Characterization of free volume in atomic models of metallic glasses

An analysis of interatomic space is presented for atomic models of amorphous ${\mathrm{Pd}}_{52}$ ${\mathrm{Ni}}_{32}$ ${\mathrm{P}}_{16}$ in the as-quenched state and in an annealed state. Interstitial voids are constructed as clusters of overlapping spheres that are placed in Delauney tetrahedra. It is found that the difference between as-quenched and annealed ${\mathrm{Pd}}_{52}$ ${\mathrm{Ni}}_{32}$ ${\mathrm{P}}_{16}$ predominantly lies in the quantity of the relatively large voids. More specifically, the number of voids surrounded by nine or less atoms (‘‘intrinsic voids’’) increases, whereas the number of voids surrounded by ten or more atoms (‘‘holes’’) strongly decreases. The interpretation is that during structural relaxation the holes break up into two or more intrinsic voids. Since in the annealed state the diffusivity is a factor 25 smaller than in the as-quenched state, the diffusion process is explained in terms of the occurrence of holes. The analysis of the volumes and shapes of the holes shows that (1) the volume distribution becomes narrower on structural relaxation, and (2) although holes with a volume of one atomic volume or more do occur, their shape is strongly nonspherical, and they certainly do not resemble crystalline vacancies. It is furthermore argued that, because of the importance of holes for the atomic mobility, the hole volume is to be regarded as the free volume appearing in the well-known free-volume model by Turnbull and Cohen.