Elasticity, shear strength, and equation of state of molybdenum and gold from x-ray diffraction under nonhydrostatic compression to 24 GPa

Abstract

Lattice strains were measured as a function of the angle $\psi$ between the diffracting plane normal and the stress axis of a diamond anvil cell in a layered sample of molybdenum and gold. The sample was compressed over the range 5–24 GPa and the lattice strains were measured using energy-dispersive x-ray diffraction. As $\psi$ is varied from 0° to 90°, the mean lattice parameter of molybdenum increases by up to 1.2% and that of gold increases by up to 0.7%. A linear relationship between $\mathrm{Q(hkl),}$ which is related to the slope of the measured d spacing versus $\text{1−3\hspace{0.05em}}{\cos }^2\mathrm{ \psi }$ relation, and $\text{3Γ(hkl),}$ a function of the Miller indices of the diffracting plane, is observed for both materials as predicted by theory. The pressure dependence of the uniaxial stress t for gold from this and other recent studies is given by $\text{t=0.06+0.015P,}$ where P is the pressure in GPa. The uniaxial stress in molybdenum can be described by $\text{t=0.46+0.13P.}$ Using gold as an internal pressure standard, the equation of state of molybdenum depends strongly on $\mathrm{\psi .}$ The bulk modulus obtained from a Birch–Murnaghan fit varies from 210 to 348 GPa as $\psi$ varies from 0° to 90°. However, an equation of state in good agreement with shock and ultrasonic isotherms is obtained for $\text{ψ=54.7°}$ where the deviatoric contribution to the lattice strain vanishes. Second-order elastic moduli for gold and molybdenum are obtained from the data. The results are generally consistent with an earlier x-ray study and with extrapolations of low-pressure ultrasonic data. The pressure dependence of the shear modulus $C_{44}$ is smaller for the x-ray data than predicted by extrapolation of ultrasonic data.