www.elsevier.com/locate/jnoncrysol

Journal of Non-Crystalline Solids 351 (2005) 1359–1365

Thermodynamic analysis of the SiO2–NiO–FeO system

R. Alejandro Cruz *, S. Antonio Romero, R. Marissa Vargas, L. Manuel Hallen

Department of Metallurgy and Materials, IPN-ESIQIE, UPALM Zacatenco, A. Postal 118-431, Mexico DF 07051, Mexico

Received 24 September 2004; received in revised form 28 February 2005

Available online 28 April 2005

Abstract

The evaluation of the thermodynamic properties and phase diagrams of the FeO–SiO2, NiO–SiO2 and SiO2–NiO–FeO systems is

presented in which a structural model is used for the liquid phase. This thermodynamic model is based on the assumption that each

metallic oxide produces the depolymerization reaction of silica network with a characteristic free energy change. A least squares

optimization program permits all available thermodynamic and phase diagram data to be optimized simultaneously for the binary

systems. In this manner, data for these binary systems have been analyzed and represented with a small number of parameters. The

binary structural model is extended to the ternary system assuming a random mixing of cations Fe2+ and Ni2+, since the FeO–SiO2

and NiO–SiO2 binary systems exhibit similar thermodynamic behavior, that is comparable free energies of mixing.

� 2005 Elsevier B.V. All rights reserved.

1. Introduction

The reduction of non-ferrous metal values from slags

is currently the subject of considerable research and

development effort in the extractive metallurgy industry.

The widespread introduction of new processes and the

trend to the production of higher-grade mattes in thecopper and nickel industries have led to increased metal

losses to the slag phase during smelting. In order to esti-

mate the loss of nickel to slags by dissolution during

smelting and converting processes it is necessary to

know the activity of nickel oxide as a function of com-

position in relevant (predominantly iron–silicate) slags.

In this context some researchers [1–3] have conducted

experimental studies of the solubility and activity ofnickel oxide in iron–silicates based slags.

Many models have been proposed to calculate the

thermodynamic properties of ordered solutions such as

liquid silicates [4]. Lin and Pelton [5] developed a struc-

tural model for binary silicate systems MO–SiO2

0022-3093/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2005.03.008

* Corresponding author. Tel.: +525557296000/54217; fax:

+525557296000/55270.

E-mail address: alex73ipn@yahoo.com.mx (R. Alejandro Cruz).

(M = Ca, Mn, Mg, etc.) where one single formalism ap-

plies over the entire composition range and accounts for

two- and three-dimensional silicate network structure.

Recently, the model has been examined in more depth

and a general empirical expression for enthalpy has been

written and an empirical non-configurational excess en-

tropy has been added [6].This structural model was also extended to ternary

systems [7]. It is shown that, for systems SiO2–AO–

BO, random mixing of cations A2+ and B2+ occurs when

the oxides AO and BO behave in a similar way with sil-

icate. If the AO–SiO2 and BO–SiO2 binary systems exhi-

bit similar thermodynamic behavior, that is comparable

free energies of mixing, the properties of the ternary

SiO2–AO–BO can be extrapolated from those binarysystems in a straightforward fashion. This condition is

found in simple silicates such as SiO2–MnO–MgO,

SiO2–FeO–MnO and SiO2–FeO–MgO systems where

the activities and liquidus temperatures calculated solely

from data on the binary sub-systems are in good agree-

ment with measured ternary data. The aim of the

present work is to apply the structural model for the

FeO–SiO2 and NiO–SiO2 binary systems and the ex-tended model to calculate activities and phase diagram

1360 R. Alejandro Cruz et al. / Journal of Non-Crystalline Solids 351 (2005) 1359–1365

of the SiO2–NiO–FeO system solely from the assessed

parameters for the binary subsystems.

2. Structural model

2.1. Structural model for binary systems

A detailed development was given previously [6].

Only a brief summary will be presented here. For binary

silicate systems it is generally accepted that all Si atoms

are tetrahedrally bonded to four oxygen atoms The

model is based on the depolymerization reaction of

SiO2:

Si–O–SiþMO ¼ Si–OO–SiM2þ

ð1Þor, in shorthand notation

O0 þO2� ¼ 2O� ð2Þwhere O0 is a bridging oxygen bonded to two silicon

atoms, O2� is a free oxygen ion, and O� is an oxygen

single bonded to one silicon atom. It is assumed that

every silicon atom is bonded to four oxygen atoms.

