In the classical Peierls–Nabarro theory of dislocation, there was a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. The dislocation energy was here calculated rigorously within the context of the full lattice theory. It was found that besides the misfit energy considered in the classical Peierls–Nabarro theory, there was an extra elastic strain energy that was also associated with the discreteness of lattice. The contradiction could be automatically removed provided that the elastic strain energy associated with the discreteness was taken into account. This elastic strain energy was very important because its magnitude was larger than the misfit energy, its sign was opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other and the width of dislocation became wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, became much smaller than that given in the classical Peierls–Nabarro theory. The results calculated here agreed with experimental data. Furthermore, based upon the results obtained, a useful formula of the Peierls stress was proposed to fully include the discreteness effects.

Dislocation Energy and Peierls Stress - a Rigorous Calculation from the Lattice Theory. S.F.Wang: Chinese Physics, 2006, 15, 1301-9