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Solubility and activity of oxygen in liquid gallium and gallium-copper alloys
of the Less-Common
Journal
0 Elsevier
Sequoia
Metals,
S.A., Lausanne
53 (1977)
- Printed
211
- 222
211
in the Netherlands
SOLUBILITY AND ACTIVITY OF OXYGEN IN LIQUID GALLIUM AND GALLIUM-COPPER ALLOYS
C. B. ALCOCK
and K. T. JACOB
Department of Metallurgy 1 A4 (Canada)
(Received
November
and Materials
Science,
University
of Toronto,
Toronto
M5S
19, 1976)
Summary The solubility of oxygen in liquid gallium in the temperature range 775 - 1125 “C and in liquid gallium-copper alloys at 1100 ‘C, in equilibrium with fi-Ga,O,, has been measured by an isopiestic equilibrium technique. The solubility of oxygen in pure gallium is given by the equation log (at.% 0) = -7380/T
+ 4.264 (kO.03)
Using recently measured values for the standard free energy of formation of P-Ga20s and assuming that oxygen obeys Sievert’s law up to the saturation limit, the standard free energy of solution of oxygen in liquid gallium may be calculated:
A G&s= -52
680 + 6.532’(+200)
cal
where the standard state for dissolved oxygen is an infinitely dilute solution in which the activity is equal to atomic per cent. The effect of copper on the activity of oxygen dissolved in liquid gallium is found to be in good agreement with that predicted by a recent quasichemical model in which it was assumed that each oxygen is interstitially coordinated to four metal atoms and that the nearest neighbour metal atoms lose approximately half their metallic cohesive energies.
Introduction As part of a larger programme of research on the thermodynamic behaviour of oxygen dissolved in metals and alloys, measurements have been made on the saturation solubility of oxygen in liquid gallium in the temperature range 775 - 1125 “C and in gallium-copper alloys at 1100 “C. A know-
212
ledge of the saturation solubility in liquid gallium has technological relevance to the design and optimization of the conditions for the preparation of solution-grown gallium-based crystals doped with oxygen. It has been reported [l] that visible luminescence of high efficiency can be achieved in gallium phosphide doped with zinc and oxygen. Moreover, in the preparation of high purity gallium phosphide and arsenide, fused quartz is frequently used as a container and purified hydrogen is sometimes employed as the gas atmosphere. Silicon contamination of the crystals under these conditions has been reported [Z, 31. The reduction of silica may be represented by the equations
SiWs) + Gasemicond + Ga2W) + Sisemicond Si%ds) + Wg)
+
HzO(!Z)
+ %emicond
If the saturation solubility of oxygen is small, it may be possible to employ a gas atmosphere of higher oxygen potential to minimize silicon contamination. Precise control of the oxygen potential during the preparation of semiconductors is now technically feasible by the use of solid oxide electrolytes. The oxygen potential corresponding to the mixture Ga(1) + /3-Ga20s has recently been measured by Klinedinst and Stevenson [4] and Smith and Chatterji [ 51, using solid oxide galvanic cells in the temperature range 550 1000 “C. Although the results of the two investigations are in fair agreement, Third Law analysis of the free energies measured by Smith and Chatterji [ 51 gives a more invariant value of AH&s for fl-Ga20,, in agreement with calorimetrically determined heats of formation [ 6, 71. This communication reports measurements of the saturation solubility of oxygen as a function of temperature, in liquid gallium and in its alloys with copper. In order to obtain a good separation between gallium oxide and the oxygen-saturated metal and to avoid errors caused by the entrapment of oxide particles by the solidifying metal, an isopiestic technique was chosen for oxygen solubility determinations. Liquid gallium or gallium-copper alloy was held in one limb of an evacuated silica cell and equilibrated via the gas phase with the mixture Ga(1) + /3-Ga20s or Ga-Cu + /3-Ga20s held in an adjacent limb. The vapour pressure of Ga20 over the Ga + Ga20s mixture has been measured by Frasch and Thurmond [8] as 1.56 X lOme atm at 800 “C and 9.9 X 10 -3 atm at 1000 “C. The vapour pressure of liquid gallium varies from 9 X lo--’ atm at 775 “C to 5.6 X 10eF5 atm at 1125 “C. The oxygen partial pressure over oxygen-saturated gallium or gallium-copper alloys at 1100 “C is below lO-‘l’ atm. The most significant vapour species is therefore Ga,O. Foster and Scardefield [9] have measured the weight loss of fusion-cast solid P-Ga2 0, after immersion in liquid gallium held in a quartz capsule for 48 - 24 h and at temperatures between 1000 and 1200 “C. Their results, published only in graphical form, indicate that the heat of solution of P-Ga203 in liquid gallium is 35.8 kcal mol-l.
213
J
GaiorGa+Cu)
Ga(orGa+cuj
/$a**,
Cell
I
Silica ampoule
Ga (Or
Ga+Cu)
Fig. 1. Schematic diagram of sealed silica cells used in isopiestic equilibration of metal with oxide.
Experimental
methods
Materials Gallium metal and p-gallium sesquioxide powder used in this study were 99.999% pure and were supplied by Apache Chemicals. Copper metal was supplied by Cominco and was 99.99% pure. Gallium and copper contained in AlaO, crucibles were reduced with high purity hydrogen at 900 “C for 12 h. The hydrogen used had been further purified by passing through palladium on alumina at 120 “C, magnesium perchlorate and phosphorus pentoxide.
