We study the thermodynamics of cubic Ti1-xAlxN using a unified clusterexpansion approach for the alloy problem. The purely configurational part ofthe alloy Hamiltonian is expanded in terms of concentration and volumedependent effective cluster interactions. By separate expansions of thechemical fixed-lattice, and local lattice relaxation terms of the orderingenergies, we demonstrate how the screened generalized perturbation method canbe fruitfully combined with a concentration dependent Connolly-Williams clusterexpansion method. Utilising the obtained Hamiltonian in Monte Carlo simulationswe access the free energy of Ti1-xAlxN alloys and construct the isostructuralphase diagram. The results show surprising similarities with the previouslyobtained mean-field results: The metastable c-TiAlN is subject to coherentspinodal decomposition over a larger part of the concentration range, e.g. fromx >= 0.33 at 2000 K.
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