Abstract
Many two-component (A,B) systems crystallize into a random solid solution (1). In such a state the atoms occupy a more or less regular array of lattice sites but each site can be A or B in a random fashion. Then, on lowering the temperature, the system will either phase separate or order, starting at some transition temperature Tc. The aim of these lectures is to present a microscopic approach to the understanding of these scientifically interesting and technologically important processes.
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References
Hansen M: Constitution of Binary Alloys. New York: McGraw Hill, 1958.
Stanley EH: Introduction to Phase Transitions and Critical Phenomena. Oxford: Clarendon Press, 1971.
Khachaturyan AG: Theory of Structural Transformations in Solids. New York: John Wiley & Sons, 1983.
Krivoglaz MA: Theory of X-ray and Thermal Neutron Scattering by Real Crystals. New York: Plenum Publishing, 1969.
Lifshitz EM and Pitaevskii LP: Statistical Physics, Part 1. New York: Pergamon Press, 3rd. edition, 1976.
Lifshitz EM: JETP 11, 253–269 (1941); (J. Phys. USSSR 7, 61 and 251 (1942).
Lyubarskii GY: Application of Group Theory in Physics. New York, Pergamon Press, 1960.
de Fontaine D: p. 73 in Solid State Physics, eds. H. Ehrenreich, F. Seitz and D. Turnbull, Vol. 34. New York: Academic Press, 1979.
Birman JL: Group Theoretical Methods in Physics (Lecture Notes in Physics), Vol. 79, eds. P. Kramer and A. Rieckers. New York: Springer-Verlag, 1980.
Levanyuk AP: Incommensurate Phases in Dielectrics, eds. R. Blinc and A. P. Levanyuk. Elsevier Science Publishers, B.V., 1986.
Sato H and Toth RS: Alloying Behavior and Effects in Concentrated Solid Solutions, ed. T. B. Massalski. New York: Gordon and Breach, 1965. Also Phys. Rev. 127, 469 (1961).
Loiseau A, Van Tendeloo G, Portier R, and Ducastelle F: J. Physique 46, 395 (1985).
Peierls RE: Quantum Theory of Solids. Oxford: Clarendon Press, 1955.
daSilva EZ, Strange P, Temmerman W, and Gyorffy BL: Phys. Rev. B 136, 3015 (1987).
de Fontaine D and Kikuchi R: Applications of Phase Diagrams in Metallurgy and Ceramics 2, 967 (1978). (NBS Special Publication 496)
Binder K: Festkorperproblem, ed. P. Grosse. New York: Springer-Verlag, XXVI, 1986.
Gyorffy BL and Stocks GM: Phys. Rev. Lett. 50, 374 (1983).
Peierls R: Phys. Rev. 54, 818 (1938).
Friedman LH: p. 185 in A Course in Structure Mechanics. Prentice Hall, Inc., 1985.
Feynman RP: Statistical Mechanics. Benjamin, 1972.
Clapp PC and Moss SC: Phys. Rev. 142, 418 (1966)
Clapp PC and Moss SC: Phys. Rev. 142, 171 (1968)
Clapp PC and Moss SC: Phys. Rev. 142, 754 (1968)
Fisher ME: J. Math. Phys. 5, 944 (1964).
Ducastelle F and Gautier F: J. Phys. F. Metal Physics 6, 2039 (1976).
Gautier F, Ducastelle F, and Giner J: Phil. Mag. 31, 1373 (1975).
Turchi PEA, Gonis A, Zhang XG, and Stocks GM: Configurational Energies in Terms of Effective Cluster Interactions in Binary Substitutional Alloys: Connection Between the Embedded Cluster Method and the Generalized Perturbation Method, this volume. Also, Sluiter M and Turchi PEA: Electronic Theory of Phase Stability in substitutional Alloys: A Comparison of the Connolly-Williams Scheme and the Generalized Perturbation Method, this volume.
Hohenberg P and Kohn W: Phys. Rev. 136, B864 (1964).
Kohn W and Sham LJ: Phys. Rev. 140, A1133 (1965).
Maruzzi VL, Janak JF, and Williams AR: Calculated Electronic Properties of Metals. New York, Pergamon Press, 1978.
Kohn W and Vashista P: Theory of the Inhomogeneous Electron Gas, eds. S. Lundquist and N.H. March. New York: Physics of Solids and Liquid Series, Plenum Press, 1983.
Williams AR and von Barth U: Theory of the Inhomogeneous Electron Gas, eds. S. Lundqvist and N.H. March. New York: Physics of Solids and Liquid Series, Plenum Press, 1983.
