New Methodology to Model Metal Chemistry at High ...

New Methodology to Model Metal Chemistry at High

Temperature

Mary Elizabeth Wagner

S.B., Massachusetts Institute of Technology (2016)

Submitted to the Department of Materials Science and Engineeringin Partial Fulfillment of the Requirements for the Degree of

Doctor of Science

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 2021

Signature of Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Department of Materials Science and EngineeringMay 12, 2021

Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Antoine AllanoreAssociate Professor of Metallurgy

Thesis Supervisor

Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Frances M. RossChair

Departmental Committee on Graduate Studies

Abstract

There is currently a lack of ability to predict which species will be reduced at the cathode and

what purity will be achieved during metal electrodeposition. Problems related to co-deposition

and contamination are usually avoided by using selective aqueous electrolytes or pre-purifying

feedstock. However, these approaches are not always possible, particularly when developing novel,

high temperature electrochemical processes where there is little experimental information about

the electrolyte. In addition, present thermodynamic modeling methods fall short of their ability

to accurately predict the properties of the multicomponent, high temperature solutions commonly

used for electrolytes. In absence of meaningful models and sufficient data, the standard state

electrochemical potential is often used as a metric to determine which reduction reaction will

dominate. However, this approach assumes every species in the electrolyte acts as if it were a pure

species, and does not accurately reflect true electrochemical behavior.

Herein, a new approach to modeling electrolytes is developed. By examining liquid solutions

in a traditional chemical thermodynamic framework, and using this as a foundation for combining

targeted experiments with calculated Gibbs energy data, deeper insights into the role of electrolytes

on cell behavior can be obtained. A quantitative link between the activity of the electrolyte

and the cathode composition is modeled. In order to expand the utility of the model, a new

reference state for activity has been derived, specifically suited to the unique challenges of electrolyte

thermodynamics. This model was tested against experimental data for several case study systems

and performed well at predicting electrochemical behavior. Activity measured relative to the new

reference state accurately informed on thermodynamic phenomena. Use of the model on systems

with limited data enabled efficient design of new electrochemical processes.

To my grandfather,

Joseph Gregory Leija

Acknowledgements

This thesis would not have been possible without the guidance and support of many. I would

especially like to acknowledge Professor Allanore, who has been my research supervisor since Jan-

uary 2013, when I joined the laboratory as an undergraduate researcher. My time in your group has

shaped me into who I am today, both scientifically and personally, and graduation is a bittersweet

moment. When I began my research with you, I was a particularly poor student in thermody-

namics. Thank you for all your time and patience over the years teaching me the subject, and for

always pushing me to improve myself. I would also like to thank you for your mentorship over the

past 8 and a half years, and for all of our illuminating discussions in that time.

I would also like to thank and acknowledge Professor Sadoway and Professor Olivetti for not

only serving on my thesis committee, but also for the outstanding guidance you both have given

me during my time at MIT. Professor Sadoway, it was on your suggestion that I first joined the

Allanore Group, and in the time since you have provided invaluable advice as if I were your own

student, on subjects as narrow as immediate research problems to as broad as philosophical outlook.

Professor Olivetti, you have been a crucial mentor, helping me ground my work in sustainability

and encouraging me not to lose sight of those goals.

A very special thank you is in order for Professor Carter, who has also mentored me as if I were

his own student. You not only taught me the fundamentals of materials computation that made

this thesis possible, but you have also been a constant source of positivity and support. Thank you

also to Professor Morita, for always being at the ready with thermodynamic advice, and Professor

Fukunaka, for all of your help in successfully navigating conferences, as well as for hosting me

during my time in Japan.

To the Allanore Group members: I want to thank you for eight years of camaraderie. You have

always been there when I needed it the most, from midnight equipment repairs, to giving your

honest feedback on my work, to helping me take much-needed breaks from the lab. I would also

like to acknowledge the DMSE staff at large, especially Angelita Mireles and Mike Tarkanian, for

the countless hours you put in helping me and everyone else succeed at MIT.

Gianluca, the story of this thesis cannot be told without your companionship. We have gone

through every step of our doctorates together since we met as first years in September 2016:

studying for quals, defining our research, and now writing our theses. Thank you for always being

there for me through the highs and lows of this journey, and for the sheer joy you bring me every

day of our life together. I love you.

Thank you also to my family, especially my parents, Cynthia and Robert, and my siblings,

Mikey and Katey. I know I can always count on you no matter what, and I am forever grateful for

that. Thank you for always reminding me to keep things in perspective, and for the support and

advice you have given every step of the way. After 9 years, I’m finally graduating “college”.

Finally, I would like to thank my grandfather, Joseph Leija, to whom this thesis is dedicated.

You have given me the values, determination, and work ethic that guide me in everything I do. It

was when you were helping me recover from my foot surgery that I first derived the models that

would become the core of this work. It is impossible for me to look at the equations in this thesis

without thinking of you, and smiling.

Contents

Abstract 3

Acknlowledgements 7

List of Figures 20

List of Tables 21

1 Introduction 23

1.1 Background on Selectivity in Electrochemistry . . . . . . . . . . . . . . . . . . . . . 25

1.2 Methods to Determine Electrolyte Activity . . . . . . . . . . . . . . . . . . . . . . . 29

1.2.1 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.2.2 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.3 Molten Sulfides: A Unique Electrolyte for Both Primary and Secondary Metal Pro-

cessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.3.1 Precious Metals and Molten Sulfide Electrolysis . . . . . . . . . . . . . . . . . 34

1.3.2 Copper Ore and Molten Sulfide Electrolysis . . . . . . . . . . . . . . . . . . . 35

1.4 The Argument for a New Approach to Thermodynamic Study at High Temperature 37

2 Hypothesis 49

2.1 Limitations of Existing Electrolyte Models . . . . . . . . . . . . . . . . . . . . . . . . 50

2.2 Scientific Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3 Statement of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.4 Framework for Validating Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.5 Assumptions and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3 Mathematical Framework for Linking Electrolyte Properties to Reduction Be-

havior 59

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.3 Derivation of Generalized Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.4 The Case for a New Reference State . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.4.1 The Wagner-Allanore Reference State . . . . . . . . . . . . . . . . . . . . . . 71

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4 Modeling Case Studies in Industrial Electrochemistry 77

4.1 Cobalt-Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.1.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.1.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2 Praseodymium-Neodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5 Thermodynamics of Ag2S−Cu2S Pseudobinary in BaS− La2S3 Electrolyte 93

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.3 Activity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.4.1 Equilibration Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.4.2 Gallium Quench Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6 Electrochemistry in Molten Sulfides 115

6.1 Ag-Cu Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.2 Fe-Cu Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7 Predicting Solution Behavior in Non-Electrochemical Systems: Rare Earth

Magnet Recycling 133

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.3 Magnet Sludge Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.3.1 Modeling Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7.4 Recycling Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

7.4.1 Modeling Methodology: Oxygen Removal . . . . . . . . . . . . . . . . . . . . 150

7.4.2 Reduction Thermodynamics Results . . . . . . . . . . . . . . . . . . . . . . . 151

7.4.3 Implication for Magnet Sludge Recycling Technologies . . . . . . . . . . . . . 153

7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

8 Future Work 165

8.1 Multiphase Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8.2 Anode Dissolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8.3 Kinetic Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

9 Conclusion 169

9.1 Demonstrated Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

9.1.1 The Wagner-Allanore Reference State . . . . . . . . . . . . . . . . . . . . . . 170

9.1.2 Predictive Electrochemical Modeling . . . . . . . . . . . . . . . . . . . . . . . 171

9.2 Method Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

9.2.1 Limitations of a Relative Reference State . . . . . . . . . . . . . . . . . . . . 172

9.2.2 Limitations of Selectivity Model . . . . . . . . . . . . . . . . . . . . . . . . . 173

9.3 Potential for Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

9.3.1 Impact on Thermodynamic Studies . . . . . . . . . . . . . . . . . . . . . . . . 174

9.3.2 A New Outlook on Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

9.4 Final Thoughts and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Appendix A Alternative Methods for Modeling the Chemistries of the Cathode

and Electrolyte 177

A.1 Introduction to Electrochemical Distribution . . . . . . . . . . . . . . . . . . . . . . 177

A.2 Interpolative Approach to Modeling Distribution . . . . . . . . . . . . . . . . . . . . 179

A.3 Predicting the Equilibrium Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 181

A.4 Perspectives on Further Model Development . . . . . . . . . . . . . . . . . . . . . . . 184

A.4.1 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

A.4.2 Extension to More Complex Systems . . . . . . . . . . . . . . . . . . . . . . . 185

A.5 Final Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Appendix B Further Investigation of Molten Sulfide Solution Properties 189

B.1 Precious Metal Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

B.1.1 Solubility in Na2S-ZnS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

B.1.2 Solubility in BaS-Cu2S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

B.2 Isothermal Study of BaS-La2S3-Cu2S Ternary . . . . . . . . . . . . . . . . . . . . . . 194

B.3 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

List of Figures

1.1 Schematic of a molten salt electrorefining cell for selective refining of uranium,

from [Ackerman1989]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.2 Interplay of models, data, and calculations that allow for expressions of Gibbs energy

to be described according to the CALPHAD method [Andersson2002]. . . . . . . . 33

1.3 Alternative method of precious metal extraction from copper-rich sources using se-

quential reduction in a molten sulfide electrorefining cell. . . . . . . . . . . . . . . . . 36

1.4 Designing models to be used in tandem with experiments, as opposed to replacing

experiments, leads to a positive feedback cycle and more efficient development of

new technologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.1 Illustration of the thermodynamic system. . . . . . . . . . . . . . . . . . . . . . . . . 54

3.1 a) exchange of species A and B through a permeable membrane separating solutions

α and β. b) species A and B must undergo a redox reaction in order to exchange

between the metal and electrolyte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Hypothetical placement of EA, EB, and ES on electrochemical potential series. In

this example, Eref = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3 Equilibrium electrochemical synthesis diagram for arbitrary binary A-B, where A is

the more noble element on the electrochemical potential series, and A and B form a

completely miscible metallic solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.4 Equilibrium electrochemical synthesis diagram for the Pr−Nd/Pr2O3−Nd2O3 sys-

tem at 1323K. At this temperature, Pr and Nd form a completely miscible liquid. . . 68

3.5 Equilibrium electrochemical synthesis diagram for the Ag−Ni/AgCl2−NiCl2 system

at 1773K. At this temperature, Ag and Ni phase separate to form two different liquid

solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.6 Comparison of Raoultian, Henrian, and Wagner-Allanore reference states. Henrian

activities are scaled according to the value of γ∞, while Wagner-Allanore activities

are scaled according to the activity coefficient of A, γA, which may not be constant

with concentration, unlike the Henrian case. The composition coordinate of the

Wagner-Allanore reference state is also rescaled along the A−B pseudobinary. . . . 74

4.1 Phase diagram of the Ni-Co system. At 823K, Ni and Co form a fully miscible FCC

solid solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.2 a) Electrochemical synthesis diagram for Ni − Co/NiCl2 − CoCl2 system at 823K

where xNiCl2 = xCoCl2 = 2wt%. b) Wagner-Allanore activity coefficient ρ for

CoCl2. : Values calculated for: ENi − ECo = 0.2V (from ideal solution), and

ENi − ECo = 0.185V (from cyclic voltammetry peaks). ;: experimental concentra-

tion of Co in Ni cathode after chronopoteniometry at 50mA/cm2, 200mA/cm2, and

500mA/cm2 [Choi2020]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.3 Wagner-Allanore activity coefficient ρCoCl2 calculated from experimental concentra-

tion of Co in Ni cathode after electrolysis at 50mA/cm2, 200mA/cm2, and 500mA/cm2,

whenxCoCl2

xNiCl2+xCoCl2

= 0.2 (W) , 0.33 (5), and 0.5 (;) [Choi2020]. . . . . . . . . . . . 82

4.4 Comparison of electrolyte composition and cathode concentration after electrolysis

at 50mA/cm2, 200mA/cm2, and 500mA/cm2, whenxCoCl2

xNiCl2+xCoCl2

= 0.2 (W) , 0.33

(5), and 0.5 (;) [Choi2020]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.5 Comparison of ρCoCl2 calculated from experimental concentration of Co in Ni cathode

after electrolysis at 50mA/cm2, to ideal solution assumption forxCoCl2

xNiCl2+xCoCl2

(W) , 0.33 (5), and 0.5 (;). Ideal solution model: [Choi2020]. . . . . . . . . . . . 84

4.6 Electrochemical synthesis diagram for for the Pr − Nd/Pr2O3 − Nd2O3 system at

1323K with: : predicted concentration of Nd in Pr based on ENi − ECo = −5mV ,

;: calculated from experimental results [Milicevic2017]. . . . . . . . . . . . . . . . 87

5.1 Standard-state electrochemical series for sulfides at 1523K, plotted v. Cu/Cu2S

reference [Bale2016, Barton1980]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.2 Electrochemical synthesis diagram for for the Ag−Cu/Ag2S−Cu2S system at 1523K

with: : predicted concentration of Cu in Ag based on EAg − ECu = 257mV. . . . . 96

5.3 a) graphite crucible and cap used for sulfide melts and equilibration experiments b)

sulfide sample and metal taken from crucible post-equilibration experiment. . . . . . 99

5.4 Left) furnace setup used for sulfide melts and equilibrium experiments. Right)

schematic of setup showing hot zone and quench zone. . . . . . . . . . . . . . . . . . 100

5.5 Measured Cu content in Ag metal after equilibration with molten BaS-La2S3-Cu2S-

Ag2S at 1523K for 24 hours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.6 Calculated activity coefficient ρCu2S in BaS-La2S-Cu2S-Ag2S after equilibration with

Ag metal at 1523K for 24 hours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.7 SEM image of typical microstructure of Ga-quenched BaS-La2S-Cu2S-Ag2S elec-

trolyte with an electroactive content of 40% Cu2S and 60% Ag2S. The “primary

phase” had an average Ag content of 65% relative to Cu, while the “secondary

phase” contained an average of 52%. No significant segregation trend was observed

in the tertiary phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.8 Measured overall Ag content relative to Cu in a BaS-La2S-Cu2S-Ag2S electrolyte

with an electroactive content of 40% Cu2S and 60% Ag2S, as a function of height

inside the crucible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.9 Measured Ag content relative to Cu in the primary and secondary phases of a BaS-

La2S-Cu2S-Ag2S electrolyte with an electroactive content of 40% Cu2S and 60%

Ag2S, as a function of height inside the crucible. . . . . . . . . . . . . . . . . . . . . 107

6.1 Left) schematic of electrochemical cell used for Cu-Ag separation experiments. Right)

cathode and electrolyte after electrolysis experiment . . . . . . . . . . . . . . . . . . 118

6.2 Chronopotentiometry measurements in a BaS-La2S3-Cu2S-Ag2S electrolyte for cath-

odes containing varying starting amounts of Cu. Cathode current density: 12mA/cm2.

Temperature: 1523 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.3 Equilibrium electrochemical synthesis diagram showing change in cathode composi-

tion before and after electrolysis for a BaS-La2S3-Cu2S-Ag2S electrolyte containing

equimolar proportions of Cu2S and Ag2S. : equilibrium Cu content in Ag cathode

for this electrolyte. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.4 Fe-Cu phase diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.5 a) Fe-Cu-C phase diagram when xCxF e+xC

= 0.17. b) equilibrium electrochemical syn-

thesis diagram for the Fe−Cu−C/FeS−Cu2S system at 1573K. At this temperature,

cast iron and Cu phase separate to form two different liquid solutions and solid C. :

predicted Cu content in cast iron (2 mol%), assuming ideal behavior in the electrolyte.125

6.6 Equilibrium electrochemical synthesis diagram for the Fe−Cu−C/FeS−Cu2S system

at 1573K for a cast iron cathode containing 19mol%C showing measured equilibrium

Cu content in cathode () as well as the cathode composition ranges after various

electrolysis experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.1 Schematic of a typical Fe-R-B magnet microstructure showing the magnetic 2-14

grains separated by a rare earth rich “other metallic phase” at the grain boundaries. 135

7.2 Overview of main processing steps in Fe-R-B magnet production. Highly oxidized

waste such as magnet sludge is produced mainly during the jet milling and machining

steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7.3 Overview of the current magnet sludge recycling process. Commercial magnet sludge

recycling occurs at the primary rare earth smelter. . . . . . . . . . . . . . . . . . . . 138

7.4 Comparison between actual magnet manufacturing (left) and the modeling steps

used herein (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.5 Calculated phase distribution in the simulated magnet after melting and casting with

no additional oxygen added (baseline case). . . . . . . . . . . . . . . . . . . . . . . . 146

7.6 Modeled distribution of rare earth elements among phases in baseline case. Rare

earth containing phases present: Dy: 100% Fe14Dy2B, Ce: 100% Ce2C3, Nd: 2%

Nd2O3, 96% Fe14Nd2B, 2% Nd2B5 Pr: 82% Pr and 18% PrAl2, La: 100% LaC2,

Gd: 14% Gd2O3, 86% GdS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

7.7 Calculated changes in phases present as oxygen content is increased from 0.09wt% to

5.4wt%. l: 2-14 phase, s: “other metallic” grain boundary phase, n: oxide phase.

After the grain boundary phase is completely oxidized near 1.8wt%, the 2-14 phase

begins to break down into oxide and more metallic phases. . . . . . . . . . . . . . . . 147

7.8 Modeled distribution of rare earth elements among phases with 5.4wt% O present.

Rare earth containing phases present: Dy: 100% Dy3Al5O12 Ce: 15% CeO2 85%

CeCrO3 Nd: 2% Nd3Al5O12, 45% NdBO3, 18% Fe14Nd2B, 35% Fe8Nd Pr: 100%

Fe8Pr Gd: 100% Gd3Al5O12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7.9 a) minimum Gibbs energy (∆G) needed to reduce equilibrated magnet sludge. b)

minimum Gibbs energy (∆G) to reduce magnet sludge with addition of the enthalpy

(∆H) to heat the material to temperature. —: modeled case where RE oxides are

separated prior to treatment. - - -: modeled case where sludge is reduced as a whole. 152

7.10 Calculated changes in phases present as O content in magnet sludge is reduced from

5.4% to 0% at 1773K. s: rare earth rich metallic phase (no Fe), n: oxide phase ,

l: metallic phases containing Fe and rare earth, u: Fe-rich metallic phase (no rare

earth). As oxygen is removed, Fe and rare earths interact to create new phases. . . . 153

7.11 Steps for direct recycling of magnet sludge. . . . . . . . . . . . . . . . . . . . . . . . 156

7.12 Ellingham diagram showing the ∆G of formation of relevant rare earth oxides and

calcium oxide, a popular choice for reductant in rare earth recycling. ∆Gf is very

similar for the various rare earths, highlighting their chemical similarity and the

resulting difficulty in purification from ore. . . . . . . . . . . . . . . . . . . . . . . . 158

A.1 Plot showing the relationship between the concentration of B in the cathode and

BX in the electrolyte, as well as the calculated distribution for each concentration.

Both metal and electrolyte are assumed to follow the regular solution model, with

T=1250K, Zmetal=10, Zelectrolyte=10, Ωmetal=300, Ωelectrolyte=-300. . . . . . . . . . . 180

A.2 a) ∆Gmix for sample metallic and electrolyte systems. b) Sum of ∆Gmixmetal and

∆Gmixelectrolyte. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

A.3 Distribution of La and Nd between a LiCl-KCl electrolyte and a Cd cathode. s:

: modeled distribution from thermodynamic data and summed Gibbs energies of

mixing La-Nd and LaCl3-NdCl3. : experimentally determined distribution. Data

from [Ackerman1991, Ackerman1993]. . . . . . . . . . . . . . . . . . . . . . . . . 183

B.1 SEM image of quenched sulfide from Ag solubility experiments in BaS-Cu2S elec-

trolyte. Primary phase composition (mol%): 37% S, 29% Ba, 29% Cu, 5% Ag.

Secondary phase composition (mol%): 39 % S, 59% Ba, 2% Cu. . . . . . . . . . . . 192

B.2 SEM image of quenched sulfide from Au solubility experiments in BaS-Cu2S elec-

trolyte. Primary phase composition (mol%): 34% S, 32% Ba, 33% Cu. Secondary

phase composition (mol%): 37% S, 60% Ba, 2% Cu. Tertiary phase composition

(mol %): 33% S, 29% Ba, 17% Cu, 21% Au . . . . . . . . . . . . . . . . . . . . . . . 193

B.3 a) BaS-La2S-Cu2S ternary concentrations tested during isothermal experiment. b)

custom-designed graphite crucible showing sample wells and drill holes. c) example

of typical “melted”, “unmelted”, and “somewhat melted” samples post-experiment. . 195

B.4 Estimated isothermal projection of BaS-La2S-Cu2S system at 1473 K based on ob-

served melting behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

List of Tables

5.1 Cu content in Ag after equilibration and measured ρCu2S . . . . . . . . . . . . . . . 104

6.1 Cu content in cathode measured before and after electrolysis at 12mA/cm2. . . . . 120

7.1 Modeled Gibbs energy of 2-14 compounds modified to limit reaction with oxygen.

Real stoichiometry: Fe(14.00018), R(1.99988), B(0.9994) . . . . . . . . . . . . . . . 141

7.2 Elemental compositions used for calculations with no additional oxygen. Initial:

compositions estimated from published reports. Post-V IM : calculated after “ini-

tial” composition was equilibrated at 1723K to simulate treatment in vacuum induc-

tion melting furnace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.3 Comparison of theoretical energy needed for the existing magnet sludge recycling

method and the alternative of direct reduction of entire sludge without primary feed

or elemental separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Chapter 1

Introduction

Development of new, sustainable methods to process metals are desperately needed by modern

society, which must reconcile the benefits of technology and industrialization with the social and

environmental costs of such development. Metals production carries the highest environmental

footprint of all materials production in terms of greenhouse gas emissions (CO2-equivalent) [1], an

impact that is only posed to climb. Recent trends predict the amount of metals in-use globally will

increase 5 to 10 times current amounts by 2050 [2].

Furthermore, the scale-up of sustainability in other industries, such as the energy sector, is

inherently coupled to the metals industry, which itself is a web of interconnected elements that are

mined or processed together. For example, wind power relies on dysprosium-containing magnets,

which must be mined and partially processed alongside other rare earths [3, 4]. The key elements

in a photovoltaic solar cell, such as indium, germanium, and tellurium, are linked to the production

of base industrial metals copper and zinc, as well as toxic arsenic and cadmium [5]. In absence of

an effort to reduce the environmental impact of metals processing, the greenhouse gasses emitted

during metal production may in fact offset the benefits of the green technologies that require

them. [6].

Electrochemical reduction of metal ores is a pathway to greener extraction [7], with the ability

to significantly reduce emissions associated with metal production. By utilizing the electron to

decompose an oxidized species, according to the reaction:

AX → A+X (1.1)

An+ + ne− → A

Xn− → X + ne− (1.2)

only electricity is necessary, meaning that the footprint of this process is tied primarily to the

method of electricity generation [8]. If renewable energy sources are used to drive electrolysis, then

the emissions of greenhouse gasses such as CO2 and SO2 from metal production can be dramatically

reduced, or even eliminated.

At the cornerstone of electrochemical metal processing, or electrometallurgy, is the electrolyte,

the media which hosts the ions that are either oxidized or reduced inside the cell. Aqueous elec-

trolytes are popular for their low-temperatures and well-established chemistries, and are the system

of choice for electrowinning or electrorefining many metals such as zinc, nickel, copper, silver, and

gold. However, low-temperature aqueous systems are often plagued by slow kinetics, which in turn

lead to the necessity of operating at high current densities. When the electrodes are solid, as in

room temperature processes, then operating this way can cause dendritic growth. These dendrites

can break off and fall to the bottom of the cell with anode slimes, a collection of species insoluble

in the electrolyte.

Slimes pose an additional challenge to metal processing sustainability. Electrolysis must be

periodically stopped, so the cell can be cleaned and the slimes collected. In the case of copper

electrorefining, these slimes can contain valuable precious metals (10.5 wt% Ag and 1.8 wt% Au

were found in slimes at Sumitomo Metal Mining Co. Ltd. [9]), and some slimes can contain up to

50wt% Cu due to dendrite break-off [10], highlighting the inefficiency of this process.

Higher temperature, non-aqueous electrolytes operating with liquid cathodes do not produce

slimes. The most industrially important electrometallurgical technology utilizing a high tempera-

ture electrolyte and a liquid cathode is aluminum production via the Hall-Heroult process [11], but

the method is used for many reactive metals, including the rare earths [12].

Recently, new electrochemical technologies are pushing the boundaries of processing conven-

tions. Novel high temperature electrolytes such as molten sulfides [13, 14] and oxides [15] generally

have greater solubility for a wider range of elements than their aqueous counterparts, and are being

investigated to develop new extraction methods for base metals such as copper and iron. The bene-

fits of using a high temperature electrolyte and liquid electrode has even led to their implementation

in new battery designs, the liquid metal battery [16].

With new technologies come new challenges, and in the case of high temperature electrolytes,

enhanced solubility is both a benefit and a detriment. When multiple species are soluble in an

electrolyte, they can compete with each other for dominance of the cell’s redox reaction. Even

if the electrolyte is well-understood, the link between electrolyte properties and the composition

of the reduced metal at the cathode is unclear, and the relationship is difficult to quantify, with

efforts so far focusing on cathode chemistry and leaving the electrolyte generalized [17]. Novel

electrolytes are even more challenging. In these cases, the composition of the final metal product

cannot be guaranteed a priori, and many experiments are required to effectively develop the new

technology. In order to move forward with newer and greener electrochemical processes, then, the

study of selectivity in high temperature electrolysis is necessary.

1.1 Background on Selectivity in Electrochemistry

Except in notable cases, such as praseodymium-neodymium production from a mixed oxide [12],

the desired electrolyzed product tends to be a nearly pure metal. Purification tends to be achieved

through either pre-processing to ensure a pure electrolysis feedstock, as in the Bayer process for

aluminum production [18], or by carefully selecting a supporting electrolyte insoluble to unwanted

species, such as silver and gold in copper anode electrorefining [19]. Therefore, if these new elec-

trometallurgical routes are to be competitive with existing technology, they must be selective to

the metal of interest.

However, pre- and post- processing to avoid selectivity issues are not always practical. When

trying to recover metals from nuclear waste, a series of processing steps will introduce more points

of possible radioactive contamination, and separation in one unified electrochemical cell is prefer-

able [20, 21]. Additionally, significant energy expenditures and waste production result from pu-

rification steps, making these routes unattractive to recycling technologies that seek to break away

from the “back-to-the-smelter” approach currently used for many metals [4, 22–24].

There is a rich body of literature on electrochemical selectivity from research on nuclear waste

processing. In 1989, the problem was addressed in a patent detailing an electrorefining cell for

separating uranium from plutonium in a molten chloride electrolyte [20]. Figure 1.1 shows the

schematic of the cell proposed in the patent. This cell featured a system of raising and lowering

cathode baskets. When a significant change in voltage was detected, indicating that plutonium

was now being deposited alongside uranium, the “pure” uranium cathode basket was raised and

an “alloy” cathode basket was lowered.

In addition to a new cell design, selectivity research in nuclear waste treatment also attempted to

probe the relationship between the electrode alloys, the electrolyte composition, and the dominating

redox reaction in hopes of enhancing the efficiency of electrorefining. Equilibration experiments

were carried out to study the partitioning of elements between a metal electrode and chloride

electrolyte [25–28]. This led to the development of “distribution” or “separation factor” as a means

of quantifying the selectivity of two elements. It is given by the ratio of two elements in the metal

electrode over the ratio of those same elements in the electrolyte after equilibrium. For elements A

and B present in the electrolyte as AX and BX such that there are two competing decomposition

reactions:

AX → A+X

BX → B +X (1.3)

Distribution can be given by:

Figure 1.1: Schematic of a molten salt electrorefining cell for selective refining of uranium, from [20].

xAxBxAXxBX (1.4)

Further discussion of the utility of a distribution-based approach to modeling electrochemical

selectivity will be given in Appendix A.

