Application of stereology to the statistical description of the spatial distribution of composition and other scalar properties in three dimensional space Original Research Article

The composition distribution in a chemically nonuniform system may be described as a set of scalar fields Xk(x, y, z), one for each component k, where Xk is the atom fraction of component k. For each component statistical information about this spatial distribution may be obtained by combining a sampling of microprobe line traces with stereological analysis. This analysis yields the volume weighted concentration distribution function, fv(Xk), where fv(Xk)dXk is the fraction of the volume of the system that has compositions in the range Xk to Xk+dXk, and Sv(Xk), the area per unit volume of structure of the isocomposition contour at each composition. The harmonic mean of the distribution of concentration gradients over each isocomposition contour can be computed from this information. The methodology also can be applied to the analysis of the distribution of any scalar property that is nonuniform in a structure.