Anharmonic contribution to the vacancy formation in Cu

Experimental data on the vacancy concentration in metals, when shown in an Arrhenius plot, give an approximate straight line as a function of $1/T$ but often with a slight upward curvature close to the melting point $T_m.$ This feature has usually been attributed to a divacancy contribution. We have performed molecular dynamics simulations on copper, using a slightly modified model potential due to Cleri and Rosato (Ref. 7). Our results show that divacancy effects are negligible, but that there is an important contribution from anharmonicity in the lattice vibrations, giving rise to the curvature in the Arrhenius plot. As a consequence, one must apply significant corrections to the vacancy formation enthalpy and entropy before they are compared with theoretical values that usually refer to zero kelvin and harmonic vibrations, respectively.