Abstract
A very accurate experimental method to determine the composition of metal-saturated sulfides has been developed and applied to Cu2-δS. The technique consists of using a high-sensitivity thermobalance which operates in a controlled atmosphere of H2-H2S gas. By this method it was shown that Cu-saturated CuxS is stoichiometric(x= 2.0000 ± 0.0002) between 700 and 1000°C. The free energy of formation for Cu2S was found to be: 2Cu(s) + 1/2 S2(g) = Cu2.0000S(s), ΔG0 = -30,610 + 6.80T (cal/mole). The sulfur partial pressure was determined over nonstoichiometric Cu2-δS for sulfur contents up to 21 pct. From the result, thermodynamic functions such as activity of copper, heats and entropies of solution were calculated as a function of nonstoichiometric composition. It was thermo-dynamically demonstrated that previous models dealing with nonstoichiometric oxides (or sulfides) based on the law of mass action,i.e., δ = const ie 67 01 (or ie 67 02), are inconsis-tent as they fail to satisfy the Gibbs-Duhem relation and also fail to account for the dis-sociation pressure over the stoichiometric composition. To resolve this dilemma, a sta-tistical thermodynamic method of constructing the grand partition function was introduced. Stoichiometry and nonstoichiometry of the Cu2-δS were then explained by postulating an ionic crystal consisting of Cu+, Cu2+, Cu0 and neutral vacancies in the copper sublattice and S2− and neutral vacancies in the sulfur sublattice.
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L. S. Darken and R. W. Gurry:J. Amer. Chem. Soc., 1945, vol. 67, p. 1398–412.
H. Rau:J. Phys. Chem. Solids, 1967, vol. 28, p. 903–16.
S. Takeuchi and K. Furukawa:Met. Soc. Conf., vol. 7, pp. 245–60, 1961 ; S. Takeuchi and K. Igaki:Sci. Rep. Res. Inst. Tohoku Univ. (Japan), 1952, vol. 4A,no. 2, pp. 164-75.
M. Hansen and K. Anderko:Constitution of Binary Alloys, McGraw-Hill, New York, 1958, and also R. P. Elliott:Constitution of Binary Alloys, First Sup- plement, McGraw-Hill, New York, 1965.
