Statistics of Jogs on Dislocations at Equilibrium

A statistical treatment is presented for the distribution of jogs on dislocations at complete thermodynamic equilibrium. General expressions for the density and average height of jogs are derived. Specific formulas for the jog density and average jog height are obtained for two separate models of the jog energy. It is found that the jog density is not given by a simple Boltzmann formula as has often been assumed. It is also found that the assumption by others that the average jog height is one atom distance, while not strictly valid, is very nearly true for reasonable values of the jog energy. The distribution of jog spacings is found and is identified with the distribution known in statistics as the geometric distribution. Some implications of these results are discussed.