Abstract
We combine the shoving model of $T$-dependent viscosity of supercooled liquids with the Zwanzig-Mountain formula for the high-frequency shear modulus, using the $g(r)$ of MD simulations of metal alloys as the input. This scheme leads to a semi-analytical expression for the viscosity as a function of temperature, which provides a three-parameter model fitting of experimental data of viscosity for the same alloy for which $g(r)$ was calculated. The model provides direct access to the influence of atomic-scale physical quantities such as the interatomic potential $\phi(r)$, on the viscosity and fragile-strong behavior. In particular, it is established that a steeper interatomic repulsion leads to fragile liquids, or, conversely, that "soft atoms make strong liquids".
Highlights
Different views of the glass transition have led to quite different descriptions of the viscosity of supercooled liquids
Upon denoting the kBT normalized integral in the Zwanzig-Mountain formula Eq (2) as I, we arrive at the following expression for the viscosity: η η0
We start from the level of the radial distribution function (RDF) g(r) and vary the repulsion steepness parameter l around the value (l = 20) that we found in the fitting of molecular dynamics (MD) simulation data [Fig. 1(b)]
Summary
Different views of the glass transition have led to quite different descriptions of the viscosity of supercooled liquids. Upon approximating the shear modulus G∞ with Born-Huang (affine) lattice dynamics (as appropriate for the high-frequency modulus), G∞ can be directly related to the short-range part of the radial distribution function (RDF) g(r) and to the interatomic potential This led to the Krausser-Samwer-Zaccone (KSZ) equation [10], which expresses the T -dependent viscosity in closedform in terms of the thermal expansion coefficient αT , the interatomic repulsion steepness parameter λ (obtained from a power-law fitting of the RDF up to the maximum of the first peak), and the activation volume Vc mentioned above. We develop a different, perhaps more sophisticated approach which combines the shoving model with the microscopic Zwanzig-Mountain formula for the G∞ of liquids This leads to semianalytical expressions for η(T ) and for m, which directly link these quantities to the g(r) and to the interatomic potential φ(r). It confirms the qualitative increasing trend of fragility m increasing with potential repulsion steepness l or λ and recovers the linear trend already seen for m(λ) in Ref. [10]
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