A refined technique for measuring crystal size distributions in thin section

Log-normal size distributions are of the form n=n(o)e(-L/alpha), where n=number density, L=crystal length, and alpha is a constant. A method for measuring three-dimensional lee-normal crystal or grain size distributions (CSDs) in thin section has been deduced from computer experiments, in which 2D sections were cut through assemblages of 3D solids. The size ranges and distributions studied were appropriate for igneous microphenocryst to megacryst populations. Conversion from 2D to 3D is based on an exact correction for spheres of uniform diameter. Cumulate numbers of polygons with length greater than or equal to L (N-2D) are converted to N-3D by the equation: ln(N-3D=ln(N-2D/[L . S])+ln(gamma)-beta/[L . S] The number density is then obtained as n=-dN/dL. The parameters S and gamma correct the measured lengths and n(o) (n(o)=number density at L=0) respectively, and are functions of crystal shape. The parameter beta is a weak function of the degree of spatial orientation of the crystals. Highly symmetrical shapes such as cubes, octahedra, and elongated prisms can be accurately measured when randomly oriented; however, rectangular solids with a not equal b not equal c cannot be accurately measured because they produce bimodal length distributions in cross section. Strongly oriented textures (trachytic or lineated) can be accurately measured regardless of crystal shape. New CSD data from alkaline rocks and a kimberlite give examples of CSDs modified by megacryst retention, xenocryst addition, phenocryst accumulation, and groundmass nucleation.