Elastic and non-linear acoustic properties and thermal expansion of cerium metaphosphate glasses

Abstract

To test predictions of the soft potential model (SPM) for the thermal and acoustic properties of glasses, the thermal expansion and the ultrasonic wave velocity and attenuation have been measured in cerium metaphosphate glasses with compositions in the vicinity of (Ce 2O 3) 0.25(P 2O 5) 0.75. The ultrasonic wave velocities have been determined as functions of temperature and hydrostatic pressure; the results provide the temperature dependences of the adiabatic elastic stiffnesses C 11 and C 44 and related elastic properties, and the hydrostatic-pressure derivatives (∂ C 11/∂ P) P=0 and (∂ C 44/∂ P) P=0 of the elastic stiffnesses and (∂ B S/∂ P) P=0 of the bulk modulus. The longitudinal ultrasonic wave velocities increase under pressure. The hydrostatic pressure derivative (∂ B S/∂ P) P=0 of the bulk modulus B S is positive: when compressed, the cerium metaphosphate glasses show a normal volume elastic response. However, the pressure derivative (∂ C 44/∂ P) P=0 of the shear modulus is negative but small, indicating weak softening of shear modes under pressure. The shear wave ultrasonic attenuation is characterised by a broad peak; the calculated relaxation parameters are consistent with phonon-assisted relaxation of two-level systems. The results found for C IJ and (∂ C IJ /∂ P) P=0 are used to determine the long-wavelength acoustic-mode Grüneisen parameters, which quantify the vibrational anharmonicity and are needed to obtain the acoustic mode contribution to thermal expansion. The temperature dependence of the shear wave ultrasound velocity, after subtraction of the relaxation and anharmonic contributions, follows a linear law as predicted by the SPM for relaxation of soft harmonic oscillators. At low temperatures the excess low-energy vibrational states provide a negative contribution to thermal expansion, which can be understood on the basis of the SPM.