Thus, mass balance considerations require that

NO0 ¼ 2XSiO2�NO�

2; ð3Þ

NO2� ¼ XMO �NO�

2; ð4Þ

where XMO and XSiO2are the mole fractions of the com-

ponents and NO0, NO� and NO2� are the number of mo-

les of the various oxygen species per mole of solution.

The first term of the configurational entropy is calcu-lated by assuming a tetrahedral quasi-lattice in which

the sites are occupied by O2� ions and Si atoms (each

associated with four oxygen atoms bonded to it); the

second term is obtained by distributing the oxygen

bridges (O0) over the neighboring Si–Si pairs

DSc ¼ �R XSiO2ln

XSiO2

XSiO2þNO2�

� ��

þNO2� lnNO2�

XSiO2þNO2�

� ���R NO0 ln

NO0

NSi–Si

� ��

þðNSi–Si �NO0Þ ln NSi–Si �NO0

NSi–Si

� ��: ð5Þ

NSi–Si is the number of moles of neighboring Si–Si pairs

per mole of solution. Since there are now O2� ions as

well as Si atoms on the quasi-lattice sites, NSi–Si is given

by

NSi–Si ¼ 2XSiO2

XSiO2

XSiO2þNO2�

� �; ð6Þ

where once again the co-ordination number of thequasi-lattice is assumed to be four. The structural model

assumes that Reaction (1) is associated with a Gibbs en-

ergy change containing an enthalpic (x) and entropic (g)term

DH ¼ NO�

2

� �x; ð7Þ

Snc ¼ NO�

2

� �g: ð8Þ

Finally, x and g are expanded as polynomials

x ¼ x0 þ x1XSiO2þ x2X

2SiO2

þ � � � ð9Þ

g ¼ g0 þ g1XSiO2þ g2X

2SiO2

þ � � � ð10ÞThe coefficients xi and gi are the parameters of the

model which are obtained by optimization of the data.Given a composition, XSiO2

, and values of the parame-

ters xi and gi, the actual value of NO� can be calculated

by minimizing the Gibbs energy at constant XSiO2, x and

g

DG ¼ DH� TðDSc þ SncÞ; ð11Þ

2oDGoNO�

� �XSiO2 ;x;g

¼ ðx� gTÞ �RT lnNO2�

XSiO2þNO2�

� ��

þ lnNO0

NSi–Si

� �� 1þ NSi–Si

XSiO2þNO2�

� �

� lnNSi–Si �NO0

NSi–Si

� ��¼ 0: ð12Þ

Substitution of Eqs. (3), (4) and (6) into (12) gives an

equation in terms of XMO (or XSiO2) and NO� , which

can be solved numerically at a fixed composition and

for given values of the parameters xi and gi to give

NO� . This value can then be substituted back into Eqs.

(3)–(5), (7) and (8) to give DS and DH.Since all integral and partial properties are expressed

in terms of the same parameters (xi and gi) all avail-

able data (phase diagrams, activities, enthalpies, etc.)

can be considered in one simultaneous least-squares

optimization. For the present model, a non-linear

least-squares optimization program was written. Copies

of this software may be obtained by contacting the

authors.

2.2. Structural model for ternary systems

Let us consider the general SiO2–AO–BO ternary sys-tem where A and B are divalent cations. Let us assume

also that these cations can mix randomly in a quasilat-

tice. The mass balance considerations (3) and (4)

requires now that

NO0 ¼ 2XSiO2�NO�

2; ð13Þ

NO2� ¼ ðXAO þXBOÞ �NO�

2: ð14Þ

R. Alejandro Cruz et al. / Journal of Non-Crystalline Solids 351 (2005) 1359–1365 1361

The total configurational entropy must contain two

terms, one for the anionic sublattice ðScaniÞ and one for

the cationic sublattice ðSccatÞ. The expression for the

Scani in the ternary model is similar to Eq. (5) which is

used in the binary systems. However, NO2� depends

now on XAO and XBO. The entropy for the cationic sub-lattice is obtained assuming random mixing of A and B

Sccat ¼ ð1�XSiO2

Þ

� �RXAO

XAO þXBO

lnXAO

XAO þXBO

� ���

þ XBO

XAO þXBO

lnXBO

XAO þXBO

� ���: ð15Þ

In the ternary solution, the depolymerization of SiO2 is

due to AO and BO. Each depolimerization reaction

is associated with a Gibbs energy change, namely(x � gT)AO–SiO2

and (x � gT)BO–SiO2.

