# Non-sphericity index (form index)

This is the ratio of the crystalâ€™s exterior surface to the surface of the sphere of the same volume.

1) Cube of side L:

2) Parallelepiped of sides A, B and C:

3) Rod of length L and cross-section S (perimeter P):

4) Plate of thickness E and surface S:

NOTE.- Use of Ins:

We always know the mass of the crystals in question and, by knowing their real density p_{s}, we know their real volume. Below, we show that when treating a more or less dispersed population, and when the surface/volume ratio must be retained, the characteristic dimension is the harmonic mean of the different classes of the particle size distribution:

In addition, if we know the form of these crystals, we can deduce their mean dimensions and thereby learn the value of the diameter d and that of volume Ms of the equivalent sphere:

The total surface of the equivalent population is:

It is important to know the total surface in crystallization, filtration and drying operations.

The non-sphericity index can reach a value in the order of 10 for an acicular or thin plate. Typically, it falls between 1 and 2.

Coulter counter readings give a direct value for the crystal volume. Equivalent sphere diameter d is immediately deduced and by knowing the crystal form, that is, I_{ns}, we obtain the surface.