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

Lattice strains were measured as a function of the angle ψ 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 ψ 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 Q(hkl), which is related to the slope of the measured d spacing versus 1 - 3 cos² ψ relation, and 3ς (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 t = 0.06+0.015P, where P is the pressure in GPa. The uniaxial stress in molybdenum can be described by t = 0.46+0.13P. Using gold as an internal pressure standard, the equation of state of molybdenum depends strongly on ψ. The bulk modulus obtained from a Birch-Murnaghan fit varies from 210 to 348 GPa as ψ varies from 0° to 90°. However, an equation of state in good agreement with shock and ultrasonic isotherms is obtained for 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 C₄₄ is smaller for the x-ray data than predicted by extrapolation of ultrasonic data.