There are empirical geometrical equations to estimate

the properties of ternary systems from the binary sub-

systems, such as that developed by Kohler [8] and that

of Topp [9], which are symmetrical and asymmetrical

with respect to the components, respectively. In this

work the asymmetrical approximation was used because

SiO2 is considered different from the metallic oxides.The interaction energy terms (x � gT) for each reaction

are known in the two binary systems from the binary

optimizations. It is then assumed that, in the ternary

solution, (x � gT)AO–SiO2and (x � gT)BO–SiO2

can be

linearly combined

ðx� gTÞtot ¼XAO

XAO þXBO

� �ðx� gTÞAO–SiO2

þ XBO

XAO þXBO

� �ðx� gT ÞBO–SiO2

: ð16Þ

The excess energy of the AO–BO binary system must be

multiplied by (1 � XSiO2) in order to consider its effect

Table 1

Thermodynamic properties relative to elements at 298.15 K

A B a

SiO2 (l) (298–1996 K) �896796 50.829 83.514

SiO2 (l) (>1996 K) �926636 9.917 85.772

SiO2 (Q) (848–1140 K) �908627 44.207 80.012

SiO2 (Tr) (390–1738 K) �907045 45.524 75.373

SiO2 (Cr) (535–1996 K) �906377 46.029 83.514

FeO(l) (298–1644 K) �234643 78.466 �18.024

FeO(l) (>1644 K) �247761 58.482 68.199

FeO(s) (298–1644 K) �265832 59.496 �18.024

NiO (s) (298–525 K) �239700 37.991 �52.622

NiO (s) (525–565 K) �235494 48.795 �33.724

NiO (s) (565–2228 K) �239687 37.070 45.622

NiO (l) (>2228 K) �178718 65.355 54.392

Fe2SiO4 (s) (298–2000 K) �1479955 150.930 248.900

Ni2SiO4 (s) (298–1818 K) �1403439 110.04 149.628

HðJ mol�1Þ ¼ AþR T

298:15 CpdT; SðJ mol�1 K�1Þ ¼ BþR T

298:15Cp

T

� �dT:

CpðJ mol�1 K�1Þ ¼ aþ bð10�3ÞTþ cð105ÞT�2 þ dT�1=2 þ eð108ÞT�3:

on the ternary system. Addition of the configurational

entropy and the excess properties gives the free energy

of mixing for the ternary liquid systems.

3. Binary systems

The thermodynamic properties of the pure oxides and

silicate compounds are given in Table 1. The sources of

these data have been previously discussed [10]. To calcu-

late binary and ternary phase diagrams is necessary to

define the free energy of each phase in the system. The

phase diagram is then calculated by treating the thermo-

dynamic expressions of all phases to determine whichcombination of phases leads to the lowest free energy

of the system.

3.1. NiO–SiO2

The phase diagram of the NiO–SiO2 system is shown

in Fig. 1. The experimental phase diagram is taken

mainly from Phillips [11] and Muan and Osborn [12].Gibbs energy of formation of the solid compound Ni2-

SiO4 is also given in Table 1. The consulate temperature

of the liquid–liquid miscibility gap has not been re-

ported. Compositions of the experimental diagram were

used as input to a least squares optimization program to

find the coefficients xi and gi which best reproduce all

the data. The resultant expressions are

x ¼ �93417þ 101537:5XSiO2þ 90582:5X2

SiO2ðJ mol�1Þ;

ð17Þ

g ¼ �55:01XSiO2þ 67:26X2

SiO2ðJ mol�1K�1Þ: ð18Þ

The NiO melting point at 1955 �C was taken from Barin[13]. The calculated eutectic was at 1655 �C with

b c d e

– �24.554 �374.693 2.801

– – – –

– �35.467 �240.276 4.917

– �59.581 – 9.583

– �24.553 �374.693 2.801

30.609 �25.333 1500.9 –

– – – –

30.609 �25.333 1500.9 –

213.15 29.776 – –

168.40 – – –

8.568 9.0063 – –

– – – –

– – �1923.9 �1.391

42.256 �16.899 – –

2000

1900

1800

1700

1600

140010 20 30 40 50 60 70 80 90 100

Mole %

Tem

pera

ture

(°C

)

Two Liquids

Cristobalite + Liquid

NiO + Cristobalite

Ni2SiO4+Cristobalite

NiO + Ni2SiO4

Liquid

1685 °C

1545 °C

NiO + Liquid

NiOSiO2

Ni 2

SiO

41500

Ni2SiO4+Tridimite

Fig. 1. Optimized NiO–SiO2 phase diagram for equilibrium with Fe.

