Abstract
In the present study, the enthalpies of mixing associated with the liquid phase in Ni-Cr-Co-Al-Ti-Cu, Au-In-Sn-Zn, and In-Pd-Sn systems at a temperature of 2000 K (1727 °C) through the six components, ternary, and quaternary geometric models are calculated. The values calculated from different geometric models are compared with those obtained in the experiments. In this respect, the results of some thermodynamic prediction methods were applied to the six-component Ni-Cr-Co-Al-Ti-Cu system, the quaternary alloy Au-In0.45-Sn0.45-Zn0.1, and the subsystem ternary alloy In-Pd-Sn in the present study in order to analytically determine the integral properties associated with the six-component alloy systems in the liquid phase. The Chou’s general solution model and the traditional models of Toop, Colinet, Muggianu, and Kohler were included in the calculation for comparison and discussion. A comparison among the results of the models and experiments carried out for ternary and quaternary systems displays good mutual agreement.
Similar content being viewed by others
References
V. S. Sudavtsova: Russian Metallurgy (Metally), 1999, vol.5, pp. 118-120.
U. Thiedemann, M. Rösner-Khun, D. M. Matson, G. Kuppermann, K. Drewes, M. C. Flemings and M. G. Frohberg: Steel Reseearch, 1998, vol.69 (1), pp. 3-7.
G. I. Batalin, V. P. Kurach and V. S. Sudavtsova: Ukr. Khim. Zh. 1983, vol.49, pp. 547-548.
L. S. Chistyakov, K. V. Grigorovich and A. Ya. Stomakhin: Izv. Vyssh. Ucheb. Zaved., Cher. Metall., 1992, vol. 2, p. 102.
L. S. Chistyakov, A. Ya. Stomakhin and K. V. Grigorovich: Izv. Rossiiskoi Akademii Nauk, metally, 1993, vol.4, pp. 20-28.
S. W. Gilby and G. R. St. Pierre:Trans. Met. Soc. AIME,1969, vol. 245,pp. 1749-1758.
S. Wagner, D. J. Shade and G. R. St. Pierre: Metall. Trans., 1972, vol.3,pp. 47-50.
E. Ichise, K. Shaw and S. Taniguchi: J. Mass. Spectrometry Soc. Japan, 1993, vol. 41, pp. 343-350.
V. V. Samokhval and A. A. Vecher:Izv. Akad. Nauk, Metally, 1971, vol.6,pp. 118-120.
W. Johnson, K. Komarek and E. Miller:Trans. Met. Soc. AIME, 1968, vol.242, pp. 1685-1691.
W. Huang and Y. A. Chang: Intermetallics 1999, vol.7, pp.863-874.
N. Dupin, I. Ansara and B. Sundman: CALPHAD 2001, vol.25, pp. 279-298.
P. Broz, J. Bursik and R. Picha: Intermetallics 2002, vol. 10, pp. 635–639.
D. Zivkovic, L. Balanovic, D. Manasijevic, A. Mitovski, A. Kostov, L. Gomidzelovi and Z. Zivkovic: J. Univ. Chem. Techn. Metallur., 2011, vol.46 (1), pp. 95-98.
D. Zivkovic and Z. Zivkovic:B. Chem. Techn. Macedonia, 2002, vol. 21 (1), pp. 65-73.
M. Palumbo, S. Curiotto and L. Battezzati: CALPHAD, 2006, vol.30,pp. 171-178.
S. Curiotto, N.H. Pryds, E. Johnson and L. Battezzati: Metallur. Mater. Trans., 2006, vol. 37A, pp. 2361-2368.
S. Curiotto, R. Greco, N.H. Pryds, E. Johnson and L. Battezzati: Fluid Phase Equilibria 2007, vol. 256, pp. 132–136.
A. Boulouiz, M. El Moudane, M. Mekkaoui and A. Sabbar:J. Mater. Environ. Sci., 2014, vol. 5 (3), pp. 815-822.
A. Milosavljević, D. Živković, and P. Stolić: 15th Int. Res. Expert Conf., TMT 2011, Prague, Czech Republic, 12–18 September 2011.
K. C. Chou: CALPHAD, 1995, vol.19 (3), pp. 315-325.
F. Kohler: Monatsh. Chem. 1960, vol. 91, pp. 738–740.
Y.M. Muggianu, M. Gambino and J.P. Bros: J. Chim. Phys. 1975, vol.72, pp. 83–88.
