Acoustic vibrational properties and fractal bond connectivity of praseodymium doped glasses

The velocities of longitudinal and shear ultrasonic waves propagated in the (Pr2O3)(x)( P2O5)(1-x) glass system, where x is the mole fraction of Pr2O3 and (1-x) is the mole fraction of P2O5, have been measured as functions of temperature and hydrostatic pressure. The temperature dependencies of the second order elastic stiffness tensor components (SOEC)C-IJ(S), which have been determined from the velocity data between 10 and 300 K, show no eviden ce of phonon mode softening throughout the whole temperature range. The ela stic stiffnesses increased monotonically, the usual behaviour associated wi th the effect of the phonon anharmonicity of atomic vibration. At low tempe ratures, strong phonon interactions with two-level systems have been observ ed. The ultrasonic wave attenuation of longitudinal and shear waves is domi nated by a broad acoustic loss peak whose height and peak position are freq uency dependent. This behaviour is consistent with the presence of thermall y activated structural relaxation of the two-level systems in these glasses . The fractal bond connectivity of these glasses, obtained from the elastic stiffnesses determined from ultrasonic wave velocities, has value between 2.32 to 2.55, indicating that their connectivity tends towards having three -dimensional character. The hydrostatic pressure dependencies of longitudin al ultrasonic waves show slight increase with pressure. As consequence, the hydrostatic pressure derivatives (partial derivativeC(11)(S)/partial deriv ativeP)(P=0) of the elastic stiffness C-11(S) and (partial derivativeB(S)/p artial derivativeP)(P=0) of the bulk modulus B-S of (Pr2O3)(x)(P2O5)(1-x) g lasses are positive. The bulk modulus increases with pressure, and thus the se glasses stiffen under pressure, which is associated with the normal elas tic behaviour. The Gruneisen parameter approach has been used to quantify t he vibrational anharmonicity of the long-wavelength acoustic phonons in the se glasses.