High pressure phase evolution under hydrostatic pressure in a single imperfect crystal due to nanovoids

Abstract

In this paper, the evolution of high pressure phase (HPP) in an imperfect single crystal due to the existence of nanovoids is investigated. The nanovoid misfit strain and its stress are properly linked to its radius. The Ginzburg-Landau coupled with elasticity equations are solved for the HPP evolution. The energy barrier between the HPP and the low pressure phase, entropy jump, transformation strain function and the relation between critical and equilibrium temperatures are determined based on the phase transformation (PT) equilibrium and instability pressures and the HPP transformation strain. The obtained PT pressure which shows an exponential reduction vs. the radius and a linear increase vs. temperature, is found mostly smaller than the theoretical solution. The HPP grows from the nanovoid surface and along the line of zero shear transformation strain. Above some critical radius, the HPP growth is promoted and continues along the boundaries. The transformation work distribution reveals a faster initial growth for larger radii. The HPP growth is evaluated based on the thermodynamic equilibrium and instability criteria. The growth rate and velocity of the HPP tip nonlinearly decrease with temperature. Interestingly, the average shear stress varies very similar to the HPP concentration. The HPP growth is also investigated for different applied pressures so that above some pressure, the HPP growth proceeds along the boundaries and the growth rate increases as the pressure increases. The current study can be used to better understand the PT nano mechanisms of various HPPs.