Non-sphericity index (form index)
This is the ratio of the crystal’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 ps, 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, Ins, we obtain the surface.