A schematic diagram of the H-shaped cells used in this study is shown in Fig. 1. In cell I the two limbs of the cell were joined by a silica capillary approximately 1 cm long with an internal diameter of 0.1 mm. A mixture of Ga + /I-GaaOs (or Ga-Cu + fi-GazO,) was contained in one limb, while the second limb contained pure Ga or Ga-Cu alloy of identical composition. The cell was sealed under a vacuum of low3 mmHg. In cell II the deoxidized Ga or Ga-Cu alloy was placed inside a silica ampoule, at the top of which a Knudsen orifice approximately 0.01 mm in diameter was made by grinding and piercing with a fine needle. This ampoule was placed inside one limb of the silica cell. The capillary connecting the two limbs in cell II had an inner diameter of 0.5 mm. The design of cell II permitted the measurement of the
214 TABLE
1
Saturation alloys
solubility
of oxygen
in liquid gallium and gallium -copper
Metal/alloy
Temperature
Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga
715 800 800 900 900 1000 1085 1100 1125 1125
0.15 0.23 0.25 0.97 0.85 3.08 6.56 7.74 10.3 9.37
1100 1100 1100 1100 1100 1100 1100 1100
4.47 1.92 0.36 0.55 0.54 0.16
Ga-Cu, X,, = Ga-Cu, X,, = Ga-Cu, X,, = Ga-Cu, X Ga-Cu , X”” Ga = G&u, X,, = Gz-Cu, X,, = Ga-Cu, X,, =
0.8 0.6 0.4 0.4 0.4 0.3 0.2 0.01
(“C)
Oxygen solubility (at.% X 102)
weight gain of the metal or alloy contained in the ampoule after the uptake of oxygen as GazO. Owing to the presence of two silica walls in one limb of cell II, the cooling rate of the metal (or alloy) was low. The introduction of the Knudsen orifice was intended to minimize the transfer of oxygen as Ga20 from the oxygen-saturated metal (or alloy) to the walls of the silica limb during quenching. Initial experiments with cell I indicated that, when dropped into water or liquid nitrogen, the quenching rates were sufficiently rapid to prevent significant transfer of oxygen via Ga,O gas, which condenses as a mixture of Ga + P-Ga20s on the inside walls of the silica cell. However, when cell II was quenched in water there was visual evidence of the deposition of a mixture of Ga + p-Ga20a on the inner surface of the silica ampoule. The escape of oxygen as Ga20 gas from the metal (or alloy) and its condensation on the inner surface of the ampoule by differential cooling could be prevented by quenching in liquid nitrogen. The solubility of oxygen, obtained by weighing the silica ampoule on a microbalance before and after equilibration, was not sufficiently reproducible and was 10 - 20% lower than values obtained by analyzing the metal (or alloy) using the inert gas fusion technique. Moreover, the weight gain was not significant when the oxygen solubility in the metal was low (e.g. at low temperatures and in copper-rich alloys). Experiments with cell II were therefore abandoned; all the values shown in Table I were obtained with cell I.
215
The cell was placed in a horizontal three-zone furnace such that the temperature of the limb containing the oxide was 2 - 3 “C below that of the limb containing the pure metal (or alloy). The temperature of the furnace was maintained within kl “C. By maintaining the oxide limb at a lower temperature, the supersaturation of the metal with oxygen or the precipitation of an oxide phase in the hotter limb due to temperature fluctuations of the furnace was avoided. The temperatures of the two limbs were measured by two Pt/Pt-Rh thermocouples. The oxide phase in equilibrium with Cu-Ga alloys at 1100 “C was found by X-ray diffraction to be P-Ga,O,. Analysis Oxygen analysis of the metal (or alloy) was carried out using a Leco RO-16 oxygen analyzer. The metal was reacted in a carbon crucible under ar arc and the carbon monoxide entrained in a controlled stream of N, was monitored by measuring the conductivity of the gas mixture. In order to minimize the volatilization of Ga,O from the sample before the completion of the carbon-oxygen reaction, oxygen-free copper [lo] was added to pure gallium and gallium-rich alloys so that the activity of gallium in the fused sample was maintained below 0.25. The alloy compositions were calculated from the weights of the component metals (copper and gallium) used.
Results In Fig. 2 the saturation solubility of oxygen in liquid gallium obtained by analysis of the metal after equilibration in cell I is plotted as a function of the reciprocal of absolute temperature. The least mean squares line through the experimental points may be representd by the equation log (at.% 0) = -7380/T The solution
of p-GazO,
+ 4.264
(kO.03)
in liquid gallium may be represented
(1) as
(2) where the standard state for oxygen in liquid gallium is an infinitely dilute solution in which the activity is equal to atomic per cent. The free energy change for the above reaction can be calculated from the relationship AG&, = -RT
In K = -4.575
= 33 767 -
19.507T
T log (at.% 0) (2160)
cal
(3)
It is assumed that oxygen dissolved in liquid gallium obeys Sievert’s law. Detailed measurements have shown that Sievert’s law is obeyed by oxygen in liquid silver, lead and tin; small negative deviations have been observed in liquid copper [ 111 and iron [ 121. These negative deviations are significant only when the oxygen concentration is greater than 1 at.%. At a concentra-
216
Fig. 2. The temperature gallium: o this study;
x
dependence of the saturation Foster and Scardefield [9].
