Unified Criterion for Temperature-Induced and Strain-Driven Glass Transitions in Metallic Glass

In a model metallic glass, we study the relaxation dynamics in both the linear and the nonlinear response regimes by numerical simulations of dynamical mechanical spectroscopy and analyze the atomic displacement statistics. We find that the primary ($\alpha$) relaxation always takes place when the most probable atomic displacement reaches a critical fraction ($\sim 20\%$) of the average interatomic distance, irrespective of whether the relaxation is induced by temperature (linear response) or by mechanical strain (nonlinear response). Such a unified scenario, analogous to the well-known Lindemann criterion for crystal melting, provides insight into the structural origin of the strain-induced glass-liquid transition.

Figure 1

Radial distribution function $g(r)$ of ${\mathrm{Ni}}_{80}{\mathrm{P}}_{20}$ MG at $T=300\mathrm{K}$. Inset: atomic volume $V_a$ as a function of temperature during the quenching process.

Figure 2

MD-DMS and structural analysis in linear response regime. (a) Loss ($E^{\prime \prime }$) modulus as a function of temperature ($T$) at a strain amplitude ${\epsilon }_A=1.25\%$. (b) Typical curves of the probability density function $p(u)$ for atomic displacement $u$ at temperatures as indicated. (c) The peak position $u_p$ as a function of temperature. (d) A 2D slice of the atomic configuration at $T=500\mathrm{K}$, $t_{\omega }=1000\text{ps}$, with color code on each atom representing the value of $u/r_p$, and the box size is about 7 nm in each dimension.

Figure 3

MD-DMS and structural analysis in nonlinear response regime. (a) Loss ($E^{\prime \prime }$) modulus and $u_p/r_p$ as a function of strain amplitude at a period $t_{\omega }=1000\text{ps}$ and $T=400\mathrm{K}$. The vertical and horizontal dashed lines indicates the peak position of $E^{\prime \prime }$, and the Lindemann criterion with $u_p/r_p=20\%$, respectively. (b) Strain amplitude effects on the temperature of $\alpha$ relaxation $T_{\alpha }$ at ${\tau }_{\alpha }=t_{\omega }=1000\text{ps}$. The dashed line is drawn as a guide to the eyes.