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 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.
Highlights
Unifying interatomic potential, g (r), elasticity, viscosity, and fragility of metallic glasses1.1
A scaling relation between atomic connectivity and packing fraction Z ∼ φ1+λ is derived. This relation is implemented in a lattice-dynamical model for the high-frequency shear modulus where the attractive anharmonic part of the e ective interaction is taken into account through the thermal expansion coe cient which maps the φ-dependence
The steepness of the viscosity rise upon approaching the glass transition, is controlled by two averaged interaction parameters: the λ interatomic-repulsion parameter introduced in [8], and the thermal expansion coe cient αT
Summary
One of the most puzzling properties of glasses is the huge increase of viscosity, by many orders of magnitude, within a narrow range of temperature T upon approaching the glass transition temperature Tg. Among the most popular pictures proposed to link the phenomenology of the Angell plot for the viscosity η versus T near Tg, is the one which associates fragile glass formers (with the steepest dependence of η on T ) to an underlying steep interparticle repulsion at contact, whereas strong glasses (with Arrhenius dependence of η on T ) are associated with softer interparticle repulsion This picture, which is largely based on the two-point correlation dynamics and local structure, and on the Weeks–Chandler–Anderson [6] idea that the repulsive part of two-body interaction is what controls the overall structure of liquids, has been demonstrated convincingly for the case of soft colloidal glasses by the Weitz group [7]. Both these global interaction parameters, λ and αT, are sensitive functions of the elemental composition and stoichiometry of the alloy, and may account for microalloying e ects as well [9]
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More From: Journal of Statistical Mechanics: Theory and Experiment
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