Other endeavors to study the factors contributing to selectivity have focused on the chemistry of

the electrolyte and the role of the supporting electrolyte. In their investigation of electrochemically

separating Mg and Mn from Al cans for recycling, Antony Cox and Derek Fray examined how

electrolyte composition affected the electrode potential of each element, and its effect on the chloride

series [29]. By only varying the concentration of the NaCl-MgCl2 supporting electrolyte by about

20wt%, the electrode potentials of Mg, Mn, and Al were observed to change by as much as 50mV.

This phenomena may be explained by changes in the activities of AlCl3, MnCl2, and MgCl2.

Although only the concentration of MgCl2 and NaCl were changed, this resulted in an overall

change in the thermodynamic properties of the entire Al-Mg-Mn-Na-Cl quinternary system. This,

in turn, changed the activities of AlCl3 and MnCl2, even if their concentration remained the same.

Consider the equation for reduction of a generic metal chloride MexCly:

yMexCly →

yMe + Cl2 (1.5)

The Gibbs energy of this reaction can be broken down into the standard state reaction, ∆G,

and the effect solution behavior will have on this reaction, measured by activity as well as fugacity

(or partial pressure assuming chlorine behaves as an ideal gas):

∆Gr = ∆G +RT lnacMepCl2abMexCly

Neglecting for the moment the effects of the gas (pCl2), if aMe > aMexCl2 , then the metallic

Me carries a higher energy of mixing in the metal phase than MexCly in the electrolyte. This will

raise the overall Gibbs energy of reaction. Conversely, if aMe < aMexCl2 , then MexCly carries a

higher energy of mixing, which will lower the Gibbs energy of reaction. The activity of MexCly

can be affected by a variety of factors, including temperature and pressure as well as the overall

electrolyte composition. Thus, even if the concentration of MexCly itself does not change, changing

the concentrations of other species will change those species’ activity, and in turn change the activity

of MexCly [30].

1.2 Methods to Determine Electrolyte Activity

Understanding the activities of electrolyte species is essential to understanding selectivity in

electrolysis. Because activity contributes to the Gibbs energy of the decomposition reaction, it will

influence which redox couple dominates during cell operation. Fortunately, the study of activity is

an established practice in thermodynamics, with a variety of methods presently in use to measure

and quantify it.

1.2.1 Experimental Methods

Equilibrium-Based Methods

In equilibrium activity measurements, the composition of a species in a known phase, or ref-

erence phase, is directly connected to its composition in an unknown phase by the equilibrium

constant for the chemical reaction of moving between phases. One common application of this

method are vapor-pressure studies.

Consider a molten salt electrolytic species AX. If the partial pressure of AX in the gaseous

phase above the liquid can be measured, than the activity of AX in the liquid electrolyte may be

determined by the equation:

alAX =pAXPAX

where PAX is the vapor pressure of pure gaseous AX. If AX cannot be assumed to be an ideal

gas, fugacity may be substituted into this relationship. This method is a popular and accurate

way to probe electrolyte activity, and has been extensively used to gather data on molten salt

electrolytes [31–33].

In theory, this principle can be extended to any system where two phases can be brought

into equilibrium with one another (i.e. liquid-solid or liquid-liquid, not only liquid-gas). The phase

under investigation is the “unknown phase”, in this case the liquid electrolyte, and the second phase

is the “reference phase”, with known properties that can be found in a database or reference text

such as [30, 34]. This method is useful when vapor pressure methods are not possible, for example,

if AX disassociates upon vaporization according to an unknown mechanism. Equilibrium methods

have been used to probe the properties of high-temperature liquids [35, 36], and are possible as

long as the equilibrium constant of the phase change reaction is known and thermochemical data

on the reference phase is available.

Electrochemical Methods

An alternative method of activity measurements is electrochemical potential difference mea-

surements (formerly electromotive force measurements). This method is attractive because the use

of a potentiostat to record potential differences allows for highly precise measurements, down to

the order of microvolts. Additionally, thermodynamic properties of high temperature systems may

be probed in-situ, unlike some equilibration measurements which must first be quenched before

evaluation.

The fundamental principle for this study is measurement of the potential difference between

electrodes. The system being probed must have a working electrode (WE) and at least one reference

electrode (RE). The difference between these two is given by:

∆Ecell = EWE − ERE

∆Ecell = −RTnF

lnaAaB

where the activity aB is known through the use of a stable and well-defined reference electrode.

This method has been used to probe systems that could be used for new innovative electro-

chemical technologies (see [37–39] for a series of studies used in development of the liquid metal

battery), as well as to inform on molten salt electrolytes (see [31, 40, 41]).

One drawback of potential difference measurements is their dependency on a reference electrode

at which a consistent and known reaction occurs. Such an electrode must be resistant to contamina-

tion by other elements that could drift or change its potential. The reactive nature of most molten

salt electrolytes makes this endeavor challenging. It is possible to inhibit transfer of problematic

species through use of a selective solid electrolyte membrane such as β”-Al2O3 (see [42] and the

references within), but the success of this method is dependent on the accuracy of the assumption

that the molten salt does not interact with membrane.

Recently, a novel method of electrochemical activity measurements using alternating current

cyclic voltammetry (ACV) has been proposed [43]. This is an attractive alternative. The enhanced

accuracy of ACV as well as its ability to segregate different electrochemical phenomena to different

Fourier harmonics, allowing for a more thorough evaluation, has been demonstrated [44–49].

1.2.2 Computational Methods

With the increase in modern computational power has come expanded interest in computational

efforts to determine thermodynamic properties. Broadly speaking, these efforts can be divided into

two categories: ab-initio, or “first principles” calculations, and CALPHAD modeling. Ab-initio

techniques attempt to solve the equations of quantum and statistical mechanics in order to define all

materials properties (see [50] for more information). However, the ability to solve these relationships

at higher temperature, when entropic contributions start to play a key role, is limited. Therefore

this discussion will focus instead on CALPHAD modeling, which is more common in studying the

thermochemistry of high temperature liquids.

CALPHAD is an acronym for “Calculation of PHAse Diagrams”, and it is an interpolation-

extrapolation method. Expressions for the Gibbs energy of pure substances are calculated first,

linearly expanded in terms of T. Such data can be calculated by fitting experimental data, by

comparison to similar systems, or from ab-initio techniques. Figure 1.2 shows the interplay of

various data sources in building CALPHAD models. Scientific Group Thermodata Europe [51]

produced one of the most comprehensive publicly available databases for pure elements, as well as

references for the data used to make their functions. This database forms the core of the models

for the two main CALPHAD softwares available today, FactSage [52] and Thermo-Calc [53].

In the CALPHAD method, pure substance data are used as end members for a binary expression,

which is determined by the software in the same matter as pure substances (fitting, comparison,

and calculation). Information on a system binary is fit to a statistical solution model that can

also be linearly expanded in terms of T. As the ultimate goal is convergence, the fitting models

are not general to the thermodynamics of every system. Instead, they must be carefully selected

by the modeler based on their assumptions. For example, solid solutions at low temperature

and off-stoichiometry compounds are commonly modeled using the Compound Energy Formalism

(CEF) [54]:

G = XAG0A +XBG

0B +RT (XAlnXA +XBlnXB) +Gex

Gex = XAXB

∑n≥0

nL(A,B)(XB −XA)n(1.9)

The summation may be expanded as necessary until convergence is reached during interpolation.

Statistical expressions of liquids are far more challenging, and they are commonly modeled using

a random-mixing Bragg-Williams approximation [55]. Models have been derived attempting to

incorporate the nonrandom nature of liquid mixing, one example being the Modified Quasichemical

Model (MQM) [56–59], adapted from the Quasichemical Model [60]. The full MQM is given by:

G = (nA,V aG0A,V a + nB,V aG

0B,V a)− T∆Sconfig +

nAB,V a2

∆gAB,V a

∆gAB = ∆g0AB +

∑i≥1

gi0ABXiAA +

∑j≥1

g0jABX

(1.10)

where Sconfig is represented by 1-dimensional Ising Model [61]. ∆g contains information about

the coordination number Z as well, although this value is used as another fitting parameter and

may be changed by the modeler in order to optimize fit.

The many complex fitting parameters demanded by this model arises from its lack of an accurate

statistical description for entropy. In order to compensate for the use of the 1-D Ising Model, all

other parameters, including end-member data, must be optimized. Unfortunately, reliance on such

fitting techniques cause challenges in accuracy of obtaining new information by extrapolating the

Thermo-Calc SoftwareThe CALPHAD method

Figure 1.2: Interplay of models, data, and calculations that allow for expressions of Gibbs energyto be described according to the CALPHAD method [53].

CALPHAD-generated Gibbs energy expression into unstudied regions. Rinzler and Allanore showed

that by expanding the definition of entropy in the quasichemical model to include just one other

mode of entropy, in this case electronic entropy, the accuracy of liquid models increased [62].

Entropic contributions are significant in molten salts. These electrolytes are high temperature,

multicomponent liquids with complex ionic and electronic interactions. Such features make CAL-

PHAD modeling challenging: even if enough data are obtained to build a model for the system, the

divergence between entropy as described in the fitted equations and entropy in the actual liquid

solution will cause inaccurate extrapolation to new concentrations and conditions. Additionally,

the success of the CALPHAD method is predicated on the existence of accurate experimental data

for the system. If an electrolyte is novel, with unknown thermochemical properties, and also reac-

tive enough that traditional activity measurements are difficult, then it cannot be modeled using

CALPHAD techniques.

1.3 Molten Sulfides: A Unique Electrolyte for Both Primary and

Secondary Metal Processing

Molten sulfides are a class of electrolyte that sit at the intersection of novel, reactive, and

high-temperature: a challenging system to study thermodynamically. Furthermore, its exceptional

solubility properties for multiple elements force the electrochemist to face issues of selectivity head-

on. However, it is molten sulfide’s ability as a high temperature solvent that enable its use in new

electrochemical technologies.

1.3.1 Precious Metals and Molten Sulfide Electrolysis

Due to solubility limitations of aqueous media, extracting precious metals, whether from copper

ore or electronic waste, must be done sequentially. Typically, these metals are separated from each

other during electrorefining, where an aqueous electrolyte soluble specifically to the species of

interest is chosen. This method starts with the more reactive metal (such as Cu), and sequentially

moves on to refine more more noble metals (Ag, followed by Au, followed by PGM). When Cu is

refined, Ag, Au and PGM collect at the bottom of the cell in the slimes.

The anode slimes take primarily the form of selenides (containing the valuable metals), and

sulfates (containing base and special metals such as lead and arsenic, as well as some copper) [10, 63–

67]. There are many differing techniques for treating slimes, extensively discussed in literature [10,

68–70]. These methods often utilize a combination of pyro- and hydrometallurgical techniques to

successfully extract metals, and are generally optimized for the typical slime composition at each

refinery. However, in all cases, this process can only be done in series, using multiple facilities and

separate streams for each metal. This is true regardless of the initial material’s status as a primary

ore or a secondary recycled waste.

Molten sulfides have already shown promise as a stable electrolyte with sufficient ionic conduc-

tivity to support electrolysis. They have been a successful media for electrolytic decomposition of

the sulfides of copper, molybdenum, and rhenium [14, 48]. Furthermore, copper, gold, silver, plat-

inum, and palladium have all been found in nature as sulfides [71–73], supporting the likelihood

that they could be solvated in a molten sulfide electrolyte. Preliminary tests of precious metal

solubility in molten sulfides will be discussed in Appendix B.

Figure 1.3 shows a possible alternative to treating and extracting precious metals from copper-

containing sources. Such a process would be enabled by the unique solvating behavior of molten

sulfides, and is inspired by the sequential refining cell proposed for nuclear waste treatment [20].

1.3.2 Copper Ore and Molten Sulfide Electrolysis

Chalcopyrite is one of the most commonly processed minerals in copper-bearing ores, with a

chemical composition of CuFeS2 [19]. Once the ore is concentrated to isolate this mineral, a product

with almost equimolar amounts of iron and copper remains.

The next step in copper processing is matte smelting in order to segregate iron to an oxide

(slag) phase and copper to a sulfide (matte) phase. The chemical reaction is given below for one

mole of chalcopyrite as:

CuFeS2 +13

8O2 →

2(Cu2S ·

2FeS) +

4FeO +

4SO2 (1.11)

molten sulfide electrorefining cell

Au Ag CuPGM

mixed feedstock

sequential electrolysis

Figure 1.3: Alternative method of precious metal extraction from copper-rich sources using sequen-tial reduction in a molten sulfide electrorefining cell.

In order to treat the remaining iron in the sulfide matte, the matte is then transferred to a

converter where oxygen rich air first helps oxidize the remaining iron, fluxing it into a silica slag,

and then reduces the copper sulfide into blister copper (99% pure Cu). These two steps are given

FeS +3

2SiO2 → FeO · 1

2SiO2 + SO2

Cu2S +O2 → 2Cu+ 2SO2

(1.12)

Considering both smelting and converting steps, 2.5 moles of SO2 are generated for every mole of

CuFeS2.

If chalcopyrite concentrate could be treated electrochemically, rather than through smelting

and converting, these emissions could potentially drop to zero. In such an electrochemical reaction,

reduction of iron and copper would take place sequentially, following the reactions:

CuFeS2 →1

2Cu2S + Fe+

2Cu2S → Cu+

(1.13)

with 1 mole of S2 generated for every mole of Cu produced. Sulfur is solid at room temperature,

indicating that it can be easily collected downstream.

Such a process would have a great environmental benefit, but being able to control the selectivity

of this process in order to compete with industry standards of less than 1% Fe in blister copper is

critical to its success [19]. Both Cu and Fe are soluble in molten sulfides, but their standard state

free energies of sulfide formation are sufficiently close to each other to make co-deposition during

electrolysis highly probable.

There is significant evidence suggesting that the behavior of Cu2S and FeS vary significantly

from standard state behavior, and that molten sulfides in general do not follow the ideal solution

model. It is not uncommon for sulfide systems to show liquid-liquid miscibility gaps [74, 75], owing

partially to changes in electronic structure and behavior [62]. Therefore, an assessment of the

thermodynamics of a molten sulfide electrolyte used for Cu and Fe extraction is necessary in order

to evaluate how feasible separation in this system may be.

1.4 The Argument for a New Approach to Thermodynamic Study

at High Temperature

The ability to quickly determine electrolyte suitability is necessary if electrochemical technolo-

gies are going to meet the demands for sustainable processing. With their improved solubility, faster

kinetics, and environmentally benign anode products if an inert anode is used, high temperature

electrochemistry offers significant improvement over existing extraction and treatment methods.

When a new electrochemical system is screened for possible use in a new technology, one of

the first items for consideration is the placement of the species of interest on the standard state

electrochemical series. The more noble species will be deposited on the cathode first, and if there is

sufficient (≈ 200mV ) difference between that species and the next one on the series, a pure product

can be expected [76]. This behavior is then confirmed or refuted through a series of thermodynamic

and electrochemical experiments targeted at understanding the cell behavior. It is not possible to

know if the technology will be successful a priori.

Modelers often approach thermodynamics with the goal of eliminating these experimental steps.

If everything about a system can be determined computationally, then laboratory tests become

redundant. Unfortunately, computational power sufficient to utilize ab-initio techniques in high-

entropy, high-temperature systems is not yet available, and the success of the CALPHAD method

is predicated on the existence of accurate data for the system of study, as well as statistical models

that capture solution behavior. While this makes CALPHAD modeling useful for well-established

technologies, such as steelmaking, its ability to evaluate a truly novel system is presently lacking.

The models that will be presented and discussed in this thesis follow an alternative approach.

Designed from the start to be run in tandem with experiments, they fall in between experimental

analysis techniques and predictive modeling methods. These models will be grounded in the rela-

tively simple equations of solution thermodynamics, meaning they can be easily solved and utilized

without significant computational power or softwares. The intended outcome of such an approach

is detailed in Figure 1.4: experiments are used to generate thermodynamic data, which are then

fed into equations of classical thermodynamics and analyzed with visualizations in order to gain

new insight on a system. These insights are then used to design future experiments. Unlike other

modeling approaches, the models put forth in this thesis require very few data to analyze a system.

As such, systems with scattered or incomplete datasets may be evaluated.

In Chapter 2, I will put forth the central hypothesis of this thesis, providing a framework to

predict selectivity in high temperature electrochemistry. The selectivity models derived in Chapter 3

are done so with this alternative approach to modeling in mind: they are intended from the start

to be an aid to the electrochemist when exploring new systems and technologies. In Chapter 4,

I will verify the accuracy of this model by comparing results to already studied systems, and in

Chapters 5 and 6, I will demonstrate the utility of this alternative approach by using it to study

a novel system: molten sulfide electrolysis for copper and precious metal extraction. Finally, I

will extend the philosophy of this modeling approach in Chapter 7, where I will analyze a non-

thermodynamic data

efficient experimentation

visualizations and models

Figure 1.4: Designing models to be used in tandem with experiments, as opposed to replacingexperiments, leads to a positive feedback cycle and more efficient development of new technologies.

electrochemical system with the same methodology of using the equations of classical and solution

thermodynamics to combine limited data in order to gain new insights on a poorly understood

system.

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Chapter 2

Hypothesis

Although electrochemistry has existed as a field for over 200 years [1], certain aspects of the

field remain ill-understood. In particular, it is presently not possible to quantitatively predict the

extent of co-deposition that may occur in an electrochemical cell [2]. As a result, electrochemical

engineers must resort to trial-and-error methods to ensure that their process results in a product

within the desired composition specification. Alternatively, a pure product can be achieved by

means of a pure feedstock (see Bayer process, [3]) or selectively soluble aqueous electrolytes (see

copper anode electrorefining, [4]). While these are effective solutions for established technologies,

lack of fundamental understanding of what drives certain species to co-deposit hinders development

of new electrochemical systems (See Chapter 1).

The core of this issue is a two-fold problem: there are real experimental challenges to accu-

rately measuring the thermodynamic properties of high temperature electrolytes, and there is an

inability to quantitatively model how these properties correlate to cell behavior. Development of

an alternative approach to electrochemical modeling could shed light upon this problem. Doing so

would enable more efficient development of electrochemical technologies by reducing trial-and-error

experimentation, and could also lead to developments that enhance the quality of metal produced

by existing processes.

2.1 Limitations of Existing Electrolyte Models

Electrolyte behavior is fundamental to overall cell performance. Therefore, it is important to

understand the thermodynamics of the system’s electrolyte before undertaking any endeavor to

model the extent of co-deposition. This may be accomplished through one of three main meth-

ods. The first method is direct activity measurements, such as electrochemical potential difference

measurements (formerly EMF). While by far the most accurate of the three methods, it requires

multiple experiments at various temperatures and concentrations to accurately map out the system.

In addition, all direct activity experiments require a thermodynamic and electrochemical reference.

This is particularly challenging for certain high temperature molten electrolytes, such as chlorides,

fluorides, and sulfides, which tend to react not only with a reference or ion-selective membrane,

but also with containment, introducing further experimental unknowns.

The second method for quantifying activity is employing ab-initio calculations such as density

functional theory (DFT). While first-principles calculations have generated a lot of excitement

due to their promise in linking atomic-level phenonoma to macroscopic materials properties, they

struggle to calculate entropic interactions that are important in high temperature liquids.

The final method for quantifying activity is the CALPHAD method (CALculation of PHAse

Diagrams) [5]. The CALPHAD method is unique in that it takes experimental measurements and

fits them to equations of statistical thermodynamics or linear expansions of classical thermodynam-

ics. It then generates an expression of total Gibbs energy, from which thermodynamic properties

may be derived. It is fundamentally an interpolation method, and thus has difficulty predicting

properties in areas far from the original interpolation, or in systems where limited data is available.

All three methods for quantifying activity have their relative strengths and weaknesses. For cer-

tain electrolytes that are high temperature, reactive, and understudied, these weaknesses overlap

and frustrate attempts to understand these solutions’ thermodynamic properties, and the elec-

trochemist is either forced to return once more to extensive experimentation or make simplifying

assumptions. One common assumption maintains that if two species are further than 200mV on the

standard state electrochemical series, then the more reactive species will not contribute at all to the

reduction reaction and there will be no significant co-deposition. Conversely, if the standard state

reduction potential of two species are closer than 200mV, codeposition will occur [6]. The major

issue with this assumption is its use of pure standard state (a=1) thermodynamic convention, which

neglects all effects of concentration and chemical interaction and treats both the electrolyte and the

cathode as if they were completely pure. In many cases, this is an erroneous assumption, as mixing

chemistry will change the Gibbs energy of formation and decomposition of oxidized species [7]. If

the concentrations of the species in the electrolyte and cathode are known, the electrochemical

series may be adjusted to an ideal series. For an oxidized specie AX being reduced to metal A and

gaseous X such that:

An+ + ne− → A

Xn− → X + ne− (2.1)

we can find its ideal decomposition potential via the equation:

Eid = E − RT

nFlnxApX

xAX(2.2)

Where E is the standard state decomposition potential of AX and X is assumed to be an

ideal gas. Although this formalism improves upon standard state, it does not take into account

interactions between AX and other species in the electrolyte, or A and other metals in the cathode.

Although certain metallic systems can be approximated as nearly ideal, most electrolytes are eutec-

tic systems with interactions that have significant deviations from ideality. These interactions are

typically represented by the Raoultian activity coefficient (γ) such that Raoltian activity a = γx,

Eid = E − RT

xAγApX

xAXγAX

Eid = E − RT

aAX(2.3)

This formalism is particularly important when one considers the fact that in commercial elec-

trolytic processes, the supporting electrolyte is present in far greater concentrations than the elec-

troactive species. For example, in the Hall-Heroult process, Al2O3 is present in the range of 2-3

wt%, dissolved in a cryolite supporting electrolyte [8]. Such concentrations are common across

other technologies, such as rare earth electrowinning [9]. At these concentrations, the molecules

of electroactive species are completely surrounded by molecules of supporting electrolyte (i.e. sol-

vated): an alumina-cryolite interaction is statistically far more common than an alumina-alumina

interaction. The significant role of the supporting molten salt electrolyte concentrations on the

electrochemical series has been observed [10], and in certain cases the changes are so severe that

the series becomes inverted. A species previously thought to reduce first may now be second or

third in the series [7, 11], and unforeseen co-deposition may become possible. These changes are

not always intuitive, and optimizing separation between two electroactive species in the presence

of a bulk supporting electrolyte has been the subject of many experimental studies [12–14].

2.2 Scientific Gap

In electrochemical production of metals, there is presently a lack of ability to predict which

metal species, and at what purity, will deposit on the liquid cathode of a high temperature electro-

chemical cell. The high temperature, reactive nature of electrolytes make gathering uncontaminated

experimental data in sufficient amounts a real challenge. To complicate the problem further, mod-

eling methods fall short of their ability to accurately predict the thermodynamic properties of high

temperature electrolytes. This stems from their inability to accurately quantify entropy, resulting

in poor treatment of high-entropy systems such as high-temperature liquid electrolytes. In absence

of meaningful models or sufficient experimental data, the standard state electrochemical potential

is used as a metric to determine if co-deposition will occur. Unfortunately, under industrial process

conditions, standard state assumptions do not often capture the true behavior of these solutions.

2.3 Statement of Hypothesis

As discussed above, quantifying the activity of electrolytes is essential to understanding the

real reduction potential of species of interest. However, even if all exact reduction potentials are

known, the link to co-deposition is still uncertain. It is hypothesized herein that the dominating

reduction reaction in a high temperature electrochemical cell can be understood by examining the

solution properties of the metal cathode and the molten electrolyte, and the equilibrium composition

established between these two phases. If a full description of activity of electrolyte species cannot be

obtained, it is proposed that measurement of the relative activity between two species is sufficient

to determine if co-deposition will occur between them.

It is a basic principle of thermodynamics that a system will seek to minimize its internal

energy. Therefore, it is further hypothesized that the chemical interactions between the cathode and

electrolyte will drive the cell towards an equilibrium composition in order to lower its overall energy.

Understanding the thermodynamic relationship between cathode and electrolyte will therefore allow

for predictions as to the extent of co-deposition, and can be used to design new electrochemical

systems.

2.4 Framework for Validating Hypothesis

In order to validate this hypothesis, a model connecting the solution thermodynamics of the

cathode and electrolyte to predicted co-deposition should be proposed. This model must be tested

against a variety of electrochemical systems to demonstrate its robustness and to determine its

limitations. It is important that these systems are industrially relevant and represent real electro-

chemical processes that cannot otherwise be described by existing modeling methods. Therefore,

this model will primarily be tested against experimental data rather than alternate models.

At the core of this hypothesis is the proposition that relative activity is sufficient to capture

the necessary thermodynamic information of electrolytes. As such, a mathematical framework for

describing activity in this way must be developed. The utility of this method should be shown

by measuring relative activity and comparing the insights from these measurements to experimen-

cathodeelectrolyte

X(g)X(g)

Figure 2.1: Illustration of the thermodynamic system.

tal observations. It is necessary to show that enough information about the thermodynamics of

electrolytes is retained, and is sufficient to predict co-deposition.

Finally, it is the goal of this work to provide an alternative method of modeling electrolysis

thermodynamics, one that does not seek to replace experimentation, but one that seeks to enhance

the efficiency of experimentation. To that end, it is important that both the co-deposition model

and the relative activity formalism should be employed in the exploration of an understudied

system, and used to guide research on that system. Molten sulfides, a promising electrolyte with

many unknown thermodynamic properties, are an ideal test case for this endeavor.

2.5 Assumptions and Boundary Conditions

As in all thermodynamic studies, careful definition of system is critical to meaningful analysis.

Herein, we define our thermodynamic system as consisting of the electrolyte and cathode. This

system is maintained at constant pressure (isobaric) and temperature (isothermal). It is a closed

system to every species except the oxidized product X(g) (Equation 2.1), and no chemical interac-

tions take place between the system and its environment, which may consist of cell containment

and electrical leads. Figure 2.1 illustrates our system as defined above.

Considering the electrolyte, it is assumed herein to be a single-phase liquid solution. There are

no conditions on the number of components the electrolyte may contain, and the anode species is

likewise left generalized in order to accommodate many different systems. Importantly, however,

this work lays the groundwork for a model for binary codeposition. Therefore, although the elec-

trolyte may contain more than two components, only two components are considered capable of

reduction (henceforth referred to as species A and B). All other species are modeled as belonging

to the supporting electrolyte, where they are stable enough not to contribute meaningfully to any

reaction. Expansion of this boundary condition will be detailed in Chapter 8.

Analogously, the metal cathode may also be modeled as multicomponent. Unlike the electrolyte,

the solution may contain any number of condensed phases so long as the Gibbs phase rule is

observed. Like the electrolyte, however, any additional species present in the electrolyte beyond A

and B are considered stable and non-reacting.

Finally, contrary to traditional electrochemical convention, all energies of reaction will be nor-

malized per mole of reduced metal. While it is true that electrochemical engineers typically nor-

malize per mole of oxidized gas, the model presented in this thesis focuses on the interactions of

a metallic cathode and liquid electrolyte. Therefore this convention was chosen for mathematical

simplicity.

2.6 Summary

Although it is well-established that electrolyte chemistry is fundamental to the performance of

electrochemical cells, a quantitative link between electrolyte properties and the final composition

of the metal produced at the cathode remains elusive. Furthermore, electrolytes used in high

temperature processes are often reactive- making gathering uncontaminated experimental data

challenging. Because these same electrolytes are usually complex multicomponent solutions, the

ability to model them with traditional thermodynamic computation methods is severely hindered,

mostly due to the increased role of entropy in these systems and the difficulty these methods have

in accurately modeling entropy.

It is hypothesized that by examining the equilibrium between the electrolyte and cathode solu-

tions, further insights may be gained about which reduction reactions will dominate in an electro-

chemical cell. The drive for the cell to reach this equilibrium will influence which species will be

reduced and when, and therefore these reactions may be predicted by modeling the thermodynamic

interactions between the electrolyte and cathode.

It is further hypothesized that, in cases where the highly reactive nature of an electrolyte make

direct activity measurements difficult, relative activity measurements between the two species being

evaluated for codeposition is sufficient.