Points from Phillips [11] and Muan and Osborn [12].

2000

1400

1900

1800

1700

1600

1500

1300

120020 40 60 80NiO FeO

liquid

(Ni, Fe)O+ liquid

(Ni, Fe) O

Weight %

Tem

pera

ture

(°C

)

Fig. 3. Optimized NiO–FeO phase diagram. Points from Von War-

tenberg and Prophet [19].

1362 R. Alejandro Cruz et al. / Journal of Non-Crystalline Solids 351 (2005) 1359–1365

XSiO2= 0.44. The calculated monotectic reaction occurs

at 1685 �C with XSiO2= 0.984. The probable maximum

inaccuracy in the assessed diagram is: ±20� for

XSiO2< 0.50 and for the miscibility gap boundary was

±80 �C.

3.2. FeO–SiO2

The calculated phase diagram shown in Fig. 2 is for

the system in equilibrium with metallic Fe and with all

Fe3+ converted to �FeO�. The experimental phase dia-

gram is from Bowen and Schairer [14], Schuhmann

and Ensio [15] and Allen and Snow [16]. The liquid mis-

cibility gap data was taken from Greig [17]. The optimi-zation also included the activities of �FeO� reported by

Schuhmann and Ensio [15] and Distin et al. [18]. The

probable maximum inaccuracy in the assessed diagram

is: ±10 �C for XSiO2< 0.45 and ±2 mol% for the silica

liquidus. The optimized parameters for the liquid phase

are

Tem

pera

ture

(°C

)

Mole % SiO2 SiO2FeO

Fe2S

iO4

FeO + Fayalite Fayalite + Tridimite

Tridimite + Liquid

Cristobalite + Liquid

Two Liquids

Liquid

FeO + Liquid

˚

˚

˚

˚

˚

Fig. 2. Optimized FeO–SiO2 phase diagram. Experimental points: (d)

[17]; (s) [14]; (j) [15]; (h) [16].

x ¼ 6770� 122724XSiO2þ 183040X2

SiO2

þ 106539X4SiO2

ðJ mol�1Þ; ð19Þ

g ¼ �34:59XSiO2þ 87:366X3

SiO2ðJ mol�1 K�1Þ: ð20Þ

3.3. NiO–FeO

It was shown by Von Wartenberg and Prophet [19]that solid NiO and FeO are completely miscible at high

temperatures. The binary NiO–FeO phase diagram

shown in Fig. 3 can be calculated assuming ideal solid

and liquid solutions. The calculated phase diagram is

in very good agreement with the measurements.

3.4. Gibbs free energy of mixing for binary systems

The Gibbs free energy of mixing for the binary sys-

tems NiO–SiO2 and FeO–SiO2 calculated in this work

at 1873 K are plotted in Fig. 4, together with those of

0.0 0.2 0.4 0.6 0.8 1.0-70

-60

-50

-40

-30

-20

-10

0FeONiO

MnO

CaOGib

bs E

nerg

y of

Mix

ing

(kJ/

mol

)

Mole fraction SiO2 SiO2 MO

Fig. 4. Calculated Gibbs free energy of mixing of the MO–SiO2 binary

systems (M = Fe, Ni, Mn and Ca) at 1873 K.

0 10 20 30 40 50 60 70 80 90 1000

20

30

40

50

60

70

80

90

1000

10

20

30

40

50

60

70

80

90

100

SiO2

NiOFeO

Two liquids

Cristobalite

Olivine

Oxide1300

14001500

16001700

1800

1900

Tridimite

(2NiO SiO2)(2FeO SiO2)

a

R. Alejandro Cruz et al. / Journal of Non-Crystalline Solids 351 (2005) 1359–1365 1363

the MnO–SiO2 and CaO–SiO2 systems reported else-

where [6]. This figure shows that the values of the

energy of NiO–SiO2 and FeO–SiO2 are very similar,

which means that the cations Ni2+ and Fe2+ should have

a similar thermodynamic behavior in the silicate net-

work. In addition, the binary phase diagram of theNiO–FeO system shows that the liquid solution is al-

most ideal. Thus, the structural model can be used

appropriately for estimating the thermodynamic proper-

ties and phase diagrams for the SiO2–NiO–FeO system

from the binary systems in a straightforward fashion.

