Abstract
Chapter 2 dealt with the phase equilibria in alloys involving only the first-order phase transitions. The Gibbs energy of a given multicomponent system is a function of its variables of state P, T, n 1 , n 2,..., n c , i.e., G = G (P, T, n 1, n 2,..., n c ). This function is continuous for the first-order phase transitions but its derivative, with respect to one of its variables, becomes discontinuous upon a first-order transition. The variable of the greatest importance is the temperature; therefore, we limit our discussion to the derivatives of G with respect to T. A first-order transition is accompanied with a discontinuity in the first derivatives of G; thus,
would show a discontinuity in the entropy or enthalpy when these properties are measured from a reference temperature such as T = 0, or often more conveniently, T = 298.15 K. Condensation and freezing of pure components provide some of the most elementary examples of first-order transitions. At a second-order transition, the second derivatives of G exhibit a discontinuity; i.e.,
In summary, S, or H, is discontinuous for the first-order phase transitions and C p is discontinuous for the second-order phase transitions.
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References
W. S. Gorsky, Z. Phys. 50, 64 (1928).
W. L. Bragg and E. J. Williams, Proc. R. Soc. London Ser. A 145, 699 (1934);
W. L. Bragg and E. J. Williams, Proc. R. Soc. London Ser. A 151, 540 (1935).
H. A. Bethe, Proc. R. Soc. London Ser. A 150, 552 (1935).
E. A. Guggenheim, Mixtures, Oxford University Press, London, Chapters IV and VII (1952).
R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, London, Chapter XII (1956).
M. A. Krivoglaz and A. A. Smirnov, The Theory of Order-Disorder in Alloys, Macdonald, London (1965);
J. M. Cowley, Phys. Rev. 120, 1648 (1960).
R. M. White and T. H. Geballe, Long Range Order in Solids, Supplement 15, Solid State Physics, Student Edition, Academic Press, New York (1983).
I. Prigogine, The Molecular Theory of Solutions, North-Holland, Amsterdam (1957).
D. de Fontaine, Solid State Phys. 34, 73 (1979);
D. de Fontaine, Acta Metall. 23, 553 (1975).
H. Sato, in Physical Chemistry: An Advanced Treatise, Volume X, edited by W. Jost, Academic Press, New York, p. 579 (1970).
N. A. Gokcen and E. T. Chang, J . Chem. Phys. 55, 2279 (1971);
N. A. Gokcen and E. T. Chang, Scr. Metall. 4, 941 (1970); A New Method for Enumerating Molecular Configurations in Propellant Mixtures, Aerospace Report No. TR-0172 (2210–10)-1, The Aerospace Corp., El Segundo, California (1971).
N. A. Gokcen, Scr. Metall. 17, 53 (1983). (The treatment presented in this reference contains minor initial statistical errors that have been corrected in this book. However, final equations and conclusions are correct in this reference.)
N. A. Gokcen, Thermodynamics, Techscience, Hawthorne, California, Chapter XI (1975).
R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, and K. K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, Ohio (1973).
D. Chipman and B. E. Warren, J. Appl. Phys. 21, 696 (1950).
H. Moser, Phys. Z. 37, 737 (1936).
C. Sykes and H. Wilkinson, J. Inst. Met. 61, 223 (1937).
R. Kikuchi, Phys. Rev. 81, 988 (1951);
R. Kikuchi, J . Chem. Phys. 60, 1071 (1974); and the intervening papers.
E. A. Guggenheim and M. L. McGlashan, Mol. Phys. 5, 433 (1962).
R. Kikuchi, J . Chem. Phys. 60, 1071 (1974);
R. Kikuchi and C. M. van Baal, Scr. Metall. 8, 425 (1974).
D. M. Burley, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green, Volume 2, Academic Press, New York, p. 329 (1972).
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Gokcen, N.A. (1986). Long-Range Order. In: Statistical Thermodynamics of Alloys. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5053-8_5
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DOI: https://doi.org/10.1007/978-1-4684-5053-8_5
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