Elastic and nonlinear acoustic properties and thermal expansion of rare-earth metaphosphate glasses

Abstract

The thermal expansions and the ultrasonic wave velocities and attenuations of (Sm₂O₃)_0.234(P₂O₅)0.776 and (La₂O₃)_0.222 (P₂O₅)_0.778 and mixed (La₂O₃)_x (Sm₂O₃)_y(P₂O₅)_0.75 (where x + y = 0.25) metaphosphate glasses have been measured as functions of temperature. The change in the ultrasonic wave velocity induced by application of hydrostatic pressure up to 0.16 GPa has also been measured at selected temperatures between room temperature and 375 K. The experimental results provide the temperature dependences of the adiabatic elastic stiffnesses C₁₁ and C₄₄ and related elastic properties and provide 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 results obtained for C _IJ and (∂C _IJ/∂P)_P=0 are used to determine the long-wavelength acoustic-mode Grüneisen parameters; these quantify the vibrational anharmonicity, which is essential information for developing the acoustic mode contribution to the thermal expansion of the glasses. Hence the ultrasonic velocity measurements in metaphosphate glasses modified with Sm³⁺ and La³⁺ ions enable separation of these acoustic-mode contributions from those due to the excess modes. Using the soft-potential model, it has been shown that, at low temperatures, the excess low-energy vibrational states provide negative contributions to the thermal expansion and to the nonlinear acoustic properties. For the mixed metaphosphate glasses of the type (La₂O₃)_x(Sm₂O₃)_y(P₂O₅)_0.75, the acoustic-mode softening induced by Sin³⁺ is negated by the addition of La³⁺; as a result the acoustic-mode Grüneisen parameters and the thermal expansion are extremely small.