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The Shear Modulus of Vit 1 in the Supercooled Liquid and Glassy State Alijeet S. Bains, Craig A. Gordon, Andrew V. Granato, Alexander B. Lebedev,1 Marissa A. LaMadrid,2 and William L. Johnson3 Physics Department, University of Illinois, Urbana, IL, U.S.A. 1 Ioffe Physico-Technical Institute, St. Petersburg, Russia. 2 Department of Molecular Biology, University of Washington, Seattle, WA, U.S.A. 3 Department of Materials Science and Engineering, California Institute of Technology, Pasadena, CA, U.S.A. ABSTRACT Using a non-contact electromagnetic-acoustic transformation (EMAT) technique, we have measured the temperature dependence of the infinite frequency shear modulus of Vit 1 at constant heating rate in the glassy and supercooled liquid states. Values of the shear softening fragility parameter –dln(G/Gg)/d(T/Tg) are compared with those obtainable from specific heat and viscosity measurements, using the interstitialcy theory of condensed matter states. There is overall agreement found between these independently measured values. INTRODUCTION The interstitialcy theory by Granato [1] has recently been applied to bot h thermodynamic and kinetic properties of bulk amorphous alloys [2]. We have made measurements of the shear modulus of the five component bulk amorphous alloy Vit 1 (Zr41.25Ti13.75Cu12.5Ni10.0Be22.5) from room temperature up to 660 K, using an EMAT technique, the results of which can be interpreted using the interstitialcy theory. The theory provides a unified framework for the treatment of crystals, liquids, and glasses. Namely, liquids and glasses are considered as crystals with a few percent of interstitialcy defects. After deriving an interstitial concentration dependent Gibbs free energy function, the shear modulus softening as a function of concentration c is derived to be G = G0 e − βc

(1)

where β = -dlnG/dc is the shear susceptibility, or diaelastic constant, and is typically about 20 to 30. In the liquid state, c increases approximately linearly with temperature and near the glass temperature Tg, G is then given by G = Gg e

γ (1−T / Tg )

(2)

where γ, called the shear softening parameter, is

γ = βTg (∂c / ∂T ) T = −(Tg / G )(∂G / ∂T ) T g

L11.5.1

g

(3)

and Gg is the shear modulus at the glass temperature. As the temperature is lowered below the glass temperature, the interstitial concentration becomes “frozen”, and the shear modulus takes on the same temperature dependence as in the crystalline state. The parameter γ plays a key role in tying together several of the predictions of the interstialcy theory on the properties of glasses. The jump in specific heat between the crystalline and glassy state is attributed to the work required to create the additional interstitials in the glass, and from this Granato derives the expression [2]

δCVg = E F (T )dc / dT = (αG g Ω)(γ / βTg )

(4)

where EF is the formation energy, Ω is the atomic volume, and α is a constant ∼ 1. The value of γ can also be related to the kinetic properties of the glass. The model of Dyre et. al. [3] relates the viscosi