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Thermodynamics of ordering alloys—III
J. Phys. C&m. So&&
Pergamon Press 1958. Vol. 6. pp. 277-279.
THERMODYNAMICS ENERGIES
OF ORDERING
OF TRANSFORMATION R. A. ORIANI
General Electric
and
Au&h,
PHASES+
W. K. MURPHY
Research Laboratory, (Receked
OF THE
ALLOYS-III
Schenectady,
New York
20 December 1957)
Abstract-Energy differences among the two superlattice and the disordered solid solution at the composition Au&Cut have been derived from calorimetric measurements of the heats of formation of the three phases. It is shown that neither of these transitions is understood in terms of quasi-chemical theory.
1. INTRODUCTION
AT the equiatomic composition in the goldcopper system there occur three solid phases: the f.c. tetragonal superlattice (I), with a critical temperature of 4OO”C, the orthorhombic superlattice (II), investigated by JOHANSSONand LINDE,~) having a critical temperature of 421°C and the essentially disordered f.c.c. solid solution (D). Each of these phases is separated from the adjacent phase by an equilibrium two-phase fieId,@*s) so that each of the two transitions is associated with a finite latent heat. Unlike the transformations of the AuCus superlattice, those at AuCu have been insufficiently investigated as to the energetic relationships. NYSTROM@) and BORELIUS et a1.W found 630 Cal/g-atom for the energy difference between I and D, but did not observe any latent heat between I and II. H~~BAYASHI(~) measured the specific heat of a number of gold-copper alloys, and for the composition of 50-S atomic per cent gold found I, 25&c 5% cd/g-atom 11 436d/g-&m D, 429°C. z
The author derivedTfby an unspecified procedure, a figure of 390 Cal/g-atom for the latent heat for II -+ D at 421°C. 2. EXPERIMRNTAL
In the present work, a well-homogenized alloy of 49*97-&0*05 atomic per cent gold was made with -* Work done on A.E.C. Contract No. W-31-109-Eng 52.
great care from copper and gold of 99.999 per cent purity. In the finished alloy, only a trace of silver was detected as impurity by emission spectrography. The alloy was reduced to &-in-diameter wire, and was cut into very short lengths for use in the calorimeter. A quantity of alloy was held under pure helium at 370-380°C for 5 days and then cooled at 20” per day to 2OO”C, whereupon the furnace power was turned off. The resulting f.c. tetragonal superIattice produced an excelIent, sharp Debye-Scherrer pattern free of extraneous lines. A small quantity of the alloy thus treated was again encapsulated and held at 408-415”C for 26 days, after which it was rapidly quenched into brine at -10°C. The resulting orthorhombic structure produced an excellent Debye-Scherrer pattern, matching that found by JOHANSSONand LINDE;@ there were also a few very faint lines of the tetragonal structure. The f.c.c. solid solution was made by holding a small quantity of the initially tetragonal alloy at 460°C for 2 days, and then rapidly quenching into brine at -15°C. This treatment produced an alloy giving a very sharp Debye-Scherrer pattern, ue = 3*8733&O-0007 A. The calorimeter employed in this work is a differential solution calorimeter previously described.(T) It can be calibrated electrically, and of special importance for this work is the feature that a metal sample can be held at temperature, to achieve thermal and internal configurational equilibrium, before it is added to the solvent bath and there dissolved at the same temperature. This
277
278
R.
A.
ORIANI
and
means that the measured heat of formation of an alloy is unambiguously relatable to the internal configuration of the alloy existing at equilibrium at that temperature. In these experiments, an amount of alloy was dissolved in one cell of the calorimeter, and an equal amount of the corresponding mechanical mixture of the pure components was simultaneously dissolved in the other cell. From the resulting differential thermocouple signal and the calibration factor, a heat of formation of the alloy referred to the pure solid components may be calculated. For each of the three phases of this alloy, four individual measurements of the heat of formation were carried out. The resulting mean heats of formation, with mean deviations as a measure of reproducibility, are shown in Table 1. Table
-
1. Heats
alloys
Heat of formation (Cal/g-atom) -1851123 -1639+12 -1259&S
evaluated at present, the best comparison between existing theory and experiment can be carried out by forming the ratio Eo/RT,, where Eo is the energy difference between a fully ordered structure and the corresponding alloy in a perfectly random state. The critical temperature, T,, for
+- 31cal/g
*
F. cc.,
437*C
atom 0rthorhomb;c.