solubility
of oxygen
in liquid
tion of 0.1 at.% the activity coefficient of oxygen is approximately 0.989, suggesting a maximum error of 1 .l% when the self-interaction of dissolved oxygen is neglected. Since the solubility of oxygen in liquid gallium is less than 0.1 at.% in the range of temperature covered in this study, the activity of gallium may be taken as being equal to unity. When eqn. (3) is combined with the standard free energy of formation of fi-GaaOs [5] obtained by the e.m.f. method: 2Ga(l) + i O,(g) + P-GaaOs AG” = -259
340 + 78.117’(?300)
(4) cal
one obtains the standard free energy of solution liquid gallium ;
G,(g) +
OGa
(5) of molecular
oxygen
in
(6)
217
4 -
1
1
I
1
o-8
C”
X
Ga
Fig. 3. Variation of the saturation copper alloys at 1100 “C.
AG” = -52
680 + 6.53T
solubility
(2200)
of oxygen
with alloy
composition
cal
The oxygen solubility can also be expressed in terms fraction of oxygen (No) and the oxygen partial pressure RT In p&l”2 = RT In No + AH, -
for gallium
TAS;
(7) of the atomic (3)
cal deg-l (g atom))r. where AH, = -52 680 cal (g atom.))’ and AS: = -15.68 The authors are unaware of measurements of the non-stoichiometry of /3-Ga,Os. However, since the standard free energy of formation of P-Ga20a used in the above calculation [5] is also obtained from oxygen potential measurements over mixtures of Ga + fl-Ga,O,, the presence of a small nonstoichiometry in the oxide does not significantly affect the accuracy of eqn. (7).
218
TABLE 2 Activity coefficients in binary Ga-Cu ailoys at 1100 "C
[13 -151
0.06 0.12
0.97 0.86
0.36 0.69 0.90 0.96 0.99 I.Ql 1.00
0.59 a,42 0.34 0.31 0.30 028 0.28
The variation of the saturation solubihty of oxygen in gallium-copper alloys at 1100 “C as a function of the alloy composition is &own in Fig, 3. The solubility of oxygen decreases with the addition of copper up to 70 at.%. The soiubility uf oxygen was too low for quantitative deter~nat~on for an alloy suntanning 80 at.% copper. The oxygen solubi~ty in an alloy eonta~n~ng 99 at.% copper was found to be slightly higher than in an alloy with 70 at.% copper. The results therefore suggest that oxygen solubility exhibits a minimum at a composition near 80 at.% copper. The ~n~rnurn shown in Fig. 3 is drawn on the basis of a theoretical model which will be discussed in the next section. From the standard free energy of formation of silica and the activity coefficient of silicon in liquid gallium calculated from the phase diagram, it can be shown that the silicon contamination of liquid gallium at the oxygen potentials corresponding to the Ga + Ga,C& equilibrium is insignificant (Xs, < 10B7 ). The ratio of the activity coefficient of oxygen in liquid gallium-copper ahoy to that in pure gallium is given by the equation
where the oxygen concentration corresponds to saturation with p-Ga203, y. = p#F (at.% 0)-l, pgf = exp (AG’&,03/3RT) (a$!)_1 and a& is the activity of gallium in the alloy. If the standard”state for oxygen is taken as a 1 at.% solution in liquid gallium, ‘Yo(oa) = 1. The variation of the activity coefficient of oxygen with alloy composition in gallium-copper alloys at 1100 “C, relative to oxygen in pure gallium, is shown in Fig. 4. The activity of gallium in the alloys is obtained from the mass spectrometric studies of Alcoek et rrl. [13] which have been extrapolated to 1100 “C (Table 2) using calorii~etric information about the heat of mixing [14,15].
219
CU
0.2
(1.4
0.6
ocs
Ga
XGa
Fig. 4. Composition dependence copper alloys, relative to oxygen
of the activity coefficient in pure gallium.
of oxygen
at 1100
“C in gallium
Discussion In Fig. 2 the saturation solubility obtained in this study of oxygen in liquid gallium is compared with the values obtained by Foster and Scardefield [9]. The solubilit~es obtained in the two studies are in good agreement, although the present results show a smaller temperature dependence. In Fig. 5 the heat and entropy of solution obtained in this study of diatomic gaseous oxygen in liquid gallium is compared with the literature values for silver [ 16, 171, copper [ll], lead [ll, 181 and tin [19]. Although the results do not
220
Fig. 5. Relationship at.%.
