Spatial correlations between parallel edge dislocations were studied. After setting up a hierarchy of equations for the many-particle density functions, via the Kirkwood superposition approximation, evolution equations were derived for the correlation functions. It was found that the resultant equations, and those governing the evolution of the density fields of total (as well as geometrically necessary) dislocations around a single edge dislocation were formally the same. The second case corresponded to the known phenomenon of Debye screening of an individual dislocation. This equivalence of the correlation functions and screened densities was also confirmed by discrete dislocation dynamics simulation results, which showed the physical correctness of the applied Kirkwood superposition approximation.

Evolution of the Correlation Functions in Two-Dimensional Dislocation Systems. P.D.Ispánovity, I.Groma, G.Györgyi: Physical Review B, 2008, 78[2], 024119