Framework for evaluating these hypotheses has been put forth, and will involve:

1. comparison of the proposed model to experimental data for multiple electrochemical systems

with different anodic species (e.g. oxides, chlorides)

2. development of a mathematical method to rigorously define relative activity in a manner

useful to thermodynamic endeavors

3. measurement of relative activity and critical evaluation of the utility of the results

4. use of relative activity together with the proposed model to probe the properties of molten

sulfides

Validation of these hypotheses would enable development of a model to predict if co-deposition

will occur in an electrochemical cell, and to what extent. Such a model could be utilized by the

electrochemist, not as a replacement for experimentation, as other thermodynamic models often

aim to do, but as a way to quickly screen new systems for feasibility, and as a guide for design of

more efficient and targeted experiments.

Bibliography

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[3] James Metson. “Production of Alumina”. In: Fundamentals of Aluminum Metallurgy. Ed. by

Roger Lumley. Cambridge: Woodhead, 2011. Chap. 2, pp. 23–48. isbn: 978-1-84569-654-2.

0-444-50206-8.

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In: Calphad 33.2 (June 2009), pp. 295–311. issn: 0364-5916. doi: 10.1016/J.CALPHAD.2008.

09.009.

[6] A. N. Baraboshkin. Elektrocrystalization from Molten Salts. Moscow: Nauka, 1976.

[7] O. Kubaschewski and Phil Habil. “Application of Chemical Thermodynamics to Practical

Problems”. In: Symposium on the Thermodynamics of High-Temperature Systems. Vol. 60.

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10643389.2012.728825.

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9781845696542.

[9] Ksenija Milicevic, Dominic Feldhaus, and Bernd Friedrich. “Conditions and mechanisms of

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Chapter 3

Mathematical Framework for Linking

Electrolyte Properties to Reduction

Behavior

In Chapter 2, I put forth the hypothesis that an electrolytic cell can be thought of as two

solutions seeking equilibrium with one another- the electrolyte and the cathode. The equilibrium

composition that both solutions want to achieve will define the limits of how the cell can operate.

This concept is familiar to the electrochemist. For example, if one wanted to deposit metallic

aluminum from an aqueous electrolyte, they would decompose water and create hydrogen long

before they could reduce aluminum ions [1]. The reason for this is simple- aluminum oxide is more

thermodynamically stable than water.

Understanding the thermodynamic limitations of an electrolytic cell becomes more complex

once additional chemical reactions become possible and interactions beyond that of pure elements

and compounds start to arise. In such cases, the thermodynamics of electrolysis can no longer be

approximated to the standard state, and solution behavior must be accounted for. In this chapter,

we put forth a mathematical framework for evaluating such solution behavior, and use the insights

gained to obtain further information about the electrolytic cell.

3.1 Introduction

The development of the CALPHAD method brought significant advances in the world of creat-

ing computer-generated phase diagrams. Minimization algorithms could compute the equilibrium

of multicomponent systems and map out their phase relations. However, in terms of visualizing

thermodynamics, not much progress has been made since the development of Pourbaix and Elling-

ham diagrams in the 1940’s [2, 3]. Both of these diagrams may be used to compare Gibbs energies

of reactions of different species, and both visualize how certain conditions effect these reaction

energies- in Ellingham’s case, temperature and partial pressure, and in Pourbaix’s case, cell poten-

tial and pH. The derivations of both diagrams, however, make the assumption that the condensed

species taking part in the reaction are in their standard state. In certain cases, this assumption

has led to discrepancies between reaction energies calculated theoretically and those observed ex-

perimentally when standard state behavior does not apply. For example, different solubilities for

oxygen among reactive metals will effect which oxide species is more thermodynamically stable [4].

In his paper “The conversion of phase diagrams of solid solution type into electrochemical syn-

thesis diagrams for binary metallic systems on inert cathodes”, G. Kaptay proposed a type of phase

diagram, called an “equilibrium electrochemical synthesis diagram” (EESD), which links the equi-

librium relationship between metals in the cathode to the reduction potential of the electrolyte [5].

This type of phase diagram is distinct from Pourbaix and Ellingham diagrams because it takes

into account the non-standard state behavior of the metal cathode. No comment is made on the

behavior of electrolytes, which are left generalized. Kaptay’s work focused on the theoretical aspect

of EESD derivation, which he derived for an ideal binary solution only, although equations were

also shown regarding application to real solutions.

In this chapter, the formalism of Kaptay will be extended and expanded to a multicompo-

nent cathode displaying real (ai 6= xi) solution behavior. Through this methodology, targeted

experimental data and classical Gibbs energy curves can be used in combination to map out the

thermodynamic nature of complex electrolytes. To facilitate this effort, a new thermodynamic ref-

erence state for activity is derived that allows one to determine electrolyte activities directly from

equilibrium electrochemical synthesis diagrams.

3.2 Background

electrolyte

Figure 3.1: a) exchange of species A andB through a permeable membrane sep-arating solutions α and β. b) species Aand B must undergo a redox reactionin order to exchange between the metaland electrolyte

Equilibrium electrochemical synthesis diagrams link

easily observable results such as cathode composition to

the less obvious thermodynamic properties of a novel elec-

trolyte. The premise arises from the isothermal, isobaric

thermodynamic equilibrium between two solutions. As

seen in Figure 3.1a, two solutions α and β, both contain-

ing elements A and B, and separated by a hypothetical

permeable membrane allowing A and B to pass through,

may be considered to be in chemical equilibrium, where

µαi = µβi and i represents A or B [6]. If one measures

the chemical potential µαA, they will also have measured

µβA, and can use the Gibbs-Duhem relation to calculate

µαB and µβB. Figure 3.1b shows an extension of this case,

where in order to cross the permeable membrane, ele-

ments A and B must undergo a redox reaction. The chem-

ical potentials of A and B in α and β are now linked by

the relationship:

µβA + µβX − µαAX = ∆GrA (3.1)

∆ErA = −∆GrAnF

Where ∆ErA is the electrochemical potential of the decomposition reaction AX → A+X, with X

being the species oxidized at the anode and A being the species reduced at the cathode (Eq. 2.1).

µαAX , the chemical potential of species AX in α (electrolyte), is an unknown quantity that is

a function of two independent variables, µβA and ∆Er. With two unknowns and one equation

(Equation 3.1), µαAX cannot be determined. If the second species, B, is reducing as well, then there

will be a unique potential ES at which the co-reduction of both elements A and B takes place, as

shown in Figure 3.2. If the mixing of A and B are energetically favored, then co-reduction of A

and B will lower the Gibbs energy of reaction such that ES takes place at a more positive potential

than either EA or EB alone. By taking this mixing behavior into account, it is possible to link the

difference between ErA and ErB to the ∆GmixA,B in β (cathode). The derivation of this relationship is

given in [5], and leads to:

∆ES =xB ∗ nB ∗ F ∗∆EB −∆GmixA,B

F [xBnB + (1− xB)nA](3.3)

where ∆EB = EB − EA, (i.e. the difference between B and A on the electrochemical series),

∆ES = ES − EA, and ni are the number of electrons required to reduce i.

If ∆ES is maximized as a function of concentration of A and B in the cathode, and A and B are

assumed to form an ideal solution as metals, ∆EB can be determined directly as a function of the

cathode composition, written here in terms of xB:

∆EB =RT

[nB lnxB − nA ln (1− xB)

](3.4)

This relationship is undoubtedly powerful in linking the alloying chemistries of the cathode to the

properties of an unknown electrolyte, here represented by ∆EB. However, it is limited to cathodes

that form only ideal solutions and are comprised of only A and B. In order to account for a full

range of possible behavior, including phase separation between A and B and the use of additional

“host” metals in the cathode, the derivation should generalized. Herein, this relationship will

be re-derived for the general case of a multicomponent cathode behaving as a real solution with

aB 6= xB.

3.3 Derivation of Generalized Model

Consider a ternary system of three elements: A, B, C. Elements A and B can be reduced from

the electrolyte into the cathode, while element C is a stable cathode host and does not interact

with the electrolyte. The concentration of A, the more noble element, is taken as the dependent

variable so concentration can be reframed in terms of B and C only. In addition, although for this

derivation C is assumed to be a single element (the cathode is modeled as three components), C

can also be any compound or alloy of fixed concentration, as long as it does not contain either A

or B. The Gibbs energy of mixing A, B, and C to produce a liquid cathode is given by:

∆Gmix = Gl − (1− xB − xC)G0A − xBG0

B − xCG0C (3.5)

G0i is the standard state Gibbs energy of pure element i at the temperature and pressure of elec-

trolysis. Gl is the Gibbs energy of a liquid cathode phase created by alloying A, B, and C. It can

be represented by

(1− xB − xC)GlA + xBGlB + xCG

lC +RT [(1− xB − xC) ln aA + xB ln aB + xC ln aC ] (3.6)

Where Gli is the Gibbs energy of element i in the pure liquid state. 1.

Element A reduces at cathode potential EA, B at EB, and both will co-reduce at a common

potential ES (Figure 3.2). Following the convention of Kaptay, A is a more “noble” species than

B, reducing at less negative potentials [5].

If mixing is favorable, there will be an energetic drive for A and B to reduce together at ES .

The shift from EA (or EB) to ES can therefore be directly equated to the contribution of A and B

to the Gibbs energy of mixing:

∆Gmix = −xBnBF (ES − EB)− (1− xB − xC)nAF (ES − EA) + xC∆GmixC (3.7)

1If pure i is liquid at the temperature of interest, Gi = Gli. If pure i is solid, but forms a liquid solution with a

cathode alloy, Gi 6= Gli

E vs. Eref/V

ΔE Β

Figure 3.2: Hypothetical placement of EA, EB, and ES on electrochemical potential series. In thisexample, Eref = 0.

∆GmixC = GlC +RT ln aC −G0C (3.8)

and ni is the number of electrons necessary to reduce species i, as in Equations 2.1 - 2.2. We can

expand and then simplify Equation 3.7 with the relations ∆EB = EB −EA and ∆ES = ES −EA,

as illustrated in Figure 3.2. This leads to:

∆Gmix = −xBnBFES + xBnBFEB − (1− xB − xC)nAF (∆ES) + xC∆GmixC +

+(xBnBFEA − xBnBFEA)

∆Gmix = −xBnBF∆ES + xBnBF∆EB − (1− xB − xC)nAF (∆ES) + xC∆GmixC (3.10)

∆Gmix = −[(1− xB − xC)nA + xBnBF ]∆ES + xBnBF∆EB + xC∆GmixC (3.11)

We can rearrange to separate ∆ES :

[(1− xB − xC)nA + xBnBF ]∆ES = xBnBF∆EB + xC∆GmixC −∆Gmix (3.12)

We can substitute in for ∆Gmix using Equation 3.5 and expanding Gl according to Equation

3.6. We also expand ∆GmixC in a similar way.

∆ES = xBnBF∆EB + xC(GlC −G0C +RT ln aC)− (1− xB − xC)(GlA −G0

A +RT ln aA)+

−xB(GlB −G0B +RT ln aB)− xC(GlC −G0

C +RT ln aC)

(3.13)

Simplifying Equation 3.13 and solving for ∆ES we have

∆ES =xBnBF∆EB − xB(GlB −G0

B)− (1− xB − xC)(GlA −G0A)

(1− xB − xC)nAF + xBnBF+

−RT (xB ln aB + (1− xB − xC) ln aA)

(1− xB − xC)nAF + xBnBF

(3.14)

Equation 3.14 evaluates ∆ES as a function of concentration of A, B, and C, while taking into

account the chemical interactions caused by alloying. Because C does not interact electrochemically,

its direct chemical contributions drop out of the equation, and it is only the activities of A and B

that determine ∆ES . Because A and B are alloyed with C, the contribution of C is contained in

the respective activity coefficients of A and B, γA and γB. This simplification will hold for any non

electroactive cathode species, meaning that more complex chemistries can be incorporated.

At a certain concentration of xB and xC , ∆ES will be maximized. This is equivalent to minimizing

∆Gmix. For a fixed cathode host composition xC , we can find the maximum ∆ES with respect to

xB with the equation:

∂∆ES∂xB

= 0 (3.15)

Solving for ∆EB and simplifying gives:

∆EB =nA∆GssB − nB∆GssA − nBRT ln[(1− xB − xC)γA] +RT ln[xBγB]

FnAnB(3.16)

Where ∆Gssi refers to the change in energy when moving from the standard state of species i

at a given T to a liquid state. This is the generalized version of Equation 3.4 that can be applied

to any liquid cathode chemistry. It details how the composition of the cathode can influence the

extent of co-deposition. When plotting xB against ∆EB, an equilibrium electrochemical synthesis

diagram is created. For clarity of plotting, xB is better plotted against −∆EB. In this notation,

more positive potential differences favor the element A with a more positive potential. In order

to facilitate comparison with other equilibrium diagrams (e.g. phase diagrams), the EESD’s in

this paper are rotated from the original design of Kaptay, placing concentration on the x-axis. An

example of an electrochemical synthesis diagram plotted in this way for a general system A and B

at temperature T is given in Figure 3.3.

Equilibrium electrochemical synthesis diagrams provide a quantitative relationship between

two metals’ willingness to alloy in the cathode and the difference in the electrochemical potentials

required to reduce them. Two metals with favorable mixing properties, such as Pr and Nd, will

have a very steep curve, indicating that very large potential differences |∆EB| >> 0 are needed

to avoid codeposition (Figure 3.4). On the contrary, two metals that phase separate, such as

Ni and Ag, will have a horizontal curve in the region of phase separation, and a much shallower

curve overall (Figure 3.5). This indicates that for there to be significant codeposition, ∆EB ≈ 0.

The tendencies of Ni and Ag to avoid mixing in the cathode result in a higher energetic barrier to

codeposition. This EESD indicates it is far easier to electrochemically separate Ag from Ni in a

molten salt than it would be to separate Pr from Nd.

To construct a simple EESD, this potential difference, ∆EB, is left generalized. Looking in

more detail, we see ∆EB is a function of the standard state electrochemical potentials of A and B,

Ε A- Ε

Figure 3.3: Equilibrium electrochemical synthesis diagram for arbitrary binary A-B, where A isthe more noble element on the electrochemical potential series, and A and B form a completelymiscible metallic solution.

as well as their activity in the electrolyte, here designated by the notation aAX and aBX , where X

is the anionic species in the electrolyte. We have:

−∆EB = EA − EB = EA −RT

nAFln aAX − (EB −

nBFln aBX) (3.17)

Although in most cases, the standard state electrochemical potentials EA and EB are known,

the activities aAX and aBX are often unknown. Direct experimental measurement of activity is

possible, but difficult if co-deposition of A and B is favored. In this case an ion-selective membrane

must be used. If the supporting electrolyte reacts with either the membrane or the reference, the

0 0.2 0.4 0.6 0.8 11200

liquid

eesd temperature

Ε Pr- Ε N

Figure 3.4: Equilibrium electrochemical synthesis diagram for the Pr−Nd/Pr2O3−Nd2O3 systemat 1323K. At this temperature, Pr and Nd form a completely miscible liquid.

T/K eesd temperature

liquid 1 + liquid 2

fcc + liquid 1

Ag NixNi

d 1 liquid 2

Ε Ag- Ε N

Figure 3.5: Equilibrium electrochemical synthesis diagram for the Ag− Ni/AgCl2 − NiCl2 systemat 1773K. At this temperature, Ag and Ni phase separate to form two different liquid solutions.

activity measurements will be contaminated. Unfortunately, many high-temperature supporting

electrolytes are highly reactive, and a compatible membrane or reference may not be available.

3.4 The Case for a New Reference State

Thermodynamic convention calls for the study of relative changes in the energy of a system:

absolute values of energy and enthalpy are not necessary within a classical framework. The energy

of the initial state of matter, then, can be chosen according to the convenience of the thermody-

namicist, as long as they remain consistent throughout their calculations.

In the equation for molar Gibbs energy,

Gi = µi = µoi (T ) +RT ln ai (3.18)

µoi is defined arbitrarily according to mathematical and experimental convenience. When ai → 1,

species i is said to be in its standard state, and µi = µoi . The deviation of the activity function

ai from unity can thus be thought of as a measurement of deviation from standard state. This

deviation may be viewed as a function of the concentration of i in a multicomponent system:

ai = xiγi, where γi is called the activity coefficient, and is the activity of species i normalized by

its concentration. When γi = 1, ai = xi and the material is said to behave ideally. When γi > 1,

ai > xi and µi > µoi and i is in a state with elevated Gibbs energy relative to its standard state.

If µoi is defined to represent the energetic state of i as a pure substance in its thermodynamically

stable phase at standard pressure (1 atm), then this behavior may be interpreted as an increase in

free energy upon mixing into a multicomponent system. If the increase in energy upon mixing is

high enough, phase separation will occur. Conversely, when γi < 1, ai < xi and µi < µoi and i is

in a state with lowered Gibbs energy relative to its standard state. The system favors interaction

between i and the other components in the system. If the interactions lower the energy sufficiently,

short range ordering and, in some cases, compound formation, will occur.

Two main reference states exist for relating the activity function to the chemical potential.

The first, and by far the most common in thermodynamics, is the Raoultian reference state. In a

Raoultian reference state:

γixi→1 = 1 (3.19)

In other words, the reference state is chosen to be one where Raoult’s law applies.

In contrast, in a Henrian reference state, the reference state is chosen to be where Henry’s law

applies:

fixi→0 = 1 (3.20)

where f is the Henrian activity coefficient.

No matter the reference state, the integral chemical potential µi does not change. Activity

framed in one reference state may be easily converted to another by a proportionality factor in-

dependent of concentration [7]. In both of these reference states, ai is quantified, and all other

activities aj can be found by Gibbs-Duhem integration. This is valid no matter how many compo-

nents the system contains.

In certain cases, it is difficult to measure the activity of species i independently. Molten sulfides,

highly reactive at elevated temperatures, are one such case, and others have been discussed in

Chapter 1. Fortunately, in order to predict the extent of co-reduction between two electroactive

species, independent activities are not necessary. It is the relative difference between the activities of

two electroactive species AX andBX that determine their relative placement on the electrochemical

series, and this in turn dictates which species will be reduced first.

3.4.1 The Wagner-Allanore Reference State

Herein, we propose a third reference state, the Wagner-Allanore reference state. This reference

state is derived specifically for multicomponent solutions where direct activity measurements are

difficult. It is a relative reference state where the activities of two species dissolved in a complex

solvent are measured relative to one another (e.g. two electroactive species in a multicomponent

supporting electrolyte).

The ratios of two activities in a solution remain constant regardless of which standard state is

used [7]. Therefore,

=aRBaRA

(3.21)

Just as aRi = γixi, we can define:

aWAi = ρiχi (3.22)

Where χi is the relative composition of i, and ρi is the Wagner-Allanore activity coefficient of

i. Considering the A−B pseudobinary, we define:

χA =xA

xA + xB(3.23)

We can then expand Equation 3.21 as:

ρBχBρAχA

=γBxBγAxA

(3.24)

In this new reference state, we set ρA = 1 such that aWAA = χA, giving:

ρBχBχA

=γBxBγAxA

(3.25)

Noting that:

χBχA

(3.26)

We can simplify and arrive at the relation:

ρB =γBγA

(3.27)

Equation 3.27 demonstrates the utility of the this new reference state. It captures how the

chemical potential of species A and B vary with respect to each other, as well as how other

components in the solution may effect this relationship. For example, if A and B are dissolved into

solvent C, and solvent C tends to bond with A (γA < 1), while phase separating with B (γB > 1),

then γB > γA and ρB > 1. In certain cases, exact calculation of γA and γB is impractical or difficult,

but ρB can be easily measured by using an EESD diagram in combination with Equation 3.17. Since

ρB is all that is needed to determine if the electrolyte solution properties favor codeposition or

purification, reframing activity in this reference state is particularly useful to electrochemists. The

Wagner-Allanore reference state can be converted to a Raoultian reference state via the equation:

aRB = aWAB γA (3.28)

The conversion factor, γA is a function of composition xA. Because the composition coordinate

χ is relative as well, there are no limits on how dilute or concentrated A and B can be in the

solvent. Thus, this new reference state has several significant advantages over Raoultian and Hen-

rian states. First, because it is a relative reference state, not an absolute reference, it is easier to

measure experimentally, particularly when very reactive solutions are involved. Second, because it

measures the pseudobinary between A and B, there are no conditions on concentration. A Raoul-

tian reference state is the simplest mathematically and experimentally when a material is very

concentrated. A Henrian reference state is the simplest mathematically and experimentally when

a material is very dilute. By defining a new composition coordinate χ, species A and B can be at

any dilution. Although the exact, independent activities of A or B cannot be determined, and thus

Gibbs-Duhem integration cannot be performed, much of the information about the solution is still

retained, such as how A and B interact with each other and with their solvent. Figure 3.6 shows

a comparison between activities reported in a Raoultian, Henrian, and Wagner-Allanore reference

state.

0.2 0.4 0.6 0.80 1

0 0.5 1

Figure 3.6: Comparison of Raoultian, Henrian, and Wagner-Allanore reference states. Henrianactivities are scaled according to the value of γ∞, while Wagner-Allanore activities are scaledaccording to the activity coefficient of A, γA, which may not be constant with concentration,unlike the Henrian case. The composition coordinate of the Wagner-Allanore reference state is alsorescaled along the A−B pseudobinary.

3.5 Summary

Re-framing activity in a relative framework is advantageous for the study of electrolytes with

activities difficult to measure directly. In combination with equilibrium electrochemical synthesis

diagrams, relative activity can be measured after equilibrating the cathode and electrolyte, as long

as the activity of the cathode has been previously determined. Fortunately, many metallic systems

have previously been studied in detail, and this information is readily available.

As will be shown in the following chapters, significant information about electrolytes can be

obtained with this method, even if direct activity is never measured. Such information can be used

to drive the design of further electrochemical experiments, as well as to quickly screen systems for

their limitations. For example, achieving a pure cathode product when two metals have a strong

Gibbs energy of mixing will be challenging, and if their ∆EB is small for a chosen electrolyte, it

may not be possible. In such cases, it will be apparent from an EESD that alternative methods

should be pursued. This valuable information for the electrochemist can now be realized far more

quickly, as only a few experiments in tandem with an EESD are required for this analysis.

Currently, the model for EESD’s have been only derived for comparison of two species in the

electrolyte (binary system). Direct comparison of three species is possible, but this would require

a third axis and would produce a three-dimensional figure similar to a complete (non-isothermal)

ternary phase diagram. It is simpler to compare three species indirectly, by first measuring ρB,

the activity coefficient relative to A, and then by measuring a third component relative to A, for

example ρD (recall that C is a non-interacting cathode specie), but this assumes negligible ternary

interactions between A, B, and D. A full discussion of possible extensions of this model is given in

Chapter 8.

Bibliography

[1] Allen J. Bard and Larry R. Faulkner. Electrochemical Methods- Fundamentals and Applica-

tions. Second. J. Wiley, 2001. isbn: ISBN 0-471-04372-9.

[2] M. Pourbaix. “Thermodynamique des solutions aqueuses diluees: Representation graphique

du role du pH et du potentiel”. PhD thesis. Technical University Delft, 1945.

[3] H.J.T. Ellingham. “Reducibility of Oxides and Sulphides in Metallurgical Processes”. In:

Journal of the Society of Chemical Industry 63.5 (May 1944), p. 133. issn: 03684075. doi:

10.1002/jctb.5000630501.

[4] O. Kubaschewski and Phil Habil. “Application of Chemical Thermodynamics to Practical

Problems”. In: Symposium on the Thermodynamics of High-Temperature Systems. Vol. 60.

Stoke-on-Trent: British Ceramic Society, 1961, pp. 67–83. isbn: 1111111111. doi: 10.1080/

10643389.2012.728825.

[6] L.S. Palatnik and A.I. Landau. Phase Equilibria in Multicomponent Systems. Ed. by Joseph

Joffe. New York: Holt, Rinehart, and Winston, Inc., 1964.

9780444007797.

Chapter 4

Modeling Case Studies in Industrial

Electrochemistry

Although production of a pure metal through electrolysis is typically achieved by using a pure

feedstock or selective solvent, there are certain cases where two species are soluble and present

in amounts that make co-deposition possible (see Chapter 1). One such case is nuclear waste

processing, where due to the radioactive nature of the components, multiple pre-purifying steps

prior to electrolysis introduce radiation contamination risks and are thus impractical. As such,

significant efforts have been expended towards investigating recycling metals from nuclear waste

in one single electrolytic cell [1–3]. In this chapter, I will investigate the separation of cobalt from

nickel in a molten chloride media, and compare model results and insights to the experimental

analysis given in [4].

Another notable system for industrial co-depositon is rare earth alloy production. Although

individual rare earths are usually produced as pure metals via electrolysis after extensive pre-

processing to ensure a pure oxide feedstock [5–7], occasionally neodymium and praseodymium are

electrolyzed together to produce a Pr-Nd alloy [8, 9]. Due to the near-exclusive production of rare

earth metals in China, little information on the actual process conditions of rare earth electrolysis

have spread beyond a select few Chinese companies, where such information is closely held as

trade secrets [7, 10]. Some published data are available, but they lack key details crucial to the

0 0.2 0.4 0.6 0.8 1273

Ni xCo Co

experiment temperature

liquid

Figure 4.1: Phase diagram of the Ni-Co system. At 823K, Ni and Co form a fully miscible FCCsolid solution.

electrolytic process, such as electrolyte composition and operating temperature [11, 12]. In their

study of Pr-Nd electrodeposition, Milicevic et al attempted to recreate industrial process conditions

and study the effect of Pr2O3 − Nd2O3 concentration on the composition of Pr-Nd alloy. Their

experimental analysis will be compared against the results obtained from modeling the system with

electrochemical synthesis diagrams in combination with the new reference state.

4.1 Cobalt-Nickel

The first case study focuses on Ni-Co separation in a LiCl-KCl molten salt electrolyte. This is

an important system in the nuclear industry, where Ni steam generators are contaminated by Co-60,

hindering their recyclability. Choi et al investigated the ability to electrochemically separate Ni from

Co in a molten salt solution at 823K [4]. Although the generalized derivation for electrochemical

synthesis diagrams focuses on liquid cathodes, where diffusion kinetics are faster and equilibrium

distribution of species is reached quickly, in the conditions of this case study, Ni-Co form a fully

miscible solid solution, as can be seen in Figure 4.1.

Such systems may be modeled without any modification of Equation 3.16, but caution should

be used when assuming the EESD is representative of the bulk cathode composition (i.e. assuming

the concentration of Co is sufficiently diffused such that it is uniform throughout the cathode). To

the author’s knowledge, there is no full thermodynamic study of the NiCl2 − CoCl2 − LiCl−KCl

system. CALPHAD models for electrolyte appear to be obtained via extrapolation from similar

chloride systems, rather than from direct measurement [13–19].

4.1.1 Results

Choi et al studied the deposition of Ni-Co alloys with three different concentration ratios of

NiCl2 − CoCl2: 2wt%NiCl2-2wt%CoCl2, 2wt%NiCl2-1wt%CoCl2, and 2wt%NiCl2-0.5wt%CoCl2.

In addition to varying the concentration, electrolysis was run at three different current densities:

50mA, 200mA, and 500mA.

The standard-state decomposition potential of liquid NiCl2 to Ni is -798mV, while the standard-

state decomposition potential of liquid CoCl2 to Co is -998mV. Note that both NiCl2 and CoCl2

are solid in their pure state, yet soluble in liquid LiCl-KCl. For this reason, thermodynamics of the

liquid should be used. The difference in decomposition potential between Ni and Co, ENi − ECo,

is 200mV if NiCl2 and CoCl2 are assumed to behave ideally with respect to each other. On the

electrochemical synthesis diagram shown in Figure 4.2a, a 200mV potential difference corresponds

to approximately 0.25 mol%Co alloyed into the Ni cathode.

