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Graphical abstract

JALCOM 28630 No. of Pages 1, Model 5G

31 May 2013

Q2

pp xxx–xxxFirst principles screening of B2 stabilizers in CuPd-basedhydrogen separation membranes: (1) Substitution for Pd

Michael C. Gao *, Lizhi Ouyang, Ömer N. Dogan

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Highlights

y of formation noticeably, namely, Mg, Al, Sc, Ti, Y, Hf, Zr, Ga, La, and Zn. � Compromise betweenbatch of potential alloying elements: V, Fe, Cr, Nb, Ta, and Mn. � Electronegativity correlatesation implying it is an important parameter in alloy design for B2 CsCl type structure for quick

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Journal of Alloys and Compounds xxx (2013) xxx–xxx

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JALCOM 28630 No. of Pages 10, Model 5G

31 May 2013

First principles screening of B2 stabilizeseparation membranes: (1) Substitution

Michael C. Gao a,b,⇑, Lizhi Ouyang c, Ömer N. Dogana National Energy Technology Laboratory, 1450 Queen Ave. SW, Albany, OR 97321, Ub URS Corporation, P.O. Box 1959, Albany, OR 97321, USAc Tennessee State University, Dept. of Physics and Mathematics, 3500 John A. Merritt

a r t i c l e i n f o

Article history:Received 26 December 2012Received in revised form 9 May 2013Accepted 16 May 2013Available online xxxx

Keywords:First-principles calculationsB2 CuPdHydrogen separation membranesElastic propertiesCharge transferElectronegativity

a b s t r a c t

We report here a screenthat can extend the CuPelements are included foLa, and Zn lowers the ensity of states, charge trbetween enthalpy andMn. To assess the effecand elastic constants of

1. Introduction

Palladium (Pd) is regarded as an excellent membrane materiafor hydrogen separation due to its high surface selectivity and higpermeability for hydrogen (for reviews, see [1–4]). However, purPd membranes are prohibitively costly since Pd is an expensivprecious metal with limited supply. Further, pure Pd is vulnerablto surface poisoning, especially in atmospheres containing H2

[5,6], an impurity typically found in gas streams from coal gasification. The high cost and surface degradation have so far preventePd membrane technology from widespread industrial adoptionFurthermore, pure Pd is prone to hydrogen embrittlement thacauses cracking [7], which is due to formation of palladium hydrid(so called b phase) within solid solution of palladium with hydrogen (so called a phase) at temperature below 300 �C and pressurbelow 20 atm [1]. Design of a single-phase alloy that eliminatephase change during the operating temperature and pressurranges can potentially avoid the low temperature embrittlemenAs a result, alloying strategies have been sought experimentall[8–10] and theoretically [11–15] to develop robust Pd-alloys witincreased chemical stability and hydrogen permeability in aggressive environments. Hydrogen permeability of various Pd-base

0925-8388/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jallcom.2013.05.126

⇑ Corresponding author at: National Energy Technology Laboratory, 1450 QueeAve. SW, Albany, OR 97321, USA. Tel.: +1 541 967 5869; fax: +1 541 918 4493.

E-mail address: michael.gao@contr.netl.doe.gov (M.C. Gao).

1

3

Contents lists availab

Journal of Allo

journal homepage: ww

Please cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), h

in CuPd-based hydrogenor Pd

., Nashville, TN 37209, USA

study using first-principles method in an attempt to identify ternary elemenphase field at reduced Pd contents and thus lower cost. A total of 37 alloyin

nbiased screening. The results show that addition of Mg, Al, Sc, Ti, Y, Hf, Zr, Glpy of formation of the B2 phase noticeably. The atomic size, electronic dener, and electronegativity are analyzed to interpret the results. Compromisbility suggests additional potential alloying elements: V, Fe, Cr, Nb, Ta, an

at SciVerse ScienceDirect

and Compounds

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example alloys at 6.25 at% solute contents.� 2013 Elsevier B.V. All rights reserve

binary, ternary and quaternary alloys are summarized in [1,3,4Several theoretical studies using first-principles density functionatheory (DFT) have addressed the ‘‘sulphur poisoning’’ phenomeno[16–20]. Thermodynamic modeling of the Cu–Pd–H [21] and Pd–[22] systems based on DFT and the CALPHAD (acronym oCALculation of PHAse Diagrams) method have also been reported

The vast majority of reports are focused on Pd-rich compostions that have a face-centered cubic (FCC) structure. Experimentastudies [5,23–25] have shown that alloying with Cu improveresistance against surface poisoning in binary Pd–Cu alloys witthe FCC structure. Pd–Cu binary alloys with the ordered bodycentered cubic (BCC) structure (Strukturbericht Designation B2should have even higher theoretical H2 permeability since thBCC lattice has a more open crystal structure compared to thFCC lattice [24–26]. Indeed, Howard et al. [24] studied the hydrogen permeability of a series of binary Pd–Cu alloys over wide compositions between 623 and 1173 K, and found that the Hpermeability for the 53 and 60 wt.% Pd alloys in B2 structure waseveral times greater than that of the FCC alloys.

The established Cu–Pd binary phase diagram is based on thdata assessed by Subramanian and Laughlin that is collected ithe ASM handbook [27]. The B2 phase has a relatively large compositional homogeneity range that is shifted to the Cu-rich side fromthe stoichiometric 50 at% Pd position. The critical point occurs aabout 40 at% Pd and 598 �C. According to the Arrhenius diffusioequation (shown below), diffusivity D increases with temperature

ttp://dx.doi.org/10.1016/j.jallcom.2013.05.126

88

D ¼ Do exp �DQRT

� �ð1Þ

9090

91 where Do is the pre-exponential coefficient, DQ is the activation92 energy, R is the gas constant, and T is the absolute temperature.93 Improving the thermal stability of the B2 phase will allow the mem-94 branes to be operated more efficiently at temperatures higher than95 598 �C in part due to higher hydrogen diffusivity.96 Therefore, it is highly desirable to design and develop new B297 PdCu-based alloys with ternary (or even higher-order) addition98 aiming to improve their thermal stability at reduced Pd contents.99 A rational approach is to combine theoretical prediction with crit-

