On estimations of the melting temperature of graphene-like compounds

Three approaches to the problem of determining the melting temperature considered as the temperature of thermal instability of a two-dimensional hexagonal structure are discussed. These approaches are (i) Naya–Iziri–Ishii’s approximation, (ii) the Lindemann criterion, and (iii) the Born criterion. The Harrison method of bonding orbitals is used for numerical estimations. Graphene, silicene, germanene, and 12 IV–IV and III–V compounds are considered. It is shown that the Lindemann and Born criteria give close and more real results in comparison to Naya–Iziri–Ishii’s approximation. To obtain rough estimates of the “bulk” and “surface” melting temperatures, the expressions $T_b\sim 10^4$ K/a$^2$ and $T_s\sim 2T_b/3$, where the spacing between the nearest neighbors a is given in $\mathring{\mathrm{A}}$, are proposed.