In their investigation of reduction potential peaks through cyclic voltammetry, Choi et al mea-

sured a potential difference of 185mV when both NiCl2 and CoCl2 are present each at 2wt% in

the supporting electrolyte [4]. On an electrochemical synthesis diagram, a 185mV difference cor-

responds to approximately 0.37 mol%Co. Chronopotentiometry experiments of this electrolyte

concentration revealed an experimental cathode concentration of 0.22, 0.53, and 1.17 mol%Co for

current densities of 50mA, 200mA, and 500mA, respectively. Figure 4.2b compares the Wagner-

Allanore activity coefficient calculated for each experiment, compared with the predicted coefficient

from the synthesis diagram. There is strong agreement between the predicted activity coefficient

and that measured with a low current density (50mA). As current density increases, the amount

of Co in the Ni cathode increases, and the measured activity coefficient strays from its equilibrium

thermodynamic prediction.

Figure 4.3 shows a comparison of the Wagner-Allanore activity coefficient as calculated for

different concentrations of NiCl2 and CoCl2. ρCoCl2 appears to be highly dependent on the cell’s

current density. It can also be seen that as the concentration of CoCl2 in the electrolyte increases,

the amount of Co deposited on the cathode also increases. Increases in Co deposition with current

density also occur for lower concentrations of CoCl2, although they are less pronounced than in

the case where xNiCl2 = xCoCl2 = 2wt%. This effect can be more readily seen in Figure 4.4. When

xCoCl2 = 0.5wt% the difference in Co content in the cathode achieved through electrolysis at 50

mA and 500 mA was ≈ 0.002. In comparison, when xCoCl2 = 2wt%, the difference in Co content

was ≈ 0.01.

If ENi−ECo is calculated with an ideal solution assumption, it will vary with electrolyte compo-

sition. Figure 4.5 shows this ∆Eideal calculated when xCoCl2 = 0.5wt%, 1wt%, and 2wt%, compared

to the corresponding data obtained from electrolysis at 50mA. As in Figure 4.2, there is good agree-

ment between experimental data and model predictions using an ideal solution assumption. Note

that when an ideal solution assumption is used, ρCoCl2 = 1 (see Chapter 3).

4.1.2 Discussion

Figure 4.2 compares the amount of Co predicted in the Ni cathode after electrolysis with

experimental results. The predicted value of 0.25 mol% is calculated using an EESD that relates

ENi − ECo to the thermodynamics of a Ni-Co alloy. Without experimental data, ENi − ECo is

unknown, however, it can be approximated by using an ideal solution model. A liquid standard

state takes into account the change in Gibbs energy upon dissolving solid NiCl2 and CoCl2 into

molten chloride electrolyte. Even when there is no further information available regarding the

electrolyte, using an EESD allows one to take into account the contribution of Ni-Co mixing in

the cathode. The value of this additional information can be seen in the agreement between the

predicted values of Co concentration read off of an EESD using ∆Eideal, and the values achieved

during low current density electrolysis (Figure 4.5).

Focusing on the set of experiments where xCoCl2 = 2wt%, the difference between the measured

Ni CoxCo

ρ CoC

Ni CoxCo

ideal solution

idealsolution

Ε Ni- Ε C

Figure 4.2: a) Electrochemical synthesis diagram for Ni−Co/NiCl2−CoCl2 system at 823K wherexNiCl2 = xCoCl2 = 2wt%. b) Wagner-Allanore activity coefficient ρ for CoCl2. : Values calculatedfor: ENi − ECo = 0.2V (from ideal solution), and ENi − ECo = 0.185V (from cyclic voltammetrypeaks). ;: experimental concentration of Co in Ni cathode after chronopoteniometry at 50mA/cm2,200mA/cm2, and 500mA/cm2 [4].

Ni xCo Co

ρ CoC

500mA500mA 500mA

50mA50mA

Figure 4.3: Wagner-Allanore activity coefficient ρCoCl2 calculated from experimental concentra-tion of Co in Ni cathode after electrolysis at 50mA/cm2, 200mA/cm2, and 500mA/cm2, when

xCoCl2xNiCl2

+xCoCl2= 0.2 (W) , 0.33 (5), and 0.5 (;) [4].

500mA200mA

200mA50mA

Ni xCo Co

Figure 4.4: Comparison of electrolyte composition and cathode concentration after electrolysis at50mA/cm2, 200mA/cm2, and 500mA/cm2, when

xCoCl2xNiCl2

+xCoCl2= 0.2 (W) , 0.33 (5), and 0.5 (;) [4].

ρ CoC

Ni xCo Co

ideal solution

0.5 wt%

1 wt% 2 wt%

Figure 4.5: Comparison of ρCoCl2 calculated from experimental concentration of Co in Ni cathodeafter electrolysis at 50mA/cm2, to ideal solution assumption for

xCoCl2xNiCl2

+xCoCl2= 0.2 (W) , 0.33 (5),

and 0.5 (;). Ideal solution model: [4].

reduction potentials of Co and Ni during cyclic voltammetry is 225mV, corresponding to 0.37

mol%Co in Ni on an EESD. This is slightly higher than the value predicted by the ideal solution

case, and higher than the composition measured after electrolysis at 50mA. Without data on the

equilibrium exchange between Co and Ni in molten chloride, one cannot determine if this difference

is due to solution interactions or kinetic and mass transport effects that arose during electrochemical

operation. However, there is some evidence to suggest that non-thermodynamic effects play a non-

negligible role in the final experimental result. First, the Ni-Co alloy is solid at 823K, which will

inevitably hinder diffusion of Co into Ni and effect the alloy chemistry. Second, independently of

CoCl2 concentration, there was good agreement between Co content predicted from an ideal solution

assumption and Co content measured after 50 mA electrolysis (Figure 4.5), suggesting that NiCl2

and CoCl2 behave ideally with respect to each other in this system and making additional solution

interactions less likely.

Furthermore, higher current density during electrolysis corresponded to higher experimental

concentrations of Co in the cathode. Higher current densities during electrolysis can push the cell

into an operation regime limited by mass transport. If there is locally increased concentration of

CoCl2 in the vicinity of the cathode, for example, then ρCoCl2 will be higher at the electrode interface

than in the bulk solution. In fact, as current density increased from 50mA to 500mA, calculated

ρCoCl2 was observed to increase correspondingly. Figure 4.3 shows that even as concentration of

CoCl2 is varied, the values of ρCoCl2 remain correlated to current density. When the concentration

of CoCl2 is low, the effect of current density on Co content in the cathode is lessened. If indeed

there are mass-transport limitations present causing gradients in the electrolyte, it is possible that

low CoCl2 concentrations overall prevent large gradients from forming. It is also possible that

other contributions could be at play, and more electrochemical studies would be needed to further

analyze the cell behavior.

4.2 Praseodymium-Neodymium

The second case study investigates Pr-Nd alloy production from a mixed rare earth oxide.

This system was selected for several notable reasons. First, Pr-Nd electrolysis takes place in a

molten fluoride electrolyte into which Nd2O3 and Pr2O3 are dissolved. The anion here is the oxide

ion, which is different from the anion of the supporting electrolyte, the fluoride ion. The additional

interactions between the two anions create additional complications that hinder modeling efforts and

frustrate attempts to measure thermodynamic properties. By re-framing the solution properties of

the oxyfluoride electrolyte into the relative Wagner-Allanore reference state, this confusion is easily

avoided and the energetic effect the molten fluoride has on the dissolved oxide species is captured

by ρ. Second, as mentioned previously, the conditions under which Pr-Nd electrolysis take place

are proprietary. Without information about the actual electrolyte composition used, and with

process conditions (temperature, current density, atmosphere) unknown, it is difficult to replicate

the conditions in a laboratory setting in order to gather thermodynamic data. Commercially

available CALPHAD models of the electrolyte are limited to binary fluoride systems, and even

then, available models are extrapolated from the data of better understood systems [20]. An

alternate method of investigating the thermodynamic properties of this electrolyte would clearly

aid researchers in understanding more about Pr-Nd alloy production methods.

4.2.1 Results

The Pr-Nd metallic system is well enough understood to build a binary CALPHAD model (Fig-

ure 3.4), which can be used to generate an electrochemical synthesis diagram for the system. At

1323K, standard state decomposition potential of liquid Pr2O3 to liquid Pr is -2.363V, while the

standard state decomposition potential of liquid Nd2O3 to liquid Nd is -2.372V. For an oxide com-

position ratio 66 mol%Nd2O3 - 33 mol%Pr2O3, potential difference EPr−ENd calculated assuming

ideal solution behavior is -5mV (Figure 4.6). Using an EESD, this corresponds to a Pr-Nd cathode

containing 53.5 mol% Nd. In Milicevic’s experiments, electrolysis from an oxyfluoride containing

66 mol%Nd2O3 - 33 mol%Pr2O3 produced a cathode composition of 71 mol%Nd - 29 mol%Pr

Pr NdxNd

Ε Pr- Ε N

Figure 4.6: Electrochemical synthesis diagram for for the Pr−Nd/Pr2O3−Nd2O3 system at 1323Kwith: : predicted concentration of Nd in Pr based on ENi − ECo = −5mV , ;: calculated fromexperimental results [8].

(Figure 4.6). Despite Pr occupying a more cathodic potential on the standard state electropoten-

tial series (EPr − ENd = 8mV ), the cathode was more enriched in Nd. From this data, ρNd2O3 is

calculated to be 4.8. ρNd2O3 > 1 indicates an energetic penalty to mix Nd2O3 in the electrolyte

relative to Pr2O3.

4.2.2 Discussion

Though considerably less information is available on Pr-Nd alloy production through electrol-

ysis, important insights can be gained by using model predictions in conjunction with published

data. Figure 4.6 shows more Nd was reduced than Pr, although Pr is the more cathodic metal.

Looking at only standard state data, one might expect the cathode to be strongly enriched in Pr.

However, by combining an ideal solution assumption with an EESD, a cathode containing 53.5

mol% Nd is predicted.

Experimentally, even more Nd was obtained via electrolysis: 71 mol% Nd. There are several

reasons why this may have occured. First, from the experimental data, ρNd2O3 ≈ 4.8. If this value

is representative of equilibrium conditions, then there is an energetic penalty for mixing Nd2O3

into the electrolyte, and the original ideal solution assumption would be invalid. Since the value of

this increased Gibbs energy of mixing is measured relative to Pr2O3, it suggests there is a driving

force to reduce the concentration of Nd2O3 in the electrolyte while increasing the concentration of

Pr2O3. This will result in increased production of Nd metal.

An alternative explanation considers that although Pr is the more cathodic metal on the elec-

tropotential series for oxides, Nd is the more cathodic metal for the fluoride series. Both PrF3 and

NdF3 are present in the fluoride supporting electrolyte [9]. If PrF3 and NdF3 were being reduced

preferentially instead of the oxides, a more Nd-rich alloy would be the result. However, in order for

rare earth fluorides to be reduced in steady state, the fluoride ion should be oxidized at the anode,

typically producing perfluorinated compounds (PFC) when the electrolyte is a molten oxyfluoride.

Literature studying PFC emissions in Pr-Nd electrolysis cells have noted that they are on average

2-3 orders of magnitude lower than CO2 production [9, 12]. Even if all PFC emissions were the

result of NdF3 electrolysis, there would not be enough Nd produced from fluoride to account for

the change in cathode composition.

A final explanation for the increased production of Nd could be the result of mass transport

limitations inside the electrolysis cell. Nd2O3 is present at nearly double the concentration of

Pr2O3. At the high current densities used for electrolysis, it is entirely plausible that in the vicinity

of the cathode, there was an even greater concentration difference between Nd2O3 and Pr3O3 [9].

This explanation concurs with the results of the Ni-Co case, where deposition of Co was noted to

increase with current density. Furthermore, available thermodynamic models for the LiF − PrF3

system and the LiF−NdF3 system suggest Nd and Pr behave similarly with respect to each other

in the electrolyte [20], which would result in an equilibrium ρ ≈ 1 and support the validity of an

ideal solution assumption. It is critical to note, however, that this is only for the thermodynamics

of the molten fluorides. To the author’s knowledge, there is currently no commercially available

thermodynamic data, experimental or modeled, for the Pr−Nd−O system. Further experimental

investigation is necessary in order to determine if Nd enrichment in the electrolyte is the result of

thermodynamic or transport phenomena.

4.3 Summary

In both the Ni-Co and Pr-Nd case studies, analyzing existing data with equilibrium electro-

chemical synthesis diagrams provided new information about the system. In addition, reframing

activity in our new relative reference state allowed for the electrolyte thermodynamics to be inves-

tigated and new information obtained. Available CALPHAD models for the Ni-Co case appear to

be derived from extrapolation and comparison to similar systems, while with the exact electrolyte

composition of the Pr-Nd oxyfluoride unknown, no activity measurements are publicly available.

The model for predicting co-deposition presented above enables the electrochemist to make use

of incomplete and scattered data. Unlike the CALPHAD method, where large amounts of data at

various conditions are necessary to build a model, data from only one experiment (as in the Pr-Nd

case) can provide valuable information about electrolysis as long as the cathode thermodynamics

are known. If no data is available, generalized EESD’s allow one to account for the effect cathode

chemistry has on co-deposition. Using this information alongside a simple model for the electrolyte

(e.g. ideal solution) can predict results close to experimental outcome (Figure 4.5, Figure 4.6).

In addition to allowing further analysis of an electrochemical system where limited data might

have prevented such efforts in the past, the co-deposition model and new reference state also

increase the information that can be obtained from experiments. In the Ni-Co case study, for

example, chronopotentiometry experiments at various current densities show the effect that non-

thermodynamic effects can have on the alloy produced during electrolysis. Thus, although EESD’s

are an equilibrium diagram, they may also be utilized to interpret kinetic effects to a limited extent.

A discussion of model expansion beyond thermodynamics is given in Chapter 8.

Bibliography

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of uranium and a mixture of uranium and plutonium from spent fuels. Nov. 1989.

[3] John P. Ackerman and Jack L. Settle. “Partition of lanthanum and neodymium metals and

chloride salts between molten cadmium and molten LiCl-KCl eutectic”. In: Journal of Alloys

and Compounds 177 (Dec. 1991), pp. 129–141. issn: 09258388. doi: 10.1016/0925-8388(91)

90063-2.

[4] Woo Seok Choi et al. “Separation behavior of nickel and cobalt in a LiCl-KCl-NiCl2 molten

salt by electrorefining process”. In: Journal of Electroanalytical Chemistry 866 (June 2020).

issn: 15726657. doi: 10.1016/j.jelechem.2020.114175.

[6] Praneet S. Arshi, Ehsan Vahidi, and Fu Zhao. “Behind the Scenes of Clean Energy: The

Environmental Footprint of Rare Earth Products”. In: ACS Sustainable Chemistry and En-

gineering 6 (2018), pp. 3311–3320. issn: 21680485. doi: https : / / doi . org / 10 . 1021 /

acssuschemeng.7b03484.

[7] H Vogel and B Friedrich. “Development and Research Trends of the Neodymium Electrolysis-

A Literature Review”. In: EMC 2015. Salzburg, 2015, pp. 1–13.

[8] Ksenija Milicevic, Thomas Meyer, and Bernd Freidrich. “Influence of electrolyte composition

on molten salt electrolysis of didymium”. In: ERES2017: 2nd European Rare Earth Resources

Conference. Santorini, 2017. doi: 10.13140/RG.2.2.13137.33122.

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Materials Series. Vol. Part F4. Springer International Publishing, 2018, pp. 1435–1441. isbn:

9783319722832. doi: 10.1007/978-3-319-72284-9_187.

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9.1 (2018), pp. 61–65. issn: 13091042. doi: 10.1016/j.apr.2017.06.006.

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(1987), pp. 509–61.

[14] C. Robelin. “Banque de donnees thermodynamiques pour la phase metallique et les sels fondus

lors du recyclage de l’aluminium”. PhD thesis. Ecole Polytechnique de Montreal, 1997.

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[16] C. Robelin, P. Chartrand, and A.D. Pelton. “Thermodynamic Evaluation and Optimization of

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doi: 10.1016/j.jnucmat.2004.07.035.

Chapter 5

Thermodynamics of Ag2S−Cu2S

Pseudobinary in BaS− La2S3

Electrolyte

In Chapter 3, I outlined a mathematical framework for describing the thermodynamic activity of

solutions in a relative way. In order to test the validity of this approach, in Chapter 4, I calculated

the activity of two different electrolyte systems (CoCl2 relative to NiCl2 in a molten chloride

supporting electrolyte, and Nd2O3 relative to Pr2O3 in a molten fluoride supporting electrolyte).

Using the calculated relative activities alongside an equilibrium electrochemical synthesis dia-

gram, it was possible to model the extent of co-deposition predicted to occur during electrolysis.

Good agreement was observed between experiment and model predictions, particularly when ex-

perimental conditions were such that the electrolytic cell was run close to equilibrium conditions

(i.e. low current density). As such, in this chapter, I will extend the approach of relative activity

measurement to investigate the solution thermodynamics of Ag2S−Cu2S dissolved in a BaS-La2S3

supporting electrolyte.

5.1 Introduction

The Ag2S − Cu2S system is of particular interest for recycling high-value metals from elec-

tronic waste due to the remarkable solubility properties of molten sulfides. Evidence suggests that

sulfides also have the unique ability to solubilize precious metals, including Au [1–3]. There are cur-

rently no known solvents that are able to dissolve multiple precious elements together, which leads

to the necessity of recovering each element sequentially in different media, resulting in increased

environmental burden [4–10].

In order to investigate molten sulfides as possible electrolytes for electronic waste recycling, a

study of the behavior of Cu and Ag sulfides was carried out. Cu and Ag co-deposition was chosen

as the system of investigation because Cu is the most plentiful base metal by weight in typical

electronic waste, and Ag is the most plentiful precious metal by weight in a typical electronic

waste [11].

On the electrochemical series plotted for several sulfides in Figure 5.1, the standard state decom-

position potentials of Cu from Cu2S and Ag from Ag2S are 257mV apart. While potential difference

is greater than the 200mV threshold commonly used to assess separation feasibility, the equilib-

rium electrochemical synthesis diagram for Ag-Cu shows considerable drive for alloying. Figure 5.2

shows that a 257mV separation corresponds to 6.2mol% Cu in Ag. However, this prediction uses

the standard state reduction potentials of Cu and Ag from their respective sulfides. As such, Cu2S

and Ag2S are assumed to be non-interacting with each other and with their supporting electrolyte.

Liquid sulfides have been shown previously to exhibit behavior that varies significantly from

standard state or ideal behavior, owing partially to changes in electronic behavior [13, 14]. There-

fore, the assumption that there are no significant interactions in the electrolyte is likely invalid. In

order to understand both the nature and extent of these interactions, it is necessary to measure the

activities of Cu2S and Ag2S in a molten sulfide supporting electrolyte. An electrolyte consisting

of BaS-La2S3 has previously shown to be a good candidate for supporting stable and successful

electrolysis of Cu from Cu2S [15]. Therefore, BaS-La2S3 was chosen as the supporting electrolyte

for the Cu2S-Ag2S system.

Eº vs. (Cu/Cu2S)/V

Cu/Cu2S

Ag/Ag2S

Pt/PtSPd/PdS

Fe/FeS

Zn/ZnS

Au/Au2S0.75

Figure 5.1: Standard-state electrochemical series for sulfides at 1523K, plotted v. Cu/Cu2S refer-ence [1, 12].

Ε Ag- Ε C

Ag CuxCu

standard stateprediction: 6.2% Cu

Figure 5.2: Electrochemical synthesis diagram for for the Ag− Cu/Ag2S− Cu2S system at 1523Kwith: : predicted concentration of Cu in Ag based on EAg − ECu = 257mV.

5.2 Background

The ability of molten sulfides to solubilize many different materials make traditional electro-

chemical activity measurements challenging. Metal references are frustrated by exchange interac-

tions and metallothermic reduction, which cause the reference to gradually change concentration

over the course of the experiment and drift electrochemical measurements. Attempts to use a Cu-

selective β”-Al2O3 membrane were unsuccessful due to exchange interactions between aluminum

and barium. The possibility of making a reference electrode inspired by aqueous capillary reference

electrodes was explored, but the supporting electrolyte reacted with the refractory materials used

to make the capillary, again causing a compositional drift.

Equilibration measurements have been successfully used in literature to determinine the activ-

ities of the CuS0.5 −MnS system, as well as the CuS0.5 −MnS− FeS system [16, 17]. In this type

of measurement, a metal is placed in contact with a solution of interest, and species are allowed

to exchange until equilibrium has been achieved. The activity of the electrolyte may be obtained

with the relation:

aAX = KaAaX (5.1)

where K is the equilibrium constant of the reaction A+X = AX.

In certain cases, the anionic species is difficult to measure and only the activities of the metal

are known. Without a sulfur-based reference electrode, it was impossible measure exactly how

much sulfur was being produced during equilibration. Additionally, no assumptions could be made

about whether sulfur was present in a gaseous or dissolved phase, in contrast to the studies in [16,

17]. Because of this, direct activity measurements were not possible, and an equilibrium synthesis

diagram was used in order to determine the decomposition potential difference of two electroactive

species as a function of their metallic concentration. This potential difference was converted to the

relative activities of the electrolyte species (see Chapter 3).

5.3 Activity Measurements

Barium sulfide (BaS, Alfa Aesar, 99.7% metals basis), lanthanum sulfide (La2S3, Strem Chem-

icals, 99.9% metals basis), copper sulfide (Cu2S, Strem Chemicals, 99.5% metals basis), and silver

sulfide (Ag2S, Alfa Aesar, 99.9% metals basis) were used to prepare the electrolyte. Based on the re-

sults of previous experiments in the BaS-La2S3-Cu2S system, the BaS-La2S3 supporting electrolyte

was fixed at 90wt% of the total electrolyte. The remaining 10% consisted of Cu2S-Ag2S.

It was observed that a homogenous sulfide melt could not be obtained if BaS, La2S3, Cu2S,

and Ag2S were mixed as powders in a crucible and melted together at high temperature. However,

BaS, La2S3, and Cu2S could be melted easily. Therefore, a two-step melting process was devised.

A 90% BaS-La2S3, 10% Cu2S mix was first melted together at 1523 K in an argon atmosphere (Ar,

Airgas, Ultra High Purity). The resulting sulfide was then crushed back into powder form in an

argon glovebox (Ar, Airgas, Ultra High Purity), and the necessary amount of Ag2S to reach the

desired final concentration was measured. Additional amounts of BaS-La2S3 were also added in

order to maintain the supporting electrolyte at 90%. This new mix was then melted a second time

in argon atmosphere.

For all melts, the sulfides were contained in a crucible machined from graphite (C, The Graphite

Store, Grade EC-16) and fitted with a graphite cap that fit tightly into the crucible in order to

limit possible sulfide volalization (Figure 5.3 a). This crucible was then loaded into an alumina

tube and placed into a vertical tube furnace (Lindberg/Blue MTM Mini-MiteTM). Inside the tube,

an alumina rod containing either a sheathed “Type R” or “Type C” thermocouple served as a stage

to both measure the temperature of the crucible as well a hold the crucible in the furnace hot zone.

The experimental setup is shown in Figure 5.4.

Pure silver (Ag, Alfa Aesar, 99.999% metals basis) was used as the metal for equilibration

experiments. Silver containing small quantities of oxygen is known to violently expel oxygen upon

solidification, and with it, small amounts of silver [18]. This phenomenon was observed to occur

in silver samples during sulfide equilibration, hindering efforts to fully analyze the metal post-

Figure 5.3: a) graphite crucible and cap used for sulfide melts and equilibration experiments b)sulfide sample and metal taken from crucible post-equilibration experiment.

argon in

argon out

sample stage with

thermocouple

graphite crucible

hot zone

quench zone

Figure 5.4: Left) furnace setup used for sulfide melts and equilibrium experiments. Right) schematicof setup showing hot zone and quench zone.

equilibrium. Therefore, the silver was de-oxygenated prior to experimentation. Approximately

0.1 g of Ag was melted in an arc melter (Compact Arc Melter MAM-1, Edmund Buhler) under

Ar atmosphere in the presence of a zirconium oxygen getter (Zr, Alfa Aesar, 99.5% metals basis

(excluding Hf), Hf 3%).

The de-oxygenated silver was then combined with the pre-melted sulfide in a graphite crucible

and after evacuating and purging with Ar three times, was allowed to equilibrate at 1523K for 24

hours. At this time, the sample was lowered from the hot zone into the cooling zone (Figure 5.4).

As the cooling zone was near the Ar inlet, the flow of Ar was increased to allow for an even

more rapid cool. Figure 5.3 b shows an example of the metal and sulfide taken from the crucible

post-equilibration. Once fully cool, the metal was mounted in epoxy, polished, and examined

by scanning electron microscopy energy dispersive X-ray spectroscopy (SEM-EDS) to determine

the Cu-Ag ratio. The sulfide was analyzed by an inductively coupled plasma atomic emission

spectrometer (ICP-AES) in order to measure the change in content of Ba, La, S, Cu, and Ag.

5.3.2 Results

Upon examining the equilibrated metal, it was found that some exchange had taken place be-

tween Ag and Cu. Figure 5.5 shows the amounts of Cu measured in the Ag metal post-experiment.

Cu content varied from as low as 3 mol% to 21 mol%. Generally, as the concentration of Cu2S

increased along the Cu2S-Ag2S pseudobinary, the more Cu was found in the metal reference. How-

ever, near 40% Cu2S, there was a notable increase of Cu concentration in Ag metal.

The Ag-Cu equilibrium electrochemical synthesis diagram from Figure 5.2 was used to determine

the equilibrium difference in reduction potentials of Ag2S and Cu2S. This potential difference

was used to compute the relative activity aCu2S . Figure 5.6 shows the Wagner-Allanore activity

coefficient ρCu2S as a function of Cu2S concentration.

On the Cu2S-rich half of the Ag2S-Cu2S pseudobinary, ρCu2S ≈ 1. This indicates that Ag2S

and Cu2S are behaving ideally with respect to one another in the BaS-La2S3 supporting electrolyte.

Although the absolute activities of Ag2S and Cu2S are still unknown, this result means that both

species interact with the supporting electrolyte in a similar way: if the absolute activity of Ag2S is

Cu2SAg2S xCu S2

Figure 5.5: Measured Cu content in Ag metal after equilibration with molten BaS-La2S3-Cu2S-Ag2Sat 1523K for 24 hours.

Cu2SAg2S xCu S2

Figure 5.6: Calculated activity coefficient ρCu2S in BaS-La2S-Cu2S-Ag2S after equilibration withAg metal at 1523K for 24 hours.

found to deviate positively from ideality, then Cu2S will also deviate positively by approximately

the same amount.

ρCu2S begins to increase on the Ag2S-rich half of the pseudobinary. At 40 mol% Cu2S, there is

a sharp increase in ρCu2S , before decreasing as Ag2S content continues to increase. However, ρCu2S

does not approach 1, as it did when the sulfide was Cu2S-rich. Instead, when Cu2S content is less

than 20%, ρCu2S increases with Ag2S content. At very low concentrations of Cu2S, ρCu2S ≈ 14.

Table 5.1 summarizes the experimental results of equilibration across the entire pseudobinary.

In order to understand why ρCu2S increased suddenly at 40% Cu2S, further experimentation was

necessary. A mix of BaS-La2S-Cu2S-Ag2S electrolyte whose electroactive portion contained 40%

Cu2S and 60% Ag2S was melted in a long cylindrical graphite crucible and allowed to equilibrate

for 24 hours. At this time, the crucible was dropped from the furnace hot zone into a small pool of

Table 5.1: Cu content in Ag after equilibration and measured ρCu2S .

Cu2S Cu ρCu2S(mol%) (mol%)

1.7 2.9 13.4

3.1 4.2 14.9

12.1 2.9 1.7

20.3 6.7 4.6

21.7 5.0 2.4

24.1 5.9 2.9

39.3 15.3 8.53

53.4 6.6 0.9

58.9 5.0 0.5

72.9 13.1 1.5

80.1 10.7 0.7

91.8 20.6 0.9

97.3 17.4 0.2

liquid gallium for a more aggressive quench. The sample was then removed from the crucible and

sectioned lengthwise before being analyzed by SEM-EDS.

