Finite size effects, potential energy surfaces

Eq. (54). These are film thickness D/(aN1/2), interaction parameter %/%c> the chemical potential difference NAp, and bare surface energies N1/2/a fsL and N1/2/a fsR. They enable [60] an easy comparison of finite size effects observed in different systems. Sometimes two such parameters, D/(aN1/2) and %/%c, are combined into the film thickness-to-interfacial width ratio D/w=3(7/7r-l)1/2D/(aN1/2). 

The GAP results for the thermal expansion coefficients obtained from the quasiharmonic approximation show excellent agreement with the LDA values. This verifies that the potential energy surface represented by the GAP model is, in fact, close to the ab initio potential energy surface, even outside the harmonic regime. In the case of Density Functional Theory, the molecular dynamics simulation would be computationally expensive, because a large supercell has to be used to minimise finite-size effects. However, with GAP, these calculations can be easily performed and the thermal expansion coefficients obtained match the experimental values well, even at high temperatures. 

---