A. N. Nesmayanov, G. I. Samal, and M. M. Pavlyuchenko:Zh. Neorg. Khim, 1967, vol. 12, pp. 1713–15.
R. Peronne, D. Balesdent, and J. Rilling:Bull. Soc. Chim. Fr., 1972, pp. 457-63.
M. Nagamori:Can. Met. Quart., 1970, vol. 9, pp. 531–33.
M. Nagamori and T. R. Ingraham:Met. Trans., 1970, vol. 1, pp. 1821–25.
M. Nagamori and M. Kameda:Trans. Jap. Inst. Metals, 1968, vol. 9, pp. 187–94.
M. Nagamori, T. Hatakeyama, and M. Kameda:Trans. Jap. Inst. Metals, 1970, vol. 11, pp. 190–94.
O. Kubaschewski, E. Ll. Evans, and C. B. Alcock:Metallurgical Thermo- chemistry, Pergamon Press, New York, 1967.
C. J. Smithells:Metals Reference Book, Plenum Press, New York, 1967.
W. R. Cook:Nat. Bur. Stand. (U.S.) Spec. Publ., 1972, no. 364, pp. 703-12.
H. H. Kellogg,Trans. TMS-AIME, 1964, vol.230, pp. 1622–34.
D. Arndt and E. Kordes:Z. Anorg. Allg. Chem., 1968, vol. 359, pp. 1–13.
E. M. Cox, M. C. Bachelder, N. H. Nachtrieb, and A. S. Skapski:Trans. AIME, 1949. vol. 185, pp. 27–31.
T. Tanaka, K. Watanabe, and J. Kurihara:Me. Fac. Eng. Hokkaido Univ. (Japan), 1950, vol. 8, pt. 1, pp. 14–22.
K. Sudo:Sci. Rep. Res. Inst., Tohoku Univ. (Japan), 1950, vol. A2, pp. 513–18.
T. Yagihashi and T. Sato:Nippon Kinzoku Gakkaishi, 1952, vol. 16, pp. 482–86.
E. Kordes and B. Rackow:Z. Phys. Chem., 1952, vol. 200, p. 129–57.
A. A. Brooks:J. Amer. Chem. Soc., 1953, vol. 75, p. 2464.
A. Kihira:Res. Rep. Fac. Eng. Nagoya Univ. (Japan), 1950, vol. 3, pp. 39–42.
F. D. Richardson and J. E. Antill:Trans. Faraday Soc., 1955, vol. 51, pp. 22–25.
R. A. Isakova and V. D. Ponomarev:Izv. Akad. Nauk Kaz. SSR, Ser. Met., Obogashch.Ogneuporov., 1959, no. 1, pp. 65-70.
D. Arndt:Diplomarbeit, Bonn, 1962.
J. Sodi and J. Elliott:Trans. TMS-AIME, 1968, vol. 242, pp. 2143–45.
V. M. Glazov and N. M. Korenchuk:Zh. Fiz. Khim., 1971, vol. 45, no. 10, p. 26–76.
O. Kubaschewski and J. A. Catterall:Thermochemical Data of Alloys, Pergamon Press, London, 1956.
V. A. Kudinova, V. V. Khromtsov, L. E. Isakova, and V. P. Kalashnikova:Uch. Zap. Ural. Gos. Univ., 1971, no. 119, pp. 58-74.
S. Djurle:Acta Chem. Scand., 1958, vol. 12, pp. 1415–26.
E. H. Roseboom:Econ. Geol., 1966, vol. 61, pp. 641–72.
A. Casalot:Semin. Etat Solide, 1969-70, no. 4, pp. 157-75.
H. Luquet, F. Guastavino, J. Bougnot, and J. C. Vaissière:Mater. Res. Bull., 1972, vol. 7, pp. 955–62.
P. Kubaschewski:Ber. Bunsenges. Phys. Chem., 1973, vol. 77, no. 2, pp. 74–80.
M. M. Kazinets:Izv. Akad. Nauk SSSR, Neorg. Mater., 1972, vol. 8, pp. 1011–14.
V. N. Konov and V. A. Kudinova:Izv. Akad. Nauk SSSR, Neorg. Mater., 1973, vol. 9, pp. 1132–37.
N. Morimoto and G. Kullerud:Amer. Mineral, 1963, vol. 48, pp. 110–23.
P. Rahlfs:Z. Phys. Chem. (Leipzig), 1936, vol. 31, pp. 157–94.
L. W. Strock:Z. Phys. Chem. (Leipzig), 1934, vol. 25, pp. 44–59 ; 1935, vol. 31, pp. 132-36.
M. Laffitte:Bull. Soc. Chim. Fr., 1959, pp. 1211-22.
G. Hägg:Nature, 1933, vol. 131, pp. 167–68.
G. Hagg and A. L. Kindström:Z. Phys. Chem. (Leipzig), 1933, vol. 22, pp. 453–64.
M. Nagamori and T. R. Ingraham:Met. Trans., 1971, vol. 2, pp. 1501–03.
M. D. Banus and T. B. Reed:The Chemistry of Extended Defects in Non- metallic Solids, L. Eyring and M. O’Keeffe, eds., pp. 488–521, American Elsevier, New York, 1970.
