Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 335–342 C A L P H A D 1 9 7 3 www.elsevier.com/locate/calphad CVM calculation of the b.c.c. Co–Cr–Al phase diagram Luiz Tadeu Fernandes Eleno 1 , Cl´ audio Geraldo Sch ¨ on ∗ Computational Materials Science Lab., Department of Metallurgical and Materials Engineering, Escola Polit´ ecnica da Universidade de S˜ ao Paulo, Av. Prof. Mello Moraes, 2463 - CEP 05508-900 S˜ ao Paulo-SP, Brazil Received 9 October 2003; received in revised form 27 November 2003; accepted 30 November 2003 This work is dedicated in memoriam to Prof. Dr. Ryoichi Kikuchi Abstract The cluster variation method (CVM) has been used as a tool for modelling the thermodynamics of the b.c.c. Co–Cr–Al system within the irregular tetrahedron approximation. The interaction parameters (nearest and next-nearest neighbour pairs, as well as tetrahedron interactions) for the three binary sub-systems have been derived following the so-called phenomenological approach, i.e. the interaction parameters have been fitted to experimental phase diagram and/or thermochemical data. As a result, the three binary phase diagrams of the system and four isothermal sections of the ternary phase diagram have been obtained. The results show that the CVM is thermodynamically self-consistent. © 2004 Elsevier Ltd. All rights reserved. Keywords: Ternary alloy systems; Order/disorder transformations; Thermodynamic and thermochemical properties; Phase diagram prediction; Ordering energies 1. Introduction Ordered intermetallics based on B2 structures (NiAl or FeAl type) have received considerable attention due to their potential for high temperature applications as structural materials. These materials show good mechanical properties at high temperatures (∼700 ◦ C), low density (∼6g/cm 3 ), and improved corrosion resistance [1]. The Co–Al system shows a large single-phase field of B2 phase at nearly equiatomic compositions. This phase melts congruently around 1640 ◦ C (1913 K) and x Al = 0.50 [2]. Materials based on this compound are suitable candidates, therefore, for structural applications at high temperatures. Addition of chromium has great potential for alloy development based on B2-CoAl compounds since both Al–Cr and Co–Cr binary systems show large stability fields of the body- centred cubic (b.c.c.) solid solution [3]. Equilibria involving the disordered phase and the B2-CoAl compound are expected to dominate over large concentration ranges of ∗ Corresponding author. Tel.: +55-11-3091-5726; fax: +55-11-3091- 5243. E-mail address: schoen@usp.br (C.G. Sch¨ on). 1 Present address: Max-Planck-Institut f¨ ur Eisenforschung, Postfach 140444, D-40074 D ¨ usseldorf, Germany. the phase diagram, allowing the production of two-phase microstructures containing a strong intermetallic and a ductile second phase (A2). Chromium may also be used to improve the corrosion resistance of these alloys. In a recent work Ishikawa et al. [4] experimentally determined four isothermal sections of the ternary Co–Al–Cr system. The experimental isothermal sections are dominated by a large two-phase field between the ordered B2-CoAl phase and the disordered chromium-rich A2 phase. The equilibrium is of second-order at low-chromium concentrations, becoming first-order at a multicritical point. The composition of this point is temperature-dependent. The extent of the two-phase field (A2 + B2) decreases as the temperature increases, but its total disappearance has not been observed in the investigation due either to temperature limitations or to competing equilibria with other phases, not based on the b.c.c. lattice [4]. In the present work the phase relationships between the B2 and A2 phases for the ternary Co–Cr–Al system using the cluster variation method (CVM) will be investigated. This kind of thermodynamic modelling allows for extrapolations to metastable equilibria outside the composition and temperature ranges where experimental data can be obtained. The CVM is based on the solution of a (factorizable) partition function [5, 6]. Its sound statistical 0364-5916/$ - see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2003.11.003