Journal of Phase Equilibria and Diffusion

, Volume 40, Issue 1, pp 104–114 | Cite as

A Modified Neumann–Kopp Treatment of the Heat Capacity of Stoichiometric Phases for Use in Computational Thermodynamics

  • Michael Schick
  • Andy WatsonEmail author
  • Moritz to Baben
  • Klaus Hack


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.


heat capacity Neumann–Kopp CALPHAD thermodynamics phase diagram 


  1. 1.
    R.A. Swalin, Thermodynamics of Solids, Wiley, London, 1962, p 60zbMATHGoogle Scholar
  2. 2.
    O. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th ed., Pergamon Press, Oxford, 1983Google Scholar
  3. 3.
    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)Google Scholar
  4. 4.
  5. 5.
    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 38-52CrossRefGoogle Scholar
  6. 6.
    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 93-98CrossRefGoogle Scholar
  7. 7.
    W. Huang and Y.A. Chang, A Thermodynamic Analysis of the Al–Re System, J. Phase Equilib., 1998, 19(4), p 361-366CrossRefGoogle Scholar
  8. 8.
    B. Hallstedt and O. Kim, Thermodynamic Assessment of the Al–Li system, Int. J. Mater. Res., 2007, 98(10), p 961-969CrossRefGoogle Scholar
  9. 9.
    SGTE 2014 intermetallic compounds database for FactSageGoogle Scholar
  10. 10.
    A.J. McAllister, The Al–Li (Aluminum–Lithium) System, Bull. Alloy Phase Diagr., 1982, 3(2), p 177-183CrossRefGoogle Scholar
  11. 11.
    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 10912ADSCrossRefGoogle Scholar
  12. 12.
    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 6137ADSCrossRefGoogle Scholar
  13. 13.
    M. Hillert, The Compound Energy Formalism, JALCOM, 2001, 320, p 161-176Google Scholar
  14. 14.
    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 35-53CrossRefGoogle Scholar

Copyright information

© ASM International 2019

Authors and Affiliations

  • Michael Schick
    • 1
  • Andy Watson
    • 2
    Email author
  • Moritz to Baben
    • 1
  • Klaus Hack
    • 1
  1. 1.GTT TechnologiesHerzogenrathGermany
  2. 2.Centre for the Built and Natural Environment, Faculty of Engineering and ComputingCoventry UniversityCoventryUK

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