Isoconfigurational Elastic Constants and Liquid Fragility of a Bulk Metallic Glass Forming Alloy

Samples of ${\mathrm{Zr}}_{46.25}{\mathrm{Ti}}_{8.25}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ were isothermally annealed and quenched near the glass transition temperature and studied by the pulse-echo overlap technique. The shear modulus $G$ of the samples shows a strong reversible dependence on annealing temperatures and, thus, on the specific configurational potential energy of the equilibrium liquid. The low-$T$ dependence of $G$ of the configurationally frozen glasses shows linear temperature dependence as expected by Debye-Grüneisen theory. The $T$ dependence of $G$ in the liquid state is directly related to the viscosity and fragility of the liquid.

Figure 1

(a) Relaxation of Vit-4 $C_S$ at 567 K. Open triangles represent the sample annealed and quenched from 567 K. The fitting parameters are for Eq. (2). After completion of relaxation at 567 K, the sample was annealed at 652 K and the $C_S$ reverted to the value initially measured at 652 K. (b) Temperature profile for the annealing.

Figure 2

(a),(b) The shear and bulk modulii of Vit-4 as measured in situ from 78 to 298 K and measured from samples quenched from the equilibrium liquid around $T_g$. Open circles represent samples annealed at 567 K, open triangles samples annealed at 665 K. Samples annealed at different temperatures, thus having different configuration states, have the same low-temperature slopes. This demonstrates that the low-temperature dependence of the elastic modulii is independent of configuration state.

Figure 3

Angell plot of the viscosity of Vit-4 as measured by Busch, Bakke, and Johnson [6] (open circles) and calculated from the measured shear modulus following Eq. (5). Above $T_g$, the viscosities match very well.