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 ( ${\overline{\Delta \theta }}^c$ ) versus the ratio of the external surface layer width to the HPP-LPP interface width ( $\overline{{\Delta }_{\xi }}$ ) is found for different boundary conditions, uniaxial pressures and transformation strains. The external surface layer reveals a similar nonlinear increase of ${\overline{\Delta \theta }}^c$ versus $\overline{{\Delta }_{\xi }}$ , in agreement with previous numerical and experimental data on thermal induced transformation/melting at the nanoscale. Without vertical constraint, ${\overline{\Delta \theta }}^c$ nonlinearly increases versus $\overline{{\Delta }_{\xi }}$ and remains constant for $\overline{{\Delta }_{\xi }}\ge 1.33$ . It also linearly reduces versus the pressure/transformation strain, independent of $\overline{{\Delta }_{\xi }}$ . With vertical constraint, ${\overline{\Delta \theta }}^c$ is larger and weakly dependent on $\overline{{\Delta }_{\xi }}$ . Under applied pressure, the transformation work linearly increases with the transformation strain for $\overline{{\Delta }_{\xi }}>0.5$ and consequently, ${\overline{\Delta \theta }}^c$ 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.