On The Atomistic Displacement Of Shear Relaxation In Solids

Typically, the word relaxation is used to describe a time-relevant behavior of solids. However, this thesis focuses on the relaxation in space due to the extra atomistic displacement upon loading. The loading, generally of the shearing type,causes the reduction of nominal elastic moduli.The Cauchy-Born rule, stating that the deformation gradient at the micro- and macro-scale are the same, is applied very often in the study of deformations. The rule,however, is not applicable for cases where there is more than one atom in the primitive cell. This work aims to study the atomistic relaxation displacement of solids under shear loadings. According to the principle of energy minimization, the atoms will go for new equilibrium positions while loaded, lowering the system potential.This leads to reduction of shear stresses while keeping the relevant macro shear strains, resulting smaller shear moduli. Since relaxation corresponds to real experiments, care must be taken on relaxation in atomistic simulations.In this thesis, the relation of elastic relaxation moduli to two factors, the force constant matrix and the derivative of virial stress to atom position, is discussed first in theory. The theory is universal since the two quantities are intrinsic to crystals. Using silicon as an example, the details of relaxation displacement are studied with atomistic simulations. It is found that the direction of relaxation displacement is perpendicular to the shearing plane in a alternating distribution style. The theory and methodologies can be extended to other types of materials.