Calculation of the average coefficient of thermal expansion in oriented cordierite polycrystals

In this work, the calculation of the average value of a physical quantity in a textured polycrystal is presented. The method is applied to the coefficient of thermal expansion in cordierite samples, presenting domain and crystal preferred orientation, and compared with experimental data. The knowledge of the experimental or simulated texture intensity function is required to calculate the orientation distribution function. Then, a sum over all oriented crystals, weighted by their population, is carried out. It is shown that this sum must be carried out differently, if different components of the physical quantity (usually a tensor) must be calculated. Results show a very good agreement between the model and the experimental data obtained (a) by neutron diffraction as a polycrystalline average and (b) by dilatometry on real cordierite materials used as diesel particulate filters. Although the method is resting on the possibility of having a simple analytical form of the texture intensity, its numerical implementation does not present any problem.