A Quantitative Investigation of Topological Structure of Grains of Pure Iron

The topological properties of annealed pure iron have been experimentally investigated by means of serial sectioning method, with emphasis on the characteristics of their distributions. The average values of basic topological parameters have been found close to those of Coxeter's statistical honeycomb or tetrakaidecahedra.The experimental distribution of the number of edges per grain face is lognormal with a mode of four.Empirical linear relations between the number of grain faces (or grain edges and grain corners) and spatial diameters of grains have been established.The experimental results also support the existing empirical linear relations between the geometric standard deviation of the distribution of grain volume and that of the distribution of the number of edges per grain face or the fraction of grain faces with no more than three edges.