Change in the vibrational properties of bulk metal glass with time

The velocity of ultrasonic longitudinal and transverse waves in ${\mathrm{Zr}}_{46.75}{\mathrm{Ti}}_{8.25}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ bulk metal glass has been measured at $298\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ after its annealing for different times at $523\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, a temperature $97\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ below its apparent ${T}_{g}$. Elastic constants and vibrational contribution to thermodynamic properties have also been determined. At $298\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the normalized value of the instantaneous bulk and shear moduli, $K$ and $G$, increases with the annealing time, $t$, according to the relation $[1\ensuremath{-}\mathrm{exp}\text{\ensuremath{-}}{(kt)}^{n}]$ with $k=7.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, $n=0.5$. 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 $298\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. 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.

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