Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition

Abstract

A method of describing the thermal fluctuations in the local atomic structure of liquid and amorphous metals in terms of the fluctuations in the atomic level stresses is proposed. The energy of the system is expressed in terms of these stresses in the elastic approximation. The temperature dependence of the second moments of the stresses is then calculated and shown to be linear with temperature. The glass transition is assumed to take place when the second moments freeze to certain values determined by computer simulation. It is shown that the pressure fluctuations and the shear fluctuations freeze at different temperatures. The glass transition, in the normal sense, is described by the freezing of the pressure fluctuation. This method provides a reasonable estimate of the glass transition temperature, and predicts it to be proportional to the product of atomic volume and bulk modulus. It furthermore provides an explanation of the different relaxation behaviours between the pressure and shear fluctuations.