100 ical experiments in order to accelerate the process. In the present101 study, a total of 37 alloying elements were chosen including all102 transition metal elements and certain non-transition metal ele-103 ments. The selection was basically unbiased while available binary104 phase diagram information [27] in particular terminal solubility in105 Pd and literature reports on Pd-based hydrogen membranes were106 also assessed. Some elements such as Tc, Hg, Re, and Pt were in-107 cluded solely for comparison purpose. The enthalpy of formation108 of a compound is usually a good indicator for its stability, which109 can be reliably calculated using first-principles DFT methods. For110 computationally affordable screening of a large number of virtual111 alloys, we used only enthalpy of formation at zero temperature112 as the pivot factor to begin with, which was estimated from the113 cohesive energies with zero-point phonon contributions ignored.114 We expect the zero point energies (ZPEs) to have very minor effects115 on the trend of enthalpy of formation as shown in our simple esti-116 mation of ZPE of example alloys based on Debye’s model (see the117 Supplementary Materials).118 Note that a ternary addition that improves the B2 lattice stabil-119 ity may not necessarily enhance the alloy’s surface affinity for120 hydrogen molecules, hydrogen diffusion within the bulk lattice,121 or resistance against sulphur poisoning. Therefore, a quaternary122 and even quinary addition may also be needed to balance these123 properties. Nevertheless, the alloying impact on these properties124 needs to be examined and addressed separately. Several theoreti-125 cal studies have detailed the methodologies in predicting hydrogen126 diffusion in binary Pd alloys [13,28–30]. As a follow-up of the pres-127 ent study, key experiments on down-selected alloys have been per-128 formed to examine the phase equilibria, corrosion resistance in129 pr130 A131 fac132 wa

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2 M.C. Gao et al. / Journal of Alloys and Compounds xxx (2013) xxx–xxx

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esence of H2S, and hydrogen permeance performance [31–33].combined experimental and DFT study on oxygen induced sur-e segregation in a B2 CuPdY alloy based on the present studys reported recently ([34]).

Computational methodology

The first-principles pseudo-potential plane-wave DFT packageVASP (Vienna ab initio simulation package) [35,36] was usedcalculate the total energies. For all calculations, we employed

e projector augmented-wave (PAW) potentials [37] as suppliedth VASP and the Perdew–Burke–Ernzerhof [38] gradient approx-ation for the exchange–correlation functional. The Brillouinne integrations were performed on the Monkhorst–Pack k-pointeshes [39] using the Methfessel–Paxton [40] method with aearing parameter of 0.2 eV. All structures were fully relaxed un-

r zero pressure at least twice (both lattice parameters and atom-coordinates) until energy converge reached 1 meV/atom.

ciprocal space (k-point) meshes of 8 � 8 � 8 were shown to befficient for structural relaxation. Plane-wave energy cutoff at0 eV was used for all systems in present study. For all transitionetal elements, the semi-core 3p, 4p and 5p electrons were explic-y treated as valence. Only collinear spin polarization was consid-ed in the calculations. The calculations showed that pure Pd wasry weakly ferromagnetic at the ground state with an atomic

ease cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), http://d

agnetic spin moment of �0.3 Bohr magnetons [22]. Magneticntribution to the total energy became noticeable only when ele-ents Cr, Mn, Fe, Co, and Ni were involved.To study the energy of alloying substitution on the lattice stabil-of B2 phase, a 2 � 2 � 2 supercell with 16 atoms in total was

nstructed. As the first step in searching for elements that stabi-e the B2 phase at lower Pd contents, only substitutions for Pdes were considered. A total of 8 compositions for each alloyingment were chosen (namely Cu8Pd8�xMx; where M denotes theoying element and x = 1–8). The energy can be sensitive to atom-configuration. For each composition, a minimum of 3 represen-tive configurations were tested except the composition of8Pd7M1. The lowest energy configuration was used later to cal-late the enthalpy of formation. After full relaxation the structureher remained cubic or became slightly distorted as permitted bye symmetry of the lattice. To calculate enthalpy of formationHf) of Cu8Pd8�xMx, a composition-weighted average of the cohe-e energies of corresponding pure elements was subtracted from

e cohesive energy of a given composition, thereby:

f ðCu8Pd8�xMxÞ �1

16fEðCu8Pd8�xMxÞ

� 8EðCuÞ � ð8� xÞEðPdÞ � xEðMÞg ð2Þ

ere E(Cu8Pd8�xMx) is the cohesive energy of B2 Cu8Pd8�xMx com-und. E(Cu), E(Pd), and E(M) is the cohesive energy per atom ofment Cu, Pd, and M in its ground state structure respectively.e resulting energy is an ‘‘enthalpy’’ because its volume is relaxedzero pressure.

Results

. Enthalpy of formation

DFT calculated formation enthalpy of stoichiometric B2 CuPd is2.0 kJ/mol of atoms (see Table 1), which agrees well with exper-ental data of �13.77 ± 0.2 kJ/mol of atoms at 769 K, 827 K, and6 K for Cu60Pd40 (at%) alloy [41] and a recent CALPHAD modelingport [42]. DFT calculated lattice parameter is 3.016 Å which alsorees well with an experimental value of 2.981 Å [43]. Our calcu-ions also agree with earlier DFT studies that reported an enthal-value of �12.35 kJ/mol of atoms at T = 0 K [15] and of �12.73 kJ/

ol of atoms at 298 K [21].The calculated enthalpies of formation and lattice parameters

r Cu8Pd7M1 at zero pressure are listed in Table 1. For comparisonrpose, atomic radii of all alloying elements studied are alsoted. Here we used the metallic radii for metals [44] for whiche coordination number is 12. For Si, Ga, Ge, Sn, and Sb, the datare taken from [45]. Mind that one may get very different resultsdifferent atomic sizes are used. Fig. 1 plots DHf and latticerameters versus the International Union of Pure and Appliedemistry (IUPAC) standard group number n of the doping ele-

