Interpretation of viscous deformation of bulk metallic glasses based on the Nabarro–Herring creep model

Superplastic-like viscous deformation of bulk metallic glass (BMG) alloy around glass transition temperature (Tg) was analyzed based on the Nabarro–Herring creep model, where the diffusional motion of atoms or vacancies through the lattice (atomic configuration) is considered. Two Zr-based and one Fe-based BMG alloys were employed in this analysis. The amorphous matrix of BMG alloys that has a randomly packed atomic configuration was assumed to behave in a manner similar to the grain boundary in polycrystalline metals so as to approximate the diffusivity of major constituent elements. The atomic volumes in the Nabarro–Herring creep equation were calculated using the covalent radius instead of the van der Waals radius of major constituent elements (Zr and Fe, respectively). Metal flow data of the BMG alloys in the supercooled-liquid state were obtained from a series of isothermal compression tests as well as literature to calculate the average diffusion path. In spite of rough approximation of the parameters in the Nabarro–Herring creep equation, a reasonable value of the diffusion path could be obtained from the metal flow data. Due to the absence of vacancy sources like grain boundaries in homogeneous metallic glasses, the calculated diffusion path was considered in this work as the average distance between tunneling centers or shear bands occurring in BMG alloys. The calculated diffusion path was comparable to the density of tunneling centers around Tg, which was suggested by M.H. Cohen and G.S. Grest based on free volume theory in 1984. Moreover, the calculated diffusion path was also comparable to the shear band spacing, which was experimentally measured by W.L. Johnson et al., in 2004. Based on these analyses, a schematic model for viscous deformation of bulk metallic glasses was proposed.