Abstract
Since the early days of phase diagram calculation, the CALPHAD community has accepted a method of data assessment that is based on using Gibbs energy expressions for stoichiometric compounds that consist of a part that represents the contributions of the reference components, the so-called Neumann–Kopp sum, and a part that represents the Gibbs energy of formation. Usually, the latter consists only of a simple A + B * T term, which implies on the one hand that enthalpy and entropy of formation of a compound are temperature independent, and on the other, that the heat capacity of the respective compound is given by the Neumann–Kopp sum of the Cps of the constituents. In most cases this method yields acceptable results, also for the heat capacity. However, if certain elementary components are involved, this is not so. The paper highlights the problem outlining a remedial treatment that can be applied to problematic heat capacity functions present in pre-existing assessments, and thus giving a suggestion of how to prevent the problem in the future.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.A. Swalin, Thermodynamics of Solids, Wiley, London, 1962, p 60
O. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th ed., Pergamon Press, Oxford, 1983
R. Mezaki, E.W. Tilleux, D.W. Barnes, J.L. Margrave, Thermodynamics of Nuclear Materials, in Proceedings of the IAEA Symposium, Vienna, p. 775 (from ref. 2) (1962)
R. Schmid Fetzer, D. Andersson, P.Y. Chevalier, L. Eleno, O. Fabrichnaya, U.R. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, and M. Zinkevich, Assessment Techniques, Database Design and Software Facilities for Thermodynamics and Diffusion: Group Report from the Ringberg Workshop on Thermodynamic Modeling and First Principles Calculations, Calphad, 2007, 31(1), p 38-52
J.-O. Andersson, A.F. Guillermet, P. Gustafson, M. Hillert, B. Jansson, B. Jönsson, B. Sundman, and J. Ågren, A New Method of Describing Lattice Stabilities, Calphad, 1987, 11(1), p 93-98
W. Huang and Y.A. Chang, A Thermodynamic Analysis of the Al–Re System, J. Phase Equilib., 1998, 19(4), p 361-366
B. Hallstedt and O. Kim, Thermodynamic Assessment of the Al–Li system, Int. J. Mater. Res., 2007, 98(10), p 961-969
SGTE 2014 intermetallic compounds database for FactSage
A.J. McAllister, The Al–Li (Aluminum–Lithium) System, Bull. Alloy Phase Diagr., 1982, 3(2), p 177-183
X.-Q. Guo, R. Podloucky, and A.J. Freeman, Phase Stability And Bonding Characteristics Of Li-Rich Al–Li Intermetallic Compounds: Al2Li3 and Al4Li9, Phys. Rev. B, 1990, 42, p 10912
M.H.F. Sluiter, Y. Watanabe, D. de Fontaine, and Y. Kawazoe, First-Principles Calculation of the Pressure Dependence of Phase Equilibria in the Al–Li System, Phys. Rev. B, 1996, 53, p 6137
M. Hillert, The Compound Energy Formalism, JALCOM, 2001, 320, p 161-176
C.W. Bale, E. Bélisle, P. Chartrand, S.A. Decterov, G. Eriksson, A.E. Gheribi, K. Hack, I.H. Jung, Y.B. Kang, J. Melançon, A.D. Pelton, S. Petersen, C. Robelin, J. Sangster, P. Spencer, and M.-A. Van Ende, FactSage Thermochemical Software and Databases 2010–2016, Calphad, 2016, 54, p 35-53
Author information
Authors and Affiliations
Corresponding author
Additional information
This invited article is part of a special issue of the Journal of Phase Equilibria and Diffusion in honor of Prof. Jan Vrestal’s 80th birthday. This special issue was organized by Prof. Andrew Watson, Coventry University, and Dr. Ales Kroupa, Institute of Physics of Materials, Brno, Czech Republic.
Rights and permissions
About this article
Cite this article
Schick, M., Watson, A., to Baben, M. et al. A Modified Neumann–Kopp Treatment of the Heat Capacity of Stoichiometric Phases for Use in Computational Thermodynamics. J. Phase Equilib. Diffus. 40, 104–114 (2019). https://doi.org/10.1007/s11669-019-00708-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11669-019-00708-0