A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies

Strain-gradient elasticity is widely used as a suitable alternative to size-independent classical continuum elasticity to, at least partially, capture elastic size effects at the nanoscale. In this work, borrowing methods from statistical mechanics, we present mathematical derivations that relate the strain-gradient material constants to atomic displacement correlations in a molecular dynamics computational ensemble. Using the developed relations and numerical atomistic calculations, the strain-gradient constants are explicitly determined for some representative semiconductor, metallic, amorphous and polymeric materials. This method has the distinct advantage that amorphous materials can be tackled in a straightforward manner. For crystalline materials we also employ and compare results from both empirical and ab initio based lattice dynamics. Apart from carrying out a systematic tabulation of the relevant material parameters for various materials, we also discuss certain subtleties of strain-gradient elasticity, including: the paradox associated with the sign of the strain-gradient constants, physical reasons for low or high characteristic length scales associated with the strain-gradient constants, and finally the relevance (or the lack thereof) of strain-gradient elasticity for nanotechnologies.