The problem of predicting stable solid solutions can be reduced to finding structures which lie on the energetic convex hull. Structures that lie on or below the convex hull are predicted to be stable at 0 K. Structures that lie above the convex hull are denoted as metastable and may be thermally accessible above 0 K. However, testing all compositions and configurations along a solid solution line can be a computationally intensive task involving many structures. Different approaches to this problem including genetic algorithms , basin-hopping , meta-dynamics , simulated annealing and particle-swarm optimisation. One approach to reduce the massive phase space may be to restrict the search to a single crystal structure type such as the spinel group which has been studied in great detail. The spinel structure (shown in Figure ) consists of a close-packed system of anions (X = O, S, Se) with one-half of octahedral and one-eighth of tetrahedral sites occupied by cations giving a reduced formula of AB 2 X 4 where A is a divalent cation and B trivalent.