It is easily shown that the expected number of particle profiles N̄A per unit area of a plane section of orientation (ø, θ) is given by: $$ {\bar{N}_{A}}\left( {\phi ,\theta } \right) = {N_{V}}\bar{D}\left( {\phi ,\theta } \right) $$ (1) in which NV is the number of particles per unit volume and D̄(ø, θ) is the average projected height of the particles on a line of orientation (ø, θ). If the
... [Show full abstract] particles are randomly oriented, then Eq. (1) can be written as $$ {\bar{N}_{A}} = {N_{V}}\bar{D} $$ (2) in which D is the projected height averaged over all orientations of a particle; i.e., $$ D = \left( {1/4\pi } \right)\int\limits_{0}^{{2\pi }} {} \int\limits_{0}^{\pi } {} \quad D\left( {\phi ,\theta } \right)\sin \phi d\phi d\theta $$ (3).
