The dependencies of the melting point of Au, Pt and Fe on the nanocrystal size and shape at different pressures

A method is proposed for calculating the dependence of the melting temperature on the size (number of atoms $N$) and the nanocrystal surface shape at the different pressures $(P)$. This method is based on the paired Mie–Lennard-Jones interatomic interaction potential, and takes into account the dependence of both the state equation and other lattice properties on the nanocrystal size and shape. For the first time, the dependences of the melting temperature $(T_m)$ on the pressure $P$, size $N$, and shape parameter $f$ of the nanocrystal were obtained. Calculations have been performed for gold, platinum and iron. It is shown that at any pressure, the $T_m(P,N,f)$ function decreases both with an isomorphic-isobaric ($f$, $P$ – const) decrease in the number of $N$ atoms, and with an isomeric-isobaric ($N$, $P$ – const) deviation of the nanocrystal shape from the energy-optimal shape. It is shown that the value of the baric derivative of the melting temperature $T'_m(P)$ for a nanocrystal at low pressures is larger and at high pressures smaller than the value $T'_m(P)$ for a macrocrystal. Moreover, the dependence of the $T'_m(P)$ function on the nanocrystal size is negligible, i. e., the functions $T_m(P,\infty)$ and $T_m(P, N, f)$ are almost parallel at constant $N$–$f$-arguments. It is indicated how this method can be applied to experimentally estimate the pressure under which a nanocrystal is confined in a refractory matrix.