Upon solidification, two main phases were observed to form: a primary phase, and a secondary

intergrain phase (Figure 5.7). Examination of each phase under SEM-EDS showed a similar segre-

gation of Ag and Cu between the two phases as that observed when looking at the variation of Cu

and Ag with crucible position. The Ag-Cu content in the first phase to form, the primary phase,

contained 65% Ag on average, while the secondary phase contained only 52%. In certain areas

of the crucible, a tertiary phase observed to occasionally form. There was no significant Cu-Ag

segregation observed in this phase.

Figures 5.8 and 5.9 show the variation in Cu and Ag content in the electrolyte from the bottom

of the crucible to the top. Figure 5.8 shows that there was a higher concentration of Ag sulfides

at the bottom of the crucible, while the electrolyte near the top was enriched in Cu sulfide. The

average Ag-Cu content in the bottom half of the crucible was 66 mol% Ag, while the average Ag-Cu

content in the top half of the crucible was only 57% Ag. The average overall Ag-Cu content was

62% Ag.

primary phase

secondary phase

ternaryphase

primary phase

Figure 5.7: SEM image of typical microstructure of Ga-quenched BaS-La2S-Cu2S-Ag2S electrolytewith an electroactive content of 40% Cu2S and 60% Ag2S. The “primary phase” had an averageAg content of 65% relative to Cu, while the “secondary phase” contained an average of 52%. Nosignificant segregation trend was observed in the tertiary phase.

sample average

Figure 5.8: Measured overall Ag content relative to Cu in a BaS-La2S-Cu2S-Ag2S electrolyte withan electroactive content of 40% Cu2S and 60% Ag2S, as a function of height inside the crucible.

phase average

Figure 5.9: Measured Ag content relative to Cu in the primary and secondary phases of a BaS-La2S-Cu2S-Ag2S electrolyte with an electroactive content of 40% Cu2S and 60% Ag2S, as a functionof height inside the crucible.

5.4 Discussion

5.4.1 Equilibration Experiments

Despite a 257mV decomposition potential difference between Ag2S and Cu2S, significant ex-

change between Cu2S and Ag was observed to occur, forming Cu and Ag2S. On the Cu2S-rich side,

ρCu2S ≈ 1 and observed Cu content in the metal was consistent with ideal-solution predictions

from the electrochemical synthesis diagrams. When Ag2S and Cu2S behave ideally relative to one

another, they are interacting with the supporting electrolyte in a similar way and electrolyte ther-

modynamics do not contribute to co-deposition. This result indicates that, when the electrolyte is

rich in Cu2S, the observed alloying of Ag and Cu comes from the thermodynamic drive for mixing

the two metals.

In contrast, when the electrolyte contains more Ag2S, the electrolyte begins to deviate from

ideality. More Cu is alloyed into the Ag than would be predicted from an EESD using an ideal-

solution assumption. The activity coefficient ρCu2S was found to deviate positively from ideality in

this concentration range. Additionally, there was a sharp increase in the activity coefficient when

the Ag2S-Cu2S fraction was equal to 0.4 Cu2S. This corresponded to a larger amount of Cu alloying

in the Ag metal.

ρCu2S > 1 signifies that Cu2S has a higher activity coefficient in the electrolyte than Ag2S.

Relative to Ag2S, Cu2S has a more positive deviation from ideality. A positive deviation from

ideality signifies an increase in Gibbs energy upon mixing, or a tendency for phase separation,

while a negative deviation from ideality signifies an increased energetic drive for mixing. Therefore,

ρCu2S > 1 indicates that the BaS-La2S3 electrolyte favors energetic bonds with Ag2S over Cu2S.

Such behavior is supported by the observation a BaS-La2S3-Ag2S electrolyte required a higher

temperature to melt successfully. Additionally, the BaS-La2S3-Ag2S electrolyte was very dense,

with the Ag metal reference floating to the top of the sulfide. Strong bonding between the sulfide

species could be one reason for the increase in density.

The sudden increase in ρCu2S at 40% Cu2S suggests similar preference for bonds between Ag2S

and the supporting BaS-La2S3 electrolyte at this composition. One possible explanation for this

phenomenon could be the formation of a compound near this composition. This would result in

short-range ordering between Ag2S and the BaS-La2S3 supporting electrolyte in the liquid after this

compound melted. Since ρCu2S is a relative value, however, it only signifies that there is a strong

preference for the supporting electrolyte to interact with Ag2S instead of Cu2S. Therefore, while

short-range ordering between Ag2S and the supporting electrolyte is possible, it is also possible

that there is phase separation between Cu2S and the supporting electrolyte.

5.4.2 Gallium Quench Experiment

During the gallium quenching experiment, it was found that there was an increased concen-

tration of Ag2S towards the bottom of the crucible, while the top of the crucible was richer in

Cu2S (Figure 5.8). This is in keeping with the observation that Ag2S-rich electrolytes were more

dense than their Cu2S counterparts. Furthermore, while the overall concentration of the sulfide

remained near the 40% Cu2S-60% Ag2S concentration, the bottom half of the crucible differed by

almost 10mol% from the top half. This result points to evidence of possible phase separation be-

tween Cu2S-rich electrolyte and Ag2S-rich electrolyte in the liquid phase, with the denser Ag2S-rich

liquid sinking to the bottom of the crucible.

Additionally, the first two phases to nucleate upon solidification also displayed similar segrega-

tion of Cu2S and Ag2S (Figure 5.9). The primary phase was Ag2S-rich, with an average composition

near that of the average composition of the Ag2S-rich bottom half of the crucible. That the Ag2S-

rich phase was the first to nucleate supports the hypothesis that there is favorable bonding between

Ag2S and the supporting electrolyte, and is consistent with observations of higher melting points

for Ag2S-rich electrolytes. The second phase to form contained higher amounts of Cu2S, similar to

the top half of the crucible.

Both micro- and macro- scale segregation of Ag2S and Cu2S was observed, with there being an

overall tendency towards Ag2S-enrichment at the bottom of the crucible, as well as the nucleation

of a Ag2S-rich phase and a Cu2S-rich phase upon solidification. These results suggest there are

very different energetic interactions between Ag2S and the supporting electrolyte, and between

Cu2S and the supporting electrolyte. These results are also consistent with increase in ρCu2S at

this concentration.

Although ρCu2S is a relative activity, it retains important information about electrolyte inter-

actions. Deviations from ideality that suggest certain phase phenomena, such as phase separation

or compound formation, are still measured. In the case of a BaS-La2S-Cu2S-Ag2S electrolyte,

these phenomena could be confirmed by microscopy, which revealed that Ag2S and Cu2S interact

differently with BaS-La2S.

By examining the results of the equilibrium experiments alongside the activity calculations and

its consequences on the electrolyte’s phase relations, it is possible to gain new insights on the BaS-

La2S-Cu2S-Ag2S system. Because of molten sulfides’ high degree of reactivity, it would be difficult

to obtain this information through conventional, direct activity measurements. However, relative

activity measurements are possible because the only condition on reactivity is that equilibrium

is reached: any degree of cross-reaction between the electrolyte and the reference can be directly

correlated to thermodynamic properties by using an equilibrium electrochemical synthesis diagram.

In the case of Cu2S-Ag2S, it could be seen that metal interactions (the drive for Cu and Ag to alloy)

dominate the reaction on the Cu2S-rich side of the pseudobinary, while electrolyte interactions (the

preference for the supporting electrolyte to mix with Ag2S over Cu2S) become more significant on

the Ag2S-rich side. From this, optimal conditions for electrolyte composition during electrolysis can

be determined. While the drive for Cu to alloy in a Ag cathode will always be present, operating

electrolysis on the Cu2S-rich prevents further complications due to electrolyte interactions. On the

Cu2S-rich side of the pseudobinary, there are no interactions in the electrolyte that favor electrolysis

of either Ag or Cu. On the Ag2S-rich side, however, unfavorable interactions between Ag2S and

BaS-La2S will push the reaction towards Cu electrolysis by raising the activity of Cu2S.

When considering molten sulfide electrolysis as a possible pathway for electronic waste recycling,

therefore, it is suggested that the electrolyte contains at least as much Cu2S as Ag2S in order to

avoid unwanted interactions between Ag2S and the supporting electrolyte. An experimental study

of Ag-Cu electrolysis in molten sulfides will be presented in Chapter 6.

5.5 Summary

Activity measurements in high temperature liquid electrolytes are challenging due to the pos-

sibility of reactivity with the references necessary for accurate measurement. Molten sulfides are

one such case. However, through measuring relative activity, it is possible to obtain useful insights

about the thermodynamics of a system. As seen in the study of BaS-La2S-Cu2S-Ag2S, activity

measurements in the Wagner-Allanore reference state provided useful thermodynamic information

about the electrolyte, which will be used in Chapter 6 to design electrochemical experiments.

Activity measurements of the system indicated a difference in mixing behavior between BaS-

La2S-Cu2S and BaS-La2S-Ag2S. This was later confirmed by quenching and microscopy, which

revealed phase separation between Cu2S and Ag2S containing phases. It was observed that when the

electrolyte contains more Cu2S, Cu2S and Ag2S behave ideally with respect to one another. Ideal

behavior minimizes unfavorable electrolyte interactions that can favor Cu deposition. Therefore,

if a pure Ag product is desired, the electrolyte should contain sufficient Cu2S to reduce risk of

codeposition.

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[11] Jirang Cui and Lifeng Zhang. “Metallurgical recovery of metals from electronic waste: A

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[14] Charles Cooper Rinzler. “Quantitatively Connecting the Thermodynamic and Electronic

Properties of Molten Systems”. PhD. Massachusetts Institute of Technology, 2017.

[16] Yun Lei et al. “Thermodynamic properties of the MnS-CuS0.5 binary system”. In: ISIJ

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[18] Manuel Eissler. The Metallurgy of Silver: A Practical Treatise on the Amalgamation, Roasting

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3rd. London: Crosby, Lockwood, and son, 1896, p. 336.

Chapter 6

Electrochemistry in Molten Sulfides

The aim of this thesis work is to develop a method for characterizing novel electrolytes in order

to facilitate development of new electrochemical processes. The derivations put forth in Chapter 3

allow the experimentalist to easily measure the activity of novel electrolytes, enabling them to

access previously unknown thermodynamic properties. Although the activity is only measured

relative to another species in the electrolyte, much of the thermodynamic information important

to determine the electrolyte’s performance is retained, as was demonstrated in Chapters 4 and 5.

In this chapter, the applications of the model are tested further. Activity measurements in the

BaS-La2S-Cu2S-Ag2S system (Chapter 5) are used to design electrochemical experiments to test

the selectivity of Ag deposition over Cu deposition. An additional system relevant to primary metal

production, Cu electrolysis from CuFeS2, will also be examined in light of the insights gained from

activity measurements in the BaS-La2S-Cu2S-FeS system. Predictions of cathode composition will

be compared to experimental electrolysis results and used to evaluate the efficacy of the proposed

model.

6.1 Ag-Cu Separation

The first experimental system studied is Ag-Cu deposition from a molten sulfide electrolyte. In

order to use molten sulfides as an effective means of recycling electronic waste, it is necessary to be

able to selectively deposit first Ag, and then Cu from the mutually soluble electrolyte. Both cathode

products should be relatively pure to minimize the need for further refinement and downstream

processing [1–3].

Based on the results of Chapter 5, a molten sulfide electrolyte containing at least as much

Cu2S as Ag2S should be used. In this concentration range, there were no measured electrolyte

interactions that would favor Cu deposition over Ag deposition, and the energetic drive for Cu to

alloy with Ag will be the only factor contributing to significant Cu production.

An electrolyte composition consisting of 90wt% BaS-La2S3 supporting electrolyte, and 10wt%

Cu2S-Ag2S was chosen based on success in previous experimental studies [4]. The Cu2S-Ag2S

portion of the electrolyte consisted of 5mol% Ag2S and 5mol% Cu2S. In this concentration range,

Cu2S as Ag2S behave ideally with respect to one another. Additionally, as the goal is to reduce

Ag2S to Ag metal first, depletion of Ag2S and the resulting concentration shift during electrolysis

will only ensure that the electrolyte composition remains favorable. As Ag2S is depleted, the

electrolyte will remain on the Cu2S-rich side of the pseudobinary. In contrast, if one were to start

with a high concentration of Ag2S instead, not only would there be an energetic drive on the

electrolyte side to deposit Cu, but as Ag2S is depleted, the electrolyte risks nearing the 60%Ag2S-

40%Cu2S concentration. Thermodynamic measurements taken at this composition indicate a large,

positive, energy of mixing for Cu2S with the supporting electrolyte, which would further favor

Cu deposition. Additionally, the concentration gradients noticed at this composition as a result

of density differences between BaS-La2S3-Cu2S and BaS-La2S3-Ag2S could have further negative

effects on the electrochemical cell: depending on the cell arrangement, there could be a different

electrolyte composition between the anode and the cathode, even without mass transfer effects.

A two-electrode setup was used for the electrolysis experiments, with a liquid metal cathode

consisting of either Ag or a Ag-Cu alloy (Ag, Alfa Aesar, 99.9985% metals basis), (Cu, Alfa Aesar,

99.999% metals basis), and a graphite anode (C, Alfa Aesar, 99.9995% metals basis). 5g of a BaS-

La2S3-Cu2S-Ag2S electrolyte was prepared using both the materials and the two-step pre-melting

process described in Chapter 5. The Ag-Cu alloy was prepared by melting approximately 5g of

metal inside an arc melter (Compact Arc Melter MAM-1, Edmund Buhler) under Ar atmosphere

in the presence of a zirconium oxygen getter (Zr, Alfa Aesar, 99.5% metals basis (excluding Hf),

Hf 3%). When an alloy was prepared, it was melted inside the arc melter 3 times, flipping the

solidified metal piece in between melts in order to ensure homogeneity.

Both the metal and sulfide were then loaded into a graphite crucible that was sheathed on

the sides by an alumina tube. A molybdenum wire (Mo, Ed Fagan Inc., ASTM B387 Type 361,

99.95% pure) was threaded into the bottom of the graphite crucible and secured with graphite

paste (PELCO High Temperature Carbon Paste, Ted Pella, Inc.) to provide electrical contact to

the cathode. This Mo wire was protected by an alumina tube that provided mechanical support to

the setup and also contained a type C thermocouple used to monitor the cell’s temperature.

A second Mo wire was threaded into the graphite anode, and after being secured with graphite

paste, was positioned just above the electrolyte, and the entire setup was loaded into a vertical

tube furnace (Lindberg/Blue MTM Mini-MiteTM) and heated to 1523 K after being evacuated and

purged with argon (Ar, Airgas, Ultra High Purity) three times.

Once the electrolyte was fully molten, the anode was lowered into the melt and galvanostatic

electrolysis was run immediately to ensure any compositional changes in the metal were a result of

electrochemistry, not equilibrium exchange. At the end of the experiment, the electrochemical cell

was immediately quenched by lowering the crucible out of the hot zone, the center of the furnace

where the heat is concentrated, to the bottom of the furnace tube where cold Ar flows in. As in the

quench methodology described in Chapter 5, the flow of Ar into the tube was increased in order to

facilitate a more rapid quench.

Electrolysis experiments were run using a Gamry Potentiostat/Galvanostat (Gamry Instru-

ments, Reference 3000), and temperature was monitored using an Omega data aquisition system

(Omega Engineering, Model QMB-DAQ-55). All electrolysis experiments were run at a low cathode

current density to minimize kinetic effects: 12mA/cm2. A schematic of the electrochemical cell

used for all experiments is shown in Figure 6.1.

Post-experiment, the metal cathode was separated from the sulfide electrolyte and was mounted

graphite crucible

aluminasheath

graphite anode

BaS-La2S3-Cu2S-Ag2S electrolyte

silver-copper alloy cathode

Figure 6.1: Left) schematic of electrochemical cell used for Cu-Ag separation experiments. Right)cathode and electrolyte after electrolysis experiment

in epoxy, polished, and examined using a scanning electron microscope’s energy dispersive X-ray

spectroscopy (SEM-EDS) to measure compositional changes from the initial Cu-Ag alloy.

6.1.2 Results

Figure 6.2 shows the total cell potential measured during a series of 12mA/cm2 chronopoten-

tiometry experiments in a BaS-La2S3-Cu2S-Ag2S electrolyte. The electroactive (non-supporting)

portion of this electrolyte contained 50% Cu2S and 50% Ag2S, and the starting cathode compo-

sition contained varying amounts of Cu, from 0mol% to 10mol%. The measured cell potential

gradually increased in magnitude over the time of the experiment, rather than stabilizing at one

single potential. The electrochemical signals displayed regular oscillations, likely a result of heating

element and thermocouple interference, but were overall very stable throughout electrolysis.

Table 6.1 shows the change in cathode composition during electrolysis, and Figure 6.3 compares

the measured composition change to the equilibrium Cu content for the chosen electrolyte. It can

be seen that when starting with a cathode of pure Ag, Cu is deposited on the cathode. When

electrolysis was only run for 1 hour, the cathode was found to contain 0.8mol%Cu. However, when

electrolysis was run for a longer amount of time, 3.5 hours, further enrichment of the cathode was

observed: the final measured composition was 1.14mol%Cu.

If the starting cathode composition contained Cu, Ag was deposited on the cathode instead. In

these cases, the shift in cathode composition appeared to be proportional to how far the composition

was from equilibrium. A large compositional shift of 2.7mol% was observed to take place when the

starting alloy contained 10mol% Cu, while smaller shifts of 0.7mol% and 0.5mol% were found when

the starting alloy contained 6mol% and 4.5mol%, respectively.

6.1.3 Discussion

It can be seen that when starting with a cathode of pure Ag, there is a strong drive for Cu

deposition in order to reach this equilibrium composition. This drive causes the reduction of Cu

over Ag, even though the measured difference in reduction potential between Cu2S and Ag2S for

this electrolyte composition should be 265mV. In order to affirm that Cu deposition was an elec-

Table 6.1: Cu content in cathode measured before and after electrolysis at 12mA/cm2.

initial Cu(mol%) 0 0 4.5 6 10

final Cu(mol%) 0.8 1.14 4.0 5.3 7.3

∆ Cu(mol%) 0.8 1.14 -0.5 -0.7 -2.7

electrolysistime (hr) 1 3.5 1 1 1

time (t/s)

10% Cu

4.5% Cu

0% Cu 0% Cu

Figure 6.2: Chronopotentiometry measurements in a BaS-La2S3-Cu2S-Ag2S electrolyte for cathodescontaining varying starting amounts of Cu. Cathode current density: 12mA/cm2. Temperature:1523 K.

Ag CuxCu

Ε Ag- Ε C

u/V 3.5 hr

electrolysis

1 hr electrolysis

Figure 6.3: Equilibrium electrochemical synthesis diagram showing change in cathode compositionbefore and after electrolysis for a BaS-La2S3-Cu2S-Ag2S electrolyte containing equimolar propor-tions of Cu2S and Ag2S. : equilibrium Cu content in Ag cathode for this electrolyte.

trochemical phenomena, the dependence of concentration shift on electrolysis time was measured.

It was found that the longer an experiment was run, the more Cu was alloyed into the cathode

(Figure 6.3).

Conversely, when starting with a cathode enriched in Cu, there is a strong drive for Ag deposi-

tion. When the starting composition contains 10mol%Cu, enough Ag is deposited during electrol-

ysis to shift the composition by 2.7%. Such a compositional shift is not possible by electrochemical

means alone, even if the cell were operating at 100% Faradaic efficiency. This indicates that Ag

was also cuprothermically reduced by the following reaction:

Ag2S + Cu→ Cu2S + Ag (6.1)

When the cathode contains 10mol% Cu, both the electrolyte and the cathode favor Ag depo-

sition. With an equilibrium concentration of 5.8% Cu, increasing Ag content through deposition

will lower the Cu concentration of the cathode and thus lower its Gibbs energy. In addition, the

electrolyte also favors Ag deposition by a 265mV potential difference. These twin driving forces

contributed to the significant cathode enrichment in Ag over the course of the experiment.

When the cathode contained moderate amounts of Cu, such as 4.5% or 6%, the cathode was

closer to its equilibrium composition and there was less of a drive for Ag deposition as a result.

The cathode was observed to increase in Ag content through both experiments.

When the cathode contained 4.5% Cu, one might expect that Cu be deposited on the cathode

instead of Ag in order to reach the equilibrium concentration. However, Ag was deposited in-

stead. There are several reasons why this may occur. First, it has been shown that the kinetic and

transport effects at play during electrolysis cannot be neglected entirely when using an equilibrium

electrochemical synthesis diagram to analyze electrochemical data (see Chapter 4). It is possible

that local concentration variations in the vicinity of the cathode caused the equilibrium concentra-

tion to shift, favoring Ag deposition instead. Given that the cell design was vertical, with the liquid

cathode at the bottom of the cell, and that BaS-La2S3-Cu2S and BaS-La2S3-Ag2S were found to

have different densities, such a concentration shift is certainly possible. Finally, in order to allow for

the anode to be lowered into the melt right at the start of electrolysis, the electrochemical cell was

open at the top. The absence of a cap may have allowed for certain elements to volatilize during

the experiment, which could shift the electrolyte concentration and in turn effect the equilibrium

Cu concentration in the cathode.

Despite these possible sources of error, the value of using the above approach to study electrolysis

can be clearly seen in Figure 6.3. The role that cathode chemistry plays in co-deposition is evident

from the difference in the amount of compositional shift, which varied depending on how far the

starting composition was from equilibrium. Additionally, by pre-screening the electrolyte with

equilibrium experiments, it was possible to gain an understanding of the electrolyte behavior, and

use this to select an appropriate concentration to run further experiments.

6.2 Fe-Cu Separation

The second molten sulfide electrochemical system considered is Fe-Cu extraction. Sufficient

separation of Fe and Cu in a molten sulfide electrolyte is essential to successful development of a

new pathway towards Cu deposition: direct electrolysis of copper-bearing sulfide ores to copper

metal [4, 5].

Chalcopyrite is one common Cu-bearing sulfide ore used in Cu production today. This mineral,

CuFeS2, contains equimolar amounts of Cu and Fe. In contrast to the oxide series, for the standard

state electrochemical series for sulfides, Fe is the more noble species (Figure 5.1). This means

that Fe must be successfully removed from the CuFeS2 before Cu can be extracted. However, the

decomposition potential difference between Cu and Fe is only 54mV at 1573K. This suggests that

separation of Cu and Fe through molten sulfide electrochemistry will be very challenging.

Analysis of the Cu-Fe system with an equilibrium electrochemical synthesis diagram, however,

indicates that electrochemical separation may be possible. At 1573 K, Cu and Fe phase separate

to form an Fe-rich solid and a Cu-rich liquid (Figure 6.4). If 17mol% (≈ 4.22wt%) carbon is added

to an iron cathode in order to depress the melting point, the region of phase separation widens. A

solution of copper and cast iron has a large positive energy of mixing, due to repulsive interactions

0 0.2 0.4 0.6 0.8 1273

Fe CuxCu

liquid

liquid + fcc

fcc(Fe) + fcc(Cu)

bcc(Fe) + fcc(Cu)

Figure 6.4: Fe-Cu phase diagram.

between Cu and both C and Fe. The effect of this thermodynamic can be seen in Figure 6.5. If the

electrolyte behaves ideally, the equilibrium cathode composition would be 2mol% Cu, less than that

predicted for Cu-Ag extraction, despite the significantly higher decomposition potential difference.

With encouraging preliminary model results indicating that Fe and Cu separation through

molten sulfide electrolysis is possible, it was necessary to confirm these predictions with experimen-

tation. Equilibrium experiments (as in Chapter 5) were run in order to measure the relative activity

of FeS and Cu2S in a BaS-La2S3 electrolyte. These results were then compared with electrolysis

experiments aimed at selectively depositing Fe from a molten sulfide electrolyte.

Graphite rods were dissolved into high purity electrolytic iron (Fe, Tophet Corporation) in an

induction melter to produce cast iron with minimal contaminants. Pieces of this cast iron were

0 0.2 0.4 0.6 0.8 1273

Fe + C CuxCu

liquid 1 + liquid 2 liquid 1 + liquid 2 + C

fcc + liquid + C

fcc 1 + fcc 2 + C

bcc + fcc + C

eesd temperature

liquid

liquid 2 + C

Fe + C CuxCu

Ε Fe- Ε C

Figure 6.5: a) Fe-Cu-C phase diagram when xCxF e+xC

= 0.17. b) equilibrium electrochemical syn-thesis diagram for the Fe − Cu − C/FeS − Cu2S system at 1573K. At this temperature, cast ironand Cu phase separate to form two different liquid solutions and solid C. : predicted Cu contentin cast iron (2 mol%), assuming ideal behavior in the electrolyte.

melted in an arc melter (Compact Arc Melter MAM-1, Edmund Buhler) under Ar atmosphere in

the presence of a zirconium oxygen getter (Zr, Alfa Aesar, 99.5% metals basis (excluding Hf), Hf

3%). LECO analysis of the cast iron found it to contain 19mol%C (≈ 5wt%).

Barium sulfide (BaS, Alfa Aesar, 99.7% metals basis), lanthanum sulfide (La2S3, Strem Chem-

icals, 99.9% metals basis), copper sulfide (Cu2S, Strem Chemicals, 99.5% metals basis), and iron

sulfide (FeS, Strem Chemicals, 99.9% metals basis) were used to prepare the electrolyte, which

contained 90wt% BaS-La2S3 and 5wt% each of FeS and Cu2S. These powders were mixed in an

argon glove box (Ar, Airgas, Ultra High Purity), and pre-melted in a graphite crucible. The melted

sulfide was then ground back into powder in the glove box before being added to an alumina cru-

cible (Al2O3, Advalue Technology) along with the cast iron. A piece of alumina was placed atop

the crucible as a loose-fitting cap to minimize volatilization, and the entire setup was loaded into

a vertical tube furnace (Lindberg/Blue MTM Mini-MiteTM). The crucible was supported by an

alumina stage containing an alumina-sheathed “Type R” thermocouple. With the exception of the

use of an alumina crucible in place of a graphite one, the equilibration setup was identical to the

one shown in Figure 5.4.

Galvanostatic electrolysis experiments were performed by colleagues in the Allanore Group and

full detail of the experimental setup will be given in an upcoming publication detailing the group’s

efforts to produce Cu from chalcopyrite by molten sulfide electrolysis. Similar to the Cu2S-Ag2S

electrolysis experiments, a pool of molten metal (C-saturated Fe) served as the cathode. Graphite

was used as the anode, and the cell setup was vertical, with the liquid cathode at the bottom and

C anode at the top. Post experiment, the composition of the cathode and sulfide were analyzed

with ICP-AES and LECO.

6.2.2 Results

After equilibration, the cast iron was found to contain 0.58mol% Cu. The electrolyte concen-

tration had shifted as well during the course of the experiment. ICP-AES analysis revealed that

the FeS-Cu2S portion of the sulfide contained approximately 76mol% FeS and 24mol% Cu2S.

These results give a value of ρCu2S = 0.46. This indicates that FeS and Cu2S do not behave

composition range of electrolysis experimentsΕ F

e- Ε C

Fe + C xCu Cu

Figure 6.6: Equilibrium electrochemical synthesis diagram for the Fe−Cu−C/FeS−Cu2S systemat 1573K for a cast iron cathode containing 19mol%C showing measured equilibrium Cu contentin cathode () as well as the cathode composition ranges after various electrolysis experiments.

ideally relative to one another in the electrolyte, rather, there is an energetic drive for the supporting

BaS-La2S3 electrolyte to mix with Cu2S instead of FeS.

During electrolysis, a small variation in Cu content was found for several different experiments.

The Cu composition in the cathode post-electrolysis ranged from 0.6mol% to 1.36mol%. A compar-

ison between cathode composition after equilibration and after electrolysis is shown in Figure 6.6.

