A model of elastically and anelastically produced temperature derivatives of acoustic wave velocities in inorganic oxide glasses

Abstract

The temperature dependence of 15 MHz ultrasonic bulk wave velocity in the range 4 to 600 K has been measured in the entire range of glasses that can be prepared by mixing MoO3 with P2O5 in open crucibles. In all cases the temperature gradients are negative. However, when the contribution to the velocity variation caused by (anelastic) two-well relaxational effects is subtracted, the residual velocity variation is always positive with respect to temperature. It is suggested that this effect, which has been reported to be present in other glasses but not in crystals, is still caused by two-well systems, but is elastic in nature. It is argued that under certain conditions the expansion of a glass due to increases in temperature softens the vibrations of particles in transverse two-well systems. In the simple case of wave propagation along a chain this leads to a positive temperature gradient of the shear modulus, and in an isotropic system positive gradients will similarly be caused in all elastic moduli. A detailed model is presented to justify the proposal quantitatively by identifying the conditions under which such behaviour could take place. One cause would be the presence of an appreciable number of two-well systems of barrier height ≪kT at room temperature. For the MoO3-P2O5 system it is estimated that 25% of cation-cation spacings contracted by between 0 to 1 % from equilibrium (crystalline) values, to produce barrier heights ⩽ 0.005 eV, would explain the observations. On the other hand an appreciable fourth-power term in the transverse force potentials (i.e. high third-order bending force constants) would cause a similar effect even if a much smaller number of barriers were present, but of height > kT indeed, such a mode softening term has exactly the opposite effect on the temperature gradients of velocity to what it has in single-well systems.