Stocks GM and Winter H: The Electronic Structure of Complex Systems, eds. P. Phariseau and W.M. Temmerman. New York: Plenum Press NATO ASI Series, Physics B113, 1984.
Korringa J: Physica 13, 392 (1947).
Kohn W and Rostoker N: Phys. Rev. 34, 1111 (1954).
Elliott RJ, Krumhansl JA, and Leath PL: Rev. Mod. Phys. 46, 465 (1974).
Ehrenreich H and Schwartz L: Solid State Physics, eds. H. Ehrenreich, F. Seitz, and D. Turnbull. New York: Academic Press, 1976.
Gyorffy BL and Stocks GM: Electrons in Finite and Infinite Structures, eds. P. Phariseau and L. Scheire. New York: Plenum Press, NATO ASI Series, Physics B 24, 1977.
Gyorffy BL and Stocks GM: Electrons in Disordered Metals and at Metallic Surfaces, eds. P. Phariseau, B.L. Gyorffy, and L. Scheire. New York: Plenum Press NATO ASI Series, Physics B 42, 1979.
Faulkner JS: Progress in Materials Science 27, 1 (1982).
Schwartz L and Siggia E: Phys. Rev. B 5, 383 (1972).
Stocks GM and Winter H: Z. Phys. B. Condensed Matter 46, 95 (1982).
Gyorffy BL, Kollar J, Pindor AJ, Stocks GM, Staunton J, and Winter H.: Eq. IV-7 in The Electronic Structure of Complex Systems, eds. P. Phariseau, W.M. Temmerman. New York: Plenum Press, 1984.
Johnson DD, Nicholson DM, Pinski FJ, Gyorffy BL, and Stocks GM: Phys. Rev. Lett. 56, 2088 (1986).
Janak JF: Phys. Rev. B 9, 3985 (1974).
Vegard L: Z. Phys. 5, 17 (1921) and Z. Kristallogr. Kristallgeom. Krystallphys. Kristalchem. 67, 239 (1928).
Johnson DD, Nicholson DM, Pinski FJ, Gyorffy BL, and Stocks GM: Phys. Rev. (submitted).
Nicholson DM, Stocks GM, Pinski FJ, Johnson DD, Gonis A, Gyorffy BL, and Wadsworth JS: Phys. Rev. Lett, (submitted).
Pindor AJ, Temmerman WM, and Gyorffy BL: J. Phys. F 13, 1627 (1983).
Schandler G, Weinberger P, Gonis A, and Klima J: J. Phys. F 15, (1985).
Stocks GM, Nicholson DM, Pinski FJ, Butler WH, Stern P, Temmerman WM, Gyorffy BL, Johnson DD, Gonis A, Chang X-G, and Turchi PEA: Mat. Res. Soc. Symp. Proc. 81, 15 (1987).
Ohshima K and Watanabe D: Acta Cryst. A 33, 520 (1977).
Moss SC: Phys. Rev. Lett. 22, 1108 (1969).
Fawcett E: Rev. Mod. Phys. 60, 209 (1988).
Wilson JA, Di Salvo FJ, and Mahajan F: Adv. Phys. 24, 117 (1975).
Doran NJ: J. Phys. C 11, L959 (1978).
Brodin D, Van Tenderloo G, Van Landwyt J, Amelinckx S, Portier R, Guymont M, Loiseau A: Phil. Mag. A 54, 395 (1986).
Loiseau A, Van Tenderloo G, Portier R, and Ducastelle F: J. Phys. 46, 595 (1985).
Miida R, Ajshimoto S, Watanabe D: Sci. Rep. RITU A29 Suppl. 1 (1981).
de Fontaine D and Kulik J: Acta Met. 33, 145 (1985).
Nicholson DM, Stocks GM, Temmerman WM, Sterne P, and Pettifor DG: (unpublished).
Varma CM and Simons AL: Phys. Rev. Lett. 51, 138 (1983).
McMillan WL: Melting Localization and Chaos, eds. R.K. Kalia and P. Yashishta. The Netherlands: North Holland Publishing, 1982.
See page 471 of Reference 5.
Cahn JW and Hi1liard JE: J. Chem. Phys. 28, 258 (1958).
van der Waals JD: J. Stat. Phys. 20, 197 (1979).
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Gyorffy, B.L., Johnson, D.D., Pinski, F.J., Nicholson, D.M., Stocks, G.M. (1989). The Electronic Structure and the State of Compositional Order in Metallic Alloys. In: Stocks, G.M., Gonis, A. (eds) Alloy Phase Stability. NATO ASI Series, vol 163. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0915-1_28
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