Acoustic Vibrational Properties and Fractal Bond Connectivity of Praseodymium Doped Glasses

Abstract

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^S _IJ , which have been determined from the velocitydata between 10 and 300 K, show no evidence of phonon mode softening throughout the whole temperature range. The elastic stiffnesses increased monotonically, the usual behaviour associated with the effect of the phonon anharmonicityof atomic vibration. At low temperatures, strong phonon interactions with two-level systems have been observed. The ultrasonic wave attenuation of longitudinal and shear waves is dominated bya broad acoustic loss peak whose height and peak position are frequencydependent. This behaviour is consistent with the presence of thermally 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 a value between 2.32 to 2.55, indicating that their connectivitytends towards having a threedimensional character. The hydrostatic pressure dependencies of longitudinal ultrasonic waves show a slight increase with pressure. As a consequence, the hydrostatic pressure derivatives ( C^S₁₁/ P)P=0 of the elastic stiffness C^S₁₁/ and (B^S/P)P=0 of the bulk modulus B^S of (Pr₂O₃)x(P₂O₅)1-x glasses are positive. The bulk modulus increases with pressure, and thus these glasses stiffen under pressure, which is associated with the normal elastic behaviour. The GrÜneisen parameter approach has been used to quantifythe vibrational anharmonicityof the long-wavelength acoustic phonons in these glasses.