I
1 F.c. tetr.
of Au,&,
379 411 437
The estimated accuracy of these figures is fl.2 per cent. The differences between these heats of formation represent the energies required to transform the alloy from one structure at one temperature to another structure at another temperature. The following scheme is obtained: 592
MURPHY
It is natural to expect that the I + II transformation should entail less energy than the II + D transformation, since the configurational change involved in the former is much less than that in the latter. Nevertheless, the energy change for the I + II transition is strikingly large in view of the fact that the step shifts that occur at every fifth atom along the [OlO] direction in the orthorhombic phase(t) do not involve a change in the number of nearest-neighbor Au-Cu bonds, if the small deviations from cubic symmetry in both phases are neglected. It is clear that other than the nearestneighbor considerations of the quasi-chemical theory must be adduced in order to explain the stability of the orthorhcmbic superlattice. Since the latent heats of transition cannot be
of formation
tetragonal (I) (II) cubic (D)
J
K.
Measuring temp. (“C)
Structure Face-centered Orthorhombic Face-centered
W.
411°C
379’C FIG. 1
3. DISCUSSION An
attempt was made to estimate the contributions to these numbers from the anomalous heat capacities in the neighborhood of the critical temperature, as measured by HIRABAYASHI,(~) but this attempt proved unsuccessful. It must be recognized that the latent heats of transition are smaller than the above numbers by an as yet undetermined amount.
I + D, if II did not intervene, may be taken for the present purpose to be 410°C. EO cannot be very different from the 950 Cal/g-atom measured by HIFWBAYASHI,@) since ROBERTS@) has shown that there is only a moderate amount of short-range order left in the Au,Cu, solid solution above Te. If, therefore, one estimates Es as 1000 Cal/g-atom, the ratio Eo/RTc = 0.73. The best theory at present, that of LI,@) which uses the tetrahedron as
THERMODYNAMICS
OF ORDERING
the local unit in the quasi-chemical treatment, gives 1.369 as the value of this ratio for the f.c. tetragonal structure at the 1 : 1 composition. It is of interest also to use the measured energies of formation to calculate values of the parameter (NU), where N is the Avogadro number and w = WAB-$(WAA+OBB). It will be remembered that w is the relevant linear combination of the interaction energies vi, between nearest neighbors i and j, and that& ali’forms of the quasi-chemical treatment ‘u is assumed to be independent of composition and of phase. From the present value of the energy of formation of the tetragonal superlattice, one calculates N;3, = 463 Cal/g-atom. From the present value of the energy of formation of the f.c.c. solution and from the measured short-range order parameter of ROBERTS,@)one obtains NV = 373 Cal/g-atom. The large difference in (NW) between the two phases points up the difficulty of treating the I -+ D transition by the quasichemical theory. This large difference in w may be ascribable to the changes in symmetry and in interatomic distances through the transition. The value of (NW) of 373 Cal/g-atom for the f.c.c. solution is in good agreement with the value of 3.50 Cal/g-
279
ALLOYS
atom obtained by Gu~MhN(lO) as giving the best fit with measurements of thermodynamic activity and of short-range-order parameter at the Au, Cu,, f.c.c. solution.
Acknowledgements-We are grateful for the help of the X-ray diffraction unit of the Metallurgy Department, and for a discussion with Dr. LBB.TER GUTTMAN.
REFERENCES 1. JOHANSSON C. H. and (L&zig) 25, 1 (1936).
LINDE
J. 0.
Ann. P&w.
2. N~wltnuc J. B. Trans. Ames. Inst. Min. (Metall,) Engrp. lti, 823 (1953). 3. ORIANIR. A. Acta Met. 2.608 (1954). J. Ark. Fys. 2, i51 (l&O).’ 4. NYSTBOM 5. BOBBLIUS G., LAWSON L. E., and SELBERC H. Ark. Fys. 2, 161 (1950).
6. HIRABAYASHX M, J. Inst. Met.Japan 15,565 (1951). 7. ORIANIR. A. and MURPHYW. K. -7. - Phvs. . Chem. in the press.
8. ROBERTS B. W. Acta Met. 2.597 (19541. ’ 9. LI Y. Y. Phys. Rev. 76,972’(194$. 10. GUTTMAN L. So&d-State Physics (Ed. F. SEITZand r). %BNBULL) Vol. 3, p. 145. Academic Press, New York (1956).