6.2.3 Discussion

Overall, very low amounts of Cu were found to alloy in the cast iron cathode. Equilibrium

experiments produced the lowest level of alloying at 0.58mol%. Even accounting for the shift in

electrolyte concentration, this Cu content is still lower than that predicted by an ideal solution

model (approximately 1mol% Cu). Therefore, it can be concluded that FeS and Cu2S interact

differently with the supporting electrolyte. These interactions favor mixing with Cu2S over FeS,

which drives the electrochemical cell towards FeS reduction.

In addition to a preference for Fe deposition due to electrolyte thermodynamics, Fe deposition

is also favored by the cathode chemistry. There is a large positive energy of mixing for Fe and

Cu metal, leading to phase separation in the cathode. This energetic is enhanced by the addition

of C and demonstrates the significant role the cathode can have in influencing an electrochemical

reaction.

More Cu was deposited on the cathode during electrolysis than equilibrium experiments (Fig-

ure 6.6). As in the other electrochemical case studies analyzed with this model, there are several

reasons why this may occur. First, the primary goal of the Fe electrolysis experiments was the

development of a new industrial process to produce Cu metal directly from chalcopyrite. Accord-

ingly, the experiments were run at larger cathode current densities (≈ 1A/cm2). It was shown in

Chapter 4 that larger current densities tend to produce a greater degree of cathode alloying, and

the results of the Fe-Cu separation experiments are consistent with that observation.

In addition, in order to test the tolerance of the system for variations that are common in

industry, but less common in the laboratory, there was variation in both FeS-Cu2S ratios as well

as C content in cast iron between the electrolysis experiments. Both compositional shifts can

be expected to influence the true equilibrium Cu content in the cathode. However, comparison of

equilibration results to electrolysis results shows that equilibrium experiments, in combination with

an equilibrium electrochemical synthesis diagram, can be used to define an approximate range of

expected cathode composition, despite small variations in system concentration. This approximate

range could be used to predict the results of electrochemistry. In the case of Fe-Cu-C, this prediction

is more accurate than present methods of estimating electrochemical outcome, which would have

discounted Fe-Cu separation from sulfides as impossible due to their minimal difference in standard

state reduction potential. This is a strong indication that although this model is an equilibrium

model, it has utility in analyzing industrial processes as well as laboratory-scale ones.

6.3 Summary

The difference between Ag2S-Cu2S separation and FeS-Cu2S separation highlights the effect

that solution thermodynamics of both the electrolyte and the cathode have on electrochemical

processes. Despite the decomposition potential difference of Fe and Cu being almost 5 times less

than that between Ag and Cu, both equilibrium and electrolysis experiments tended to produce

greater separation of Fe from Cu than Ag from Cu.

The Ag2S-Cu2S system has a standard state decomposition potential difference of 257mV, but

a strong drive for Ag-Cu alloying in the liquid cathode as well as an electrolyte that tends to

favor mixing with Ag2S over Cu2S. Both of these factors together lead to a greater increase in Cu

deposition than would be expected from standard state thermodynamics alone.

In contrast, the FeS-Cu2S system has a standard state decomposition potential of 54mV. This

alone should indicate that Cu and Fe will be very difficult to separate using molten sulfide electrol-

ysis. However, energetic repulsions between Cu and cast iron, along with an electrolyte that favors

mixing with Cu2S over FeS, lead to less Cu deposition than standard state thermodynamics would

indicate.

Considering the high reactivity of sulfides and their relatively unknown thermodynamic proper-

ties, it would be difficult to come to such a conclusion without relative activity measurements and

equilibrium electrochemical synthesis diagrams. Equilibrium electrochemical synthesis diagrams

show directly the influence different cathode concentrations have on a system’s drive to either co-

deposit or separate. Such a method of analysis can be used to iterate quickly through different

possible cathodes in order to find one that best suits the desired electrochemical outcome. For

example, increasing C content in the cathode should enhance electrochemical separation of Cu and

Relative activity measured in the Wagner-Allanore reference state allows for the quick ther-

modynamic study of new electrolytes. By only considering the activity of the two species being

investigated for co-deposition, the measurement is intuitive to the electrochemist seeking to quickly

understand if his electrolyte is optimal for his desired result. The sulfide studies in this thesis focus

on the behavior of FeS, Cu2S, and Ag2S in a BaS-La2S3 electrolyte. From a comparatively smaller

amount of experiments than would be necessary for a traditional activity analysis, it was possible

to gain a useful understanding of how the supporting electrolyte interacts with the electroactive

species, and to use this understanding to design future electrochemical experiments.

Further experimentation is necessary in order to determine the effect of concentration on FeS-

Cu2S thermodynamics, as well as to investigate the behavior of other more complex solutions

that are relevant to both electronic waste recycling as well as direct reduction from ore: namely,

FeS-Cu2S-Ag2S thermodynamics.

Bibliography

1007/s11837-014-1114-9.

174328509X431463.

0-444-50206-8.

0013-4651. doi: 10.1149/2.0821603jes.

Chapter 7

Predicting Solution Behavior in

Non-Electrochemical Systems: Rare

Earth Magnet Recycling

7.1 Introduction

The overarching goal of this work has been to present an alternative to traditional thermody-

namic modeling methods of high temperature solutions. Although the focus has been primarily on

application to electrolytes, it is critical to note that this is by no means the limit of this approach.

By using the equations of classical thermodynamics to merge select high-quality data with limited

calculations, new insights on any material may be gained. In this chapter, that methodology, which

forms the core of my electrochemical model, is applied to a non-electrochemical system.

As in Chapter 4, the rare earth system is used to verify this approach. Like rare earth electrol-

ysis, the data surrounding rare earth magnet metallurgy is scattered and incomplete. There is no

commercially available CALPHAD model for the complete rare earth magnet system, but certain

binaries and ternaries, for example, Fe-Nd-B and Nd-Pr, have been optimized separately [1–5], with

limited integration of multiple rare earth elements alongside iron and boron. The case is further

complicated by a lack of a solution model able to accommodate both additives (e.g. Al, Ga, Nb)

as well as impurities (e.g. C, O, S). In addition, gathering experimental data is hindered because

the process conditions of rare earth magnet production are kept proprietary by the companies that

manufacture them, and so the experimental data available was measured under a variety of different

conditions. While this lack of data may be discouraging for those wishing to perform a traditional

fully computational or experimental analysis, in this chapter I demonstrate how, with the hybrid

approach to modeling, valuable information can still be obtained for the system.

7.2 Motivation

Rare earth magnets of the Fe-R-B type (iron, rare earth, boron) have become increasingly

popular for their use in everything from small electronics to turbines. The rare earth elements in

these magnets are alloyed to achieve a composition of more than 60% iron, producing an iron-rich

microstructure not unlike that of hypoeutectoid steel. In place of pearlite, the large grains are an

Fe-R-B compound phase, called the 2-14 phase for its stoichiometry: Fe14R2B. The 2-14 grains are

separated not by ferrite, but by a metallic rare earth rich solid-solution grain boundary phase [6,

7]. Figure 7.1 shows a schematic of the typical microstructure found in an Fe-R-B type magnet.

Unlike pearlitic steel, this alloy must be rapidly quenched for this microstructure to appear: at low

temperature an iron solution is favored over the Fe14R2B compound. If processed correctly, this

iron-based alloy has demonstrated unique bulk magnetic performances, creating the opportunity

to miniaturize magnets for extremely powerful magnetic fields. Figure 7.2 gives an overview of

the main processing steps involved in Fe-R-B magnet manufacturing. Ultimately, the cast alloy

is jet milled into a fine powder and sintered into its final form. Magnet production, therefore,

incorporates many areas of ferrous metallurgical knowledge, from casting to powder metallurgy. At

the core of this process is the chemistry of the cast alloy. This composition dictates the elemental

distribution in the final microstructure, and in turn, the magnetic performance. As in high-end

steel production, elemental compositions are controlled below a fraction of a weight percent at

casting and problematic impurities like Si and P are kept to an absolute minimum.

In its methods of casting, powder metallurgy, and impurity control, the rare earth magnet in-

Figure 7.1: Schematic of a typical Fe-R-B magnet microstructure showing the magnetic 2-14 grainsseparated by a rare earth rich “other metallic phase” at the grain boundaries.

dustry drew inspiration from the technology of the steel industry to improve and expand. However,

rare earth metals have a supply pipeline and market very different from steel because primary

production occurs mostly in one country, China. Because most rare earth mines and smelters are

concentrated in this single country, the market is exposed to the political, environmental, and social

risks that arise from not having sufficient alternative sources readily available in other regions of the

world [8, 9]. In addition to the geographical limitations of mining and processing rare earths, their

chemistry provides other challenges. The rare earths are f-block metals, and can be divided into

two subgroups: light rare earths (lanthanum through samarium) and heavy rare earths (europium

through lutetium). Elements within these subgroups are known for their chemical similarity- a trait

that makes separating these elements difficult. Producing purified rare earths in a primary smelter

is expensive, energy intensive, and creates radioactive and acidic waste that require extensive treat-

ment to mitigate their environmental impact [9]. Despite the issues with primary production, the

development of newer, smaller, and faster electronics push for more virgin material to be mined

and processed. For this reason, the effort to recycle magnets has gained increasing interest recently.

Most efforts for magnet recycling focus on bulk magnet waste, which comes from large decom-

missioned equipment such as turbines. Typically still in one piece, their contamination is often

limited to their surface and they have not reacted much with oxygen. Beyond the traditional hy-

Fe-R-B magnet process steps

vacuum induction melting and strip casting

hydrogen decrepitation(embrittlement)

jet milling into powder

pressing and sinteringpowder into block

grinding and polishing block into sellable form

highly oxidized waste (sludge) produced

Figure 7.2: Overview of main processing steps in Fe-R-B magnet production. Highly oxidized wastesuch as magnet sludge is produced mainly during the jet milling and machining steps.

drometallurgical recycling methods, hydrogen reduction [10, 11], chlorination [12], metallothermic

reduction with calcium (Ca) [13] and phase separation with liquid magnesium (Mg) [14] have been

proposed, among others [8]. Magnet sludge created when manufacturing smaller magnets is more

difficult to treat. This is the highly oxidized factory waste produced during jet milling, machining,

and grinding magnets down to their final sellable form (Figure 7.2). Magnet sludge is different

from bulk end-of-life magnets. It has higher levels of oxygen alongside other contaminants from

machining, such as carbon from lubrication. If magnet sludge is recycled, its high levels of oxygen

and other impurities mean it is treated similarly to a mined rare earth ore. Figure 7.3 outlines this

commercial recycling process.

The sludge is first cleaned with acid before being sent back to primary rare earth smelters

where it is mixed with mined ore prior to solvent extraction. Ultimately, pure rare earth metals

are obtained via molten salt electrolysis [8]. During the leaching step, all of the sludge is oxidized,

including portions that may have originally still been metallic. Additional energy is required to

re-reduce these metals to create suitable rare earth metal or alloy feedstock. Despite the challenge

of being highly contaminated, efforts have been made to develop a recycling process targeted

specifically at magnet sludge. Research into these new methods mostly focus on Ca reduction

because of the sludge’s high oxygen levels [13, 15–18].

Recycling sludge by mixing with primary feed aims at recovering the rare earth metal value, and

the end goal is to obtain a purified product that can be sold to downstream production companies

like magnet manufacturers. This strategy may be criticized with two sustainability arguments.

First, if the goal of recycling is to avoid the environmental and economic costs of primary rare

earth production, treating sludge alongside primary feed will link the secondary rare earth content

value to the primary rare earth value. This is analogous to the connection between scrap steel

price and primary steel price. Second, the rare earth sludge is treated as a type of rare earth ore,

when in fact, at greater than 60 wt% Fe, the sludge is closer in elemental composition to a heavily

oxidized scrap iron alloy [18, 19].

Herein, an alternative approach is adopted. Noting the high Fe content, the sludge and magnet

manufacturing wastes are considered as iron-based materials with essentially the correct metal

Industrial Recycling

acid dissolutionpre-treatment

sludge added to primaryfeed from rare earth mines

solvent extraction of primary feed/sludge mix

molten salt electrolysis

oxidized magnet sludge

Figure 7.3: Overview of the current magnet sludge recycling process. Commercial magnet sludgerecycling occurs at the primary rare earth smelter.

composition needed to produce a magnet, and a process for producing a magnet directly from

such wastes is explored. As in earlier chapters, modeling the underlying chemical thermodynamics

enables a new perspective on materials processing. Therefore, a comprehensive thermodynamic

assessment of two parts is proposed. In the first, the reaction of magnet sludge with oxygen is

modeled. In the second, the reduction energy needed to remove this oxygen and return the magnet

back to its original composition is estimated. Although magnet sludge is also contaminated by

cutting media and lubricant, studies dedicated to sludge recycling have shown promising results in

cleaning away these impurities, which are not typically chemically bonded to the magnet [16, 18].

Since oxygen chemically reacts with the metals in the magnet, it poses a true chemical metallurgy

challenge to recycling. Thus, treating oxygen is the focus of this chapter. In absence of a complete

solution model able to accommodate all elements present in a typical magnet, thermodynamic

calculations herein involve only standard state Gibbs energies of pure components and compounds.

Using standard state to study oxidation has a rich history in ferrous thermodynamics in the form

of Ellingham and Kellogg diagrams, which both relate the oxidation behavior of a pure metal or

compound to the atmosphere and temperature of its environment.

7.3 Magnet Sludge Model

7.3.1 Modeling Methodology

The “Equilib” module of FactSage 7.3 was used to minimize the Gibbs energy and predict

which pure components and compounds were stable under a given temperature and pressure. The

standard-state elements and compounds used were divided into three phase subgroups:

1. the magnetic “2-14” phase consisting of Fe14R2B where R may be Pr, Nd, or Dy;

2. the “other metallic” phase, which consists mostly of rare earths along with additives and

impurities that make up the intergrain region between the 2-14 phase [6, 20]

3. any oxides present.

The “other metallic” phase was modeled using the FactPS database in FactSage [21], with the

exception of R-B compounds, R-Fe compounds, and non 2-14 Fe-R-B compounds [22]. The oxide

phase was modeled using FactPS and Fe-R-B-O compounds optimized by Jakobsson et. al [23].

The 2-14 phase has been reported to initially oxidize less than other magnet components [24, 25].

This limited oxidation did not appear to be accounted for in published thermodynamic models [1,

3, 4], and so herein is assumed to be of a kinetic origin. In order to account for this behavior

and add this constrain on phase stability, the ∆Hf for Fe14Pr2B, Fe14Nd2B, and Fe14Dy2B were

modified from their originally optimized values [1, 3, 4]. For each compound, ∆Hf was lowered by

increments of 10 kJ until overall 2-14 phase formation was favored over competing Fe-intermetallics,

e.g. Fe2Ti. The Gibbs energy functions for the modified compounds are presented in Table 7.1.

Initial Melting of the Rare Earth Magnet

As most magnet producers use proprietary alloy concentrations, a detailed compositional anal-

ysis of feedstock for magnet production could not be found. Lixandru et. al. [19] measured the

major and minor elements contained in laptop speaker magnet waste through ICP-OES: Fe, Nd,

Pr, Dy, Gd, Co, Nb, Cu, Al, Ga, Zn, B. The average composition measured fell within the range

suggested by prior art [6]. Therefore, these published results inform the basis of the present case

study. In order to include the contribution of impurities, four main feedstocks were identified: elec-

trolytic iron, ferroboron, ferroniobium, and praseodymium-neodymium alloy. Commercial sources

of these feedstocks often disclose the composition of impurities such as O and C, and impurity

levels often vary depending on feed grade and source. The commercial sources used were chosen on

the basis of report thoroughness and overall purity: a source that disclosed O, C, Si, and P content

would be chosen over a source that only disclosed C content. When deciding between two equally

well-detailed sources, the one with the lowest impurity content was chosen to reflect a magnet

manufacturing strategy based on premium material grades. The impurity compositions found in

this manner were then added to the total mass balance [26–28]. This method worked well for all

elements except for Si and P. Their estimated weight percent in the initial mass balance was so high

they impeded formation of the 2-14 phase, and as such their amounts in the final mass balance were

reduced to 10% of their originally estimated value. From a ferrous metallurgy consideration, it can

Table 7.1: Modeled Gibbs energy of 2-14 compounds modified to limit reaction with oxygen.Real stoichiometry: Fe(14.00018), R(1.99988), B(0.9994)

Phase T −Range(K) ∆G(T )

Fe14Pr2B 298.15− 500 −489604.7 + 2668.6 ∗ T − 491.2 ∗ T lnT + 8.3E−2 ∗ T 2− 5.1E−5 ∗T 3 + 3334946.8 ∗ T−1 − 62399762 ∗ T−2

500− 800 −466493 + 2120.4 ∗ T − 399.1 ∗ T lnT − 7.3E−2 ∗ T 2 − 3.3E−6 ∗T 3 + 2320237.7 ∗ T−1 − 62399762 ∗ T−2

800− 1068 −261189.6 − 191.5 ∗ T − 59.8 ∗ T lnT − 0.3 ∗ T 2 + 3E−5 ∗ T 3 −20855972 ∗ T−1 − 62399762 ∗ T−2

1068− 1204 −1415268.7 + 10423.7 ∗ T − 1565.5 ∗ T lnT + 0.5 ∗ T 2 − 6.3E−5 ∗T 3 + 1.4E8 ∗ T−1 − 62399762 ∗ T−2

1204− 1811 −492027.2 + 2410.9 ∗ T − 439.3 ∗ T lnT − 6.3E−2 ∗ T 2− 8.3E−7 ∗T 3 + 2320237.7 ∗ T−1 − 62399762 ∗ T−2

1811− 1812 −849221.2+4855.8∗T −754.1∗T lnT −1.5E−3∗T 2 +1237197.8∗T−1 − 62399762 ∗ T−2

1812− 2350 317721.9− 619.7 ∗ T − 110.1 ∗ T lnT − 1.5E−3 ∗ T 2 + 1237197.8 ∗T−1 − 62399762 ∗ T−2

2350− 2800 −316246.8−615.1∗T−110.6∗T lnT−1.4E−3∗T 2+1830376.6∗T−1

2800− 3000 −397703.3− 843.8 ∗ T − 85.9 ∗ T lnT

Fe14Nd2B 200− 450 −491095.8 + 2024.7 ∗T − 360.1 ∗T lnT − 0.3 ∗T 2 + 4.1E−5 ∗T 3−1226885.5 ∗ T−1

450− 576 −3359228.3 + 63255.1 ∗ T − 10474 ∗ T lnT + 15.5 ∗ T 2 − 4.6E−3 ∗T 3 + 1.5E8 ∗ T−1

567− 618 −9697023.9+264314.3∗T−44496.2∗T lnT+69.7∗T 2−1.8E−2∗T 3

618− 3000 −462765.3 + 2524.3 ∗ T − 470 ∗ T lnT

Fe14Dy2B 298− 450 2.2E13 − 1.1E11 ∗ T − 360.1 ∗ T lnT − 0.3 ∗ T 2408333.3 ∗ T 3 +1.2E−4 ∗ T−1

450− 592 −5.3E13 + 1.4E11 ∗T − 10474 ∗T lnT + 15.5 ∗T 2− 4.6E−3 ∗T 3 +1.5E8 ∗ T−1

592− 616 −5.3E13 + 1.4E11 ∗T − 44496.1 ∗T lnT + 69.7 ∗T 2− 1.8E−2 ∗T 3

616− 3000 −5.3E13 + 1.4E11 ∗ T − 470 ∗ T lnT

be assumed that advanced magnet producers would source specialty feed low in Si and P content.

Gd, Dy, Cu, Al, Ga, Zn, and Co were present at such low concentration that any impurities in

their respective feedstock were neglected. Table 7.2 summarizes the composition of the feedstocks

and initial input used in this case study.

This initial input was allowed to equilibrate at 1723 K and 0.5 bar Ar containing 1ppm O2, CO

and H2O; and 5ppm N2 [29] using FactSage’s Equilib software. This step simulated the conditions

in the vacuum induction melting (VIM) furnace, the first step in magnet production. Temperature

and atmospheric conditions were taken from prior art [6, 20]. The results after the melting step

are presented in Table 7.2. This high temperature step refined the magnet composition, as species

were allowed to volatilize off and react with oxygen impurities in the Ar atmosphere.

Strip Casting Kinetic Simulation

In practice, as illustrated in Figure 7.4, after a magnet is melted in the VIM, it is rapidly cooled

via strip casting. This rapid cooling inhibits the formation of ferrite and promotes the 2-14 phase

instead. As in other rapid cooling methods of ferroalloys, carbon rejection and graphite precipitation

are also prevented. The lack of ferrite and graphite creates a metastable alloy. FactSage allows for

modeling of kinetically metastable phases by enabling the user to “de-select”, or suppress certain

phases. If suppressed, the “de-selected” phase will not form and the next stable phase will form

instead. An instructive example can be seen in steel modeling. If graphite is suppressed, cementite

will form instead. To obtain the metastable phases created through rapid cooling, herein all pure

Fe and pure C phases were selected as “suppressed” phases and were not allowed to form. This

led to the formation of iron compounds and carbides. To further simulate rapid cooling, no gas

evolution was allowed. It was at this point in the model that the modified 2-14 compounds were

incorporated in order to account for their kinetic stability. A full comparison between industrial

practice and our results is presented in Figure 7.4.

Table 7.2: Elemental compositions used for calculations with no additional oxygen. Initial: com-positions estimated from published reports. Post-V IM : calculated after “initial” composition wasequilibrated at 1723K to simulate treatment in vacuum induction melting furnace.

Element Initial Post-V IM(wt %) (wt %)

Pr 6.69% 6.72%

Nd 23.46% 23.59%

La 0.02% 0.02%

Ce 0.02% 0.02%

Fe 65.06% 65.41%

Al 0.66% 0.66%

Si 0.01% 0.01%

Mo 0.02% 0.02%

W 0.02% 0.02%

Ti 0.02% 0.02%

Ca 0.003% 0.002%

Mg 0.01% 0.00%

S 0.01% 0.01%

C 0.02% 0.02%

B 0.96% 0.96%

P 0.01% 0.01%

Mn 0.06% 0.05%

Cr 0.005% 0.005%

O 0.09% 0.09%

Nb 0.05% 0.05%

Ta 4E−5% 4E−5%

Dy 1.67% 1.67%

Gd 0.06% 0.06%

Co 0.44% 0.45%

Cu 0.12% 0.12%

Ga 0.05% 0.04%

Zn 0.50% 0.00%

Industrial Practice

VIM1573-1773 K

vacuum or inert atmosphere

Fe, R, B +contaminants & additives

rapid cooling stripcasting to inhibit

ferrite and promote2-14 phases

cast magnet flakeat least 80vol% 2-14

R-rich intergrainminimal oxidation

Thermodynamic ModelFe, R, B +

contaminants & additives

FactSage Equilib1723K, 0.5 bar Ar

no elementssuppressed

289 K, 1 barpure Fe, C and all

gasses suppressedweighted 2-14 phase

calculated baselinephase distribution

90.62wt% 2-148.72wt% intergrain

0.65wt% oxide

Figure 7.4: Comparison between actual magnet manufacturing (left) and the modeling steps usedherein (right).

Oxidation Model

The elemental oxygen content in the condensed phases present post-furnace were incrementally

increased, with a total O content ranging from 0.1wt% to 5.4wt%. The ratios of all other elements

were kept constant. New phases were calculated using Equilib at 298 K with gas phases and all

pure Fe (ferrite) and C (graphite) phases suppressed. The kinetically modified 2-14 compound data

were used, and the Fe14Pr2B phase was suppressed. Fe14Pr2B was not predicted form in the initial

case without added oxygen, and so it was assumed it could not reasonably form on its own at

298K with an increase in oxygen. Because the model was based in standard-state thermodynamics

using only compounds and pure elements, no model for dissolved oxygen was used. All oxygen was

modeled as incorporated in an oxide compound phase.

7.3.2 Results

Simulated Magnet after Melting and Casting

The output from the VIM model at 1723K and 0.5 bar Ar shows minor changes to the overall

magnet composition. Most notably, all of the Zn and Mg were predicted to volatilize off. Starting

with one tonne of initial feedstock, 107g Mn, 64g Ga, 11g Dy, 9g Ca, 3g Cu, and 2g Nd also

volatilized off. This new composition (Table 7.2) was then used to calculate the baseline phase

distribution.

Figure 7.5 shows the calculated weight percent of each phase (oxide, 2-14, and “other metallic”)

and Figure 7.6 shows the distribution of each rare earth element among these three phases. The

oxide phase, present overall at 0.65%, is comprised of Gd2O3 and Nd2O3. The 2-14 phase, at 90.63%,

consists of Fe14Nd2B and Fe14Dy2B. Finally, the “other metallic” phase, with the remaining rare

earth and boron, additives, and impurities, contains GdS, Ce2C3, Nd2B5, LaC2, Pr, Nd, and PrAl2,

among other non-rare-earth containing compounds. The model inputs and outputs at each stage

in the baseline calculation are given in detail elsewhere [30].

Figure 7.5: Calculated phase distribution in the simulated magnet after melting and casting withno additional oxygen added (baseline case).

Figure 7.6: Modeled distribution of rare earth elements among phases in baseline case. Rareearth containing phases present: Dy: 100% Fe14Dy2B, Ce: 100% Ce2C3, Nd: 2% Nd2O3, 96%Fe14Nd2B, 2% Nd2B5 Pr: 82% Pr and 18% PrAl2, La: 100% LaC2, Gd: 14% Gd2O3, 86% GdS.

Figure 7.7: Calculated changes in phases present as oxygen content is increased from 0.09wt% to5.4wt%. l: 2-14 phase, s: “other metallic” grain boundary phase, n: oxide phase. After thegrain boundary phase is completely oxidized near 1.8wt%, the 2-14 phase begins to break downinto oxide and more metallic phases.

Addition of Oxygen

Oxygen was incrementally added to the magnet until 5.4wt% O was achieved. As the oxygen

content increases, the predicted phase distribution changes, as presented in Figure 7.7. The rare

earth elements in the “other metallic” intergrain phase oxidize at the lowest levels of oxygen,

converting into oxide until the “other metallic” phase drops from 8.1% to 0.8wt% at 1.8% O. At

this oxygen level, the 2-14 phase begins to decompose into oxide and various metallic phases. The

2-14 phase continued to decrease with increasing O, until it became the minor phase: 15.2% at

5.4%O.

Figure 7.8 shows that for an oxygen content of 5.4%, the distributions of rare earths among the

phases change significantly from the baseline case (Figure 7.6). The heavy rare earths, Dy and Gd,

are completely oxidized, while some of the lighter rare earths, most notably Nd and Pr, remain in

a metallic state bonded with Fe. Overall, 40% of the rare earth elements by weight are oxidized,

while 60% remain in the metallic phase.

Figure 7.8: Modeled distribution of rare earth elements among phases with 5.4wt% O present.Rare earth containing phases present: Dy: 100% Dy3Al5O12 Ce: 15% CeO2 85% CeCrO3 Nd: 2%Nd3Al5O12, 45% NdBO3, 18% Fe14Nd2B, 35% Fe8Nd Pr: 100% Fe8Pr Gd: 100% Gd3Al5O12

7.3.3 Discussion

Melting and Casting Model Performance

The initial, post-furnace composition of the magnet used in the simulation was estimated to

contain 0.09% O and 0.02% C. This calculated oxygen level is below that reported for finished mag-

net products [7, 18]. It has been observed that oxygen levels in a magnet increase during processing,

particularly during the powder metallurgy steps [24]. Predicting a cast alloy oxygen content below

the level in sintered magnets indicates sufficient performance of the proposed VIM model. The

carbon level 0.02% was also just below the experimentally measured values of 0.03% [18].

In order to produce a material with magnetic performances to the specifications of prior art,

the 2-14 phase should comprise at least 80% of the rare earth magnet by volume, and the “other

metallic” grain boundary phase should be rare earth rich [6, 20, 25]. A weight fraction of 90.63%

for the 2-14 phase was predicted by the initial casting model. The “other metallic” phase predicted

by the model was 82.5% rare earth. Both the initial magnet composition and modeled phase

distribution show good agreement with experimental data available in literature, supporting the

validity of the casting model, and, in a more general sense, the utility of a thermodynamics-based

analysis even when the available data is not complete.