ents in the periodic table for period 3, 4, 5 and 6. Note that 4dd 5d transition metal elements have similar atomic size andctronegativity except for n = 11 and 12. As expected, for enthal-, the trends in period 5 and 6 are also quite similar, which showcreasing enthalpy with n at beginning, reaching peak at n = 7 andcreasing thereafter. The trends in the supercell lattice parameterersus n for transition metals are strikingly similar to the trendsenthalpy albeit in the opposite direction. The apparent correla-n between DHf and lattice parameter a is further examined in. 1c. Although the data points are rather scattered, for modelsth doping elements in the same period, a general trend towards

er DHf as a increases is evident. Among the compounds withest DHf (<�17 kJ/mol of atoms), we found that they all have lar-

r lattice parameters than pure B2 CuPd with the exception of

x.doi.org/10.1016/j.jallcom.2013.05.126

213 Cu8Pd7Al1. The decrease in lattice parameter with lowered214 enthalpy of formation for Cu8Pd7Al1 suggests formation of stronger215 bonds. Fig. 1d shows a close-to-linear dependence between the216 metallic atomic radius of the doping element M (only transition217 metals are included in the plot) and the corresponding supercell218 lattice parameter a. This is consistent with the elastic model for di-219 lute alloy in which the volume change is linearly related to the220 apparent atomic size of the alloy element [46]. The apparent atom-221 ic size of the doping element supposedly depends on the host ma-222 trix. In our case, the metallic atomic radius is shown to be a good223 approximation for the apparent atomic size used in those elastic224 models.225 The composition dependent enthalpies of the virtual ternary al-226 loys (Fig. 2) show that addition of most transition metal elements227 makes the enthalpy of formation positive. The exception is the228 Group IIIB, IVB and IIB elements including Sc, Y, La, Ti, Zr, Hf and229 Zn. Their addition lowers the enthalpy of formation making it more230 negative (some are limited to alloying contents up to 25 at%). For231 the 9 non-transition metal elements studied (Al, Si, Ga, Ge, Mg,232 As, In, Sb, and Sn), their addition also lowers the enthalpy of forma-233 tion except As. Consequently, 10 alloying elements (Mg, Al, Sc, Y,234 -235 o236 e,237

2383.2. Electronic structure

239The electronic density of states (DOS) was examined in order to240help understand the predicted stabilizing tendency of these ele-241ments. A comparison of DOS and orbital resolved partial DOS of242representative compositions of CuPd, Cu8Pd7Mg1, Cu8Pd7Al1, Cu8-

243Pd7Sc1 and Cu8Pd7Ru1 is shown in Fig. 3. We used states/eV/atom244as the unit for DOS unless otherwise specified. We chose Mg, Al,245Sc and Ru in the comparison since they represent s-metal, sp-me-246tal, low d-occupancy transition metal, and high d-occupancy tran-247sition metal respectively. Note that they all have electronegativity248no greater than Pd.249Partial density of states (PDOS) of pure B2 CuPd revealed that250the top of the valence band is formed mainly by the 3d and 4d elec-251trons from Cu and Pd, respectively. The Fermi level locates at the252middle of the top edge of the d-electron band and the correspond-253ing DOS is about 0.70. Above the d-electron band, DOS becomes254significantly lower. Alloying with Mg, Al, Sc or Ru raises the Fermi255level but the overall shape of the d-electron band contributed from256Cu and Pd remains similar. For a Mg atom with 2 free-electron-257alike valence electrons, the Fermi level of the alloy shifts to about2580.3 eV above the d-electron band and DOS at the Fermi level be-259comes about 0.25. As expected from simple valence electron count-260ing, for Al, a sp-metal with 3 valence electrons, the Fermi level of261the alloy shifts higher to about 0.4 eV above the d-electron band262and the corresponding DOS is about 0.33. For a Sc atom with 3 va-263lence electrons (i.e. 2 s-electrons and 1 d-electron), the Fermi level264is about 0.6 eV above the d-electron band and its DOS is about 0.28.265Note that the band due to the d electrons of Sc is above the Fermi266level and significantly higher than that of Cu or Pd. For Ru, the Fer-267mi level is located at the bottom edge of the conduction band and268its DOS is about 1.22. The calculated enthalpies are �17.9, �19.0,269�21.2 and �1.9 kJ/mol of atoms for Cu8Pd7Mg1, Cu8Pd7Al1, Cu8Pd7-

270Sc1, and Cu8Pd7Ru1, respectively. Apparently, low DOS at Fermi le-271vel is associated with low enthalpy of formation (i.e. more272negative). Similar trends are observed for all other doping ele-273ments in this study. However, there is no linear correlation be-274tween DOS at Fermi level and the enthalpy of formation as in the275case of free electron gas.

2763.3. Charge analysis

277The less electronegative doping element replacing the Pd site is278expected to be positively charged and donate electrons to lattice279matrix. How much it affects the average charges on the Cu and280Pd sites however requires further analysis. To quantify the charge281transfer in the ternary alloys, Bader charge analysis [47] was per-282formed for CuPd and example compositions Cu8Pd7M1 (M = Mg,283Al, V, Sc, Ru). The average effective charges for Cu and Pd atoms284are listed in Table 2. In pure CuPd, Cu sites are positively charged285and Pd sites are negatively charged. The results of Cu8Pd7M1 show286that doping causes significant alteration of the average charges on287both Cu and Pd sites. For all ternary alloys analyzed, the signs of288their charges are reversed, indicating that on average Cu atoms289gain electrons and Pd atoms lose electrons to minimize the electro-290static interaction with the positively charged doping sites. Note291that, however, in general, average charge transfer does not increase292with decreased electronegativity of the doping elements. If we only293compare the sp-metal (namely Mg and Al), we found that the ele-294ment with higher electronegativity (i.e. Al) leads to increased mag-295nitudes of average charges on both Cu and Pd sites but decreased296magnitude ratio (see the R = |Q(Cu)|/|Q(Pd)| value in Table 2). The297t298d299e300o

Table 1DFT calculated enthalpy of formation (DHf, kJ/mol of atoms), lattice parameter (a),and percentage difference in lattice parameter (with respect to B2 CuPd) ofhypothetical B2 Cu8Pd7M1 structures, atomic radii (r) of ternary elements, andpercentage difference in atomic radius with respect to Pd (D(Pd)) and Cu (D(Cu)). Thelattice parameter for pure B2 CuPd measured by Yusenko et al. [43] is 2.981 Å. Anatomic radius of 1.28 Å and 1.37 Å was used for Cu and Pd respectively.