between
partial heat and entropy
of oxygen
in liquid metals
at 1
support a linear relationship between entropies and heats of solution, as found by Kubaschewski [20] for integral values of binary alloys, there is a clear correlation between the two parameters. Since their partial properties refer to infinite dilution where the configurational contributions to the entropy would be similar for the different metals, the decrease in partial entropy with partial heat (or stronger metal-oxygen bonds) may be ascribed to increasing vibrational frequency. Available values for the solution of oxygen in liquid iron, cobalt and nickel show considerable scatter and do not fit this correlation. It is conceivable that the narrow range of temperature in which the activity of oxygen has been measured and the experimental errors inherent in physicochemical measurements at temperatures above 1500 “C! preclude reliable estimates of partial heats and entropies of oxygen. Alternatively, the unfilled d shells of these metals might influence the behaviour of dissolved oxygen. An analysis of the results obtained so far supports the qualitative correlation suggested by Richardson [21] between partial heats of solution of oxygen and the heat of formation of the corresponding oxides. In Fig. 4 the experimental values for the activity coefficient of oxygen in liquid Ga-Cu alloys at 1100 “C are compared with the values calculated
221
using a recent quasichemical model proposed by Jacob and Alcock [22] in which each oxygen atom is assumed to bond with n metal atoms. Because of strong bonding between the metal and oxygen atoms, the electronic configuration around the metal atoms bonded to oxygen would be distorted, so that the strength of metal-metal bonds made by these atoms is reduced by a factor 1 - 01. The activity coefficient of oxygen dissolved in a binary alloy may then be predicted from a knowledge of the activity coefficients in the three bounding binary systems, using the formula 01
X Ga
-fGa(Ga+Cu) ___Y tgGL3,
r”Cu(Ga
1
+ ‘A)=
(10)
+ XC” d;Ga+
Y $2u,
Cu)
where XGa and Xc, are the mole fractions of gallium and copper, To(&), are the activity coefficients of oxygen in pure gallium, YO(Cu) and YO(Ga+&) copper and copper-gallium alloys, respectively, and yoa(oa + cuj and 7Cu(oa+Cu) are the activity coefficients in binary gallium-copper alloys. It has been shown earlier [ 221 that the experimental data for a number of ternary solutions containing oxygen and sulphur are in good agreement with the above equation for IZ = 4 and 01 = %. Measurements of the diffusion coefficient of oxygen in liquid metals suggest that oxygen dissolves interstitially. It may be seen from Fig. 4 that the agreement between the measurements and the predicted values is close, suggesting that the model may be used to extrapolate from the present measurements to copper concentrations above 70 at.%. The free energy of formation of cuprous gallate, CuGaOz, has recently been measured [23] using a solid oxide galvanic cell. For the reaction Cu,O(s) + Ga,Oa(P) AG” = -3 Combining CuzO [ll] reaction
375 + 2.6T
(+lOO) cal
(II)
this information with the standard free energies of formation of and p-GaaO, [5], the free energy change for the displacement
2GasOs(P) is obtained
--f 2CuGaO,(s)
+ 3Cu(l)
+ 3CuGaOa(s)
+ Ga(1)
as
L?.G” = 55 750 The displacement gallium when log %, < -12
3.067’
reaction 185/T
(*300)
cal
would therefore + 0.668
(12) occur only at low activities
of (13)
Using a value of 0.05 for the activity coefficient of gallium at infinite dilution in copper at 1100 ‘C, it can be shown that the CuGaOz phase is stable only below a gallium concentration of 0.12 at. ppm.
222
Acknowledgments The authors wish to thank the National Research Council of Canada for financial support and Mr. C. K. Kim for help with the oxygen analysis.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
R. A. Logan, H. G. White and F. A. Trumbore, Appl. Phys. Lett., 10 (1967) 206. C. N. Cochran and L. M. Foster, J. Electrochem. Sot., 109 (1962) 149. J. M. Woodall, Trans. Metall. Sot. AIME, 239 (1967) 378. K. A. Klinedinst and D. A. Stevenson, J. Chem. Thermodyn., 4 (1972) 565. J. V. Smith and D. Chatterji, J. Am. Ceram. Sot., 56 (1973) 288. A. D. Mah, U.S. Bur. Mines, Rep. Invest., 5965, 1962. S. N. Gadzhiev and K. A. Sharifov, 4th Vop. Met. Fiz. Poluprov. Tr. Soveshch., 1959, (1961) 43. C. J. Frash and C. D. Thurmond, J. Phys. Chem., 66 (1962) 877. L. M. Foster and J. Scardefield, J. Electrochem. Sot., 116 (1969) 495. K. T. Jacob. S, K. Seshadri and F. D. Richardson, Trans. Inst. Min. Metall. (London), Sect. C, 79 (1970) C274. K. T. Jacob and J. H. E. Jeffes, Trans. Inst. Min. Metall. (London), Sect. C, 80 (1971) C32. T. P. Floridis and J. Chipman, Trans. Am. Inst. Min. Metall. Pet. Eng., 212 (1958) 549. C. B. Alcock, R. Sridhar and R. C. Svedberg, J. Chem. Thermodyn., 2 (1970) 255. K. Itagaki and A. Yazawa, Trans. Jpn. Inst. Met., 35 (1971) 383. B. Predel and D. W. Stein, Acta Metall., 20 (1972) 515. C. Diaz, C. R. Mason and F. D. Richardson, Trans. Inst. Min. Metall. (London), 75 (1966) C183. E. H. Baker and M. I. Talukdar, Trans. Inst. Min. Metall. (London), 77 (1968) C128. C. B. Alcock and T. N. Belford, Trans. Faraday Sot., 60 (1964) 822. C. B. Alcock and T. N. Belford, Trans. Faraday Sot., 61 (1965) 442. 0. Kubaschewski, E. L. Evans and C. B. Alcock, Metallurgical Thermochemistry, 4th edn., Pergamon Press, Oxford, 1967, p. 65. F. D. Richardson, J. Iron Steel Inst. London, 166 (1950) 144. K. T. Jacob and C. B. Alcock, Acta Metall., 20 (1972) 2‘21. K. T. Jacob and C. B. Alcock, Rev. Int. Hautes Temp. Refrect., 13 (1976) 37.
