  We study the thermodynamics of cubic Ti1-xAlxN using a unified cluster
expansion approach for the alloy problem. The purely configurational part of
the alloy Hamiltonian is expanded in terms of concentration and volume
dependent effective cluster interactions. By separate expansions of the
chemical fixed-lattice, and local lattice relaxation terms of the ordering
energies, we demonstrate how the screened generalized perturbation method can
be fruitfully combined with a concentration dependent Connolly-Williams cluster
expansion method. Utilising the obtained Hamiltonian in Monte Carlo simulations
we access the free energy of Ti1-xAlxN alloys and construct the isostructural
phase diagram. The results show surprising similarities with the previously
obtained mean-field results: The metastable c-TiAlN is subject to coherent
spinodal decomposition over a larger part of the concentration range, e.g. from
x >= 0.33 at 2000 K.