M DHf a (Å) D% (a) r (Å) D% (Pd) D% (Cu)

CuPd �12.0 3.016Sc �21.2 6.071 0.6 1.62 18.2 26.6Ti �14.8 6.033 0.0 1.47 7.3 14.8V �7.8 6.016 �0.3 1.34 �2.2 4.7Cr �8.0 6.028 �0.1 1.28 �6.6 0.0Mn �12.1 6.025 �0.1 1.27 �7.3 �0.8Fe �7.9 6.009 �0.4 1.26 �8.0 �1.6Co �5.8 6.000 �0.5 1.25 �8.8 �2.3Ni �8.4 5.994 �0.6 1.24 �9.5 �3.1Zn �15.4 6.014 �0.3 1.34 �2.2 4.7Y �19.6 6.131 1.6 1.8 31.4 40.6Zr �17.0 6.087 0.9 1.6 16.8 25.0Nb �8.4 6.054 0.4 1.46 6.6 14.1Mo �1.5 6.034 0.0 1.39 1.5 8.6Tc �0.7 6.024 �0.1 1.36 �0.7 6.3Ru �1.9 6.020 �0.2 1.34 �2.2 4.7Rh �7.3 6.023 �0.1 1.34 �2.2 4.7Ag �11.2 6.052 0.3 1.44 5.1 12.5Cd �13.8 6.069 0.6 1.51 10.2 18.0La �16.8 6.176 2.4 1.87 36.5 46.1Hf �18.1 6.074 0.7 1.59 16.1 24.2Ta �9.2 6.049 0.3 1.46 6.6 14.1W �0.2 6.033 0.0 1.39 1.5 8.6Re 1.5 6.023 �0.1 1.37 0.0 7.0Os 1.2 6.019 �0.2 1.35 �1.5 5.5Ir �5.2 6.023 �0.1 1.355 �1.1 5.9Pt �11.9 6.033 0.0 1.385 1.1 8.2Au �12.7 6.054 0.4 1.44 5.1 12.5Hg �11.1 6.076 0.7 1.51 10.2 18.0Mg �17.9 6.046 0.2 1.6 16.8 25.0Al �19.0 6.013 �0.3 1.43 4.4 11.7Si �14.1 6.003 �0.5 1.02 �25.5 �20.3Ga �16.3 6.021 �0.2 1.32 �3.6 3.1Ge �13.6 6.028 �0.1 1.14 �16.8 �10.9As �12.0 6.039 0.1 1.06 �22.6 �17.2In �15.2 6.073 0.7 1.67 21.9 30.5Sn �14.9 6.079 0.8 1.62 18.2 26.6Sb �13.3 6.088 0.9 1.59 16.1 24.2

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Hf, Zr, Ga, La, Zn and Ti,) were down-selected, based on the criterion of enthalpy of formation, for further computational study tpredict the electronic structure, charge transfer, equation of statand elastic properties.

Please cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), h

decrease in the magnitude ratio is primarily due to the fact thathe valence electrons of sp-metals tend to be nonlocal and spreaover all atoms and that the increase in free electron alike chargcontributed by the doping element is distributed more evenly t

ttp://dx.doi.org/10.1016/j.jallcom.2013.05.126

301 m302 m303 ca

304ele305th306de

Fig. 1. Plots of DFT calculated results versus group number in the periodic tables. Shapes of the symbols, star, disk, triangle, and diamond, represent periods 3, 4, 5, and 6,respectively. (a) Calculated enthalpy of formation (kJ/mol of atoms) of Cu8Pd7M1. (b) Calculated cell parameter of Cu8Pd7M1. (c) Calculated enthalpy of formation versus cellparameter. (d) Cell parameters versus metallic atomic radius.

d8-xMx alloys. The dashed horizontal line is for the reference purpose.Q6

4 M.C. Gao et al. / Journal of Alloys and Compounds xxx (2013) xxx–xxx

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inimize the electrostatic potential energy. As for the transitionetals, the changes to the average charge on Cu and Pd atomsused by ternary doping become smaller with increase of the

Fig. 2. Calculated enthalpy of formation (kJ/mol of atoms) of virtual Cu8P

ease cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), http://d

ctronegativity of the doping element as expected. Furthermore,e decrease of electronegativity appears to coincide with the or-r of lowering the enthalpy of formation. This is due to the fact

x.doi.org/10.1016/j.jallcom.2013.05.126

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Fig. 3. Calculated density of states of CuPd, Cu Pd Mg , Cu Pd Al , Cu Pd Sc and Cu8 d-rtic

f.’’iss

ofe

that d-electrons of transition metals are more localized and thathe charge contributed by the less electronegative doping elemen

8 7 1 8 7 1 8 7 1

PDOS of the element are arranged in increased order of elevation. The dashed ve

Table 2Bader charge analysis [47] of Cu8Pd7M1 where M = Mg, Al, Sc, V, Ru, and Pd. ‘‘condenotes the valence electron configuration, ‘‘En’’ denotes the electronegativity, ‘‘Q’’the average charge with a unit of number of electrons per site (a negative value meanlose of electrons and a positive value means gain of electrons), ‘‘R’’ is the ratioabsolute charge of Cu over than of Pd (i.e., R = |Q(Cu)|/|Q(Pd)|), and ‘‘DHf’’ is thenthalpy of formation (kJ/mol of atoms).