Journal
0 Elsevier
Sequoia
Metals,
S.A., Lausanne
53 (1977)
- Printed
211
- 222
211
in the Netherlands
SOLUBILITY AND ACTIVITY OF OXYGEN IN LIQUID GALLIUM AND GALLIUM-COPPER ALLOYS
C. B. ALCOCK
and K. T. JACOB
Department of Metallurgy 1 A4 (Canada)
(Received
November
and Materials
Science,
University
of Toronto,
Toronto
M5S
19, 1976)
Summary The solubility of oxygen in liquid gallium in the temperature range 775 - 1125 “C and in liquid gallium-copper alloys at 1100 ‘C, in equilibrium with fi-Ga,O,, has been measured by an isopiestic equilibrium technique. The solubility of oxygen in pure gallium is given by the equation log (at.% 0) = -7380/T
+ 4.264 (kO.03)
Using recently measured values for the standard free energy of formation of P-Ga20s and assuming that oxygen obeys Sievert’s law up to the saturation limit, the standard free energy of solution of oxygen in liquid gallium may be calculated:
A G&s= -52
680 + 6.532’(+200)
cal
where the standard state for dissolved oxygen is an infinitely dilute solution in which the activity is equal to atomic per cent. The effect of copper on the activity of oxygen dissolved in liquid gallium is found to be in good agreement with that predicted by a recent quasichemical model in which it was assumed that each oxygen is interstitially coordinated to four metal atoms and that the nearest neighbour metal atoms lose approximately half their metallic cohesive energies.
Introduction As part of a larger programme of research on the thermodynamic behaviour of oxygen dissolved in metals and alloys, measurements have been made on the saturation solubility of oxygen in liquid gallium in the temperature range 775 - 1125 “C and in gallium-copper alloys at 1100 “C. A know-
212
ledge of the saturation solubility in liquid gallium has technological relevance to the design and optimization of the conditions for the preparation of solution-grown gallium-based crystals doped with oxygen. It has been reported [l] that visible luminescence of high efficiency can be achieved in gallium phosphide doped with zinc and oxygen. Moreover, in the preparation of high purity gallium phosphide and arsenide, fused quartz is frequently used as a container and purified hydrogen is sometimes employed as the gas atmosphere. Silicon contamination of the crystals under these conditions has been reported [Z, 31. The reduction of silica may be represented by the equations
SiWs) + Gasemicond + Ga2W) + Sisemicond Si%ds) + Wg)
+
HzO(!Z)
+ %emicond
If the saturation solubility of oxygen is small, it may be possible to employ a gas atmosphere of higher oxygen potential to minimize silicon contamination. Precise control of the oxygen potential during the preparation of semiconductors is now technically feasible by the use of solid oxide electrolytes. The oxygen potential corresponding to the mixture Ga(1) + /3-Ga20s has recently been measured by Klinedinst and Stevenson [4] and Smith and Chatterji [ 51, using solid oxide galvanic cells in the temperature range 550 1000 “C. Although the results of the two investigations are in fair agreement, Third Law analysis of the free energies measured by Smith and Chatterji [ 51 gives a more invariant value of AH&s for fl-Ga20,, in agreement with calorimetrically determined heats of formation [ 6, 71. This communication reports measurements of the saturation solubility of oxygen as a function of temperature, in liquid gallium and in its alloys with copper. In order to obtain a good separation between gallium oxide and the oxygen-saturated metal and to avoid errors caused by the entrapment of oxide particles by the solidifying metal, an isopiestic technique was chosen for oxygen solubility determinations. Liquid gallium or gallium-copper alloy was held in one limb of an evacuated silica cell and equilibrated via the gas phase with the mixture Ga(1) + /3-Ga20s or Ga-Cu + /3-Ga20s held in an adjacent limb. The vapour pressure of Ga20 over the Ga + Ga20s mixture has been measured by Frasch and Thurmond [8] as 1.56 X lOme atm at 800 “C and 9.9 X 10 -3 atm at 1000 “C. The vapour pressure of liquid gallium varies from 9 X lo--’ atm at 775 “C to 5.6 X 10eF5 atm at 1125 “C. The oxygen partial pressure over oxygen-saturated gallium or gallium-copper alloys at 1100 “C is below lO-‘l’ atm. The most significant vapour species is therefore Ga,O. Foster and Scardefield [9] have measured the weight loss of fusion-cast solid P-Ga2 0, after immersion in liquid gallium held in a quartz capsule for 48 - 24 h and at temperatures between 1000 and 1200 “C. Their results, published only in graphical form, indicate that the heat of solution of P-Ga203 in liquid gallium is 35.8 kcal mol-l.
213
J
GaiorGa+Cu)
Ga(orGa+cuj
/$a**,
Cell
I
Silica ampoule
Ga (Or
Ga+Cu)
Fig. 1. Schematic diagram of sealed silica cells used in isopiestic equilibration of metal with oxide.
Experimental
methods
Materials Gallium metal and p-gallium sesquioxide powder used in this study were 99.999% pure and were supplied by Apache Chemicals. Copper metal was supplied by Cominco and was 99.99% pure. Gallium and copper contained in AlaO, crucibles were reduced with high purity hydrogen at 900 “C for 12 h. The hydrogen used had been further purified by passing through palladium on alumina at 120 “C, magnesium perchlorate and phosphorus pentoxide.
