Theoretical foundations of resonant ultrasound spectroscopy at high pressure

The theory of free-vibration acoustic resonance (FVAR) of solids at high pressure is developed within the framework of nonlinear elasticity and the calculus of variations. The FVAR state is formulated as a generalization of the conventional theory that was originally developed by Rayleigh and Ritz in the sense that it includes geometrical and material nonlinearities as well as the potential energy of external pressure. Magnetic point groups and quasi-harmonic approximation are used so as to obtain a natural extension of normal mode phonons in the high-pressure regime. The numerical analysis of eight different cubic-symmetry crystals reveals that FVAR frequencies depend linearly on the pressure, and the slopes vary with the FVAR modes, including the sign. We estimated the mode Grüneisen parameter up toN =2400 and proved that the high-frequency limitγ ∞ is equivalent to the conventional Grüneisen parameterγ . Quantitative agreement of the parameters demonstrates that nearly the entire third-order elastic constants tensor can be determined from high-pressure ultrasound spectroscopy experiments.