M Conf. En Q(Cu) Q(Pd) Q(M) R DHf

Mg 3s2 1.31 0.2854 �0.0812 �1.7146 3.5 �17.9Al 3s23p1 1.61 0.4255 �0.1473 �2.3730 2.9 �19.0Sc 3d14s2 1.36 0.9632 �0.8360 �1.8541 1.2 �21.2V 3d34s2 1.63 0.6832 �0.5576 �1.5652 1.2 �7.8Ru 4d75s2 2.20 0.0490 �0.0121 �0.3076 4.0 �1.9Pd 4d105s0 2.20 �0.2421 0.2421 0.2421 1.0 �12

largely goes to the nearest neighbors.Fig. 4 shows the deformed charge density, which is the differ-

ence between the calculated electron density and the sum of atom-ic charge density, of the above selected systems in the (110) planethat is the close-packed plane in the bcc structure. For Pd atomsneighboring with the doping element, reduced charge on Pd andweaker Cu–Pd bond appear to be associated with enhancedM–Cu bond. The overlapping charges on the M–Cu bonds is in anincreasing order by the doping element M, namely Mg < Al <Sc < Ru < V, which is not in the same order of either the numberof d electrons or the electronegativity differences between Pdand M. Among the 5 doping elements plotted, V shows the stron-gest Cu–M bond and weakest Cu–Pd bond, while Mg shows weak-est bonding between Mg and Cu and it also has the least impact onthe Cu–Pd bond. The calculated enthalpy of formation is in a differ-ent but increased order by the alloy element M (Sc < Al < Mg < V < -Ru). In summary, our charge analysis indicates consistencebetween electronegativity and charge transfer. The enthalpy of for-mation of Cu8Pd8�xMx is the consequence of the complex interplay

Please cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), h

328S,329-330

331

332e333d334d

l1,d

ofd,

between ternary doping elements and the matrix, including DOelectronegativity, charge transfer, and atomic size mismatch, instead of simple nearest neighbor interactions.

3.4. Equation of state (EOS)

The elastic properties of the alloys are useful information to thprocessing and performance of the membranes, since it is relateto the intrinsic ductility. As brittle intermetallics, the B2 CuP

Pd7Ru1 and Cu8Pd7V1. The elevated curves representing the l-decomposed s-, p-, andal line indicates the Fermi level of the alloy. M is the doping element.

Fig. 4. Calculated deformed charge density of CuPd, Cu8Pd7Mg1, Cu8Pd7ACu8Pd7V1 Cu8Pd7Sc1, and Cu8Pd7Ru1 in the close-packed (110) plane. Selectecenters of the Cu and Pd are labeled. A color bar on the right shows the scaleelectron density. (For interpretation of the references to color in this figure legenthe reader is referred to the web version of this article.)

ttp://dx.doi.org/10.1016/j.jallcom.2013.05.126

335 phase could be potentially ductilized to certain degree by doping336 ternary or higher order element(s). Ductility facilitates processing337 such as rolling. Furthermore, high ductility is usually correlated338 favorably with fracture toughness. Therefore, we calculated the339 pressure–volume equation of state (EOS) and their elastic con-340 stants for the down-selected Cu8Pd7M1 compositions.341 For the EOS, a set of 15 different volumes that were isotropically342 expanded or contracted from the fully relaxed structure was cre-343 ated and then their atomic positions and lattice shape were al-344 lowed to relax at the fixed volume. The resulting enthalpy of345 formation versus the volume is illustrated in Fig. 5. The data for346 pure B2-CuPd is also shown for comparison. The resulting energy347 and volume data set were then used to fit the third-order Birch–348 Murnaghan pressure–volume EOS [48]:349

P ¼" # " #( )

351351

352

353 bu354 an355 Pd356 Y357 bo358 sli

359 3.5

360

361 ela362 lat363 pa364 di365 th366 ar367 Th368 ar369

370 ta371 bil372 C1

373 na374 ba375 an376 m

377Pd7La1. That implies the addition of Y and especially La perhaps378will result in some unique mechanical properties if they are soluble379in B2 CuPd phase.

3804. Discussions

381The main objective of the present study was to screen potential382B2 stabilizers at reduced Pd contents using DFT method as the first383step of a series of computational and experimental studies. A wide384range of doping elements were selected from group IIA, IIIA, IVA,385and all transition metals (including a few light rare earth elements)386for unbiased screening. Their enthalpies of formation were esti-387mated without zero point energy correction for computational388affordability. The results suggested substitution of 10 elements389fo390no391if392fo393als394of395tiv396op397th398we399at400pr401th402pa

Q4

6 M.C. Gao et al. / Journal of Alloys and Compounds xxx (2013) xxx–xxx

JALCOM 28630 No. of Pages 10, Model 5G

31 May 2013

Pl

3Bo

2Vo

V

� �7=3

� Vo

V

� �5=3

1þ 34ðB1 � 4Þ Vo

V

� �2=3

� 1

ð3Þ

The obtained EOS parameters such as equilibrium volume andlk modulus are listed in Table 2. Addition of Sc, Ti, Y, Zr, La, Hfd Mg expands the equilibrium atomic volume of B2 CuPd; Cu8-

7La1 expands the atomic volume the most by 7.4% followed bywith 5% due to the much larger atomic size (metallic radii) ofth La and Y compared to Cu and Pd. Addition of Al, Ga and Znghtly decreases atomic volume.

. Elastic constants

To further examine their mechanical and lattice stabilities, the 4034.1

404

405rig406va407Fermi level is adjusted to the change of number of valence elec-408tro409loy410Cu411ab412d-413m414gr415Ho416IV417m

4184.2

419

420ele421an422M423po424B2425wi426be427ba428tra429ne430th431m432m433va434pe435to

stic constants of the down-selected compositions were calcu-ed using the finite difference method supplied with the VASPckage. The elastic tensor is determined by performing six finitestortions of the lattice and deriving the elastic constants frome strain–stress relationship [49]. The polycrystalline propertiese estimated using the Voigt–Reuss–Hill approximation [50].e calculated elastic properties for Cu, Pd and B2 compoundse listed in Table 3.

