Unifying interatomic potential, g (r), elasticity, viscosity, and fragility of metallic glasses: analytical model, simulations, and experiments

Abstract

An analytical framework is proposed to describe the elasticity, viscosity and fragility of metallic glasses in relation to their atomic-level structure and the effective interatomic interaction. The bottom-up approach starts with forming an effective Ashcroft–Born–Mayer interatomic potential based on Boltzmann inversion of the radial distribution function g (r) and on fitting the short-range part of g (r) by means of a simple power-law approximation. The power exponent λ represents a global repulsion steepness parameter. A scaling relation between atomic connectivity and packing fraction Z∼ϕ1+λ is derived. This relation is then implemented in a lattice-dynamical model for the high-frequency shear modulus where the attractive anharmonic part of the effective interaction is taken into account through the thermal expansion coefficient which maps the ϕ-dependence into a T-dependence. The shear modulus as a function of temperature calculated in this way is then used within the cooperative shear model of the glass transition to yield the viscosity of the supercooled melt as a double-exponential function of T across the entire Angell plot. The model, which has only one adjustable parameter (the characteristic atomic volume for high-frequency cage deformation) is tested against new experimental data of ZrCu alloys and provides an excellent one-parameter description of the viscosity down to the glass transition temperature.