Premium
Quantifying the dispersion of mixture microstructures
Author(s) -
LUO Z. P.,
KOO J. H.
Publication year - 2007
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.2007.01722.x
Subject(s) - log normal distribution , dispersion (optics) , standard deviation , range (aeronautics) , sigma , particle (ecology) , mean free path , physics , probability density function , mathematics , materials science , analytical chemistry (journal) , mathematical analysis , statistics , optics , chemistry , composite material , chromatography , quantum mechanics , oceanography , scattering , geology
Summary A general method to quantify the inclusion dispersion of mixture microstructures has been developed. The dispersion quantity, D , is defined as the probability of inclusion particle free‐path spacing falling into a certain range of the mean spacing μ, according to the particle spacing data frequency distribution. Two quantities, D 0.1 and D 0.2 , are proposed, which are the probabilities of the particle free‐path spacing falling into the ranges of μ± 0.1 μ and μ± 0.2 μ, respectively. Both normal and lognormal distributions are discussed, and in both cases, the quantities D 0.1 and D 0.2 are specified as monotonous increasing functions of μ/σ, where μ and sigma; are the mean particle free‐path spacing and standard deviation, respectively. Examples of composite are presented to quantify the dispersion of foreign reinforcements based on the proposed method.