The Concept of Strain Tensor at Atomic Level

An atomic strain concept is formulated that allows calculation of continuum quantities directly within a discrete atomic (molecular) system. The concept is based on the Voronoi tessellation of the molecular system and calculation of atomic site strains, which connects continuum variables and atomic quantities when the later are averaged over a sufficiently large volume treated as a point of the continuum body. The atomic strain tensor is applied to investigate deformation of regular and disordered molecular systems. It is shown that disordered systems exhibit significant non-affine deformations which can be captured by a proper correction of the strain tensor.