The double sum runs over all positions of defect pairs k and l , Δ Δ r → → k , l = r → → k − − r → → l measures the distance between the dislocations. b → → is the Burgers vector and denotes the orientation of the dislocation at position Orte r → → k . The second term in the brackets brings dislocations to arrange preferentially antiparallel due to energetic reasons. Its contribution is small and can be neglected for large distance between defects. The main contribution stems from the logarithmic term (the first one in the brackets) which describes, how the energy of a dislocation pair diverges with increasing distance. Since the shortest distance between two dislocations is given approximatively by the average particle distance a , the scaling of distances with a prevents the logarithm ln ⁡ ⁡ Δ Δ r → → k , l a to become negative. The strength of the interaction is proportional to Young's modulus Y given by the stiffness of the crystal lattice. To create a dislocation from an undisturbed lattice, a small displacement on a scale smaller than the average particle distance a is needed. The discrete energy associated with this displacement is usually called core energy Energie E c and has to be counted for each of the N l o c dislocations individually (last term).