G.W. Toop: Trans. AIME,1965, vol.233, pp. 850–855.
C. Colinet: Ph.D. Thesis, Facultedes Sciences, Universitede Grenoble, 1967.
C. K. Behera and M. Shamsuddin: Metall. Mater. Trans. B. 2008, vol. 39B pp. 551-560.
A. Boulouiz and A. Sabbar: Thermochimica Acta, 2014, vol.575, pp. 151–158.
C. Luef, H. Flandorfer and H. Ipser: Thermochimica Acta, 2004, vol.417, pp.47–57.
G. H. Zhang, L. J. Wang and K. C. Chou: CALPHAD, 2010, vol.34, pp.504–509.
G. H. Zhang and K. C. Chou: J. Solution Chem., 2010, vol. 39, pp. 1200-1212.
K. C. Chou and S. K. Wei: Metall. Mater. Trans. B, 1997, vol.28, pp. 439–445.
Z. Qiang, L. Wenchao and X.Hong: J. Mining Metall., 2000, vol.36, pp. 1–2.
H. Arslan: Physica B, 2014, vol.438, pp. 48-52.
H. Arslan, A. Dogan and T. Dogan: The Physics of Metals and Metallography, 2013, vol. 114(12), pp. 1053–1060.
L. Kaufman and H. Nesor: Z. Metallkd.1973, vol.64 pp. 249-257.
L. Kaufman and H. Nesor: CALPHAD, 1978, vol.2, pp. 325-348.
Z. Liang and Z. Jin: CALPHAD, 1993, vol. 17(4), pp. 415-425.
T.Miki, F. Ishii and M. Hino: Mater. Trans., 2003, vol. 44 (9), pp.1817-1823.
J. C. Schuster and Y. Du: CALPHAD, 1999, vol.23, pp.393–408.
X. J. Liu, Z. P. Jiang, C. P. Wang and K. Ishida: J. Alloys and Comp., 2009, vol.478, pp. 287-296.
L. Kaufman and H. Nesor: CALPHAD, 1978, vol. 2, pp. 81–108.
A.V. Davydov, U. R. Kattner, D. Josell, J. E. Blendell, R. M. Waterstrat, A. J. Shapiro and W. J. Boettinger (2001) Metall. Mater. Trans.,A, 32:2175–2186.
W. T. Witusiewicz, A. A. Bondar, T. Hecht and T. Y. Velikanova:J. Alloys Compd., 2009, vol. 472, pp. 133–161.
L. Gomidzelovic, I. Miajlovic, A. Kostov and D. Zirkovic: Hem. Ind., 2013, vol.67, pp. 157-164.
K. Kumar, I. Ansara, P. Wollants and L. Delaey:Z. Metallkd., 1996, vol.87, 666-672.
D. Dezellus, R. Arroyave and S. Fries: Int. J. Mater. Res, 2011, vol.102, pp. 286-297.
R. Arroyave, T. W. Eagar and L. Kaufman: J. Alloys Compd., 2003, vol.351, pp. 158–170.
S. Hassam, D. Boa and J. Rgez: J Alloys and Comp., 2012, vol. 520, pp. 65-71.
J. Wang, C. Leinenbach and M. Roth: J Alloys and Comp., 2009, vol.481 pp. 830-836.
H.S. Liu, C.L. Liu, K. Ishida and Z.P. Jin: J Electronic Materials,2003, vol.32, pp. 1290-1295.
H. S. Liu, K. Ishida, Z. P. Lin and Y. Du: Intermetallics, 2003, vol.11, pp. 987-994.
R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, and K.K. Kelley: in Selected Values of the Thermodynamic Properties of Binary Alloys, ASM In., Metals Park, OH, 1973.
M. Rechchach, A. Sabbar, H. Flandorfer and H. Ipser: Thermochimica Acta, 2010, vol.502 pp. 66–72.
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted May 14, 2014.
Rights and permissions
About this article
Cite this article
Dogan, A., Arslan, H. Comparative Thermodynamic Prediction of Integral Properties of Six Component, Quaternary, and Ternary Systems. Metall Mater Trans A 46, 3753–3760 (2015). https://doi.org/10.1007/s11661-015-2888-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11661-015-2888-2