β Scribed by Gunther Schoeck
No coin nor oath required. For personal study only.
Dislocations aligned along closeβpacked directions in a crystal lattice experience when moving periodic variations of their energy with the period of the lattice cell. This can be described in the framework of the Peierls model when the generalized stackingβfault energy in the glide plane β the Ξ³βsurface β has been derived. The maximum energy variation is called the Peierls energy E~P~. As consequence of these energy variations there exists also a finite stress β the Peierls stress Ο~P~ β necessary to displace a straight dislocations over the distance of a lattice cell without the aid of thermal fluctuations. It is commonly assumed that these energy variations result from changes in the atomic misfit energy E~A~ in the glide plane and as consequence Ο~P~ is defined by the maximum gradient of E~A~. This assumption is inconsistent, however. When the dislocation moves in isothermal thermodynamic equilibrium the width w of the dislocation changes during displacement. An increase in misfit energy E~A~ by an increase in width w is overcompensated by a corresponding decrease in elastic energy E~el~. As result the variation in total energy β the Peierls energy β will be smaller as compared to the situation where no structural relaxation occurs during the movement.
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