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

The elastic and structural properties of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ are investigated from first principles. full tensors moduli both phases at $0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ computed in the framework semilocal density-functional theory. We determine mechanical instabilities by evaluating stiffness tensor under load for a range hydrostatic pressure values. While phase transition $\ensuremath{\beta}$ to $\ensuremath{\alpha}$ is found be energetically favored $2.6\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa}$, we show that mechanically unstable only much higher pressures $(&gt;30\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa})$, which agrees well with experimental results. Our employed approach based on Born stability criterion, independent crystal symmetry, thus can readily applied different materials.