Oxidation Model Performance

The magnet oxidation model results in Figure 7.7 show two important O compositions. First,

at 0.8% O, the phase fraction of oxide overtakes the phase fraction of the grain boundary. In his

study of FeNdB magnet recycling, Lalana noted both virgin and recycled magnets appear to reach

an equilibrium oxygen concentration of 0.55% [24]. Kim et. al found that magnets with O levels

greater than 0.6% showed a higher resistance to further oxidation [31]. These observations suggest

a barrier preventing the magnet from easily up-taking oxygen near 0.55%-0.6%. The crossover near

0.8% in Figure 7.7 indicates that such a barrier may be reproduced with the sole use of chemical

thermodynamics.

The second important composition in Figure 7.7 is at 1.8% O, above which the 2-14 composition

breaks down significantly. It is well-documented that the 2-14 phase remains stable until a signif-

icant portion of the intergrain region has been oxidized. At this point the 2-14 phase decomposes

into iron and rare earth oxide [24, 25]. The model results show a similar behavior, demonstrating

agreement with experimental literature. A phase fraction of 80% by volume for the 2-14 phase is

considered to be the threshold to achieve satisfactory magnet performance [25]. Past this threshold,

the magnet likely becomes unusable and must be either sent to landfill or recycled alongside oxide

feed at the smelter. Our chemical thermodynamic results thus explain the difficulties with recycling

heavily oxidized magnet material [8]. Eventually, at 3.6%, most of the 2-14 phase has decomposed

into rare earth oxide and metallic iron.

The model’s agreement with literature supports the utility of the weighted 2-14 phases. By

lowering ∆Hf of 2-14 compounds until their formation was favored over competing ferrous inter-

metallics, the correct phase distribution was achieved without needing to “suppress” those inter-

metallic phases. This enabled them to re-emerge as oxygen content was increased and the 2-14 phase

decomposed. If all competing phases were suppressed instead, the 2-14 phase would not decompose

and the magnet would saturate in oxygen before reaching 5.4% O, an outcome in contradiction

with literature [16, 18, 32].

7.4 Recycling Model

The thermodynamic model has shown good agreement with available literature, both to re-

produce melting and casting behavior at low oxygen content, and to predict the effects of higher

oxygen content (oxidation) on magnet waste. With both low oxygen and high oxygen cases pre-

dicted accurately solely by thermodynamic means, we can confidently extend this approach to an

unstudied area, as we did in Chapter 6. Herein, we use a thermodynamic-based analysis to evaluate

and compare the feasibility of possible recycling pathways.

7.4.1 Modeling Methodology: Oxygen Removal

In order to remove oxygen, herein modeled as oxide compounds, it was necessary to calculate

the chemical (Gibbs) energy required to reduce the oxide phases to metal and oxygen gas. This ∆G

decreases with increasing temperature for metal oxides. This energetic benefit with temperature is

offset by the energy (enthalpy) cost of heating the sludge, ∆H. Both ∆G and ∆H were considered.

First, condensed phases obtained from the 5.4wt% oxidation model were allowed to reach internal

equilibrium at room temperature. Pure Fe and pure C phases were allowed, and unweighted 2-

14 phases were used. This simulated the changes in the sludge during the pre-reduction steps

and heating from room temperature to the target reduction temperature. At a finite temperature

above room temperature, it is expected that the oxidized sludge will reach internal equilibrium,

redistributing C, O, Fe, and R across the most stable phases. Once equilibrated, ∆H was calculated

as the energy required to heat the newly equilibrated material to processing temperature. ∆G was

found as the energy required to completely decompose the oxidized sludge to metal + (O, O2,

and O3) at the processing temperature. Other gas phases such as CO, CO2, and SO2 were also

permitted, but gaseous metal oxides were not. When calculating the amount of energy needed

to remove O completely from the magnet, 5.4 wt% O was chosen as the starting total oxygen

content in the sludge. This level was similar to experimentally measured values available in the

literature [16, 18, 32].

7.4.2 Reduction Thermodynamics Results

In the study of energy needed to reduce all of the oxides contained in the 5.4wt% O sludge, two

different case studies were considered:

1. the energy to heat and reduce only the rare earth oxides initially contained in magnet sludge,

assuming that the rare earth oxides were first separated from the rest of the waste prior to

treatment.

2. the energy to heat and reduce 1 tonne of simulated waste material at 5.4wt% O.

Figure 7.9 compares these two cases, looking first at the ∆G to reduce the material and second at

how ∆H influences the energy requirements. For consistency, all cases have been normalized by

the mass of oxidized rare earth metal present in each case. This normalization was chosen so the

results could be easily compared with analyses of existing recycling methods [9, 33].

For Case 1, which models the case where rare earth oxides would be first separated from the

magnet before reduction, the amount of oxidized rare earth is fixed at 0.123 tonne RE/tonne waste.

For Case 2, which models the entire magnet waste (including rare earth metals not oxidized initially

due to kinetics), the amount of oxidized rare earth at equilibrium varies with temperature. It can

be seen in Figure 7.9 that less energy is needed to reduce the rare earth oxides if reduced alongside

the rest of the magnet waste than to reduce the rare earth oxides alone. This is true regardless if

∆H is considered. If ∆H is considered, the benefit to reducing the entire magnet waste is lessened

at higher temperatures as more energy is expended to heat the whole magnet as opposed to just the

oxidized fraction. Above 2000K a crossover point will occur where it is more energetically favorable

to treat only the oxides.

Figure 7.10 shows the predicted phase distribution at 1773K as simulated magnet waste is

deoxidized from 5.4%O to 0%O. Fe-rich metallic phases containing no rare earths and oxide phases

containing mostly rare earth oxides are the dominating phases at 5.4%O. As deoxidation proceeds,

the newly reduced rare earth metals combine with iron to form Fe-R metal compounds such as

Figure 7.9: a) minimum Gibbs energy (∆G) needed to reduce equilibrated magnet sludge. b)minimum Gibbs energy (∆G) to reduce magnet sludge with addition of the enthalpy (∆H) to heatthe material to temperature. —: modeled case where RE oxides are separated prior to treatment.- - -: modeled case where sludge is reduced as a whole.

Figure 7.10: Calculated changes in phases present as O content in magnet sludge is reduced from5.4% to 0% at 1773K. s: rare earth rich metallic phase (no Fe), n: oxide phase , l: metallic phasescontaining Fe and rare earth, u: Fe-rich metallic phase (no rare earth). As oxygen is removed, Feand rare earths interact to create new phases.

Fe17R2 and Fe4RB4. Eventually these compounds become the dominating phases.

7.4.3 Implication for Magnet Sludge Recycling Technologies

In the most highly oxidized case of 5.4%O, rare earth elements are only 30wt% of the magnet,

and 89% of the remaining material is iron. Although past recycling efforts have focused on pro-

cessing the material from a rare earth perspective, bearing in mind that magnet scrap is Fe-rich

may offer new outlooks on its end of life treatment and is the core focus of this case study. From a

purely energetic standpoint, as shown in Figure 7.9, less energy is needed to reduce the rare earths

if they are treated alongside the entire magnet material than to reduce only the rare earth oxide.

This benefit results from favorable interactions between iron and rare earth metals. If only oxidized

rare earths are treated, no iron is present. Instead, if iron is kept, Fe-R compounds are quick to

form as the rare earth is deoxidized as shown in Figure 7.10. The two competing reactions can be

described as:

yRxOy →

yR+O2 (7.1)

yRxOy + zFe→ FezR 2x

y+O2 (7.2)

where ∆G 7.2 < ∆G 7.1 at the processing temperatures considered. It is important to note that

at 1773K, the temperature of the deoxidation analysis in Figure 7.10, the magnet should be mostly

liquid [24]. Because herein we do not account for liquid solution behavior, there is no depression

of the melting point and thus the model considers mostly solids alongside liquid compounds with

a standard state melting temperature below 1773K. For example, the stable form of pure iron at

1773K is BCC solid, and so all of the pure iron in the model at 1773K is considered to be BCC.

It is well-known in thermodynamics that metals which are ordered compounds in the solid state

immediately below their melting point will display short-range ordering at the stoichiometry of the

compound in the liquid immediately above the melting point. Although Fe17R2 will not exist in

the liquid state, favorable interactions between iron and rare earth will remain after melting, and

thus despite these approximations the model still informs trends in energy requirements during

deoxidation.

Reducing the entire magnet material carries another benefit: no additional energy for mechani-

cal or hydrometallurgical separation is required. This separation energy is significant. An estimated

average 19.2 GJ/tonne rare earth is required to operate the hydrometallurgical pumps needed to

separate rare earth species to prepare them for molten salt electrolysis [33]. Including the cost of

water treatment and the energy needed for solvent handling and consumption, LCA analyses for

hydrometallurgical treatment have estimated a contribution of 58 GJ/tonne rare earth to the foot-

print of rare earth processing [34]. We can calculate the energy required for molten salt electrolysis

of one mole of rare earth metal using the Nernst equation:

∆V = −∆G

nF(7.3)

where ∆V is estimated as a theoretical minimum of around 4.0 volts and the metal ion valency

n is assumed to be 3 [33]. A molar mass of 144.5 g/mol rare earth mix is calculated using the

relative concentrations of Dy, Ce, Nd, Pr, La, and Gd present in this case study. This predicts a

theoretical minimum of 8 GJ/ tonne rare earth required for electrolytic production of rare earth

metals. Combining the theoretical minimum energy requirements for hydrometallurgical treatment

(19.2 GJ) and for electrolysis (8 GJ) gives a total estimate of at least 27.2 GJ/tonne rare earth

required for the traditional processing route shown in Figure 7.3.

This value can be compared to the range of 6-9 GJ/tonne rare earth required for heating

and reducing magnet sludge whole (Figure 7.9). This estimate is similar in magnitude to the

electrolysis minimum, suggesting that most of the energetic savings can be gained by avoiding

elemental separation and hydrometallurgical treatment. Figure 7.11 shows what such a direct

processing route could look like. Accounting for enthalpy, it can be seen in Figure 7.9 that between

1800K and 1900K, ∆H increases with temperature due to melting and boiling of various elements.

These results indicate an optimal temperature for a bulk magnet recycling process near 1700K,

where the ∆G requirements are low but the ∆H costs have not yet started to sharply increase.

Table 7.3 compares the existing sludge recycling process to the energetics needed to completely

remove the oxygen from the magnet at 1700K. Eliminating the hydrometallurgical step and reducing

the material directly would result in an estimated minimum energy saving of 78%.

The direct reduction of magnet sludge would be a streamlined “magnet-to-magnet” recycling

method. Rather than completely break down and separate the waste into its 25+ elements, only

to be re-mixed into a new magnet, one can envision a route (Figure 7.11) where the waste is

treated whole. Only minor elemental additions would be necessary to correct the stoichiometry

to be commercially acceptable. Furthermore, the optimal temperature, 1700K, is near the 1723K

temperature used in the initial melting and casting step, and within the range proposed by various

patents [6, 20, 25]. One can envision a unified process where the recycled material is reduced in-situ

before being directly cast into a new magnet.

Metallothermic reduction is one possible high-temperature deoxidation method. Figure 7.12

shows the ∆G to reduce the rare earths present in this case study. La and Ce, which require

Whole Sludge Recycling

cleaning pre-treatmentto remove lubrication

high temperaturereduction

oxidized magnet sludge

Figure 7.11: Steps for direct recycling of magnet sludge.

Table 7.3: Comparison of theoretical energy needed for the existing magnet sludge recycling methodand the alternative of direct reduction of entire sludge without primary feed or elemental separation.

Feedstock Product Process Theoreticalminimum

energy

Theoreticalminimum

energy(GJ/tonne) MWh/tonne

ExistingMethod

magnetsludge andprimary feed

individuallypurified,separateREEs

hydro-metallurgicalseparationand moltensaltelectrolysis

27.2 7.6

AlternativeMethod

magnetsludge

mixed REand iron nearproportionsneeded formagnet

directreductionprior tovacuum meltand strip cast

7.5 2.1

less energy to reduce, are not shown. The similarity in reduction energy among Pr, Nd, and Gd

highlights the challenge in separating and purifying these elements. Ca, which has often been

suggested as a possible reductant for rare earth magnet recycling, is also pictured [16, 18]. Dy

cannot be reduced by Ca at 1700K. If Dy is left in an oxidized form and removed via slagging,

there would be a loss of 14% of the total RE value [35]. In order to recover this value, the slag

would need to be subjected to further processing, or an alternative to metallothermic reduction,

such as electrolysis, should be considered. Electrochemical deoxidation has been shown to be an

effective method at increasing the chemical potential of Ca so it can reduce Dy and other reactive

rare earths [36].

7.5 Summary

Although rare earth magnets are widespread in modern technology, their recycling methods are

far from modern. Currently, magnet sludge is often sent back to its primary processing feed and

mixed with ore: all metallic material is oxidized via hydrometallurgy before being reduced and

purified. Often, all this effort is expended only to re-mix the metals into a new magnet. While the

Figure 7.12: Ellingham diagram showing the ∆G of formation of relevant rare earth oxides andcalcium oxide, a popular choice for reductant in rare earth recycling. ∆Gf is very similar for thevarious rare earths, highlighting their chemical similarity and the resulting difficulty in purificationfrom ore.

heavy environmental cost of rare earth processing is well-known, and is the source for significant

drive to develop greener methods, innovation is hindered by a fundamental lack of data. Without

an understanding of the chemical interactions in the rare earth magnet system, it is difficult to

know a priori if a new recycling path is viable. By making use of what is known about the rare

earth magnet system, and combining this information with the fundamental equations of chemical

thermodynamics, new understandings of the system may come to light. In turn, this will allow for

experimentalists to gather more targeted data, feeding even more precise predictions.

The rare earth magnet case study is an instructive example into the utility of this approach.

In absence of a full model detailing the interactions of all 25+ elements typically found in a rare

earth magnet, a hybrid model based in standard state classical thermodynamics was adopted.

Through this, the behavior of magnet material as it is melted in the VIM and as it oxidizes

during sludge production could be accurately represented. Comparison with literature shows correct

prediction of certain phenomena, such as delayed breakdown of the 2-14 phase and correlation of

oxidation resistance to oxygen saturation of non 2-14 phases. By extending the modeling effort into

screening for possible recycling technologies, it was predicted that significant energy savings (78%)

could arise if magnet separation and purification steps are skipped in favor of reducing the sludge

whole. An early screen of possible alternatives was conducted: it was found that Ca reduction or

electrochemical deoxidation are promising pathways for more sustainable magnet recycling. Further

work should continue to use this methodology to continue screening for alternatives, and to advise

further experimentation on the subject.

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[32] Ken-ichi Machida et al. “Effective Recovery of Nd–Fe–B Sintered Magnet Scrap Powders

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elsevier.com/retrieve/pii/S092583889800807X.

Chapter 8

Future Work

A model linking the solution properties of a metal cathode to the thermodynamics of an elec-

trolyte has been derived, and the utility of using this model to quickly study and screen electrolytes

has been demonstrated. Additionally, the value of re-framing activity in terms of a new reference

state, the Wagner-Allanore reference, state was shown in Chapters 5 and 6, where it was used to

study a new process: molten sulfide electrolysis.

Electrochemistry is a complex field, with multiple competing phenomena contributing to overall

cell behavior [1, 2]. Thermodynamics, kinetics, transport, heat transfer, and surface interactions

all come into play, and each influences the other. The models and methods put forth in Chapter 3

are thermodynamic. The role of thermodynamics in high temperature liquid systems is significant,

as can be seen by the model agreement with test cases. However, further development of this

research to incorporate more complex systems and phenomena would certainly be beneficial and

would undoubtedly increase agreement between model predictions and experimental results.

8.1 Multiphase Systems

Both electrochemical synthesis diagrams and our new reference state define the properties of one

species relative to another. Expanding modeling efforts beyond the binary would enable analysis

of higher-order systems. For electrochemical synthesis diagrams, this extension would be similar

to ternary phase diagram derivations. A three-dimensional potential surface would need to be

maximized, producing a three-dimensional synthesis diagram. Furthermore, the interplay of three

electroactive species, and their effect on each other, must be considered.

Finally, although our expanded synthesis diagram derivation can accommodate non-ideal solu-

tion models, we have not incorporated the effect of compound formation in the cathode. It would

likely have the opposite effect of phase separation- a vertical discontinuity in the synthesis diagram

and a prediction of difficult separation. However, more work is needed to fully investigate.

8.2 Anode Dissolution

Modeling efforts so far have focused only on the relationship between the cathode and the

electrolyte in order to understand the dominating reduction reaction. The anode is assumed to

be inert, with the anodic product gaseous and pressure held constant. In certain electrochemical

processes, the anode can also influence the solution thermodynamics of the cell. For example, in

electrorefining, one species is selectively dissolved from a mixed metal anode and then deposited

on a more pure cathode. The characteristics of the anode’s alloy will certainly effect which species

is dissolved first, or if two species are co-dissolved. Depending on the cathode and electrolyte

chemistry, there will be an interplay between all three solutions that will influence the overall

thermodynamics of the cell. Therefore, expanding modeling efforts to include anode chemistry is

an important direction for future work.

8.3 Kinetic Contributions

It was demonstrated in Chapter 4 that non-thermodynamic effects will shift experimental out-

comes away from model predictions. In the Ni-Co case study, for example, increasing current density

increased the amount of alloyed Co in excess of what the equilibrium electrochemical synthesis dia-

gram predicted. It was hypothesized that this result was due to mass-transport limitations, which

was supported by the relative activity coefficient ρCoCl2 increasing with current density. It is likely

that the relative activity measurements captured a local concentration, representative of electrolyte

conditions in the vicinity of the cathode, rather than the bulk. More experimentation is neces-

sary to confirm this hypothesis. It is suggested that future work looks at comparing equilibration

and chronopotentiometry results for a system with well-understood thermodynamics and kinetics.

Voltammetric studies aimed at determining the rate-limiting step in electrolysis will also be useful

in this effort. Alternating current cyclic voltammetry studies, which can separate various kinetic

contributions into different Fourier harmonics, are an ideal experimental method.

Once the influence of non-thermodynamic contributions on an equilibrium electrochemical syn-

thesis diagram are better understood, it could be possible to incorporate them in a re-derivation

of the model. A total cell voltage Ecell can be described in terms of the theoretical thermodynamic

voltage (E) alongside a series of kinetic overpotentials (η):

Ecell = E + ηmt + ηct + ηΩ (8.1)

where ηmt is the overpotential due to mass transport, ηct, charge transfer, and ηΩ, solution resis-

tance. If all overpotentials can be quantified and combined with the thermodynamic E, then Ecell

can be fully modeled. A blended kinetic-thermodynamic diagram would be the result, similar to

phase diagrams showing spinodal decomposition regions.

Bibliography

[1] Allen J. Bard and Larry R. Faulkner. Electrochemical Methods- Fundamentals and Applica-

tions. Second. J. Wiley, 2001. isbn: ISBN 0-471-04372-9.

[2] John Bockris, Amulya Reddy, and Maria Gamboa-Aldeco. Modern Electrochemistry Volume

2A. Second. New York, NY: Kluwer Academic Publishers, 2000.

Chapter 9

Conclusion

Studying the thermodynamics of a system is an essential step in the research and development

of new technologies. It is only by understanding where energy wants to flow that we can come to

understand how it will flow in practice. In high temperature electrolysis, transport and kinetics are

generally fast and thermodynamic effects typically dominate. Understanding the thermodynamics

of a molten salt electrolysis process, then, should help inform on overall cell behavior. Due to the

complexity of the solutions and interactions at play, however, there has been very little success on

quantifying the link between thermodynamics and electrolytic product.

The models derived in Chapter 3 represent the first semi-quantitative method to predict which

species will deposit on the cathode. It is important to note that the model is not fully quantitative,

due to the limitations in system definition for the derivation and the lack of non-thermodynamic

effects as well as anode influence (see Chapter 8). However, this model is an important step forward

for electrochemical modeling, a step away from qualitative “trial-and-error” methods or standard

state simplifications.

9.1 Demonstrated Outcomes

9.1.1 The Wagner-Allanore Reference State

Molten salt electrolytes are typically multicomponent systems with complex interactions be-

tween highly reactive species. Efforts to model or measure their activity with respect to Raoultian

or Henrian reference states can be challenging. The Wagner-Allanore reference state, derived in

Chapter 3, was derived specifically for electrolytes. It was demonstrated in Chapter 5 that much of

the important information about a system’s thermodynamics is retained when activity is measured

in the Wagner-Allanore reference state, even though it is only a relative reference state.

Measuring relative activity has several key trade-offs to measuring traditional absolute activ-

ity. While absolute activity carries information about the entire system (through Gibbs-Duhem),

relative activity only captures data about two species in that system. Nevertheless, relative activ-

ity data is significantly easier to measure from an experimental standpoint (no thermodynamic or

electrochemical reference is needed). Additionally, being fixed along a pseudobinary, it is intuitive

to understand even if the electrolyte is complex. Its use alongside equilibrium electrochemical syn-

thesis diagrams makes a powerful combination: the electrochemist can quickly measure a system’s

activity as it pertains to co-deposition, and use this information to determine how efficient a novel

technology may be at electrochemical separation.

It is interesting to note that very little assumption is made regarding the behavior of the

electrolyte species. For the purposes of representing activity, the electrolyte is given as AX/BX,

rather than as an ionic form (AnA+/BnB+). Similarly, any anion complexes that may form through

solvation are not considered. This simplistic formalism is adopted for the purposes of integration

with thermodynamic models. In the past, much confusion has arisen in the literature due to the

discrepancy between this formalism, which is the convention for electrolyte thermodynamics, and

the true ionic nature of the electrolyte (see [1–3] for series of exchanges in the literature debating this

topic). It is worth re-stating here, however, that relative activity is calculated from measurements

of EA − EB, which is purposefully left generalized [4]. By measuring AX relative to BX, any

issue with ill-definition of electrolyte reference can be assumed to be “normalized out”, as long

as both AX and BX are referenced to the same standard state (i.e. both must be thought of

as oxidized compounds, rather than one as an ion AnA+ and one as a compound BX). Further

research must be done to determine if this assumption holds, and if relative activity is a valid

framework for electrolyte thermodynamics, in cases where the nature of A and B in the electrolyte

are substantially different: for example, if A is complexed as a cation and B as an anion.

9.1.2 Predictive Electrochemical Modeling

The expanded equilibrium electrochemical synthesis diagram derivation (Chapter 3) is the first

semi-quantitative model for predicting which species will be reduced at the cathode. If thermo-

dynamic information about the electrolyte is known, then the composition of the alloy formed at

the cathode can be estimated. Chapter 4 demonstrated that even simple assumptions about elec-

trolyte behavior, such as an ideal solution model, will generate predictions close to experimental

outcome. This is because the energetics of cathode alloying play a very significant role in overall

cell performance.

In Chapter 6, this new predictive model was utilized in the development of molten sulfide elec-

trolysis for two systems: Fe-Cu and Ag-Cu. It was found that by taking into account cathode

alloying as well as relative activity measurements, it was possible to realize the limitations on sep-

aration for both systems. Fe-Cu, predicted to co-deposit by standard state thermodynamics, was

found to achieve separation close to the concentration of blister Cu due to the energetic repulsions

between metallic Fe and Cu, enhanced by the presence of C. On the contrary, the favorable interac-

tions between Ag and Cu, leading to a negative energy of mixing, results in significantly more Cu

deposited in Ag than standard state thermodynamics would predict. Additionally, in the Ag-Cu

study, it was shown that relative activity measurements could be used to pre-screen an electrolyte

in order to find the optimal composition to begin experimentation.

Blending experimentation, classical thermodynamic relations, and CALPHAD-modeling allows

for greater insight on a system than could be obtained by one of these approaches alone. Although

there is little information available on the process conditions of rare earth electrolysis, the equi-

librium electrochemical synthesis diagrams in Chapter 4 were used to understand the behavior of

Pr-Nd co-deposition with only limited, scattered data. The benefits of this method are applicable

beyond electrochemical systems. In Chapter 7, it was demonstrated how this approach to model-

ing was able to reveal new information about magnet sludge and even propose new pathways to

recycling and recovering the rare earths from this sludge.

9.2 Method Limitations

9.2.1 Limitations of a Relative Reference State

The greatest advantage of the Wagner-Allanore reference state, its relative nature, is also its

biggest limitation. The activity of one species is measured relative to another, i.e. its value is

pinned to the value of a second species. Analysis of a system is thus limited to studying how two

species change with respect to another: this new reference state cannot scale to study how three

species may simultaneously interact. It is also for this reason that Gibbs-Duhem may not be used

to find the activities of all other species.

This new reference state may be converted to a Raoultian reference state if a Gibbs-Duhem

integration is desired. However, just as converting a Henrian reference to a Raoultian one requires

knowledge of the Raoultian activity coefficient γ∞, converting the Wagner-Allanore reference re-

quires γA, where A is the more noble species (more positive reduction potential on the electrochem-

ical series). Unlike the Henrian case, however, γA cannot be assumed to be constant and must be

measured across the composition range. In such cases, it is preferable to simply measure activity

directly in the Raoultian reference state. If the two relative species in question are sufficiently dilute

and display Henrian behavior, then γA = γ∞ and the Wagner-Allanore reference state simplifies to

the Henrian reference state.

In addition, defining activity in a relative way causes limitations in defining activity at concen-

tration extremes. As the activity coefficient ρ is defined by:

ρB =γBγA

if γA → 0, then ρB will be undefined. Because electrolytes do not always obey Henry’s law, it is

possible that this condition may occur when xA → 0 [5]. It is worth noting that if both A and B

are extremely dilute in the electrolyte, then both γA and γB will approach 0. Although both γ may

be small, if they have similar orders of magnitude, then a relative activity framework may provide

a better resolution for the behavior of A and B in such regions than an absolute framework. Such

dilute solutions were not studied in the course of this thesis but would be an interesting future

direction to test the limits of the new reference state.

9.2.2 Limitations of Selectivity Model

While the expanded derivation of equilibrium electrochemical synthesis diagrams has shown

that the model can provide valuable insight into electrochemical processes, it does possess certain

inherent limitations beyond the need for expansion/improvement as discussed in Chapter 8. In

particular, it relies on the cathode chemistry being well-known. In order to compute an EESD, the

activities of the species in the cathode must be known across the entire binary. Preferably, these

activities will have been modeled in a CALPHAD software: this will allow the generator of the EESD

to build a diagram with a high resolution along the composition axis, which will then increase the

accuracy of the analyses made with an EESD. Unfortunately, this ties the performance of EESD’s

to the robustness of the CALPHAD solution model. If one decides to use only experimental activity

data to create an EESD, then they must decide between limiting the resolution of their diagram

to that of their data (e.g. every 5 mol%), or use curve-fitting/interpolation to fill in the gaps along

the composition axis. Interpolation-based methods should be approached with caution, however,

as they can easily deviate from actual values in areas where data are scarce. This is a particular

concern at concentration extremes (x → 0 or x → 1). Further discussion on the limitations of

interpolating experimental data will be given in Appendix A.

Finally, as mentioned in Chapter 8, the current derivation for synthesis diagrams are purely

thermodynamic, with no kinetic contributions taken into account. Therefore, synthesis diagrams

should be used to study electrochemistry in regimes where thermodynamic effects dominate: high

temperature, liquid systems. Solid cathodes or electrolytes will result in concentration gradients

generated by slow species diffusion. Until kinetic effects on synthesis diagram predictions are better

understood, the extent to which these gradients will shift experimental cell behavior from model

predictions are unknown.