A schematic diagram of the H-shaped cells used in this study is shown in Fig. 1. In cell I the two limbs of the cell were joined by a silica capillary approximately 1 cm long with an internal diameter of 0.1 mm. A mixture of Ga + /I-GaaOs (or Ga-Cu + fi-GazO,) was contained in one limb, while the second limb contained pure Ga or Ga-Cu alloy of identical composition. The cell was sealed under a vacuum of low3 mmHg. In cell II the deoxidized Ga or Ga-Cu alloy was placed inside a silica ampoule, at the top of which a Knudsen orifice approximately 0.01 mm in diameter was made by grinding and piercing with a fine needle. This ampoule was placed inside one limb of the silica cell. The capillary connecting the two limbs in cell II had an inner diameter of 0.5 mm. The design of cell II permitted the measurement of the
214 TABLE
1
Saturation alloys
solubility
of oxygen
in liquid gallium and gallium -copper
Metal/alloy
Temperature
Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga
715 800 800 900 900 1000 1085 1100 1125 1125
0.15 0.23 0.25 0.97 0.85 3.08 6.56 7.74 10.3 9.37
1100 1100 1100 1100 1100 1100 1100 1100
4.47 1.92 0.36 0.55 0.54 0.16
Ga-Cu, X,, = Ga-Cu, X,, = Ga-Cu, X,, = Ga-Cu, X Ga-Cu , X”” Ga = G&u, X,, = Gz-Cu, X,, = Ga-Cu, X,, =
0.8 0.6 0.4 0.4 0.4 0.3 0.2 0.01
(“C)
Oxygen solubility (at.% X 102)
weight gain of the metal or alloy contained in the ampoule after the uptake of oxygen as GazO. Owing to the presence of two silica walls in one limb of cell II, the cooling rate of the metal (or alloy) was low. The introduction of the Knudsen orifice was intended to minimize the transfer of oxygen as Ga20 from the oxygen-saturated metal (or alloy) to the walls of the silica limb during quenching. Initial experiments with cell I indicated that, when dropped into water or liquid nitrogen, the quenching rates were sufficiently rapid to prevent significant transfer of oxygen via Ga,O gas, which condenses as a mixture of Ga + P-Ga20s on the inside walls of the silica cell. However, when cell II was quenched in water there was visual evidence of the deposition of a mixture of Ga + p-Ga20a on the inner surface of the silica ampoule. The escape of oxygen as Ga20 gas from the metal (or alloy) and its condensation on the inner surface of the ampoule by differential cooling could be prevented by quenching in liquid nitrogen. The solubility of oxygen, obtained by weighing the silica ampoule on a microbalance before and after equilibration, was not sufficiently reproducible and was 10 - 20% lower than values obtained by analyzing the metal (or alloy) using the inert gas fusion technique. Moreover, the weight gain was not significant when the oxygen solubility in the metal was low (e.g. at low temperatures and in copper-rich alloys). Experiments with cell II were therefore abandoned; all the values shown in Table I were obtained with cell I.
215
The cell was placed in a horizontal three-zone furnace such that the temperature of the limb containing the oxide was 2 - 3 “C below that of the limb containing the pure metal (or alloy). The temperature of the furnace was maintained within kl “C. By maintaining the oxide limb at a lower temperature, the supersaturation of the metal with oxygen or the precipitation of an oxide phase in the hotter limb due to temperature fluctuations of the furnace was avoided. The temperatures of the two limbs were measured by two Pt/Pt-Rh thermocouples. The oxide phase in equilibrium with Cu-Ga alloys at 1100 “C was found by X-ray diffraction to be P-Ga,O,. Analysis Oxygen analysis of the metal (or alloy) was carried out using a Leco RO-16 oxygen analyzer. The metal was reacted in a carbon crucible under ar arc and the carbon monoxide entrained in a controlled stream of N, was monitored by measuring the conductivity of the gas mixture. In order to minimize the volatilization of Ga,O from the sample before the completion of the carbon-oxygen reaction, oxygen-free copper [lo] was added to pure gallium and gallium-rich alloys so that the activity of gallium in the fused sample was maintained below 0.25. The alloy compositions were calculated from the weights of the component metals (copper and gallium) used.
Results In Fig. 2 the saturation solubility of oxygen in liquid gallium obtained by analysis of the metal after equilibration in cell I is plotted as a function of the reciprocal of absolute temperature. The least mean squares line through the experimental points may be representd by the equation log (at.% 0) = -7380/T The solution
of p-GazO,
+ 4.264
(kO.03)
in liquid gallium may be represented
(1) as
(2) where the standard state for oxygen in liquid gallium is an infinitely dilute solution in which the activity is equal to atomic per cent. The free energy change for the above reaction can be calculated from the relationship AG&, = -RT
In K = -4.575
= 33 767 -
19.507T
T log (at.% 0) (2160)
cal
(3)
It is assumed that oxygen dissolved in liquid gallium obeys Sievert’s law. Detailed measurements have shown that Sievert’s law is obeyed by oxygen in liquid silver, lead and tin; small negative deviations have been observed in liquid copper [ 111 and iron [ 121. These negative deviations are significant only when the oxygen concentration is greater than 1 at.%. At a concentra-
216
Fig. 2. The temperature gallium: o this study;
x
dependence of the saturation Foster and Scardefield [9].
