A computer code was developed for the dislocation-density evaluation of a single-crystal ingot during annealing. In this code, the temperatures in a single-crystal ingot were used as input data and were obtained from a transient heat-conduction analysis of an ingot. A dislocation kinetics model (Haasen–Sumino) was used as the constitutive equation. In this model, the creep strain-rate was related to the dislocation density, and this model was extended to a multi-axial stress state based upon the theory of crystal plasticity. A 3-dimensional finite-element model was used to take account of crystal anisotropy in the elastic constants and specific slip directions. Dislocation density analyses were performed, using this code, for an ingot of 10cm-diameter, and time variations in the dislocation density and resolved shear stress and the residual stress after ingot annealing were obtained.

Development of Three-Dimensional Dislocation Density Analysis Code for Annealing Process of Single Crystal Ingot. N.Miyazaki, H.Kutsukake, A.Kumamoto: Journal of Crystal Growth, 2002, 243[1], 47-54