Premium
The homogeneity of phase repartition in TiB 2 –Fe composites using variance and covariance analysis
Author(s) -
MISSIAEN J. M.,
CHAIX J. M.
Publication year - 1994
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.1365-2818.1994.tb03485.x
Subject(s) - covariance , variogram , materials science , porosity , homogeneity (statistics) , mathematics , covariance mapping , monte carlo method , covariance function , statistics , statistical physics , mineralogy , mathematical analysis , kriging , physics , composite material , chemistry , covariance intersection
Summary The microstructure of a sintered TiB 2 –Fe material has been studied by image analysis. The dispersion of phases, with particular attention to porosity, is investigated using chord lengths, covariance functions and variance of volume fractions. An extension of the usual point covariance analysis is made by sampling series of 10 contiguous fields, and measuring the covariance in the direction of field alignment. A model of a multiscale structure is proposed to interpret the different transitions of the variogram as composition fluctuations at different scales. Boolean models are used to give a geometrical representation of these fluctuations: the dispersion of porosity can be seen either as 20–30‐μm pore clusters or as the result of TiB 2 +Fe 30–50‐μm clusters, probably formed during the elaboration process. Complementary information is obtained from the evolution of measured variance versus field size: a model is proposed to analyse the shape of the experimental curves. At small scales, ‘short’ integral ranges are determined, also obtained from the covariance. At very large scale (> 300 μm), composition fluctuations of about 2% are detected.