Determination of texture from individual grain orientation measurements

We present a technique for determining the texture of a polycrystalline mat erial 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 orien tation data sets, using the March-Dollase function for a total of five diff erent texture parameters, r(init). Using the maximum-likelihood method, we solved for the texture parameter, r', that best fits each simulated data se t in order to determine the distribution of r' and evaluate the precision a nd accuracy with which r' can be determined, The 90% confidence limits of t he ratio r'/r(init) vary as N-1/2 but were independent of r(init). Using th e texture of slightly textured Al2O3 as determined by X-ray diffraction, we calculated the 90% confidence limits for measurements of 131 grains. The o rientations of 131 grains in textured Al2O3 were measured by electron backs catter diffraction, and the texture determined from those measurements lay within these 90% confidence limits.