Determination of Texture From Individual Grain Orientation Measurements

We present a technique for determining the texture of a polycrystalline material based on the measurement of the orientation of a number of individual grains. We assumed that the sample has fiber (i.e. axisymmetric) texture and that the texture can be characterized by a function (the March-Dollase function) with a single parameter. We simulated a large number, N, of orientation data sets, using the March-Dollase function for a total of five different texture parameters, r. Using the maximum likelihood method we solved for the texture parameter, r′, that best fits each simulated data set in order to determine the distribution of r′ and evaluate the precision and accuracy with which r′ can be determined. The 90% confidence limits of the ratio r′/r varied as N but were independent of r. Using the texture of slightly textured alumina as determined by x-ray diffraction we calculated the 90% confidence limits for measurements of 131 grains. The orientations of 131 grains in textured alumina were measured by electron backscatter diffraction and the texture determined from those measurements lay within these 90% confidence limits.