Pergamon Press 1958. Vol. 6. pp. 277-279.
THERMODYNAMICS ENERGIES
OF ORDERING
OF TRANSFORMATION R. A. ORIANI
General Electric
and
Au&h,
PHASES+
W. K. MURPHY
Research Laboratory, (Receked
OF THE
ALLOYS-III
Schenectady,
New York
20 December 1957)
Abstract-Energy differences among the two superlattice and the disordered solid solution at the composition Au&Cut have been derived from calorimetric measurements of the heats of formation of the three phases. It is shown that neither of these transitions is understood in terms of quasi-chemical theory.
1. INTRODUCTION
AT the equiatomic composition in the goldcopper system there occur three solid phases: the f.c. tetragonal superlattice (I), with a critical temperature of 4OO”C, the orthorhombic superlattice (II), investigated by JOHANSSONand LINDE,~) having a critical temperature of 421°C and the essentially disordered f.c.c. solid solution (D). Each of these phases is separated from the adjacent phase by an equilibrium two-phase fieId,@*s) so that each of the two transitions is associated with a finite latent heat. Unlike the transformations of the AuCus superlattice, those at AuCu have been insufficiently investigated as to the energetic relationships. NYSTROM@) and BORELIUS et a1.W found 630 Cal/g-atom for the energy difference between I and D, but did not observe any latent heat between I and II. H~~BAYASHI(~) measured the specific heat of a number of gold-copper alloys, and for the composition of 50-S atomic per cent gold found I, 25&c 5% cd/g-atom 11 436d/g-&m D, 429°C. z
The author derivedTfby an unspecified procedure, a figure of 390 Cal/g-atom for the latent heat for II -+ D at 421°C. 2. EXPERIMRNTAL
In the present work, a well-homogenized alloy of 49*97-&0*05 atomic per cent gold was made with -* Work done on A.E.C. Contract No. W-31-109-Eng 52.
great care from copper and gold of 99.999 per cent purity. In the finished alloy, only a trace of silver was detected as impurity by emission spectrography. The alloy was reduced to &-in-diameter wire, and was cut into very short lengths for use in the calorimeter. A quantity of alloy was held under pure helium at 370-380°C for 5 days and then cooled at 20” per day to 2OO”C, whereupon the furnace power was turned off. The resulting f.c. tetragonal superIattice produced an excelIent, sharp Debye-Scherrer pattern free of extraneous lines. A small quantity of the alloy thus treated was again encapsulated and held at 408-415”C for 26 days, after which it was rapidly quenched into brine at -10°C. The resulting orthorhombic structure produced an excellent Debye-Scherrer pattern, matching that found by JOHANSSONand LINDE;@ there were also a few very faint lines of the tetragonal structure. The f.c.c. solid solution was made by holding a small quantity of the initially tetragonal alloy at 460°C for 2 days, and then rapidly quenching into brine at -15°C. This treatment produced an alloy giving a very sharp Debye-Scherrer pattern, ue = 3*8733&O-0007 A. The calorimeter employed in this work is a differential solution calorimeter previously described.(T) It can be calibrated electrically, and of special importance for this work is the feature that a metal sample can be held at temperature, to achieve thermal and internal configurational equilibrium, before it is added to the solvent bath and there dissolved at the same temperature. This
277
278
R.
A.
ORIANI
and
means that the measured heat of formation of an alloy is unambiguously relatable to the internal configuration of the alloy existing at equilibrium at that temperature. In these experiments, an amount of alloy was dissolved in one cell of the calorimeter, and an equal amount of the corresponding mechanical mixture of the pure components was simultaneously dissolved in the other cell. From the resulting differential thermocouple signal and the calibration factor, a heat of formation of the alloy referred to the pure solid components may be calculated. For each of the three phases of this alloy, four individual measurements of the heat of formation were carried out. The resulting mean heats of formation, with mean deviations as a measure of reproducibility, are shown in Table 1. Table
-
1. Heats
alloys
Heat of formation (Cal/g-atom) -1851123 -1639+12 -1259&S
evaluated at present, the best comparison between existing theory and experiment can be carried out by forming the ratio Eo/RT,, where Eo is the energy difference between a fully ordered structure and the corresponding alloy in a perfectly random state. The critical temperature, T,, for
+- 31cal/g
*
F. cc.,
437*C
atom 0rthorhomb;c.
