Determination of the discreteness correction in dislocation equations for sphalerite crystals

Abstract The discreteness correction for simple lattices has been determined, however, there is still no detailed and rigorous derivation of the discreteness correction for compound lattices due to the relatively complex structure (simple lattices have only one set per slip system, while complex lattices have at least two sets). A lattice dynamics model which takes into account the energy increments caused by changes in bond length and bond angle is constructed for sphalerite crystals and the relationships between discreteness parameters and elastic constants are determined for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>110</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mfenced close="}" open="{" separators=""> <mml:mrow> <mml:mn>111</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> slip system. Compared to glide set, the discreteness correction for shuffle set is much larger due to it is mainly contributed by the interactions between nearest neighbor atoms. Based on the results obtained from the model, the dislocations in ZnS crystal are investigated. The theoretical prediction result of Peierls stress for shuffle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>60</mml:mn> <mml:mi mathvariant="normal">°</mml:mi> </mml:math> dislocation closely matches the experimental critical shear stress. It is inferred that the initial plastic deformation of ZnS is closely related to the movement of shuffle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>60</mml:mn> <mml:mi mathvariant="normal">°</mml:mi> </mml:math> dislocations.