Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classicalPeierls--Nabarro (P-N) theory of dislocation,there is a long-standing contradiction that the stable configurationof dislocation has maximum energy rather than minimum energy. Inthis paper, the dislocation energy is calculated rigorously in thecontext of the full lattice theory. It is found that besides themisfit energy considered in the classical P-N theory, there is anextra elastic strain energy that is also associated with thediscreteness of lattice. The contradiction can be automaticallyremoved provided that the elastic strain energy associated with thediscreteness is taken into account. This elastic strain energy isvery important because its magnitude is larger than the misfitenergy, its sign is opposite to the misfit energy. Since the elasticstrain energy and misfit energy associated with discreteness canceleach other, and the width of dislocation becomes wide in the latticetheory, the Peierls energy, which measures the height of theeffective potential barrier, becomes much smaller than that given inthe classical P-N theory. The results calculated here agree withexperimental data. Furthermore, based on the results obtained, auseful formula of the Peierls stress is proposed to fully includethe discreteness effects.

Dislocation energy and Peierls stress: a rigorous calculation from the lattice theory

In the classicalPeierls--Nabarro (P-N) theory of dislocation,there is a long-standing contradiction that the stable configurationof dislocation has maximum energy rather than minimum energy. Inthis paper, the dislocation energy is calculated rigorously in thecontext of the full lattice theory. It is found that besides themisfit energy considered in the classical P-N theory, there is anextra elastic strain energy that is also associated with thediscreteness of lattice. The contradiction can be automaticallyremoved provided that the elastic strain energy associated with thediscreteness is taken into account. This elastic strain energy isvery important because its magnitude is larger than the misfitenergy, its sign is opposite to the misfit energy. Since the elasticstrain energy and misfit energy associated with discreteness canceleach other, and the width of dislocation becomes wide in the latticetheory, the Peierls energy, which measures the height of theeffective potential barrier, becomes much smaller than that given inthe classical P-N theory. The results calculated here agree withexperimental data. Furthermore, based on the results obtained, auseful formula of the Peierls stress is proposed to fully includethe discreteness effects.