Correlating the properties of amorphous silicon with its flexibility volume

For metallic glasses, ``flexibility volume'' has recently been introduced as a property-revealing indicator of the structural state the glass is in. This parameter incorporates the atomic volume and the vibrational mean-square displacement, to combine both static structure and dynamics information. Flexibility volume was shown to quantitatively correlate with the properties of metallic glasses [J. Ding et al., Nat. Commun. 7, 13733 (2016)]. However, it remains to be examined if this parameter is useful for other types of glasses with bonding characteristics, atomic packing structures, as well as properties that are distinctly different from metallic glasses. In this paper, we tackle this issue through systematic molecular-dynamics simulations of amorphous silicon $(a$-Si) models produced with different cooling rates, as $a$-Si is a prototypical covalently bonded network glass whose structure and properties cannot be characterized using structural parameters such as free volume used for metallic and polymeric glasses. Specifically, we demonstrate a quantitative prediction of the shear modulus of $a$-Si from the flexibility for atomic motion. This flexibility volume descriptor, when evaluated on the atomic scale, is shown to also correlate well with local packing, as well as with the propensity for thermal relaxations and shear transformations, providing a metric to map out and explain the structural and mechanical heterogeneity in the amorphous material. This case study of a model of covalently bonded network $a$-Si, together with our earlier demonstration for metallic glasses, points to the universality of flexibility volume as an indicator of the structure state to link with properties, applicable across amorphous materials with different chemical bonding and atomic packing structures.