A general methodology using atomic clusters is applied to three problems connected to the study of alloy phase stability. The cluster method proposed by Allen and Cahn is applied to non-ideal hcp structures under tetrahedral approximation using multiatom interactions. The possible ground-state structures which are stable at absolute zero temperature are obtained. A geometrical representation in 4D parameter space of the possible strengths of multiatom interactions permitted for these structures is illustrated in terms of a 2D analogue. Extending these ideas, the cluster variation method (CVM) proposed by Kikuchi is applied to fcc structures under tetrahedral approximation to find the effect of multiatom interactions on the topology of the coherent phase diagrams in which all the phases present are derivable by mere rearrangement of atoms on the parent disordered structure. In addition, the possible invariant reactions are identified in such coherent phase diagrams. Finally the CVM is applied for calculating a model incoherent phase diagram, that of Ti-Zr system, where disordered hcp and bcc phases are present. The free energies of hcp and bcc phases are formulated using CVM procedures respectively under tetrahedral-octahedral and tetrahedral approximations. The CVM is shown to be in better agreement with the thermodynamic data and to be able to reproduce the correct value of measured enthalpy of transformation compared to that given by the regular solution model, which significantly overestimates the same.