Crystal Research and Technology
Cryst. Res. Technol. 42, 300 (2007) - Abstract -

Three-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetry

K. Böttcher and K. A. Cliffe*

Institute for Crystal Growth (in the Forschungsverbund Berlin e.V.), Max-Born-Str. 2, 12489 Berlin, Germany
*School of Mathematical Sciences, Nottingham University, University Park, Nottingham NG7 2RD, United Kingdom

Keywords thermoelastic stresses, hexagonal crystal symmetry, off-axis orientation, Fourier Finite Element Method
PACS 02.60.Cb, 02.70.Dh, 46.25.Hf
DOI 10.1002/crat.200610817

A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle #phi of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal.




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