Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 28–37 www.elsevier.com/locate/calphad Thermodynamic models for crystalline phases. Composition dependent models for volume, bulk modulus and thermal expansion Bengt Hallstedt a,∗ , Nathalie Dupin b , Mats Hillert c , Lars H ¨ oglund c , Hans Leo Lukas d , Julius C. Schuster e , Nuri Solak d a RWTH Aachen, Aachen, Germany b Calcul Thermodynamique, Orcet, France c Royal Institute of Technology, Stockholm, Sweden d Max-Planck-Institut f¨ ur Metallforschung, Stuttgart, Germany e Universit¨ at Wien, Vienna, Austria Received 14 February 2006; accepted 17 February 2006 Available online 22 March 2006 Abstract The thermodynamic modelling of solid (crystalline) phases forms a central topic within the Calphad approach and a variety of aspects have been discussed at previous Ringberg workshops. At the present Ringberg workshop, modelling of volume and its temperature, pressure and composition dependence formed a major part of the discussions. In addition, modelling of the heat capacity above the (equilibrium) melting temperature, sublattice modelling of complex phases, modelling of ordering and interstitial solutions in the bcc lattice and the effect of magnetism were addressed. c  2006 Elsevier Ltd. All rights reserved. 1. Introduction The development of thermodynamic models for crystalline phases, elements, compounds and solutions, along with recommendations for data sources and evaluation has been discussed at all previous Ringberg workshops. Modelling of the heat capacity [1,2] and contributions from magnetic ordering [3] were discussed in 1995, the Murnaghan equation of state in 1997 [4], and use of ab initio calculations in the Calphad environment in 1999 [5]. Sublattice modelling of complex intermetallic phases was discussed in 1996 [6] and 1997 [4], while modelling of carbides and nitrides [7] and interstitial solutions in the hcp host lattice [8] were discussed in 1999. Order–disorder modelling has been frequently discussed [4,8, 9]. Ionic solutions were discussed in 1996 [10] and 1999 [5,11] and semiconductors in 1996 [12] and 1997 [4]. ∗ Corresponding author. E-mail addresses: hallstedt@mch.rwth-aachen.de (B. Hallstedt), nathdupin@wanadoo.fr (N. Dupin), mats@mse.kth.se (M. Hillert), lars@mse.kth.se (L. H ¨ oglund), lukas@mf.mpg.de (H.L. Lukas), julius.schuster@univie.ac.at (J.C. Schuster), solak@mf.mpg.de (N. Solak). So far, few serious attempts to include volume and pressure dependence in conventional Calphad modelling have been made. The discussion of modelling of volume and pressure dependence formed a major topic at the present workshop. In this context, the modelling of the liquid phase was also discussed. 2. Treatment of volumes within the Calphad approach 2.1. Motivation Including volumes in a thermodynamic database enables the calculation of volume changes on for example heating or melting, volume fractions, lattice mismatch in cubic structures and phase diagrams at increased pressure. Pressure independent volumes can be used up to about 1 GPa. At pressures above 1 GPa the pressure dependence of the volumes must be included by using a proper equation of state (EOS). Volumes can be easily added to thermodynamic databases by adding a PV -term to the existing G(T ) expressions. To avoid inconsistencies, PV - terms should be added to all element and compound energies in 0364-5916/$ - see front matter c  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2006.02.008