Introduction to Crystallization of Fine Chemicals and Pharmaceuticals - Molecules: Nucleation, Aggregation and Crystallization - page 157

based on the total number, mass or surface area of the particles, as a den-
sity distribution, or as a histogram. The average crystal size can be repre-
sented by the mean size, the median size or the peak value. The mean size
of crystals can refer to the number, surface area or volume (mass) distri-
bution of the particles. The median size is the size where the cumulative
distribution passes 50% of the total amount. The spread in the distribution
is given as the coefficient of variation (CV), defined as the ratio of stan-
dard deviation to mean size.
Crystal shape
Together with particle size, particle shape, or habit , is of major importance
to the filtering and washing of the crystals, and thus also to the purity of
the product. Filtering of thin, flat particles is very time-consuming in com-
parison to filtering of more or less spherical particles. The habit of crys-
tals can also be important depending on the use of the product. Crystal
habit depends on two main factors. The inner, crystalline structure deter-
mines the faces the crystal can present; this is covered in the field of crys-
tallography. Growth conditions, however, determine the relative size of
each face, and hence also the overall shape.
Based on crystalline structure, crystalline materials are divided into
32 symmetry classes. These classes are generally divided into seven
different systems, designated regular (cubic), tetragonal, orthorhombic,
monoclinic, triclinic, trigonal and hexagonal. In order to be able to dis-
cuss how the crystal surfaces are related to one another, a system of
coordinates is introduced with the axes x , y , z . These axes are generally
not perpendicular to one another, but are aligned with the edges of
the unit cell , a geometrically defined block encapsulating a unit of
the crystal structure by which the entire crystal structure can be con-
structed through repetition. The seven crystal systems differ with
regard to the angles between the axes and the relative length of the lin-
ear dimensions of the unit cell. Using the crystallographic axes as ref-
erence, the various crystal faces are named according to the so-called
Miller indices.