A common theory of line broadening and rocking curves

Abstract

X-ray diffraction peak broadening is discussed in terms of line broadening and rocking-curve broadening in a novel theoretical description. The nonlocal strain tensor is factorized by using the method of polar decomposition instead of the more conventional separation into symmetrical and antisymmetrical components. A number of X-ray line-broadening and rocking-curve experiments on the same single crystals or individual grains in bulk polycrystals prove that plastic deformation produces strained subgrains mutually rotated by rigid-body rotations. The novel theoretical description appropriately accounts for the rigid-body rotation and strain at the same time and provides straightforward separation of the two effects of line and rocking-curve broadening in the radial and normal directions of the diffraction vector. The mathematical results are discussed in terms of experiments of X-ray diffraction, Laue asterism and electron backscatter diffraction. From the experimental results it is shown that the simultaneous evaluation of line and rocking-curve broadening provides qualitative information about the redundant and geometrically necessary character of dislocations, not available if only one or the other is accessible.