solubility
of oxygen
in liquid
tion of 0.1 at.% the activity coefficient of oxygen is approximately 0.989, suggesting a maximum error of 1 .l% when the self-interaction of dissolved oxygen is neglected. Since the solubility of oxygen in liquid gallium is less than 0.1 at.% in the range of temperature covered in this study, the activity of gallium may be taken as being equal to unity. When eqn. (3) is combined with the standard free energy of formation of fi-GaaOs [5] obtained by the e.m.f. method: 2Ga(l) + i O,(g) + P-GaaOs AG” = -259
340 + 78.117’(?300)
(4) cal
one obtains the standard free energy of solution liquid gallium ;
G,(g) +
OGa
(5) of molecular
oxygen
in
(6)
217
4 -
1
1
I
1
o-8
C”
X
Ga
Fig. 3. Variation of the saturation copper alloys at 1100 “C.
AG” = -52
680 + 6.53T
solubility
(2200)
of oxygen
with alloy
composition
cal
The oxygen solubility can also be expressed in terms fraction of oxygen (No) and the oxygen partial pressure RT In p&l”2 = RT In No + AH, -
for gallium
TAS;
(7) of the atomic (3)
cal deg-l (g atom))r. where AH, = -52 680 cal (g atom.))’ and AS: = -15.68 The authors are unaware of measurements of the non-stoichiometry of /3-Ga,Os. However, since the standard free energy of formation of P-Ga20a used in the above calculation [5] is also obtained from oxygen potential measurements over mixtures of Ga + fl-Ga,O,, the presence of a small nonstoichiometry in the oxide does not significantly affect the accuracy of eqn. (7).
218
TABLE 2 Activity coefficients in binary Ga-Cu ailoys at 1100 "C
[13 -151
0.06 0.12
0.97 0.86
0.36 0.69 0.90 0.96 0.99 I.Ql 1.00
0.59 a,42 0.34 0.31 0.30 028 0.28
The variation of the saturation solubihty of oxygen in gallium-copper alloys at 1100 “C as a function of the alloy composition is &own in Fig, 3. The solubility of oxygen decreases with the addition of copper up to 70 at.%. The soiubility uf oxygen was too low for quantitative deter~nat~on for an alloy suntanning 80 at.% copper. The oxygen solubi~ty in an alloy eonta~n~ng 99 at.% copper was found to be slightly higher than in an alloy with 70 at.% copper. The results therefore suggest that oxygen solubility exhibits a minimum at a composition near 80 at.% copper. The ~n~rnurn shown in Fig. 3 is drawn on the basis of a theoretical model which will be discussed in the next section. From the standard free energy of formation of silica and the activity coefficient of silicon in liquid gallium calculated from the phase diagram, it can be shown that the silicon contamination of liquid gallium at the oxygen potentials corresponding to the Ga + Ga,C& equilibrium is insignificant (Xs, < 10B7 ). The ratio of the activity coefficient of oxygen in liquid gallium-copper ahoy to that in pure gallium is given by the equation
where the oxygen concentration corresponds to saturation with p-Ga203, y. = p#F (at.% 0)-l, pgf = exp (AG’&,03/3RT) (a$!)_1 and a& is the activity of gallium in the alloy. If the standard”state for oxygen is taken as a 1 at.% solution in liquid gallium, ‘Yo(oa) = 1. The variation of the activity coefficient of oxygen with alloy composition in gallium-copper alloys at 1100 “C, relative to oxygen in pure gallium, is shown in Fig. 4. The activity of gallium in the alloys is obtained from the mass spectrometric studies of Alcoek et rrl. [13] which have been extrapolated to 1100 “C (Table 2) using calorii~etric information about the heat of mixing [14,15].
219
CU
0.2
(1.4
0.6
ocs
Ga
XGa
Fig. 4. Composition dependence copper alloys, relative to oxygen
of the activity coefficient in pure gallium.
of oxygen
at 1100
“C in gallium
Discussion In Fig. 2 the saturation solubility obtained in this study of oxygen in liquid gallium is compared with the values obtained by Foster and Scardefield [9]. The solubilit~es obtained in the two studies are in good agreement, although the present results show a smaller temperature dependence. In Fig. 5 the heat and entropy of solution obtained in this study of diatomic gaseous oxygen in liquid gallium is compared with the literature values for silver [ 16, 171, copper [ll], lead [ll, 181 and tin [19]. Although the results do not
220
Fig. 5. Relationship at.%.
