Viscous relaxation in metallic glasses

Recent theories of icosahedral ordering in supercooled liquids are used to define a model dynamics to describe the relaxation of momentum fluctuations in these systems. Glassy behavior of the system at microscopic distances is enforced by introducing a phenomenological relaxation parameter ${\Gamma }^B$ which is anomalously small and strongly dependent upon temperature. Macroscopic consequences of this microscopic slowing down are examined. It is found that there is an upper bound on the magnitude of the translational correlation length, below which microscopic sluggishness is ineffective in producing a large macroscopic viscosity. If the correlation length is larger than this upper bound, then the macroscopic viscosity acquires a strong temperature dependence increasing like 1/${\Gamma }^B$ as the temperature falls. Binary metallic glasses have a correlation length which is just above this bound.