Change in the melting temperature baric dependence during the transition from macro to nanocrystal

Abstract

In this work we present new analytical (i.e., without computer modeling) method for calculating the dependence of the nanocrystal melting temperature both on pressure and on the size (number of atoms N) and surface shape of the nanocrystal. 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 size and shape of the nanocrystal. For the first time, the dependences of the melting temperature on the pressure P, size N, and shape f of the nanocrystal were obtained. Calculations have been performed for gold, platinum and iron. It is shown that at any pressure, the melting point Tm(P, N, f) 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 Tm′(P) for a nanocrystal at low pressures is greater, and at high pressures less than the Tm′(P) value for a macrocrystal. At this, the dependence of the Tm′(P) function on the nanocrystal size is insignificant, i.e., at constant N-f-arguments, the baric dependences Tm(P, ∞) and Tm(P, N, f) are practically parallel. It is indicated how this method can be applied for experimental evaluation of the pressure under which a nanocrystal is located in a refractory matrix.