Transition pressures and enthalpy barriers for the cubic diamond→β-tin transition in Si and Ge under nonhydrostatic conditions

Abstract

We present an ab-initio study of the phase transition cd→β-tin in Si and Ge under hydrostatic and non-hydrostatic pressure. For this purpose we have developed a new method to calculate the influence of non-hydrostatic pressure components not only on the transition pressure but also on the enthalpy barriers between the phases. We find good agreement with available experimental and other theoretical data. The calculations have been performed using the plane-wave pseudopotential approach to the density-functional theory within the local-density and the generalized-gradient approximation implemented in VASP.

Stress induced phase transitions in silicon

“…Nanoindentation studies with various indenter-shapes 2 have shown that non-hydrostatic conditions lower the transformation stress, which is in accordance with theoretical considerations by Gilman (1993a) as well as various atomistic studies (cf. Lee et al, 1997;Cheng et al, 2001;Cheng, 2003;Gaál-Nagy and Strauch, 2006), which suggest a linear relationship between the transformation pressure p and applied von Mises equivalent stress S q := √ 3 /2 S . Transformation events during unloading appear on the force-displacement (P−h) curve (see Fig.…”

“…This choice reproduces the experimentally observed phase transition under hydrostatic compression (Hu et al, 1986), without predicting transformations in hydrostatic tension. Further, the linear relationship between equivalent stress S q and pressure p on the limit surface suggested by MD simulations (Cheng et al, 2001;Cheng, 2003;Gaál-Nagy and Strauch, 2006;Lee et al, 1997) can be smoothly approximated with an arbitrary order of accuracy. The corresponding flow potential is also chosen to be a hyperboloid of revolution, albeit not necessary the same one.…”

Phase transformation in Si from semiconducting diamond to metallicβ-Snphase in QMC and DFT under hydrostatic and anisotropic stress

“…The linear coefficient is similar for all three functionals and close to the values determined previously for the LDA and PW91 functional. 17,18 Considering that the mechanical strength of silicon under uniaxial compression at ambient conditions is about 7 GPa, 58 it may be reasonable to assume that deviatory stresses on the order of 0.5 GPa could be present in the diamond-anvil cell experiments with a pressure medium and even larger deviatory stresses without a pressure medium. This would lower the observed transition pressure by 1.2 GPa compared to perfect hydrostatic compression.…”

“…Stress anisotropy in the sample can lower the transition pressure by stabilizing the ␤-Sn phase over the diamond phase. 17,18 We determine the effect of nonhydrostatic stresses on the transition pressure following the approach by Cheng et al 17 The phase transformation from the diamond to the ␤-Sn phase occurs when…”

“…The transition pressure decreases linearly with increasing deviatory stresses along one of the cubic axes. 17,18 In this study, we perform QMC and DFT calculations to benchmark semilocal and hybrid exchange-correlation functionals for the diamond to ␤-Sn transformation in Si and determine how nonhydrostatic stress affects the transition pressure. Section II introduces the DFT and QMC methods.…”