Abstract
Phase diagrams showing very unlikely boundaries, while not explicitly violating thermodynamic principles or phase rules, are discussed. Phase rule violations in proposed phase diagrams often become apparent when phase boundaries are extrapolated into metastable regions. In addition to phase rule violations, this article considers difficulties regarding an abrupt change of slope of a phase boundary, asymmetric or unusually pointed liquidus boundaries, location of miscibility gaps, and gas/liquid equilibria. Another frequent source of phase diagram errors concerns the initial slopes of liquidus and solidus boundaries in the very dilute regions near the pure elements. Useful and consistent prediction can be made from the application of the van’t Hoff equation for the dilute regions.
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Cited References
F.N. Rhines,Phase Diagrams in Metallurgy, McGraw-Hill, New York, 340p(1956).
L.H. Beck and C.S. Smith, “Copper-Zinc Constitution Diagram, Redetermined in the Vicinity of the Beta Phase by Means of Quantita- tive Metallography,”Trans. AIME, 194(10), 1079–1083 (1957).
M. Hansen and K. Anderko,Constitution of Binary Alloys, originally published by McGraw-Hill, reprinted and available from Genium Publishing Corporation, 1145 Catalyn Street, Schenectady, New York 12303 (1958).
R.P. Elliot,Constitution of Binary Alloys, First Supplement, originally published by McGraw-Hill, reprinted and available from Genium Publishing Corporation, 1145 Catalyn Street, Schenectady, New York 12303 (1965).
A. Prince,Alloy Phase Equilibria, Elsevier Publ. Co., London (1966).
P. Gordon,Principles of Phase Diagrams in Material Systems, McGraw-Hill, New York, 232p (1968).
E. Rudy,Ternary Phase Equilibria in Transition Metal-Boron- Carbon-Silicon Systems, Part V. Compendium of Phase Diagram Data, Air Force Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, OH, 214–215 (1969).
F.A. Shunk,Constitution of Binary Alloys, Second Supplement, originally published by McGraw-Hill, reprinted and available from Genium Publishing Corporation, 1145 Catalyn Street, Schenectady, New York 12303 (1969).
R. Thummel and W. Klemm, “Behavior of Alkali Metals in Me- talsof Group IIIB,”Z. Anorg. Allg. Chem.,376,44–63(1970).
R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley, and D.D. Wagman,Selected Values of the Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, OH (1973).
S. Wagner and D.A. Rigney, “Binary Systems Involving the ‘Catatectic’ Reaction Solid 1 Cooling ↔ Heating Solid 2 + liquid,”Metall. Trans., 5(10), 2155–2160(1974).
C.B. Alcock, K.T. Jacobs, S. Zador, O. von Goldbeck, H. Nowot- ny, K. Seifert, and O. Kubaschewski,Zirconium, Physico-Chemical Properties of Its Compounds and Alloys, O. Kubaschewski, Ed., Atomic Energy Review Special Issue No. 6, International Atomic Energy Agency, Vienna (1976).
W.G. Moffatt, Handbook of Binary Phase Diagrams, Genium Publishing Corporation, Schenectady, New York (1978) and Supple- ments.
D.A. Goodman, J.W. Cahn, and L.H. Bennett, “The Centennial of the Gibbs-Konovalov Rule for Congruent Points,”Bull Alloy Phase Diagrams, 2(1),29–34(1981).
T. Nishizawa and M. Hasebe, “Computer Calculation of Phase Diagrams of Iron Alloys (1),”Tetsu to Hagane, 67(11), 1887–1898 (1981).
J.F. Smith, “The Sn-V (Tin-Vanadium) System,”Bull Alloy Phase Diagrams, 2(2), 210–214 (1981).
K.A. Gschneidner, Jr. and F.W. Calderwood, “The Ce-Pr (Cerium-Praseodymium) System,”Bull Alloy Phase Diagrams, 3(2), 187–188 (1982).
M.W. Chase, “Heats of Transition of the Elements,”Bull. Alloy Phase Diagrams, 4(1), 123–124 (1983).
A.A. Nayeb-Hashemi and J.B. Clark, “The Mg-Sb (Mag- nesium-Antimony) System,”Bull Alloy Phase Diagrams, 5(6), 579- 584(1984).