between
partial heat and entropy
of oxygen
in liquid metals
at 1
support a linear relationship between entropies and heats of solution, as found by Kubaschewski [20] for integral values of binary alloys, there is a clear correlation between the two parameters. Since their partial properties refer to infinite dilution where the configurational contributions to the entropy would be similar for the different metals, the decrease in partial entropy with partial heat (or stronger metal-oxygen bonds) may be ascribed to increasing vibrational frequency. Available values for the solution of oxygen in liquid iron, cobalt and nickel show considerable scatter and do not fit this correlation. It is conceivable that the narrow range of temperature in which the activity of oxygen has been measured and the experimental errors inherent in physicochemical measurements at temperatures above 1500 “C! preclude reliable estimates of partial heats and entropies of oxygen. Alternatively, the unfilled d shells of these metals might influence the behaviour of dissolved oxygen. An analysis of the results obtained so far supports the qualitative correlation suggested by Richardson [21] between partial heats of solution of oxygen and the heat of formation of the corresponding oxides. In Fig. 4 the experimental values for the activity coefficient of oxygen in liquid Ga-Cu alloys at 1100 “C are compared with the values calculated
221
using a recent quasichemical model proposed by Jacob and Alcock [22] in which each oxygen atom is assumed to bond with n metal atoms. Because of strong bonding between the metal and oxygen atoms, the electronic configuration around the metal atoms bonded to oxygen would be distorted, so that the strength of metal-metal bonds made by these atoms is reduced by a factor 1 - 01. The activity coefficient of oxygen dissolved in a binary alloy may then be predicted from a knowledge of the activity coefficients in the three bounding binary systems, using the formula 01
X Ga
-fGa(Ga+Cu) ___Y tgGL3,
r”Cu(Ga
1
+ ‘A)=
(10)
+ XC” d;Ga+
Y $2u,
Cu)
where XGa and Xc, are the mole fractions of gallium and copper, To(&), are the activity coefficients of oxygen in pure gallium, YO(Cu) and YO(Ga+&) copper and copper-gallium alloys, respectively, and yoa(oa + cuj and 7Cu(oa+Cu) are the activity coefficients in binary gallium-copper alloys. It has been shown earlier [ 221 that the experimental data for a number of ternary solutions containing oxygen and sulphur are in good agreement with the above equation for IZ = 4 and 01 = %. Measurements of the diffusion coefficient of oxygen in liquid metals suggest that oxygen dissolves interstitially. It may be seen from Fig. 4 that the agreement between the measurements and the predicted values is close, suggesting that the model may be used to extrapolate from the present measurements to copper concentrations above 70 at.%. The free energy of formation of cuprous gallate, CuGaOz, has recently been measured [23] using a solid oxide galvanic cell. For the reaction Cu,O(s) + Ga,Oa(P) AG” = -3 Combining CuzO [ll] reaction
375 + 2.6T
(+lOO) cal
(II)
this information with the standard free energies of formation of and p-GaaO, [5], the free energy change for the displacement
2GasOs(P) is obtained
--f 2CuGaO,(s)
+ 3Cu(l)
+ 3CuGaOa(s)
+ Ga(1)
as
L?.G” = 55 750 The displacement gallium when log %, < -12
3.067’
reaction 185/T
(*300)
cal
would therefore + 0.668
(12) occur only at low activities
of (13)
Using a value of 0.05 for the activity coefficient of gallium at infinite dilution in copper at 1100 ‘C, it can be shown that the CuGaOz phase is stable only below a gallium concentration of 0.12 at. ppm.
222
Acknowledgments The authors wish to thank the National Research Council of Canada for financial support and Mr. C. K. Kim for help with the oxygen analysis.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
R. A. Logan, H. G. White and F. A. Trumbore, Appl. Phys. Lett., 10 (1967) 206. C. N. Cochran and L. M. Foster, J. Electrochem. Sot., 109 (1962) 149. J. M. Woodall, Trans. Metall. Sot. AIME, 239 (1967) 378. K. A. Klinedinst and D. A. Stevenson, J. Chem. Thermodyn., 4 (1972) 565. J. V. Smith and D. Chatterji, J. Am. Ceram. Sot., 56 (1973) 288. A. D. Mah, U.S. Bur. Mines, Rep. Invest., 5965, 1962. S. N. Gadzhiev and K. A. Sharifov, 4th Vop. Met. Fiz. Poluprov. Tr. Soveshch., 1959, (1961) 43. C. J. Frash and C. D. Thurmond, J. Phys. Chem., 66 (1962) 877. L. M. Foster and J. Scardefield, J. Electrochem. Sot., 116 (1969) 495. K. T. Jacob. S, K. Seshadri and F. D. Richardson, Trans. Inst. Min. Metall. (London), Sect. C, 79 (1970) C274. K. T. Jacob and J. H. E. Jeffes, Trans. Inst. Min. Metall. (London), Sect. C, 80 (1971) C32. T. P. Floridis and J. Chipman, Trans. Am. Inst. Min. Metall. Pet. Eng., 212 (1958) 549. C. B. Alcock, R. Sridhar and R. C. Svedberg, J. Chem. Thermodyn., 2 (1970) 255. K. Itagaki and A. Yazawa, Trans. Jpn. Inst. Met., 35 (1971) 383. B. Predel and D. W. Stein, Acta Metall., 20 (1972) 515. C. Diaz, C. R. Mason and F. D. Richardson, Trans. Inst. Min. Metall. (London), 75 (1966) C183. E. H. Baker and M. I. Talukdar, Trans. Inst. Min. Metall. (London), 77 (1968) C128. C. B. Alcock and T. N. Belford, Trans. Faraday Sot., 60 (1964) 822. C. B. Alcock and T. N. Belford, Trans. Faraday Sot., 61 (1965) 442. 0. Kubaschewski, E. L. Evans and C. B. Alcock, Metallurgical Thermochemistry, 4th edn., Pergamon Press, Oxford, 1967, p. 65. F. D. Richardson, J. Iron Steel Inst. London, 166 (1950) 144. K. T. Jacob and C. B. Alcock, Acta Metall., 20 (1972) 2‘21. K. T. Jacob and C. B. Alcock, Rev. Int. Hautes Temp. Refrect., 13 (1976) 37.