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A Relation Between Fragility, Specific Heat, and Shear Modulus Temperature Dependence for Simple Supercooled Liquids

Published online by Cambridge University Press:  10 February 2011

A. V. Granato
A. V. Granato*
Affiliation:
University of Illinois, Dept. of Physics, Urbana, IL 61801, [email protected]
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Abstract

It is often said that the fragility and specific heat discontinuity at the glass transition are related characteristic features of glasses. We give a relation between these quantities for simple liquids, and also find that the temperature dependence of the shear modulus should be closely related to these quantities. According to the Interstitialcy Theory, the liquid state shear modulus G = Go, exp (-βc) = Go exp {-γ[(T/To)-l ]}, where Gois the shear modulus at a reference temperature To, which can be taken to be the glass temperature. In these relations, βis the diaelastic shear susceptibility, c is the interstitialcy concentration, T is the temperature, and dc/dT = γ/βTo. It has been proposed by Dyre, Olsen and Christensen that U in the viscosity η = ηo exp (U/kT) be given as the work done in shoving aside particles during a diffusion step, and therefore be proportional to the (liquid state) shear modulus. If so, then combining the above relations, the fragility F = [d log η/d (Tg/T]T=Tg becomes F=(1+γ) log [η (Tg)/ηo], where γ = - (Tg/G)(dG/dT). Then, since δCv, = UF(dc/dT), where UF is the interstitialcy formation energy, one obtains further with reasonable simplifying approximations δCv/Cv∼γG(T)/Goo, where Goo is the zero temperature crystalline shear modulus. For a typical fragile glass γ ∼ 2 (F ∼ 50) with G(Tg)/Goo ∼ 1/2, then δCv/Cv, ⊼ 1, ut close to zero for strong glasses, in fair agreement with available experimental results. The perspective given by the Interstititialcy Theory is then that the fragility is given phenomenologically by the temperature dependence of the shear modulus, or microscopically by the rate of increase of the equilibrium interstitialcy concentration with temperature.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 554: Symposium MM – Bulk Metallic Glasses , 1998 , 299
Copyright
Copyright © Materials Research Society 1999

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