Optimizing the experimental design of texture goniometry

Pole figure measurements with an X-ray texture goniometer equipped with a point detector are rather time consuming: depending on the angular resolution to be recorded, of the order of several hours per pole figure. Conventionally, the pole hemisphere is scanned along latitudinal small circles according to a regular grid of constant step sizes in both the azimuthal and the polar angle. In the case of sharp textures an adaptive successive local refinement strategy of the pole hemisphere may offer a better performance in less time. Then the measurement positions of the grid are highly irregularly distributed over the pole hemisphere. To avoid erratic movements when turning the specimen, the scanning order is optimized by means of resolving a travelling salesman problem such that the total travelling time is minimized. Several algorithms are described resolving the travelling salesman problem with respect to the irregular grid to be applied for each pole figure and for each step of successive refinement. A practical application to pole figure measurements exposes total savings of about 1/8 compared to the conventional scanning order. Successive local refinement of the experimental design and optimization of the order of its measurement positions are well suited to the purpose of controlling a texture goniometer.