There are only 3 independent elastic constants for cubic crys-ls, namely C11, C12 and C44. Three generally accepted elastic sta-ity criteria for a cubic crystal [51] are, C11 + 2C12 > 0, C44 > 0,1 � C12 > 0, which are connected to the bulk, shear and tetrago-l shear moduli respectively. The calculations show that C11 isrely larger than C12 for those Cu8Pd7M1 alloys. Both Cu8Pd7La1

d Cu8Pd7Y1 soften B2 CuPd by lowering the bulk modulus, shearodulus, and Young’s modulus significantly especially with Cu8-

Fig. 5. Calculated enthalpy–volume plot of down-selected Cu8Pd7M1.

ease cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), http://d

r the Pd sites lowers the enthalpy of formation of the B2 phaseticeably, and thus they may potentially stabilize the B2 phase

they are soluble in the B2 phase. These candidate elements wereund to be s-metals, sp-metals, group IIIB and IVB transition met-

with one exception, Zn, which is in the IIB group. DOS analysisexample ternary alloys revealed that all alloys with more nega-e enthalpy of formation have lower Fermi level DOS while theposite holds for alloys with more positive enthalpy of formationan pure B2 CuPd (see Table 3 and Fig. 3). Note that it has beenll known that stable transitional metals tend to have low DOSthe Fermi level [52]. Given the reliability of accurate first-

inciples DFT calculations on the electronic structure and thuse total energies of metallic alloys, it would be interesting to com-re the present calculation results with several empirical rules.

. DOS from the rigid band model

Let’s first compare DFT calculated electronic structure with theid band model [53]. In the rigid band model, which is consideredlid at dilute alloying limit, the electronic DOS is fixed while the

ns due to alloying. Indeed, the d-electron band of Cu8Pd7M1 al-s appears to be quite similar to that of the stoichiometric B2Pd, but ternary element M from transition metals causes notice-le modification. Additional valence electrons from M will fill theelectron band and move the Fermi level to the diffusive band ofuch lower DOS. By simple counting of d-electron number, onlyoup IB and IIB elements have more valence electrons than Pd.wever, from the DOS analysis, we found that group IIIB and

B transition metals, s-metal, and sp-metal can also shift the Fer-i level higher into the band with low DOS.

. Electronegativity

Our charge analysis has demonstrated the importance of thectronegativity, which by definition describes the tendency ofatom to attract electrons in the formation of an ionic bond.

any important ionic crystals such as CsCl and intermetallic com-unds such as Ni(Co,Fe)Al and AlY(rare earth) possess the simple

crystal structure. Generally speaking, any alloying elementsth lower electronegativity than the substituted Pd sites shouldable to contribute more valence electrons to fill the d-electron

nd. This criterion appears to have most s-metals, sp-metals andnsitional metals satisfied since Pd has a large Pauling electro-gativity of 2.20 which is the same as hydrogen. Furthermore,ose elements that have very low electronegativity, such asetallic elements from groups IA, IIA, IIIB, IVB and rare earth ele-ents, are expected to have the strongest capability to contributelence electrons to form stronger bonds, and accordingly are ex-cted to lower the enthalpy of formation significantly. This seemsagree with the present DFT screening study. On the other hand,

x.doi.org/10.1016/j.jallcom.2013.05.126

436 -437 :438 :439 e440 -441 h442 s.443 l-444

445 y446 t447 n448

449

450 ll451 e452 y453 y454 n455 s456 y457 s458 e459 -460 -461 y462 o463 -464 e465

466 n467 s468 -469 l-470 ;471 -472 ;473

474

475

476

477

478

479

480

481

482

483e484e485r486r487–488%489r490e491i-492d493

494y495e496i-497h498t499-500t501

502

503a504-505-506.507t508d509n510e511s.5122513d514r515r,516n517t-518ir519

520f

Table 3DFT calculated equilibrium volume (Vo, Å3/at) and bulk modulus (BEOS, GPa) and Bo (GPa 1

compositions and pure CuPd. DOS(Ef) signifies the calculated DOS (states/eV/atom) at Fer m)are estimated using the Voigt–Reuss–Hill approximation [50].

Vo Bo B1 BEOS DOS(Ef)

CuPd 13.82 151.33 5.26 153.8 0.70Sc 14.08 143.11 5.10 145.5 0.28Ti 13.82 151.99 5.13 154.4 0.68Zn 13.71 147.96 5.21 150.4 0.25Y 14.51 134.36 5.13 136.7 0.28Zr 14.18 148.86 5.09 151.2 0.48La 14.84 125.79 5.16 128.2 0.26Hf 14.10 151.47 5.08 153.8 0.47

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JALCOM 28630 No. of Pages 10, Model 5G

31 May 2013

those 10 down-selected elements all have Pauling electronegativity that is also much smaller than Cu (1.9) except Ga (La: 1.10, Y1.22, Hf: 1.3, Mg: 1.31, Zr: 1.33, Sc: 1.36, Ti: 1.54, Al: 1.61, Zn1.65, Ga: 1.81), hinting that they might prefer to substitute thCu sites. By comparing the enthalpy of formation of each substitution scenario, Benn et al. [15] predicted that transition metals sucas Nb and Ta favor substitution for the Cu sites over the Pd siteThe electronegativity analysis and DFT prediction [15] are in quaitative agreement with established phase diagrams [27] that showformation of extremely stable compounds between Pd and manearly transition metals and rare earth elements. Conversely, mostransition metals have very low solubility in Cu and they oftedo not form compounds with Cu.

4.3. Solubility consideration

Ideally, the substitution of Pd atoms by a doping element winot only lower the enthalpy of formation but also maximize thentropy at finite temperatures. More negative Gibbs free energof the doped B2 phase will enhance its thermodynamic stabilitand thus increase the likelihood of expanding its phase field itemperature and/or composition. Evaluating total entropy involvedetermination of vibrational entropy and configurational entropof the doped alloys. Accurate determination of the latter requirereliable prediction of the solubility of the doping element in thB2 CuPd phase, which inevitably requires knowledge of those competing phases in each individual Cu–Pd–M ternary system. Therefore, entropy calculations are not included in our screening studfor simplicity, but phonon and solubility calculations remain tbe an important topic as follow-up study once potent doping elements are determined that show promise in not only the B2 phasstability but also hydrogen permeation performance.