H. Okamoto and T.B. Massalski, “The Au-Sb (Gold-Antimony) System,”Bull. Alloy Phase Diagrams, 5(2), 166–171 (1984).
R.W. Olesinski and G.J. Abbaschian, “The C-Ge (Carbon- Ger- manium) System,”Bull. Alloy Phase Diagrams, 5(5), 484–486 (1984).
A. Palenzona, P. Manfrinetti, and S. Cirafici, “The Th-In Phase Diagram,”J. Less-Common Met.,97, 231–236 (1984).
T.B. Massalski, J.L. Murray, L.H. Bennett, and H. Baker,Binary Alloy Phase Diagrams, 1st ed., American Society for Metals, Metals Park, OH (1986).
H. Okamoto and T.B. Massalski, “The Au-U (Gold-Uranium) System,”Bull. Alloy Phase Diagrams, 7(6), 532–535 (1986).
H. Okamoto and T.B. Massalski, “Phase Relationships and Thermodynamic Modeling in Several Binary Systems Based on Gold,”Noble Metal Alloys: Phase Diagrams, Alloy Phase Stability, Thermodynamic Aspects, Properties and Special Features, T.B. Mas- salski, W.B. Pearson, L.H. Bennett, and Y.A. Chang, Ed., Metallurgi- cal Society, Inc., Warrendale, PA, 265–288 (1986).
C.B. Alcock, P.G. Komorowski, V.P. Itkin, and M. Itkin,Micro Tbank, University of Toronto, Toronto, Canada (1987).
V.P. Itkin, C.B. Alcock, P.J. van Ekeren, and H. A. J. Oonk, “The Al-Ca (Aluminum-Calcium) System,”Bull. Alloy Phase Diagrams, 9(6), 652–657 (1988).
Z. Moser, J. Dutkiewicz, L. Zabdyr, and J. Salawa, “The Bi-Cd (Bismuth-Cadmium) System,”Bull. Alloy Phase Diagrams, 9(4), 445–448(1988).
A. Palenzona and S. Cirafici, “The Phase Diagram of the U-Au System,”J. Less-Common Met.,143, 167–171 (1988).
P.R. Subramanian and D.E. Laughlin, “The Cu-Lu (Copper- Lutetium) System.,”Bull. Alloy Phase Diagrams, 9(3a), 358–361 (1988).
A.B. Gokhale, A. Munitz, and G.J. Abbaschian, “The Ge-Pr (Germanium-Praseodymium) System,”Bull. Alloy Phase Diagrams, 10(3), 241–246 (1989).
: J.M. Howe, “The Al-Se (Aluminum-Selenium) System,”Bull. Alloy Phase Diagrams, 10(6), 650–652(1989).
R.C. Sharma and Y.A. Chang, “Thermodynamic Analysis and Phase Equilibria Calculations for the Cd-Te, Cd-Se, and Cd-S Sys- tems,”J. Electrochem. Soc.,136(5), 1536–1542 (1989).
O.N. Carlson, “The Al-B (Aluminum-Boron) System,”Bull. Alloy Phase Diagrams, 11(6), 560–566 (1990).
A.T. Dinsdale, “SGTE Pure Elements Transformation Data,” T13-T15, reprinted in [90Mas].
U.R. Kattner, “Al-Ta (Aluminum-Tantalum),” reprinted in [90Mas].
T.B. Massalski, H. Okamoto, P.R. Subramanian, and L. Kacprzak,Binary Alloy Phase Diagrams, 2nd ed., ASM Internation- al, Materials Park, OH(1990).
M.F. Singleton, J.L. Murray, and P. Nash, “Al-Ni (Aluminum- Nickel),” in, 181,183-184 (1990).
M. Venkatraman and J.P. Neumann, “The Cr-Os (Chromium- Osmium) Phase Diagram,”Bull. Alloy Phase Diagrams, 11(1), 8–11 (1990).
M. Venkatraman and J.P. Neumann, “The C-Cr (Carbon- Chromium) Phase Diagram,”Bull. Alloy Phase Diagrams, 11(2), 152–159(1990).
H. Okamoto, “The P-Pd (Phosphorus-Palladium) System, to be published inJ.Phase Equilibria (1991).
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Okamoto, H., Massalski, T. Thermodynamically Improbable Phase Diagrams. JPE 12, 148–168 (1991). https://doi.org/10.1007/BF02645711
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DOI: https://doi.org/10.1007/BF02645711