切片長さ測定値分布による3次元的な結晶粒度分布の評価

Abstract

A new method is proposed to estimate the three-dimensional grain size distribution from the measured linear intercept length distribution. The method is developed on the assumption that the grain size distribution in three dimensions is a log-normal distribution. The three-dimensional grain size distribution is expressed as that of the “grain diameter” D defined as the equivalent volume diameter; the distribution of D is estimated from the arithmetic mean lnDg and the arithmetic standard deviation lnσg for the logarithm of D, lnD (where Dg is the geometric mean of D and σg is the gometric standard deviation for D). The estmation is based upon the theoretical distribution of linear intercept lengths which is derived from the numerical calculation in the tetrakaidecahedron grain structure model with a diameter distribution in a log-normal form. The values of Dg, and lnσg are determined by applying the discrete least squares method to the measured linear intercept length distribution on the basis of the calculated results. The present method enables us to evaluate the fundamental parameters of Dg, and lnσg defining three-dimensional distribution of grain size from measurements of linear intercept length distribubon.