Fig. 4 also shows that the energy of the CaO–SiO2 sys-

tems is much lower than the other systems. This means

that Ca2+ must play a role in the silicate network differ-ent from that of Ni2+, Mn2+ and Fe2+ in the silicate

network [7].

Weight %

(a) Experimental [20]

20

30

40

50

60

70

80

90

1000

10

20

30

40

50

60

70

80

SiO2

Two liquids

Cristobalite

Olivine

Oxide1300

Tridimite

a

(2NiO SiO2)(2FeO SiO2)

4. The SiO2–NiO–FeO system

4.1. Phase diagram

In order to calculate the thermodynamic properties

and phase diagram of this ternary system, the asymmet-

ric method was used with no ternary interaction terms.

That is, the only data entering the calculations were

those for the binary systems. There exists a solid solu-

tion between Fe2SiO4 and Ni2SiO4 which is considered

a regular with the following excess free energy in order

to reproduce the measured univariant lines in the ter-nary phase diagram

0

1090

100

14001500

16001700

18001900

GE ¼ 3347XFe2SiO4XNi2SiO4

ðJ mol�1Þ: ð21Þ

0 10 20 30 40 50 60 70 80 90 100 NiOFeO

Weight %

(b) Calculated

Fig. 5. (a) Experimental [20] and (b) Calculated liquidus surface of the

SiO2–NiO–FeO system. Temperature in �C.

The experimental SiO2–NiO–FeO phase diagram re-ported by Grutzeck and Muan [20] is compared with

the calculated diagram in Fig. 5. The invariant point

�a� in this ternary diagram was calculated at 1574 �C,36 wt% SiO2 and 17 wt% FeO which is very close

to the experimental invariant point located at 1571 �C,34 wt% SiO2 and 19 wt% FeO. Experimental iso-

therms are in good agreement with the calculated

values.

4.2. Activities of NiO

Activities of NiO in the liquid were measured byNagamori [21] by equilibration of FeO–Fe2O3–SiO2

slags in pure nickel crucibles under a CO–CO2 at tem-

peratures of 1200 and 1300 �C. The CO2/CO ratios

were varied up to values corresponding to magnetite

saturation. Grimsay and Biswas [22] estimated the

NiO activities in the FeO–Fe2O3–SiO2 liquid sys-

tem at 1300 �C using silica crucibles. Equilibrium

with liquid Ni–Au–Fe alloys and CO–CO2 gas was

achieved.

We take the NiO activity results obtained by Naga-

mori [21] and Grimsay and Biswas [22] with low CO2/

CO, which gave an oxygen partial pressure between

10�9 and 10�10 atm in order to consider strongly reduc-

ing conditions and thus very small amounts of Fe asFe2O3. The calculated and experimental activities of

NiO in liquid SiO2–NiO–FeO, relative to the pure

liquid standard state, are shown in Figs. 6 and 7 at

1300 �C. The structural model shows a good agreement

with the NiO activities obtained experimentally for low

oxygen partial pressures. Calculated activities of NiO in

the liquid solution at 1600 and 1800 �C are shown in

Fig. 8.

0.05 0.1

0.005

0.005

0.016

0.016

0.035

20 30 40 50 6020

30

40

50

60

70

8020

30

40

50

60

70

800 10

SiO2

NiOFeOMole %

Fig. 6. Calculated activity of NiO in liquid SiO2–NiO–FeO (liquid

standard state) at 1573 K compared to data of Nagamori [21].

20 30 40 50 6020

30

40

50

60

70

8020

30

40

50

60

70

800 10

SiO2

NiOFeOMole %

0.05 0.1

0.005

0.003

0.003

0.07

0.07

0.08

0.07

0.07

0.07

0.07

Fig. 7. Calculated activity of NiO in liquid SiO2–NiO–FeO (liquid

standard state) at 1573 K compared to data of Grimsay and Biswas

[22].

