Abstract
Enormous progress has been made in the calculation of phase diagrams during the past 30 years. This progress will continue as model descriptions are improved and computational technology advances. Improvement has been made in the model descriptions in the CALPHAD method, the coupling of phase diagrams with kinetic process modeling, computer programs for easy access to phase diagram information, and the construction of databases used for calculating the phase diagrams of complex commercial alloys.
Similar content being viewed by others
References
T.B. Massalski, ed., Binary Alloy Phase Diagrams, 2nd ed., vol. 1–3 (Materials Park, OH: ASM, 1990).
B. Predel, Phase Equilibria, Crystallographic and Thermodynamic Data of Binary Alloys, 5, subvol. a–g, ed. O. Madelung (Berlin, Germany: New Series, Springer, 1991–1997).
Phase Equilibria Diagrams, vol. IX–XII (Westerville, OH: American Ceramic Society, 1992–1996).
Phase Diagrams for Ceramists, vol. I–VIII (Westerville, OH: American Ceramic Society, 1964–1990).
P. Villar, A. Prince, and H. Okamoto, Handbook of Ternary Alloy Phase Diagrams, 1–10 (Materials Park, OH: ASM, 1995).
Ternary Alloys: A Comprehensive Compendium of Evaluated Constitutional Data & Phase Diagrams, 1–15, ed. G. Petzow and G. Effenberg (Weinheim, Germany: VCH Verlagsgesellscahft, 1988–1995).
J. Hertz, J. Phase Equilibria, 13 (1992), pp. 450–458.
J.J. van Laar, Z. Phys. Chem., 63 (1908), pp. 216–253; 64 (1908) pp. 257–297.
J.H. Hildebrand, J. Amer. Chem. Soc., 51 (1929), pp. 66–80.
J.L. Meijering, Philips Res. Rep., 5 (1950), pp. 333–356; 6 (1951), pp. 183–210.
J.L. Meijering and H.K. Hardy, Acta Metall., 4 (1956), pp. 249–256.
J.L. Meijering, Acta Metall., 5 (1957), pp. 257–264.
L. Kaufman and M. Cohen, Trans. AIME, 206 (8) (1956), pp. 1393–1401.
L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals (New York: Academic Press, 1970).
R. Kikuchi, Phys. Rev., 81 (1951), pp. 986–1003.
D. de Fontaine, Solid State Physics, 47 (1994), pp. 33–176.
E.A. Schoefer, Weld. J., Res. Suppl., 39 (1974), pp. s10-s12.
C.T. Sims, “Prediction of Phase Composition,” Superalloys II, eds. C.T. Sims, N.S. Stoloff, and W.C. Hagel (New York: John Wiley & Sons, 1987), pp. 217–240.
A. Engstrom, L. Höglund, and J. Ågren, Metall. Mater. Trans. A, 25A (1994), pp. 1127–1134.
H. Du and J. Ågren, Metall. Mater. Trans. A, 27A (1996), pp. 1073–1080.
M. Kajihara, C. Lim, and M. Kikuchi, ISIJ Inter., 33 (1993), pp. 498–507.
A. Engstrom, J.E. Morral and J. Ågren, Acta Mater., 45 (1997), p. 1189.
T. Helander and J. Ågren, Metall. Mater. Trans. A, 28A (1997), pp. 303–308.
J. Ågren, Scand. J. Met., 19 (1990), pp. 2–8.
Z.-K. Liu et al., Metall. Trans. A, 22A (1991), pp. 1745–1752.
T. Kraft, M. Rettenmayr, and H.E. Exner, Modelling Simul. Mater. Sch. Eng., 4 (1996), pp. 161–177.
N. Saunders, Proc. 4th Decennial Int. Conf. Solidification Processing, ed. J. Beech and H. Jones (U.K.: University of Sheffield, 1997), pp. 362–366.
D.K. Banerjee et al., Proc. 4th Decennial Int. Conf. Solidification Processing, ed. J. Beech and H. Jones (U.K.: University of Sheffield, 1997), pp. 354–357.
A.T. Dinsdale, CALPHAD, 15 (1991), pp. 317–425.
M. Hillert and L.-I. Staffansson, Acta Chem. Scand., 24 (1970), pp. 3618–3626.
F. Sommer, Z. Metallkd., 73 (1982), pp. 72–76.
C. Wagner und W. Schottky, Z. Phys. Chem., B11 (1930), pp. 163–210.
W.L. Bragg and E.J. Williams, Proc. Royal Soc. A, London, 145 (1934), pp. 699–730; 151 (1935), pp. 540–566.
