Statistical Mechanics of Metallic Glasses and Liquids

It is difficult to formulate the statistical mechanical theory of liquids and glasses, because phonons, which are the basis for the statistical mechanics of lattice dynamics in crystals, are strongly scattered and have a very short lifetime in liquids and glasses. Instead computer simulation and the free-volume theory are most frequently used in explaining experimental results on metallic glasses. However, both of them suffer from serious problems, as discussed in this article. We propose an alternative approach based upon the dynamics of the atomic level stresses. We review recent progress with this approach and show that it is possible to calculate thermodynamic quantities, including the glass transition temperature and the kinetics of structural relaxation, by this approach.