Elastic stability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>Ga</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:math>: Addressing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> phase transition from first principles
Konstantin Lion, P. Pavone, Claudia Draxl
Abstract
The elastic and structural properties of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ are investigated from first principles. The full elastic tensors and elastic moduli of both phases at $0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ are computed in the framework of semilocal density-functional theory. We determine mechanical instabilities of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ by evaluating the full stiffness tensor under load for a range of hydrostatic pressure values. While a phase transition from the $\ensuremath{\beta}$ to $\ensuremath{\alpha}$ phase is found to be energetically favored at $2.6\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa}$, we show that the $\ensuremath{\beta}$ phase is mechanically unstable only for much higher pressures $(>30\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa})$, which agrees well with experimental results. Our employed approach is based on the Born stability criterion, is independent of crystal symmetry, and thus can be readily applied to different materials.