Applicable scope of estimation of three-dimensional particle size distribution by the Goldsmith-Cruz-Orive and improved methods

Microscopic observation is commonly performed on particle sections when the internal structure and/or inclusion is of interest in a given field, and the particles in question include sand, grain, cell, void, crystal, etc. components for example. However, in practice, the particle size distributions determined by two-dimensional (2D) observation of particle sections differ from the actual three-dimensional (3D) particle size distributions, due to the stereological difference between 2D and 3D observation. Among the various methods of estimating 3D from 2D size distributions, the Goldsmith-Cruz-Orive method (GCO) is known to provide high estimation accuracy. In this study, the GCO and a newly improved GCO method (MGCO) were systematically investigated to determine their applicable scope in terms of the range of size distributions, unusually-shaped (step-like) size distributions, the axis length ratio of ellipsoidal particles, and input data errors. Among the study's results, the MGCO method showed greater estimation accuracy than GCO irrespective of the range of size distributions, reasonable estimation accuracy in the case of step-like size distributions (while GCO did not), greater robustness than GCO with respect to the axis length ratio of ellipsoidal particles, and more sensitivity to input data errors than GCO. Elucidation of the applicable scopes of the respective methods facilitates the practical use of the GCO methods for various types of particles. [Display omitted] •3D particle size distribution can be estimated by the GCO and improved GCO (IGCO) methods.•The IGCO method was modified (MGCO) to improve its estimation accuracy.•The applicable scopes of the GCO and MGCO methods were determined through systematic simulations.•A complementary method was tested for use with samples exceeding the GCO methods' scope of applicability.