Vickers hardness corresponds to the force F required to pierce the material. The indenter has the force of a pyramid with an angle of 136° at the summit:
dj and d2 are the two diagonal angles of the indent left by the indenter.
F is measured in Newtons and Hv in Pascals.
A simple ratio was proposed by Orovan [ORO 49]:
n : number of atoms in the molecule
cc: molar concentration in the crystal (kmol.m-3)
N A : Avogadro number E : elasticity modulus (Pa).
Gahn [GAH 97] proposed a measurement based on the work of plastic deformation.
F*: critical force required for fissure formation.
p is the shear modulus. Expressed in GPa, its value is between 1 and 20.
v is the Poisson modulus, typically close to 0.3.
Attrition in a stirred vessel [MER 01]
Collisions with the impeller give rise to fragments whose minimum size is:
The mass distribution of fragment dimensions is, disregarding 1/Lmax in favor of 1/Lmin:
Attrition reduces the speed of crystal growth that we can write out as:
П = 0.15 for very hard crystals (SiO2)
П = 0.5 for less hard crystals (NaCl, KCl, KF, LiCl, LiBr).
Indeed, attrition provokes wear equivalent to negative growth and proportional to the square of the crystal’s dimensions.
Note that Mersmann [MER 01, p. 196] proposed an expression for: Lmax
Wpi is the energy of plastic deformation
a„ : radius of the area of plastic deformation (m)