Investigating the effect of external surface layer on high pressure phase evolution in a single crystal: A mechanics-based phase field study

Abstract

In this paper, effect of the external surface layer on low pressure phase (LPP)-high pressure phase (HPP) transformation in a single crystal is investigated using a phase field model. It consists of a kinetic equation to represent the LPP-HPP transformation and another one to introduce the external surface layer between the bulk and surrounding phase within which the surface energy is properly distributed. After resolving a stationary layer, the coupled elasticity and phase field equations are solved to capture the HHP evolution. The variation of the critical thermal driving force ([Formula: see text]) versus the ratio of the external surface layer width to the HPP-LPP interface width ([Formula: see text]) is found for different boundary conditions, uniaxial pressures and transformation strains. The external surface layer reveals a similar nonlinear increase of [Formula: see text] versus [Formula: see text], in agreement with previous numerical and experimental data on thermal induced transformation/melting at the nanoscale. Without vertical constraint, [Formula: see text] nonlinearly increases versus [Formula: see text] and remains constant for [Formula: see text]. It also linearly reduces versus the pressure/transformation strain, independent of [Formula: see text]. With vertical constraint, [Formula: see text] is larger and weakly dependent on [Formula: see text]. Under applied pressure, the transformation work linearly increases with the transformation strain for [Formula: see text] and consequently, [Formula: see text] reduces. The obtained results help to understand the effect of the external surface layer on the HPP evolution in relation to other key parameters depending on its width.