9.3 Potential for Impact

9.3.1 Impact on Thermodynamic Studies

The derivation of a new reference state specifically for the unique challenges of electrolytes has

the potential for significant impact on the future of thermodynamic studies of electrolytes. Relative

activity can be quickly and easily measured, making it ideal for screening new systems. With only

absolute activity available, experimentalists must chose between trial-and-error style experimental

approach for new electrolytes or investing significant time and energy into developing a suitable

reference for a full activity study. The trial-and-error route is inefficient because the electrochemist

has little information on whether he is choosing a suitable system. A good electrolyte may eventually

be found after numerous experiments on various solutions narrow down viable candidates, however,

without a model for linking these results together in a meaningful way, such an approach will always

be qualitative. In contrast, full activity studies take time to develop proper experimental methods

and generate enough data. When used for electrolyte screening, this approach is impractical because

effort is being expended to fully study a system that later experimentation may reveal unsuitable

for electrolysis.

Relative activity measurements in the Wagner-Allanore reference state represent a “middle

ground” between the two existing electrolyte research methods. Targeted thermodynamic data

specific to electrolysis can be quickly measured and used to make determinations about further

experiments, speeding the development of new technologies. If relative activity measurements

became a mainstream method for thermodynamic study, it would enable more experimental study

of reactive solutions, including molten salts. This, in turn, would result in more available data

on such solutions, assisting others in the scientific community who may be studying the same or

similar systems.

9.3.2 A New Outlook on Modeling

The thermodynamic approach outlined in this thesis differs from modern, computational-focused

approaches. Equilibrium electrochemical synthesis diagrams are similar in nature to Pourbaix

Diagrams or Ellingham Diagrams- they are all graphical representations of classical thermodynamic

expressions. Because the electrolyte properties are left generalized when building such a diagram,

and because it only captures the effect of thermodynamics on cell behavior, it is more of a tool to

analyze experimental data than a predictive model. This is in keeping with its semi-quantitative

nature.

While modeling efforts are typically oriented around the goal of replacing experiments, the

models and methods contained herein are inseparable from them. This is not a limitation, but

rather a different goal: to increase both the efficiency and amount of obtainable information from

each experiment.

9.4 Final Thoughts and Perspectives

New electrochemical technologies will undoubtedly play a significant role in developing new

metal production processes. If on one hand, using the electron instead of carbon as the reductant

will reduce the greenhouse gas emissions associated with metal processing, then on the other, opti-

mizing electrochemical selectivity will increase product quality. This has the dual effect of making

electrochemical routes more competitive, as well as further reducing the environmental burden (less

post- or pre-processing purification steps). Through understanding the how the thermodynamics

of the electrolyte and cathode solutions interact, new insights on cell behavior may be obtained.

Both solutions become engineering parameters that can be used either to push the cell towards

separation or co-deposition. Since metal chemistries generally have more data than molten salts,

a constant cathode chemistry can also be used to make determinations about electrolyte thermo-

dynamics. This is particularly useful for developing new technologies where little or no data is

available regarding the electrolyte.

Bibliography

[1] John F. Elliott, David C. Lynch, and Tracy B. Braun. “A Criticism of the Flood-Grjotheim

Ionic Treatment of Slag-Equilibria”. In: Metallurgical Transactions B 6B (1975), pp. 495–501.

[2] Tormod Førland and Kai Grjotheim. “Thermodynamics of Slag-Metal Equilibrium”. In: Met-

allurgical Transactions B 8B (1977), pp. 645–50.

[3] Milton Blander. “Inconsistencies in a Criticism Flood-Grjotheim Treatment of of the Slag

Equilibria”. In: Metallurgical Transactions B 8B (1977), pp. 529–30.

9780444007797.

Appendix A

Alternative Methods for Modeling the

Chemistries of the Cathode and

Electrolyte

The modeling methods discussed in this thesis have focused on an approach that expands and

generalizes electrochemical synthesis diagrams, building upon the methods of G. Kaptay [1]. While

its merits have been shown, this model cannot be used in cases where the full binary of the metal

cathode has not been determined. In this Appendix, a second model has been explored. This model

has the potential to be applicable in systems where the metal binary is not fully determined, and

is built upon the derivations of Ackerman and Moriyama [2–5], which focus on the distribution, or

partitioning, of species between the cathode and electrolyte.

A.1 Introduction to Electrochemical Distribution

The distribution, or separation factor, of a species between the cathode and electrolyte is given

by the ratio of two elements in the metal electrode over the ratio of those same elements in the

electrolyte after equilibrium. For elements A and B present in the electrolyte as AX and BX such

that there are two competing decomposition reactions:

AX → A+X

BX → B +X

AX +B → BX +A

Distribution can be given by:

xAxBxAXxBX

D =xAxBXxBxAX

This can be linked to the equilibrium constant keq for the exchange reaction in A.1, noting that:

keq =xAγAxBXγBXxBγBxAXγAX

Resulting in:

D = keqγBγAXγAγBX

Ackerman argued that the relationship between distribution and the equilibrium constant as

outlined in Equation A.4 allowed for D to be treated mathematically the same as keq [2]. Similarly

to how the equilibrium constant of a chemical reaction B → C could be found by subtracting the

reaction A → C from A → B, the distribution between B and C could be found indirectly by

studying the distribution between A and B and between A and C:

DA−B = kA−BγBγAXγAγBX

DA−C = kA−CγCγAXγAγCX

DB−C =kA−BγBγAXγAγBX

∗ γAγCXkA−CγCγAX

=kB−CγBγCXγCγBX

The ability to indirectly measure distribution rests on the accuracy of the assumption that

species A, B, and C are all sufficiently dilute in the supporting electrolyte and cathode host such

that their thermodynamics are governed by solvent interactions. Under such an assumption, γA in

the cathode host will not change regardless of whether it is alloyed alongside γB or γC .

If the metal and electrolyte display Henrian behavior, then all activity coefficients γ are constant,

and D can be expressed as a constant in terms of Henrian coefficients. The data measured by

Ackerman and others showed a scattering with no consistent trend in concentration, supporting

this hypothesis [2–5].

A.2 Interpolative Approach to Modeling Distribution

Noting the relationship between activity and distribution, it is proposed that distribution can

be modeled directly from activity data. Such a model would be an alternate method to determine

equilibrium cathode and electrolyte composition from solution properties, similar to equilibrium

electrochemical synthesis diagrams.

We use the definition of the equilibrium constant (Equation A.3) to write:

= keqaBXaAX

Noting that this relationship may be expressed as a function of the concentrations of B and

BX, respectively:

(xB) = keqaBXaAX

(xBX) (A.9)

We can define two functions, f(x) and g(x):

0.0 0.2 0.4 0.6 0.8 1.0

Figure A.1: Plot showing the relationship between the concentration of B in the cathode and BXin the electrolyte, as well as the calculated distribution for each concentration. Both metal and elec-trolyte are assumed to follow the regular solution model, with T=1250K, Zmetal=10, Zelectrolyte=10,Ωmetal=300, Ωelectrolyte=-300.

f(xB) = keqg(xBX) (A.10)

This allows for the expression of the concentration xB in terms of xBX :

(xB) = f−1(keqg(xBX)) (A.11)

This relationship can be solved analytically if a solution model, such as the regular solution

model, is available. It can also be solved graphically by interpolating the activity curves for both

B and BX. Figure A.1 shows the link between electrolyte composition and cathode composition,

as well as the distribution at each composition, calculated with Equation A.11.

A.3 Predicting the Equilibrium Distribution

In order to use distribution relationships to predict the equilibrium concentrations of the elec-

trolyte and the metal, a mathematical framework is put forth based on simultaneously minimizing

the Gibbs energy of both solutions.

The change in molar Gibbs energy upon mixing A and B in a metal cathode is given by:

∆Gmixmetal = RT (xA ln aA + xB ln aB) (A.12)

Likewise, the change in molar Gibbs energy upon mixing AX and BX in the electrolyte can be

given by:

∆Gmixelectrolyte = RT (xAX ln aAX + xBX ln aBX) (A.13)

It is proposed herein that by simultaneously minimizing the molar Gibbs energy of mixing both

the electrolyte and the metal, that an equilibrium composition may be determined. The two Gibbs

energies are added and the sum is then minimized in order to minimize the total Gibbs energy of

the system:

∆Gmixtotal = RT (xA ln aA + xB ln aB) +RT (xAX ln aAX + xBX ln aBX) (A.14)

Figure A.2 shows an example of how such an analysis would work for a sample metal system

paired with a chloride electrolyte.

This methodology was tested against one of the distribution cases studied by Ackerman: parti-

tioning of Nd and La in between a Cd cathode host and a LiCl-KCl eutectic electrolyte at 773 K.

In absence of a Nd-La-Cd model in CALPHAD, the metal was fit to a regular solution model using

the Henrian activity coefficients from [6]. The activity data for NdCl3 and LaCl3 in the LiCl-KCl

electrolyte was measured for various amounts of dilute NdCl3 and LaCl3 [7]. In order to keep the

electrolyte model generalized and avoid fitting it to a regular solution model, the activity of the

electrolyte was interpolated as a function of concentration using Wolfram Mathematica.

0 0.2 0.4 0.6 0.8 1

ΔGmix(electrolyte)

ΔGmix(metal)

AX xBX BX

Figure A.2: a) ∆Gmix for sample metallic and electrolyte systems. b) Sum of ∆Gmixmetal and∆Gmixelectrolyte.

LaCl3 xNdCl3 NdCl30.2 0.4 0.6 0.8 1.00

Figure A.3: Distribution of La and Nd between a LiCl-KCl electrolyte and a Cd cathode. s: :modeled distribution from thermodynamic data and summed Gibbs energies of mixing La-Nd andLaCl3-NdCl3. : experimentally determined distribution. Data from [2, 3].

In this way, Gibbs energy curves of both the La-Nd and LaCl3-NdCl3 pseudobinaries in Cd and

LiCl-KCl, respectively, were generated. The sum of both of these curves were minimized, and the

concentration of NdCl3 at this minimum energy was taken as the equilibrium concentration. This

value was then used to find D, the distribution parameter, through equations A.2 and A.11. Fig-

ure A.3 shows the value of the calculated distribution compared to the experimentally determined

values from Ackerman [2, 3].

These preliminary results are encouraging. The modeled result is within the range of error for

the experimental values, both in concentration of NdCl3 as well as in distribution.

A.4 Perspectives on Further Model Development

The expansion of the distribution model proposed above shows promise for correctly predicting

electrochemical outcomes. However, it is critical to note that further study is necessary to refine

the model and correctly determine its limitations. Additional case studies should be tested to verify

this approach. From the preliminary study, specific shortcomings of the model became apparent:

these shortcomings must be addressed before further development and implementation can occur.

A.4.1 Boundary Conditions

One of the strengths of this model is the ability to work independently of CALPHAD models

and generate Gibbs energy curves directly from experimental data. To facilitate this, the Gibbs

energies of mixing are re-framed along the pseudobinary of the species in question. In the La-Nd

case, for example, the concentrations of LaCl3 and NdCl3 was constrained at 0-2.64 mol% in the

LiCl-KCl eutectic. The concentrations of La and Nd were also limited to the same amount in the

Cd cathode. 2.64 mol% was the highest available concentration for which there was activity data.

Such a cap kept the development of an expression for activity in the interpolation range, rather

than in the extrapolation range.

However, if the data range was narrowed even further, to 2 mol% electroactive species in the

supporting electrolyte, then the modeled distribution value was observed to change. Distribution

shifted from its original value of 1.04 (Figure A.3) to 1.6. The predicted concentration of NdCl3

also shifted, albeit by a smaller amount: from 81 mol% NdCl3 to 80 mol%. Similar shifts were also

noticed with changes in interpolation step size.

Although the results of this shift were still within the range of experimental error, the shift

itself causes concern. It suggests that the initial boundary conditions of the model are ill-defined.

One possible explanation could be issues with the interpolating functions used. The expression

developed for the activities of LaCl3 and NdCl3 were used in Equation A.11 to calculate distribution

at each composition. Errors in defining activity between data points by using interpolation would

propogate through the inverse function calculations. Such errors would also impact calculations of

the minima or common tangents for Gibbs energy curves, and would be most pronounced at the

edges of the interpolation regime (minimum or maximum concentration).

A second explanation could be that imposing such a boundary condition on the concentration of

metal and electrolyte is not possible. The equilibrium distribution of two species between the metal

and electrolyte may not exist within the pre-defined boundaries (i.e. the equilibrium electrolyte or

metal composition may be greater than 2.64 mol%). For this reason, the consequences of adding two

Gibbs energy curves defined along a molar pseudobinary is not quite clear. Further mathematical

and thermodynamic analyses are necessary in order to understand the limitations of this method,

and if the entire concentration regime must be defined before modeling (similarly to how equilibrium

electrochemical synthesis diagrams are modeled).

The small concentration regimes studied are also a cause for concern. The distribution studies

referenced focused on solutions that were dilute both in the Cd cathode as well as the chloride

electrolyte. If the changes in modeled distribution as a function of boundary condition are in

fact due to propogated errors from interpolation, then the magnitude of these errors would be

exaggerated as the concentration regimes studied tend towards dilution. For example, if the La-Nd

species were concentrated at 90 mol% of the total solution, then model deviations by 0.5mol% would

mean roughly 0.6% error. If La-Nd were dilute at 2.5 mol% of the total solution, then the same

amount of deviation would cause a 20% error. A comparison of model tolerance for concentrated

and dilute cases is therefore necessary.

A.4.2 Extension to More Complex Systems

Once the boundary conditions of the model have been appropriately defined and possible sources

for error are clarified, the next important step in model development is testing it on other systems

and case studies. Validation in other electrolytes, such as fluorides or oxides, should be considered.

Special attention should be paid to ensure accurate modeling of phase phenomena, such as phase

separation or compound formation.

In the distribution experiments cited above, as well as in the model derived in this appendix,

the case studies focused on instances where one mole of metal produced one mole of electrolyte:

La to LaCl3 and Nd to NdCl3. This stoichiometry is fortuitous because it not only allows the

Gibbs energies of mixing to be defined on the same molar basis, but also the exchange between La

and Nd does not result in production of additional species, such as Cl2. In order to accommodate

electrolytes with other stoichiometries, the derivation should be generalized and the model should

be rigorously tested using these cases.

A.5 Final Thoughts

Distribution modeling represents a complement to the electrochemical synthesis diagram mod-

eling discussed in this thesis. Both models share significant similarities, and both aim to link the

properties of two solutions (electrolyte and metal) by minimizing the Gibbs energy of these solu-

tions. Synthesis diagrams are limited by their dependence on a complete solution model for the

cathode. As such, they cannot be used when the properties of the cathode alloy are unknown.

However, no activity data is required for the electrolyte.

In contrast, distribution models use limited experimental data for both solutions. Thus, while

they rely on the availability of absolute activity measurements in the electrolyte, significantly less

information is needed on the metal side. Early results of this model are encouraging, but they have

only been applied to one system and the limitations are not entirely clear yet. Further investigation

is needed before distribution modeling can be more broadly applied to understanding the behavior

of electrochemical solutions.

Bibliography

8388(93)90430-U.

[4] M Kurata et al. “Distribution behavior of uranium, neptunium, rare-earth elements (Y, La,

Ce, Nd, Sm, Eu, Gd) and alkaline-earth metals (Sr,Ba) between molten LiC1-KC1 eutectic

salt and liquid cadmium or bismuth”. In: Journal of Nuclear Materials 227 (1995), pp. 110–

83. issn: 09258388. doi: 10.1016/S0925-8388(01)00973-2.

[6] Masaki Kurata, Yoshiharu Sakamura, and Tsuneo Matsui. “Thermodynamic quantities of

actinides and rare earth elements in liquid bismuth and cadmium”. In: Journal of Alloys and

Compounds 234.1 (1996), pp. 83–92. issn: 09258388. doi: 10.1016/0925-8388(95)01960-X.

[7] Jinsuo Zhang et al. Rare Earth Electrochemical Property Measurements and Phase Diagram

Development in a Complex Molten Salt Mixture for Molten Salt Recycle. Tech. rep. US De-

partment of Energy, 2018, p. 193. url: https://www.osti.gov/servlets/purl/1432448.

Appendix B

Further Investigation of Molten

Sulfide Solution Properties

Molten sulfides are particularly attractive as a novel electrolyte, partially because of their ability

to solubilize a wide array of elements. Among these are precious metals and copper, making

the electrolyte attractive for new methods of treating Cu-rich electronic waste. One of the main

energetic drawbacks in current electronic waste treatment is the need for sequential processing due

to limited mutual solubility of copper and precious metals in aqueous media (see Chapter 1 as well

as references [1–5]).

While efforts to directly sulfidize gold have thus far been unsuccessful [6], sulfides of gold-silver

alloys have been obtained: uytenbogaardtite (Ag3AuS2) and petrovskaite (AgAuS), and can even

be found in nature [7, 8]. The ability for sulfides to simultaneously host Ag and Au offers a

significant advantage over current electrorefining media: gold does not dissolve in the nitric acid

used for silver refining, and silver forms an insoluble chloride in aqua regia [9].

Further experimentation was necessary to study possible molten sulfide supporting electrolytes

and develop a new electrorefining process. In order to test the behavior of Ag and Au in a molten

sulfide supporting electrolyte, solubility experiments were run in two test electrolytes: Na2S-ZnS

and BaS-Cu2S. Additionally, in order to determine an optimal electrolysis temperature, the melting

behavior of the BaS-La2S3-Cu2S ternary was studied at 1473 K. This Appendix will highlight the

results of these preliminary screening experiments.

B.1 Precious Metal Solubility

B.1.1 Solubility in Na2S-ZnS

Na2S-ZnS was chosen as the supporting electrolyte for the first test case because of its lower

melting point compared to BaS-based electrolytes. This allowed for a lower operating temperature

by about 400 K, which enabled easier screening experiments to verify the literature’s observation

that Au could form a sulfide with other metals.

Na2S (sodium sulfide, Alfa Aesar, anhydrous, 95% minimum purity) was mixed with ZnS (zinc

sulfide, Alfa Aesar, 99.99% metals basis) to obtain the eutectic composition (54 mol% Na2S). The

sulfides were mixed in an Ar glove box (argon, Airgas, Ultra High Purity) before being placed in an

alumina crucible alongside a metal sample of either Ag (silver, Alfa Aesar, 99.9% metals basis) or

Au (gold, Alfa Aesar, 99.999% metals basis). This sample was placed into a vertical tube furnace

(Lindberg/Blue MTM Mini-MiteTM) and heated to 1073 K under Ar flow. The sulfide and metal

were allowed to equilibrate for 8 hours at temperature. The metal loss at the end of the experiment

was used to estimate solubility in the sulfide.

Both Ag and Au demonstrated high solubility in the Na2S-ZnS electrolyte, with SEM-EDS

analysis showing no metallic regions in the sulfide post-experiment. After an 8-hour equilibration

at 1073 K, the measured solubility of Ag was 135 g/L, while the measured solubility of Au was

278 g/L. In comparison, Moebius and Thum cells for Ag electrorefining typically have a solubility

range of 30-100 g/L for Ag, while Wohrwill cells for Au electrorefining have a solubility of 80-100

g/L for Au [9–11].

B.1.2 Solubility in BaS-Cu2S

Encouraged by the preliminary results indicating that molten sulfides could not only solubilize

precious metals, but also that they displayed a higher level of solubility than the industrial aqueous

electrolytes currently in use, the experiments were re-run in a BaS-Cu2S electrolyte at 1488 K.

Barium sulfide (BaS, Alfa Aesar, 99.7% metals basis) and copper sulfide (Cu2S, Strem Chemi-

cals, 99.5% metals basis) were mixed together in an Ar glove box (argon, Airgas, Ultra High Purity)

and pre-melted in a graphite crucible (C, The Graphite Store, Grade EC-16) under Ar flow before

being placed in a graphite crucible alongside a metal sample of either Ag (silver, Alfa Aesar, 99.9%

metals basis) or Au (gold, Alfa Aesar, 99.999% metals basis). Both Ag and Au were pre-melted in

an arc melter (Compact Arc Melter MAM-1, Edmund Buhler) under Ar atmosphere in the presence

of a zirconium oxygen getter (Zr, Alfa Aesar, 99.5% metals basis (excluding Hf), Hf 3%) in order

to remove any residual oxygen from the metal. The graphite crucible was loaded into a vertical

tube furnace (Mellen, SS15R-2.50X6V- 1Z) and heated to 1488 K under Ar flow. After an 8-hour

hold at temperature, the sample was quenched by lowering from the central, heated area of the

tube to the lower, colder end of the tube (Chapter 5). Post-experiment, the metal and sulfide were

separated and weighed. Solubility was estimated by metal weight loss and the sulfide was crushed

into a powder, mounted in epoxy, polished to 2000 grit, and examined under SEM-EDS to ensure

there were no metallic regions present.

Upon cooling, it was found that the BaS-Cu2S electrolyte separated into BaS-rich and Cu2S-rich

regions. Figure B.1 shows the typical microstructure of the electrolyte after equilibration with Ag.

Ag was found to segregate to the Cu-rich phase, with an overall measured solubility of 53 g/L.

Figure B.2 shows the typical microstructure observed after Au solubility experiments. In con-

trast to Ag, Au did not segregate to the Cu-rich phase, but rather formed a phase of its own

with moderate amounts of Ba, Cu, and S. The solubility of Au in the BaS-Cu2S electrolyte was

relatively lower than that measured in Na2S-ZnS: 26 g/L after 8 hours. However, it is likely that

equilibrium solubility was not achieved in 8 hours in this electrolyte. A follow-up experiment held

at temperature for 24 hours resulted in total dissolution of the gold sample. This indicates that

Au has a solubility in the BaS-Cu2S electrolyte greater than 160 g/L, a value more similar to that

observed in Na2S-ZnS.

While Ag appeared to dissolve in the Cu-rich phase of the electrolyte, in which Ag ions could

have possibly substituted for Cu to form a BaS-Cu2S-Ag2S phase, Au showed a different behavior.

It is possible that the Au-rich sulfide phase was an entirely new compound, Au4Cu3Ba6S6, which

primaryphase

secondary phase

primaryphase

Figure B.1: SEM image of quenched sulfide from Ag solubility experiments in BaS-Cu2S electrolyte.Primary phase composition (mol%): 37% S, 29% Ba, 29% Cu, 5% Ag. Secondary phase composition(mol%): 39 % S, 59% Ba, 2% Cu.

primary phase

secondary phase

primary phase

tertiary phasesecondary

Figure B.2: SEM image of quenched sulfide from Au solubility experiments in BaS-Cu2S electrolyte.Primary phase composition (mol%): 34% S, 32% Ba, 33% Cu. Secondary phase composition(mol%): 37% S, 60% Ba, 2% Cu. Tertiary phase composition (mol %): 33% S, 29% Ba, 17% Cu,21% Au

would be in keeping with current observations about Au-sulfides. It has been observed that while

Au2S is generally unstable, Au combined with other metals form more stable sulfides [6–8].

B.2 Isothermal Study of BaS-La2S3-Cu2S Ternary

Research on Cu electrolysis from BaS-Cu2S electrolyte indicated that addition of a third elec-

trolyte, La2S3 may improve the properties of the supporting electrolyte, promoting ionic conduc-

tivity and lowering the vapor pressure [12]. In order to understand the melting behavior of this

new electrolyte, an isothermal study of the material near electrolysis temperature (1473 K) was

Sulfide at various concentrations of barium sulfide (BaS, Alfa Aesar, 99.7% metals basis), cop-

per sulfide (Cu2S, Strem Chemicals, 99.5% metals basis), and lanthanum sulfide (La2S3, Strem

Chemicals, 99.9% metals basis) were mixed in an Ar glove box and loaded into a specially designed

graphite crucible (C, The Graphite Store, Grade EC-16) that could accommodate 0.5 g of each

composition. Figure B.3a details the tested concentrations along the ternary, and Figure B.3b

shows the design of the crucible used. A custom-designed cap for the crucible that fit tightly into

each sample well was used to limit volatilization. Small screws that fit into the four drill-holes in

each arm of the cross further tightened the seal. The setup was loaded into a vertical tube furnace

(Carbolite, model PVT 18/100/350) and temperature was monitored with a “type C” thermocouple

using an Omega data aquisition system (Omega Engineering, Model QMB-DAQ-55). The furnace

was allowed to heat up to 1473 K before being held at temperature for 4 hours under a flow of Ar

to ensure an inert atmosphere.

After the 4-hour hold, the the crucible was slow-cooled to room temperature and then removed

from the furnace. It was kept in the Ar glovebox until it was ready to be opened. Upon opening,

the resulting compositions were photographed and moved to storage vials. These vials were then

transferred back to the glovebox, where the final contents were weighed. Visual inspection was

used to determine if the samples were “entirely melted”, “unmelted”, or “somewhat melted”.

(Figure B.3c). This information was used to determine a preliminary phase diagram by separating

Figure B.3: a) BaS-La2S-Cu2S ternary concentrations tested during isothermal experiment. b)custom-designed graphite crucible showing sample wells and drill holes. c) example of typical“melted”, “unmelted”, and “somewhat melted” samples post-experiment.

regions of the isotherm into solid, liquid, and two-phase, and combining the results with data on

end members and binaries [13, 14].

Figure B.4 shows the results of the experimental study plotted on the ternary phase diagram

for BaS-La2S-Cu2S. The boundary lines drawn are estimated from the experimental data points:

further investigation is required in order to determine the exact boundaries between phases far from

the binary axes. Nevertheless, this work represents an important preliminary step in determining

the thermodynamic properties of molten sulfide electrolytes, particularly with respect to finding an

optimal electrolysis temperature.

B.3 Perspectives

The work presented in this appendix represent a series of preliminary studies aimed at deter-

mining the feasibility of using molten sulfide electrolytes for precious metal processing. While more

experiments are needed, the early results are promising. Solubility tests indicate that molten sul-

fides have a high solubility for copper, silver, and gold, and may be able to support electrolysis of

all three metals in just one electrolyte. This ability does not exist in the aqueous media currently

used in industrial electrorefining. Future studies should focus on more firmly establishing solubility

limits in molten sulfide electrolytes, including in BaS-La2S-Cu2S electrolytes.

While it is likely that there can be simultaneous solubility for all three metals of interest (Au,

Ag, and Cu), this should also be verified with future experiments. Investigations of the Au-Ag-

Cu-Ba-La-S system are particularly important due to the many unknowns about the behavior of

gold sulfides. A possible path for future study could follow the methods of Chapter 5, which would

provide valuable insight on the activity of gold sulfides and their decomposition potential in this

electrolyte. Such information could then be used for development and design of Au electrorefining

technologies in molten sulfides.

Further experimental effort to determine the thermodynamics of the BaS-La2S-Cu2S ternary is

also necessary. More detailed experiments in the style of [13] would be particularly useful in deter-

mining phase boundaries and composition across a variety of temperatures. Such research would

Figure B.4: Estimated isothermal projection of BaS-La2S-Cu2S system at 1473 K based on observedmelting behavior.

advise electrochemists on the best temperature and composition to ensure that their electrolyte is

a stable liquid, ideally with a low vapor pressure. Future isothermal studies are also recommended

to focus on the areas of the ternary where liquid and solid phases are predicted to be in equilibrium,

in order to further refine the estimated ternary projection.

Bibliography

10.3103/S1067821212050070.

174328509X431463.

1007/s11837-014-1114-9.

[6] Mark D. Barton. “The Ag-Au-S System”. In: Economic Geology 75 (1980), pp. 303–316. issn:

0361-0128. doi: 10.2113/gsecongeo.75.2.303.

[9] K G Fisher. “Refining of Gold At the Rand Refinery”. In: Extractive Metallurgy of Gold in

South Africa. Ed. by G.G. Stanley. Johannesburg: South African Institution of Mining and

Metallurgy, 1987. Chap. 10, pp. 615–653. isbn: 978-1468484274.

[10] C. L. Mantell. Electrochemical Engineering. Fourth. New York, NY: McGraw-Hill, 1960. isbn:

0-07-040028-8.

[11] Umicore AG & Co. KG. Precious Materials Handbook. 1st ed. Hanau-Wolfgang: Umicore AG

& Co, KG, 2012. isbn: 978-3-8343-3259-2.

[14] N V Sikerina et al. “Phase equilibria in the BaS-Cu2S-Gd2S3 system”. In: Zh. Neorg. Khim.

pp. 2099–2103.

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