E. Hirahara:J. Phys. Soc. Jap., 1951, vol. 6, pp. 422–27.
V. Wehefritz:Z. Phys. Chem., N.F., 1960, vol. 26, pp. 339–58.
K. Weiss:Ber. Bunsenges. Phys. Chem., 1969, vol. 73, pp. 338–44.
K. Okamoto and S. Kawai:Jap. J. Appl. Phys., 1973, vol. 12, pp. 1130–38.
N. Nakayama:J. Phys. Soc. Jap., 1968, vol. 25, pp. 290–91.
G. B. Abdullaev, Z. A. Aliyarova, E. H. Zamanova, and G. A. Asadov:Phys. Status Solidi, 1968, vol. 26, pp. 65–68.
S. Martinuzzi, M. Gaign, and W. Palz:Phys. Status Solidi A, 1970, vol. 2, pp. K9–11.
N. A. Vlasenko and Ya. F. Kononetz:Ukr. Fiz. Zh., 1971, vol. 16, no. 2, pp. 237–43.
O. P. Astakhov, V. V. Lobankov, I. V. Sgibnev, and B. M. Surkov:Teplofiz., Vys. Temp., 1972, vol. 10, pp. 654–55.
T. Kushida:J. Sci. Hiroshima Univ., 1952, Ser. A16, pp. 75–80.
L. Eisenmann:Ann. Phys., 1952, vol. 10, pp. 129–52.
J. B. Wanger and C. Wagner:J. Chem. Phys., 1957, vol. 26, pp. 1602–06.
K. Okamoto, S. Kawai, and R. Kiriyama:Jap. J. Appl. Phys., 1969, vol. 8, no. 6, pp. 718–24.
J. P. Delmaire, H. Lebrusq, A. Duquesnoy, and F. Marion:C. R. Acad. Sci. Paris, Ser. C, 1970, vol. 270, pp. 1411–14.
H. LeBrusq, J. P. Delmaire, A. Duquesnoy, and F. Marion:C. R. Acad. Sci. Paris, Ser. C, 1970, vol. 270, pp. 1757–59.
J. Bougnot, F. Guastavino, H. Luquet, and D. Sodini:Phys. Status SolidiA, 1971, vol. 8, pp. K93–96.
A. V. Tarasov, I. T. Gulydin, and A. N. Krestovnikov.Izv. Vyssh. Ucheb. Zaved. Tsvet. Met., 1970, vol. 13, no. 2, pp. 78–82.
O. P. Astakhov and V. V. Lobankov:Teplofiz. Vys. Temp., 1972, vol. 10, no. 3, pp. 905–06.
V. M. Glazov and A. S. Burkhanov:Fiz. Tekh. Poluprov, 1973, vol. 7, pp. 1401–05.
V. M. Glazov, A. N. Krestovnikov, A. S. Okhotin, A. S. Burkhanov, and S. A. Bezekovich:Izv. Vyssh. Ucheb. Zaved., Tsvet. Met., 1970, vol. 13, no. 4, pp. 27–31.
R. Routie and J. Mahenc:Rev. Chim. Miner., 1969, vol. 6, pp. 991–1003.
R. Routie and J. Mahenc:J. Chim. Phys. Physicochim. Biol., 1969, vol. 66, no. 6, pp. 1103–08.
R. Routie and J. Mahenc:Electrochim. Acta, 1970, vol. 15, pp. 1201–07.
J. Mahenc, R. Routie, and P. Taxil:J. Chim. Phys. Physicochim. Biol., 1970, vol. 67, no. l,pp. 73–77.
P. Kofstad:Nonstoichiometry, Diffusion, and Electrical Conductivity in Binary Metal Oxides, Wiley-Interscience, New York, 1972.
J. J. Adou and J. Baudet:J. Chim. Phys., 1967, vol. 64, pp. 1540–46.
M. O’TCeeffe and F. S. Stone:Proc. Roy. Soc. (London), 1962, vol. A267, pp. 501–17.
M. O’Keeffe and W. J. Moore:J. Chim. Phys., 1961, vol. 35, pp. 1324–28.
A. Dumon, A. Casalot, E. Poquet, and S. Gromb:C. R. Acad. Sci. Paris, Ser. B, 1969, vol. 269, pp. 835–37.
H. J. Mathieu and H. Rickert:Z. Phys. Chem. N.F., 1972, vol. 79, pp. 315–30.
R. Fowler and E. A. Guggenheim:Statistical Thermodynamics, Univ. Press, Cambridge, 1965.
E. A. Guggenheim:Mixtures, Clarendon Press, Oxford, 1952.
G. S. Rushbrooke:Introduction to Statistical Mechanics, Clarendon Press, Oxford, 1951.
G. G. Libowitz:The Chemical Structure of Solids, N. B. Hannay, ed., vol. 1, pp. 335–85, Plenum Press, New York, 1973.
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Formerly Postdoctorate Fellow, National Research Council of Canada, Ottawa, Ontario
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Nagamori, M. A thermodynamic study of digenite solid solution (cu2-δs) at 600 to 1000°c and a statistical thermodynamic critique on general nonstoichiometry. Metall Trans B 7, 67–80 (1976). https://doi.org/10.1007/BF02652821
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DOI: https://doi.org/10.1007/BF02652821