The estimation of size distribution and density of precipitates from electron micrographs of thin foils

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Abstract
A method is described for deriving estimates of the density and spatial size distribution of precipitates in a thin foil from measurements of their projected sizes from electron micrographs. It applies to spherical particles (or sections thereof) and corrects for precipitates centred outside the foil but contributing a projected image less than the true diameter. The projected circles with diameters lying in the largest size interval are assumed to arise only from spheres with diameters within that same interval. The contributions to smaller class intervals from spheres of the largest size centred outside the foil but intersecting it are then calculated and subtracted from the number of particles in each of the remaining size intervals. This process is then repeated making the same assumptions about the next largest class of spheres until corrected values have been obtained for all sizes. This procedure can be applied where the particle size is comparable to the thickness of the foil so that overlaps can be neglected and near-overlaps detected visually. Measurements of precipitates of plate- or rod-like form provide the most favourable case.