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 ^init. 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 ^init vary as N ^-1/2 but were independent of r ^init. Using the texture of slightly textured Al₂O₃ as determined by X-ray diffraction, we calculated the 90% confidence limits for measurements of 131 grains. The orientations of 131 grains in textured Al₂O₃ were measured by electron backscatter diffraction, and the texture determined from those measurements lay within these 90% confidence limits.