On the sampling of three-dimensional polycrystalline microstructures for distribution determination

How to sample three-dimensional microstructure and effectively reduce experimental error is a challenging problem. Taking seven single-phase polycrystalline structures generated by 400x400x400 Potts Monte Carlo simulation as the study object, effects of sampling strategy on the determination of various characteristic parameters of the grain size distribution and grain topology distribution are studied. The mean voxel value ( or volume) of individual grains in the three-dimensional simulated microstructure varies from 4.56x10(4) to 1.0x10(3), and the number of grains contained in the structure varies from 63 901 to 1403. The results show that, a minimum of 200 sampled grains can ensure the relative error to be less than 5% for determination of the mean grain volume, the mean grain face number and the coefficient of variance of the distribution of grain size and the grain face number. Whereas for the coefficient of the skewness and the kurtosis of grain size distribution or grain face number distribution, a minimum of 800 sampled grains are required for the same error level. However, if some exceptional big grains appear, e.g. a grain larger than with eight multiples of mean grain volume and/or three multiples of mean grain face number, abnormal values of the two parameters would be resulted, even the number of examined grains is over 1000.