Strength and equation of state of boron suboxide from radial x-ray diffraction in a diamond cell under nonhydrostatic compression

Abstract

Using radial x-ray diffraction techniques together with lattice strain theory, the behavior of boron suboxide $({\mathrm{B}}_{6}\mathrm{O})$ was investigated under nonhydrostatic compression to $65.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ in a diamond-anvil cell. The apparent bulk modulus derived from nonhydrostatic compression data varies from $363\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}124\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ depending on the orientation of the diffraction planes with respect to the loading axis. Measurement of the variation of lattice spacing with angle, $\ensuremath{\psi}$, from the loading axis allows the $d$ spacings corresponding to hydrostatic compression to be obtained. The hydrostatic $d$ spacing obtained from a linear fitting to data at 0\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} is consistent with direct measurements at the appropriate angle $(\ensuremath{\psi}=54.7\ifmmode^\circ\else\textdegree\fi{})$ to within 0.5%, which suggests that even two measurements ($\ensuremath{\psi}=0\ifmmode^\circ\else\textdegree\fi{}$ and 90\ifmmode^\circ\else\textdegree\fi{}) are sufficient for accurate hydrostatic equation of state determination. The hydrostatic compression data yield a bulk modulus ${K}_{0}=270\ifmmode\pm\else\textpm\fi{}12\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and its pressure derivative ${K}_{0}^{\ensuremath{'}}=1.8\ifmmode\pm\else\textpm\fi{}0.3$. The ratio of differential stress to shear modulus ranges from 0.021 to 0.095 at pressures of $9.3--65.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Together with estimates of the high-pressure shear modulus, a lower bound to the yield strength is $26--30\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ at the highest pressure. The yield strength of ${\mathrm{B}}_{6}\mathrm{O}$ is about a factor of 2 larger than for other strong solids such as ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$. The ratio of yield stress to shear modulus derived from lattice strain theory is also consistent with the result obtained by the analysis of x-ray peak width. This ratio might be a good qualitative indicator of hardness as it reflects the contributions of both plastic and elastic deformation.