Elasticity ofω-phase zirconium

Abstract

Compressional $({V}_{P})$ and shear wave $({V}_{S})$ velocities as well as unit-cell volumes of the $\ensuremath{\omega}$ phase of Zr have been measured at high pressure $(6.9--10.9\phantom{\rule{0.3em}{0ex}}\mathrm{GPa})$ at room temperature using ultrasonic interferometry in conjunction with synchrotron x radiation. Both ${V}_{P}$ and ${V}_{S}$ as well as the adiabatic bulk $({K}_{S})$ and shear $(G)$ moduli exhibit monotonic increase with increasing pressure. Using a finite strain equation of state approach, the elastic bulk and shear moduli and their pressure derivatives are derived from the directly measured velocities and densities, yielding ${K}_{S0}=104.0\phantom{\rule{0.3em}{0ex}}(16)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${G}_{0}=45.1\phantom{\rule{0.3em}{0ex}}(9)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${K}_{S0}^{\ensuremath{'}}=2.8$ (2), and ${G}_{0}^{\ensuremath{'}}=0.6$ (1) independent of pressure calibration. The low pressure dependence of ${K}_{S0}$ and ${G}_{0}$ may be attributed to the pressure-induced progressive $s\text{\ensuremath{-}}d$ electron transfer in the $\ensuremath{\omega}\text{\ensuremath{-}}\mathrm{Zr}$ as suggested by previous Raman studies as well as static compressions at high pressure.