Surface induced melting of long Al nanowires: phase field model and simulations for pressure loading and without it

Abstract

In this paper, melting of long Al nanowires is studied using a phase field model in which deviatoric transformation strain described by a kinetic equation produces a promoting driving force for both melting and solidification and consequently, a lower melting temperature is resolved. The coupled system of the Ginzburg–Landau equation for solidification/melting transformation, the kinetic equation for the deviatoric transformation strain and elasticity equations are solved using the COMSOL finite element code to obtain the evolution of melt solution. A deviatoric strain kinetic coefficient is used which results in the same pressure as that calculated with the Laplace equation in a solid neglecting elastic stresses. The surface and bulk melting temperatures are calculated for different nanowire diameters without mechanical loading which shows a good agreement with existing MD and analytical results. For radii R > 5 nm, a complete surface solid-melt interface is created which propagates to the center. For smaller radii, premelting occurs everywhere starting from the surface and the nanowire melts without creating the interface. The melting rate shows an inverse power relationship with radius for R < 15 nm. For melting under pressure, the model with constant bulk modulus results in an unphysical parabolic variation versus pressure in contrast to the almost linear increase of the melting temperature versus pressure from known MD simulations. Such drawback is resolved by considering the pressure dependence of the bulk modulus through the Murnaghan’s equation due to which an almost linear increase of the melting temperature versus pressure is obtained. Also, a reduction of the interface width and a significant increase of the melting rate versus pressure are found. The presented model and results allow for a better understanding of the premelting and melting of different metallic nanowires with various loading conditions and structural defects.