Therefore here we discuss the solubility of doping elements ithe B2 CuPd phase in accordance with the Hume-Rothery rule[54] instead, which are widely used to address alloy solubility issue. They mainly consist of the following 4 rules regarding the soute and solvent: (1) the atomic size difference is no more than 15%(2) the crystal structures must match; (3) complete solubility requires the same valency and solute of higher valency is preferred

Mg 13.91 139.56 5.18 142.0 0.25Al 13.69 150.27 5.18 152.7 0.33Ga 13.74 147.55 5.27 150.0 0.36

and (4) the electronegativity should be similar. Now let’s focus onntodiseg,

521-522s523y524t525means addition of Ag, Ni or Co likely stabilizes the FCC phase over526-527e528

529is530e

the atomic size effect, which usually has the biggest influence isolubility. According to the data listed in Table 1, the elements thaexceed the 15% limit in atomic size difference with respect teither Pd or Cu are Sc, Y, Zr, La, Hf, Mg, Si, Ge, As, In, Sn, Sb, anCd. There are 19 elements for which the atomic size differencewithin the 15% limit with respect to both Cu and Pd, and therare 13 elements satisfied if we use 10% as the threshold (excludinTc, Hg, Re and Pt). These 13 elements are V, Cr, Mn, Fe, Co, Ni, ZnMo, Ru, Rh, W, Os, and Ir.

Please cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), h

Apparently, six of those 10 down-selected elements, whosadditions lower the enthalpy noticeably, violate the atomic sizcriterion of Hume-Rothery rules, suggesting that they will suffefrom low solubility in B2 CuPd at least at low temperatures. Oufollow-up experimental study on phase equilibria showed [3133] that only Al showed a solubility of 5.3 at% while it is 2.5 atfor Ti, and 0.9 at% for Mg at 400 �C in the B2 CuPd phase. As foLa and Y, their solubility is basically zero at 400 �C. Although thobserved solubility seems to suggest the importance of the size crterion, the stability of the competing phases should be considerefor a thorough analysis.

However, exclusively relying on the size criterion alone maeasily discard potentially important alloying elements becausthe entropy effect including vibrational and configurational contrbutions can be important in certain systems. For example, althouga Y atom is larger than Pd by 31.4%, Pd can dissolve about 10% Y aT P 504 �C and �5 at% Y even at 40 �C [27]. It is known that the Pd10 wt% Y alloys can achieve a hydrogen permeability 3.8 times thaof pure Pd [3,15].

4.4. Compromise between enthalpy and solubility

Taking solubility into consideration for alloy design requirescompromise between enthalpy and solubility. This suggests a second batch of doping elements that also deserve further experimental and theoretical studies, which includes V, Cr, Fe, Nb, Ta, and MnDoping these elements that artificially substitute the Pd sites a6.25 at% results in an enthalpy of formation between �9.2 an�7.8 for V, Cr, Fe, Nb and Ta, and �12.1 kJ/mol of atoms for M(see Table 1). Elements V, Cr, Fe, Nb and Ta all have a BCC structurat low temperatures and are known to be strong BCC stabilizerAlthough the enthalpies are less negative than that of pure BCuPd, their atomic size differences with respect to both Cu anPd are all within 15%, implying favorable solubility. As a matteof fact, a previous study by Benn et al. [15] recommended Fe, CNb, Ta, V, Mo, and W as potential B2 CuPd stabilizers based oDFT calculated enthalpies of formation while considering the latice size difference of pure elements as guidance to estimate thesolubility in B2 CuPd.

Although alloy Cu8Pd7M1 (M = Ag, Ni, Co) has an enthalpy o�11.2, �8.4, and �5.8 kJ/mol of atoms and the atomic size difference between the dopant and Cu and Pd are small, these elementare well-known FCC stabilizers. For example, complete miscibilitexists for Pd–Ag, Pd–Ni, Pd–Co, and Ni–Cu binaries [27]. Tha

) and B1 (GPa) via the Birch–Murnaghan EOS parameters for down-selected B2 Cu8Pd7Mmi level. Bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (

C11 C12 C44 B G E m

173.8 143.5 88.9 153.6 44.8 122.4 0.367158.1 139.5 93.4 145.7 40.0 110.0 0.374161.5 148.3 93.5 152.7 36.9 102.3 0.388166.3 140.9 96.4 149.4 44.7 122.0 0.364148.9 130.5 83.8 136.6 36.8 101.4 0.376158.0 149.1 92.1 152.1 33.7 94.0 0.397136.1 123.4 73.1 127.6 30.2 84.1 0.39159.1 151.5 94.9 154.1 33.7 94.2 0.398159.2 132.0 95.8 141.0 45.5 123.3 0.354161.7 147.1 96.8 152.0 38.7 107.1 0.383154.9 146.7 93.2 149.5 33.6 93.7 0.395

the B2 phase mainly due to the contribution to the Gibbs free energy from the configurational entropy in the FCC phase at finittemperatures.

As Fig. 1a shows, the enthalpy of formation of Cu8Pd7M1

much lower for Mn than Cr or Fe. We think this is probably du

ttp://dx.doi.org/10.1016/j.jallcom.2013.05.126

531 to532 un533 m534 pe535 [2536 15537 po538 sc539 de540 Cu541 tw542 �1543 at544 M545 re546 Th547 te548 low549 du550

551 ior552 so553 FC554 Fe555 fo556 Cr557 th558 en559

560 on561 na562 ph563 Cu564 an565 DF566 all567 ity568 wh569 cu570 ex571 to572 ea573 dr574 du

575 5.

576

577 on578 po579 du580 tra581 su

582ru583co

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608Di

609

610agency of the United States Government. Neither the United States

TabDFandsol

8 M.C. Gao et al. / Journal of Alloys and Compounds xxx (2013) xxx–xxx

JALCOM 28630 No. of Pages 10, Model 5G

31 May 2013

Pl

the fact that the Mn-Pd interaction is strikingly strong, which isusual if compared to the other FCC stabilizers (Ag, Ni, Co), or BCC

etals such as Cr and Fe which locate next to Mn in period 4 of theriodic table. According to established binary phase diagrams7], the B2 MnPd phase has a congruent melting point of15 �C. In contrast, Cr or Fe forms significantly weaker com-unds with Pd. For instance, CrPd decomposes to Pdss (the post-ript ‘‘ss’’ signifies solid solution) and Crss at 570 �C, and FePd3

composes to FCC (Fe,Pd)ss at 821 �C. As for the interaction with, Cr and Cu are nearly immiscible, and the mutual solubility be-een Cu and Fe is very limited. Conversely, Cu can dissolve7 at% Mn at T 6 200 �C and they become completely miscibleT P 704 �C. The noticeable contrast in the phase diagrams of

n with Pd and Cu compared with those of Cr/Fe with Cu/Pdspectively reveals the uniqueness of Mn in alloying behavior.is seems to be consistent with the uniqueness of pure Mn in

rms of its physical properties (e.g., a melting point substantiallyer than any other early 3d transition metals), which is believed

e to the unusually large 3d–3d repulsive interaction of pure Mn.

le 4T calculated enthalpy of formation (DHf, kJ/mol of atoms), lattice parameter (a, Å)

average magnetic spin moment per atom (lB, Bohr magnetons) of dilute solidution of Cr, Mn, and Fe (3.125 at%) in FCC Cu and Pd.

