  Pseudobinary heterostructural alloys of ZnO with MgO or CdO are studied by
composing the system locally of clusters with varying ratio of cations. We
investigate fourfold (wurtzite structure) and sixfold (rocksalt structure)
coordination of the atoms. By means of density functional theory we study a
total number of 256 16-atom clusters divided into 22 classes for the wurtzite
structure and 16 classes for the rocksalt structure for each of the alloy
systems. The fraction with which each cluster contributes to the alloy is
determined for a given temperature T and composition x within (i) the
generalized quasi-chemical approximation, (ii) the model of a strict-regular
solution, and (iii) the model of microscopic decomposition. From the cluster
fractions we derive conclusions about the miscibility and the critical
compositions at which the average crystal structure changes. Thermodynamic
properties such as the mixing free energy and the mixing entropy are
investigated for the three different statistics. We discuss the consequences of
the two different local lattice structures for characteristic atomic distances,
cohesive energies, and the alloys' elasticities. The differences in the
properties of Mg_x Zn_{1-x} O and Cd_x Zn_{1-x} O are explained and discussed.
