In the crystallography, distribution times are key figures of the crystal size distribution. These are the times of the distribution of the crystal size. The i {\displaystyle i} -the moment of distribution n {\displaystyle n} is thus given by: m i = & # x222B; 0 & # x221E; x i n ( x ) d x {\displaystyle m_{i}=\int _{0}^{\infty }x^{i}\,n(x)\,{\rm {d}}x}
Distribution moments are used to obtain analytical solutions for population balance. This method is implemented in processes described using population balance, such as crystallization.
For crystallization, the first five moments are related to measurable physical properties of the distribution, as shown in the table below. The shape factors ka and kv relate the crystal length to the corresponding surface and volume respectively.
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