III. Dislocation densities in some annealed and cold-worked metals from measurements on the X-ray debye-scherrer spectrum

Abstract Two basic equations are derived for deducing the dislocation density in powdered materials from the particle size and strain breadth measured from the Debye-Schemer spectrum. In the particle size estimate, it is assumed that the material has a block structure similar to that found in microbeam studies and that the dislocations lie along the block surfaces. The number of dislocations along each face, n, is not known. In the strain broadening estimate the x-ray line broadening from a dislocation array is calculated in terms of the broadening due to an isolated dislocation and a strain energy factor F, which allows for the effect of dislocation arrangement. Both methods involve an unknown quantity but by equating the two results it is possible in most cases to get both a narrow bracket for the dislocation density and considerable information on the dislocation arrangement. In annealed metals the values of p range from 2 × 107 cm of dislocation line per cm3 for aluminium to 3 × 108 for tungsten and molybdenum, the majority of dislocations being ‘random’, i.e. the number along each edge is approximately 1. There is some correlation between p and the purity and annealing treatment of the powder. High purity and high annealing temperatures result in smaller dislocation densities. In cold-worked metals the dislocation density is more variable. A precise analysis is possible for aluminium; high purity aluminium filed at room temperature gives p=4·5 to 7·6 × 109 with evidence for recovery, possibly by polygonization. Commercially pure aluminium filed at both room temperature and liquid air give p = 5 × 109 to 2·7 × 1010 and p = 1·5 × 1010 to 3·2 × 1011 respectively. Some dislocation array such as a ‘pile-up’, which causes an increase in the strain energy of dislocations exists in both these samples as with all the other metals examined. Dislocation densities are also given for tungsten, molybdenum, iron and α-brass. In α-brass, the only alloy considered, p is higher than for the pure metals and there is strong evidence that the dislocations are effectively random and that each dislocation is attached to a stacking fault.