∆E ss for the substitution scheme therefore differs from that of the swapping routine as the substitution energy is not dependent on the energy of the previous structure but on the two (stable) end members. When a substitution event occurs then, there is a high likelihood that the energy difference will be positive. This makes acceptance of a substitution event less likely than the acceptance of a swap. Using this energy with the Metropolis criterion allows for the acceptance of substitution with consideration of thermal effects. More advanced implementations such as the energy above the convex hull could also be used to get more accurate relative stabilties, but for this system the solid solution energy is equivalent to the convex hull energy as the spinel disproportionates into the two end members which lie on the convex hull.