Attrition

Crystal hardness

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 H_v in Pascals.

Fracture resistance

A simple ratio was proposed by Orovan [ORO 49]:

n : number of atoms in the molecule

c_c: 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/L_max in favor of 1/L_min:

with:

Attrition reduces the speed of crystal growth that we can write out as:

We propose:

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: L_max

W_pi is the energy of plastic deformation

a„ : radius of the area of plastic deformation (m)