Phase stabilities and spinodal decomposition in the Cr 1x Al x N system studied by ab initio LDA and thermodynamic modeling: Comparison with the Ti 1x Al x N and TiN/Si 3 N 4 systems R.F. Zhang, S. Veprek * Department of Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Munich, Germany Received 9 November 2006; received in revised form 13 April 2007; accepted 13 April 2007 Available online 6 June 2007 Abstract The total energies and lattice constants of binary hexagonal close-packed (hcp)- and face-centered cubic (fcc)-CrN, AlN and ternary Cr 0.5 Al 0.5 N phases are calculated using the Vienna Ab-initio Simulation Program. The calculated total energies of the structures are then used to calculate the lattice stabilities of binary hcp- and fcc-CrN and AlN, and the interaction parameters of the ternary hcp- and fcc- Cr 1x Al x N solution phases. These results are used in the sublattice thermodynamic model to construct the Gibbs free energy diagram of the immiscible quasi-binary CrN–AlN system at different temperatures. Based on these results, we discuss the relative phase stability of the metastable ternary hcp- and fcc-Cr 1x Al x N solid solutions over the entire range of compositions. The predictions are compared with and supported by the published results from physical and chemical vapor deposition experiments. The constructed Gibbs free energy diagrams show that metastable fcc-Cr 1x Al x N coatings may undergo spinodal decomposition into coherent fcc-CrN and fcc-AlN, but there is a relatively large barrier for a direct formation of the stable hcp-AlN. A comparison with the Ti 1x Al x N and TiN–Si 3 N 4 systems shows that the phase segregation will be more difficult and, therefore, the solid solution more stable in the Cr 1x Al x N case. Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanocomposite; Spinoidal decomposition; Ab initio electron theory; Thermodynamics; Modeling 1. Introduction In the past few decades, theoretical investigation of hard transition metal carbides and nitrides attracted much inter- est of researchers. These studies can be divided into two major categories: (i) first-principle ab initio calculation; and (ii) thermodynamic modeling. An example of the ab initio calculations of the phase stabilities of several tran- sition metal nitrides and carbides is the work of Hugosson et al. [1,2]. The thermodynamic modeling is typically done by means of the CALPHAD and other empirical numeric methods [3,4]. From these studies, it can be clearly seen that the advantage of the ab initio calculation method is the fact that no experimental input data are needed, differ- ent crystalline structures can be dealt with and a much dee- per physical insight can be obtained. However, its applications are limited to a temperature of 0 K unless a much larger CPU effort is acceptable in the quantum molecular dynamics, and are restricted to just a few struc- tures and compositions because the theoretical modeling is based on reciprocal space methods, which require modeling perfect stoichiometric crystal structures. The thermodynamic modeling is much simpler and fas- ter, it can cover the whole composition range and account for variable chemical activities and different temperatures. Such calculations require the knowledge of the relative sta- bility of different structures and of the interaction parame- ter between the constituent components. This is usually obtained from the fitting of experimental thermodynamic data. However, such data are available only for a small number of concerned systems which are miscible or whose 1359-6454/$30.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.04.029 * Corresponding author. Tel.: +49 89 2891 3624; fax: +49 90 2891 3626. E-mail address: veprek@ch.tum.de (S. Veprek). www.elsevier.com/locate/actamat Acta Materialia 55 (2007) 4615–4624