Abstract
A quantitative optical microscopy study was made on the grain size distribution in one-, two- and three-dimensions in recrystallized titanium (0.2% Oeq) by the linear intercept, planimetric and serial sectioning methods. Analysis of the results revealed that all the size distributions were logarithmic-normal and that the mean values of the chord length l, grain area A, and grain volume \barV were in good agreement with the values associated with the maximum of the distribution curves (which were approximately l, A and V at 50% of the cumulative frequency). There existed an intrinsic spatial distribution of grain sizes, which could not be deduced from either one- or two-dimensional measurements quantitatively without knowledge of the shape and size of the constituent grains. The interrelations of \barl, \barA and \barV were expressed by the equations
\barl=α(\barA)1⁄2, \barl=β(\barV)1⁄3 and \barA=γ(\barV)2⁄3
where α, β and γ are approximately unity. It was therefore concluded that the grain size measured either in one- or two- dimensions could be utilized to establish the three-dimensional grain size. The construction of three-dimensional grains by stacking serial sections revealed that the number of faces, vertices and edges of a polyhedral grain increased with increase in grain size (namely the cumulative frequency) and the larger the grain size the more isotropic the grain became.
