Change in the vibrational properties of bulk metal glass with time

The velocity of ultrasonic longitudinal and transverse waves in Zr46.75Ti8.25Cu7.5Ni₁₀Be27.5 bulk metal glass has been measured at 2980.3em0exK after its annealing for different times at 5230.3em0exK, a temperature 970.3em0exK below its apparent Tg. Elastic constants and vibrational contribution to thermodynamic properties have also been determined. At 2980.3em0exK, the normalized value of the instantaneous bulk and shear moduli, K and G, increases with the annealing time, t, according to the relation [1-exp-(kt)ⁿ] with k=7.4×10^-60.3em0exs, $n=0.5$. It is found that $K(t)=a+bG(t)$, where a and b are constants. In terms of a recent model for viscous flow, an extrapolated increase in G with t corresponds to an approximate three-fold increase in viscosity and 5% decrease in the mean-square atomic displacement at 2980.3em0exK. The increase in K and G corresponds to a 2.4% increase in the Debye frequency, and 0.3% and 2.4% decrease, respectively, in the Debye heat capacity and entropy, and 0.86% increase in the Debye energy. The Poisson's ratio decreases with t, i.e., the glass becomes laterally stiffer. The $K(t)=a+bG(t)$ relation is consistent with a relation obtained for Lennard-Jones interactions. In the potential energy landscape paradigm, annealing appears to shift the state point of a glass to a deeper and more-curved minimum.