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

0.1NiO

0.2

0.30.40.570

80

90

1000

10

20

30

40

50

60

70

80

90

100

a

0.1NiO

0.2

0.30.40.5

0.6

0.7

a

(a) T = 1873 K

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

1000

10

20

30

40

50

60

70

80

90

100

SiO2

SiO2

NiOFeO

NiOFeO

Mole %

(b) T = 2073 K

Fig. 8. Calculated NiO iso-activity curves at (a) 1873 K and (b)

2073 K in liquid SiO2–NiO–FeO solution (liquid standard state).

1364 R. Alejandro Cruz et al. / Journal of Non-Crystalline Solids 351 (2005) 1359–1365

5. Conclusions

An evaluation of the available thermodynamic and

phase diagram data for the FeO–SiO2 and NiO–SiO2

systems has been carried out with a structural model.The extended structural model for ternary silicate melts

was used to estimate the phase diagram of the SiO2–

NiO–FeO system as well as the activity of NiO. The

model assumes that a random mixing of cations Ni2+

and Fe2+ occurs since the NiO and FeO oxides behave

in a similar way with silicate. This means that the

NiO–SiO2 and FeO–SiO2 binary systems exhibit similar

thermodynamic behavior, that is comparable free ener-gies of mixing. The activities and liquidus temperatures

calculated solely from data on the binary sub-systems

are in good agreement with measured ternary data.

Acknowledgement

The authors wish to thank the Institutions CONA-

CyT, SNI, COFAA and IPN for their permanent

assistance to the Process Metallurgy Group at ESI-

QIE-Metallurgy and Materials Department.

References

[1] B.S. Terry, C.L. Harris, Trans Inst. Min. Metall. (Section C:

Mineral Process. Extr. Metall.) 104 (1995) C81.

[2] A.R. Burkun, Extractive Metallurgy of Nickel, John Wiley, 1985.

[3] S. Lee, S. Moon, J. Park, D. Min, Metall. Mater. Trans. B 26B

(1995) 55.

[4] A.D. Pelton, M. Blander, M.T. Clavaguera-Mora, M. Hoch, L.

Hoglund, H.L. Lukas, P. Spencer, B. Sundman, Calphad 21

(1997) 155.

[5] P.L. Lin, A.D. Pelton, Metall. Trans. B 10B (1979) 667.

R. Alejandro Cruz et al. / Journal of Non-Crystalline Solids 351 (2005) 1359–1365 1365

[6] A. Romero-Serrano, A.D. Pelton, Metall. Mater. Trans. B 26B

(1995) 305.

[7] A. Romero Serrano, A. Pelton, ISIJ Int. 39 (5) (1999) 399.

[8] F. Kohler, Monatsh. Chemie 91 (1960) 738.

[9] G.W. Toop, C.S. Samis, Trans. TMS-AIME 224 (1962) 878.

[10] P. Wu, G. Eriksson, A.D. Pelton, J. Am. Ceram. Soc. 76 (1993)

2059.

[11] B. Phillips, J.J. Hutta, I. Warshaw, J. Am. Ceram. Soc. 46 (1963)

579.

[12] A. Muan, F. Osborn, Phase Equilibria among Oxides in

Steelmaking, Addison Wesley, Reading, MA, 1965.

[13] I. Barin, Thermochemical Data of Pure Substances, VCH

Verlagsgesellschaft, Germany, 1989.

[14] N.L. Bowen, J.F. Schairer, Am. J. Sc. 24 (1932) 177.

[15] R. Schuhmann, P. Ensio, J. Met. 3 (1951) 401.

[16] W.C. Allen, R.B. Snow, J. Am. Ceram. Soc. 38 (1955) 264.

[17] J.W. Greig, Am. J. Sci. 13 (1927) 133.

[18] P.A. Distin, S.G. Whiteway, C.R. Masson, Can. Metall. Q. 10

(1971) 73.

[19] H. Von Wartenberg, E. Prophet, Z. Anorg. Allg. Chem. 208

(1932) 369.

[20] M. Grutzeck, A. Muan, J. Am. Ceram. Soc. 75 (6) (1992)

1342.

[21] M. Nagamori, Metall. Trans. 5 (1974) 539.

[22] E. Grimsey, A. Biswas, Trans. Inst. Mining Metall. 86 (1976)

C200.