Fir-tree patterns elastic distortions and application to X-ray topography

Abstract

Observations by means of the Bitter colloid and the Lang techniques of fir-tree patterns (closure domains attached to 180° walls) are described. Three types of closure domains may be distinguished according to their elastic behaviour in the vicinity of the 180° wall: half-chevrons (one branch), asymmetrical chevrons (two branches of unequal lengths), symmetrical chevrons (two branches of equal lengths). However, the contrast observed on Lang topographs along the intersections of the branches with the surface is identical for all types.

Branches are limited inside the sample by a curved coherent but strained boundary. The decomposition of this boundary into plane wall segments shows that the elastic stresses due to it may be described as the sum of the stresses due to a succession of twist quasi-disclinations (rotation dislocations with Frank vector perpendicular to the line). Surface relaxation is taken into account. Qualitative conclusions, in fair agreement with the experiment, concerning the contrast, on X-ray topographs, of branch boundaries are deduced from this decomposition.