A revised thermodynamic model for crystal surfaces. I. Theoretical aspects

A revised thermodynamic model to explain the deviation of the surface composition from that of the bulk (i.e., segregation) is proposed. This phenomenological model is based both on the multilayer approach (i.e., the crystal is treated as an infinite set of layers of formula units (f.u.), each layer potentially having a different composition) and on the recent findings on the behaviour of the free energy per f.u. in the proximity of a crystal surface. The model is developed for a binary solid solution, but can be extended to any number of components. The free energy of the whole system is derived and minimized varying the atom fractions of each layer. The effect of the different parameters of the model on the surface composition is successively evaluated by using a homemade calculation program. We also investigate how sensitive is the surface composition in respect to the variations of that of the bulk crystal.