The creation free enthalpy of flat crystal embryos (round in cross-section and of radius r) from a supersaturated solution is:
Yc edge energy (J.m-1) h: embryo height (m)
Q: molar volume of solute (m3.molecule-1).
Let us regard the derivation of AG2 in order to find the maximum for this function
We have added coefficient v, which is the number of ions that correspond to the possible dissociation of an electrolyte.
Spiral growth [BUR 51]
AH : molar dissociation heat (J.molecule-1)
Let us specify the use of the exponential term here.
A physical or chemical phenomenon, and in particular crystallization, that is significantly faster when exothermic, or less endothermic (which is essentially equivalent).
Since dissolution is the inverse path of crystallization, crystallization that is somewhat endothermic corresponds to dissolution that is somewhat exothermic.
In other words, if AH is the positive heat released by dissolution, the crystallization rate is a decreasing function of AH, which effectively announces the exp factor (-AH/RT).
Ds: surface diffusion (m2.s-1)
a: dimension of one molecule (part of a multilayer) (m)
e: base of natural logarithms (2.3026)
v: fundamental vibration frequency of the molecule (s-1)
The vibration frequency v decreases with the molecule size. It is in the order of 1014 for a monatomic molecule (see [MUT 01])
o: relative supersaturation (see section 2.1.1)
We note that this value differs only slightly from:
This result is very high. In reality, intense nucleation multiplies the seeds, significantly decreasing supersaturation. If a becomes equal to 0.005, we arrive at the following results:
The growth rate is divided by more than 1,000.
In any case, these rates are significantly greater than those resulting from crossing the diffusion layer (see section 2.3.5), which is consequently limiting.