I
1 F.c. tetr.
of Au,&,
379 411 437
The estimated accuracy of these figures is fl.2 per cent. The differences between these heats of formation represent the energies required to transform the alloy from one structure at one temperature to another structure at another temperature. The following scheme is obtained: 592
MURPHY
It is natural to expect that the I + II transformation should entail less energy than the II + D transformation, since the configurational change involved in the former is much less than that in the latter. Nevertheless, the energy change for the I + II transition is strikingly large in view of the fact that the step shifts that occur at every fifth atom along the [OlO] direction in the orthorhombic phase(t) do not involve a change in the number of nearest-neighbor Au-Cu bonds, if the small deviations from cubic symmetry in both phases are neglected. It is clear that other than the nearestneighbor considerations of the quasi-chemical theory must be adduced in order to explain the stability of the orthorhcmbic superlattice. Since the latent heats of transition cannot be
of formation
tetragonal (I) (II) cubic (D)
J
K.
Measuring temp. (“C)
Structure Face-centered Orthorhombic Face-centered
W.
411°C
379’C FIG. 1
3. DISCUSSION An
attempt was made to estimate the contributions to these numbers from the anomalous heat capacities in the neighborhood of the critical temperature, as measured by HIRABAYASHI,(~) but this attempt proved unsuccessful. It must be recognized that the latent heats of transition are smaller than the above numbers by an as yet undetermined amount.
I + D, if II did not intervene, may be taken for the present purpose to be 410°C. EO cannot be very different from the 950 Cal/g-atom measured by HIFWBAYASHI,@) since ROBERTS@) has shown that there is only a moderate amount of short-range order left in the Au,Cu, solid solution above Te. If, therefore, one estimates Es as 1000 Cal/g-atom, the ratio Eo/RTc = 0.73. The best theory at present, that of LI,@) which uses the tetrahedron as
THERMODYNAMICS
OF ORDERING
the local unit in the quasi-chemical treatment, gives 1.369 as the value of this ratio for the f.c. tetragonal structure at the 1 : 1 composition. It is of interest also to use the measured energies of formation to calculate values of the parameter (NU), where N is the Avogadro number and w = WAB-$(WAA+OBB). It will be remembered that w is the relevant linear combination of the interaction energies vi, between nearest neighbors i and j, and that& ali’forms of the quasi-chemical treatment ‘u is assumed to be independent of composition and of phase. From the present value of the energy of formation of the tetragonal superlattice, one calculates N;3, = 463 Cal/g-atom. From the present value of the energy of formation of the f.c.c. solution and from the measured short-range order parameter of ROBERTS,@)one obtains NV = 373 Cal/g-atom. The large difference in (NW) between the two phases points up the difficulty of treating the I -+ D transition by the quasichemical theory. This large difference in w may be ascribable to the changes in symmetry and in interatomic distances through the transition. The value of (NW) of 373 Cal/g-atom for the f.c.c. solution is in good agreement with the value of 3.50 Cal/g-
279
ALLOYS
atom obtained by Gu~MhN(lO) as giving the best fit with measurements of thermodynamic activity and of short-range-order parameter at the Au, Cu,, f.c.c. solution.
Acknowledgements-We are grateful for the help of the X-ray diffraction unit of the Metallurgy Department, and for a discussion with Dr. LBB.TER GUTTMAN.
REFERENCES 1. JOHANSSON C. H. and (L&zig) 25, 1 (1936).
LINDE
J. 0.
Ann. P&w.
2. N~wltnuc J. B. Trans. Ames. Inst. Min. (Metall,) Engrp. lti, 823 (1953). 3. ORIANIR. A. Acta Met. 2.608 (1954). J. Ark. Fys. 2, i51 (l&O).’ 4. NYSTBOM 5. BOBBLIUS G., LAWSON L. E., and SELBERC H. Ark. Fys. 2, 161 (1950).
6. HIRABAYASHX M, J. Inst. Met.Japan 15,565 (1951). 7. ORIANIR. A. and MURPHYW. K. -7. - Phvs. . Chem. in the press.
8. ROBERTS B. W. Acta Met. 2.597 (19541. ’ 9. LI Y. Y. Phys. Rev. 76,972’(194$. 10. GUTTMAN L. So&d-State Physics (Ed. F. SEITZand r). %BNBULL) Vol. 3, p. 145. Academic Press, New York (1956).