O. Redlich and A.T. Kister, Indust. Eng. Chem., 40 (1948), pp. 345–348.
H.L. Lukas, J. Weiss, and E.-Th. Henig, CALPHAD, 6 (1982), pp. 229–251.
B. Sundman and J. Ågren, J. Phys. Chem. Solids, 42 (1981), pp. 297–301.
J.-O. Andersson et al., Acta Metall., 34 (1986), pp. 437–445.
I. Ansara, B. Sundman, and P. Willemin, Acta Metall., 36 (1988), pp. 977–982.
I. Ansara et al., J. Alloys Compd., 247 (1997), pp. 20–30.
S.-L. Chen, C.R. Kao, and Y.A. Chang, Intermetallics, 3 (1995), pp. 233–242.
M. Hillert, Physica, 103B (1981), pp. 31–40.
H.L. Lukas, E.-Th. Henig, and B. Zimmermann, CALPHAD, 1 (1977), pp. 225–236.
D.W. Marquardt, J. Soc. Indust. Appl. Math., 11 (1963), pp. 431–441.
E. Königsberger, CALPHAD, 15 (1991), pp. 69–78.
M. Hillert, CALPHAD, 4 (1980), pp. 1–12.
Y.-M. Muggianu, M. Gambino, and L.P. Bros, J. Chim. Phus., 72 (1975), pp. 85–88.
L. Kaufman and H. Nesor, CALPHAD, 2 (1978), pp. 325–348.
H. Okamoto, J. Phase Equilibria, 14 (1993), pp. 257–259.
G. Eriksson and K. Hack, Metall. Trans. B, 21B (1990), pp. 1013–1023.
R.H. Davies et al., Applications of Thermodynamics in the Synthesis and Processing of Materials, eds. P. Nash and B. Sundman (Warrendale, PA: TMS, 1995), pp. 371–384.
B. Sundman, B. Jansson, and J.-O. Andersson, CALPHAD, 9 (1985), pp. 153–190.
E. Königsberger and G. Eriksson, CALPHAD, 19 (1995), pp. 207–214.
B. Sundman, User Aspects of Phase Diagrams, ed. F.H. Hayes (London, UK: Institute of Metals, 1991), pp. 130–139.
B. Sundman, Thermo-Calc Newsletter no. 18 (Stockholm, Sweden: Royal Institute of Technology, 1995).
U.R. Kattner, W.J. Boettinger, and S.R. Coriell, Z. Metallkd., 87 (1987), pp. 522–528.
J. Ågren, ISIJ International, 32 (1992), pp. 291–296.
G. Eriksson, H. Sippola, and B. Sundman, CALPHAD, 18 (1994), pp. 345–345.
SGTE Solution Database: SGTE (France: St. Martin d’Hères).
Al-DATA, Fe-DATA, Ni-Data, Ti-DATA: ThermoTech Ltd. (U.K.: Surrey).
C.W. Bale and G. Eriksson, Canad Metall Quarterly, 29 (1990), pp. 105–132.
C.W. Bale, “Web Sites in Inorganic Chemical Thermodynamics,” http://www.crct.polymtl.ca/fact/websites.html.
L. Kaufman, ed., User Applications of Alloy Phase Diagrams (Metals Park, OH: ASM, 1987).
F.H. Hayes, ed., User Aspects of Phase Diagrams (London: IOM, 1991).
K. Hack, ed., The SGTE Casebook, Thermodynamics at Work (London: IOM, 1996).
U.R. Kattner and W.J. Boettinger, J. Electron. Mater., 23 (1994), pp. 603–610.
N. Saunders, Materials Science Forum, 217–222 (1996), pp. 667–672.
Author information
Authors and Affiliations
Additional information
Editor’s Note: A hypertext-enhanced version of this article can be found at http://www.tms.org/pubs/journals/JOM/9712/Kattner-9712.html.
Author’s Note: In this article, commercial products are identified as examples. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that they are necessarily the best available for the purpose.
Ursula R. Kattner earned her Ph.D. in metallurgy at the University of Stuttgart, Germany, in 1982. She is currently a physical scientist at the National Institute of Standards and Technology.
Rights and permissions
About this article
Cite this article
Kattner, U.R. The thermodynamic modeling of multicomponent phase equilibria. JOM 49, 14–19 (1997). https://doi.org/10.1007/s11837-997-0024-5
Issue Date:
DOI: https://doi.org/10.1007/s11837-997-0024-5