DHf a (Å) lB

Cu31Cr1 2.6 7.253 0.12Cu31Mn1 1.1 7.252 0.13Cu31Fe1 2.1 7.239 0.10Pd31Cr1 �0.4 7.894 0Pd31Mn1 �3.3 7.913 0.34Pd31Fe1 �2.2 7.906 0.38

To further demonstrate the uniqueness of Mn in alloying behav-, here we calculated the enthalpy of formation of dilute solid

lution at 3.125 at% (i.e. placing one solute atom in a 2 � 2 � 2C supercell) in Pd and Cu respectively for element Cr, Mn and. The results (see Table 4) show that the enthalpy is the lowestr Pd31Mn1 (�3.3 kJ/mol of atoms), followed by Pd31Fe1. The Pd–interaction is the weakest (�0.4 kJ/mol of atoms). As expected,

eir interactions with Cu are all repulsive evidenced by positivethalpies, but Cu31Mn1 has the lowest value.It is worth emphasizing that the B2 phase stability also dependsthe energies of competing phases in individual Cu–Pd–M ter-

ry system including the possibility of formation of ternaryases, substitution of ternary element M for the Cu site in B2Pd phase, substitution of ternary element M in the FCC phase,d extension of other binary phases into the ternary. Our ongoingT calculations have been performed in the scenario of ternaryoying elements substituting Cu sites as well as the phase stabil-

of example Cu–Pd–M ternary systems at zero temperature,ich deserve in a separate presentation. Mind that accurately cal-

lating complex ternary phase diagrams at finite temperaturesclusively based on DFT methods remains at its infant stage evenday. Therefore, careful examination of the phase equilibria ofch Cu–Pd–M ternary system using experiments is necessary toaw a thorough conclusion on the phase stability of the B2 CuPde to ternary addition.

Conclusions

In summary, first-principles DFT calculations were performedvirtual ternary alloys Cu8Pd8�xMx (x = 1–8) aiming to identify

tential doping elements that stabilize the CuPd B2 phase at re-ced Pd contents and thus the cost. Electronic structure, chargensfer, and elastic properties were analyzed to interpret the re-

lts. Rigid band model, electronegativity, and the Hume-Rothery

Gombilneorrigcewireorprte

Ac

grgrTeMcaCafuSuTeDMEnFo

Ap

th12

ease cite this article in press as: M.C. Gao et al., J. Alloys Comp. (2013), http://d

les are further discussed in light of the DFT results. The followingnclusions were reached:

(1) Addition of 10 elements lowers the enthalpy of formationnoticeably, namely, Mg, Al, Sc, Ti, Y, Hf, Zr, Ga, La, and Zn.

(2) DOS analysis of example ternary alloys revealed that allalloys with more negative enthalpy of formation have lowerFermi level DOS while the opposite holds for alloys withmore positive enthalpy of formation than pure B2 CuPd.

(3) Electron charge analysis showed significant alteration incharge distribution due to doping. For transition metals,the changes to the average charge on Cu and Pd atoms areconsistent with the electronegativity of the doping element.For sp-metals, their valence electrons tend to be nonlocaland spread over all atoms which causes smaller disturbanceto the charge of Cu and Pd atoms.

(4) Electronegativity correlates well with the enthalpy of forma-tion implying it is an important parameter in alloy design forB2 CsCl type structure for quick screening.

(5) Solubility was analyzed using the atomic size difference asguidance. Compromise between enthalpy and solubilityleads to a second batch of potential alloying elements: V,Fe, Cr, Nb, Ta, and Mn.

(6) Pressure–volume EOS, single-crystal elastic constants, andpolycrystalline bulk and shear moduli of 10 example compo-sitions at 6.25 at% were calculated.

sclaimer

This report was prepared as an account of work sponsored by an

611vernment nor any agency thereof, nor any of their employees,612akes any warranty, express or implied, or assumes any legal lia-613ity or responsibility for the accuracy, completeness, or useful-614ss of any information, apparatus, product, or process disclosed,615represents that its use would not infringe privately owned616hts. Reference herein to any specific commercial product, pro-617ss, or service by trade name, trademark, manufacturer, or other-618se does not necessarily constitute or imply its endorsement,619commendation, or favoring by the United States Government620any agency thereof. The views and opinions of authors ex-621essed herein do not necessarily state or reflect those of the Uni-622d States Government or any agency thereof.

623knowledgments

624This technical effort was performed in support of the Fuels Pro-625am as well as the Innovative Processing and Technologies Pro-626am of Strategic Center for Coal at DOE National Energy627chnology Laboratory under the RES contract DE-FE0004000.628CG thanks Drs. David Alman and De Nyago Tafen at NETL for629refully reviewing this manuscript and Prof. Michael Widom at630rnegie Mellon University and Dr. Bryan Morealle at NETL for use-631l discussions. This work used the computing facility at Pittsburgh632percomputing Center (PSC) through Award DMR110001P and633xas Advanced Computing Center (TACC) through Award#634R120048 by the Extreme Science and Engineering Discovery635vironment (XSEDE), which is supported by National Science636undation Grant Number OCI-1053575.

637pendix A. Supplementary material

638Supplementary data associated with this article can be found, in639e online version, at http://dx.doi.org/10.1016/j.jallcom.2013.05.6406.

Q5

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