Unusual pressure effect on the shear modulus in MgAl₂O ₄ spinel

Compressional (V_P) and shear (V_S) wave velocities of polycrystalline MgAl₂O₄ spinel have been measured up to 14 GPa and 900 K using ultrasonic interferometry and in situ X-ray diffraction techniques. Here, we observed a weaker pressure dependence in shear modulus (G) for MgAl₂O₄ spinel, as compared to a stronger ∂G/∂P for magnesium silicate/germanate counterpart. Our first-principles calculations show that the tetragonal shear modulus C _S = (C₁₁-C₁₂)/2 decrease with pressures, indicating acoustic mode softening, which further supports our observed experimental results. Using a finite strain equation of state approach the elastic bulk and shear moduli, as well as their pressure and temperature derivatives, are derived from the directly measured velocities and densities, yielding K_S0 =196.0(9) GPa, G₀ = 109.0(4) GPa, ∂K_S/∂P = 4.60(9), and ∂G/∂P = 0.58(3) independent of pressure calibration. The temperature derivatives for the bulk and shear moduli were tightly constrained from acoustic velocity measurements as ∂K_S/∂T = -0.022(3) GPa/K and ∂G/∂T = -0.014(1) GPa/K. In addition, the mechanism for the unusual pressure effect on the shear modulus in MgAl₂O₄ spinel has been addressed by the coupling between atomic displacements and shear strains, namely a better accommodation of the AlO₆ octahedral distortion and shear strains, as well as the pressure-induced tilting/distortion and/or symmetry changes in MgAl₂O₄ spinel.