Probability distribution functions as descriptors for long range randomness in non-crystalline solids

Probability distribution functions (PDF) can be useful descriptors for the random structure of non-crystalline solids. The lognormal PDF has provided a good description of the distribution of interstitial site sizes in non-crystalline solids, both metallic and nonmetallic. The utility of this descriptor to characterize the ring statistics of vitreous silica under a wide range of pressures has been evaluated. In fact, the normal (Gaussian) PDF is a better descriptor for ring statistics for pressures up to 23 GPa. Although the average ring size is largely unchanged (slightly less than 6.0) over the entire pressure range, the standard deviation of the ring size distribution rises sharply at 9 GPa serving as a sensitive indicator of the onset of plastic deformation.