Optional Reading:

Berner E. K. and Berner R. A. (1987) The global water cycle: Geochemistry and Environment: Prentice-Hall, Inc., Englewood Cliffs, NJ, Pages 142-155.

Berner R. A. (1980) Early Diagenesis: A theoretical approach: Princton University Press, Princton, NJ, Pages 90-117.

Mineral precipitation and dissolution.

The overall chemical process of clay mineral precipitation can be viewed in terms of

1. Nucleation mechanisms
2. Crystal growth mechanisms
3. Dissolution mechanisms

The entire process can be understood by examining the energetic changes associated with crystallization.

Consider the edge of a clay structure, where ions or molecules are bound to the surface. Because only one side is bound, it has a greater amount of energy than the same ion in the interior of the clay.

For example potassium in illite:

-----------------------------------------> edge of xtal

It takes excess energy to move an atom of potassium from the interior of the structure.

For this reason, one mole of a fine illite has more energy than one mole of coarse illite.

This excess energy is known as interfacial free energy.

This energy depends upon the nature of the material in contact with the surface. For example the interfacial energy of the surface in contact with an aqueous solution is going to be different then the same surface in contact with air.

For crystals larger than about 2 µm, the interfacial free energy is very small, relative to the bulk free energy (DGbulk). However, for the crystallization of a phase from solution, the free energy of formation (DGn) for a crystallite can be expressed as:

DGn = DGbulk + DGinterf (1)

where:

bulk and interf refer to the bulk and interfacial free energies.

Recalling that W is the saturation index (ratio of ion concentration activity product to the ion equilibrium activity product, then it can be shown that for the case of super-saturation,

DGbulk = -nkBTlnW (2)

where:

n = number of atoms of ion ppt to form the crystal

kB = Boltzmann constant

T = absolute temperature

A new parameter may be defined which is the specific interfacial free energy between crystal and solution (s).

Where,

s = ^{dG interf} / _dA (3)

and A = surface area of the crystal.

Estimated values for interfacial free energy of solids in water (from table 5-1 Berner 1980)

Substance	s (erg/cm2)
Calcite	80
Gypsum	76
Silica glass	46
Sylvite	30
Hematite	1200
Goethite	1600

Note: Low values for salts of carbonate and sulfate.

High value for oxides and hydroxides.

Clay values???

If s is not a function of A, then the above equation can be integrated and combined with equation (1) to show that:

DG_n = -nk_BTlnW + sA (4)

Now if the area (A) is defined as

A = b V^2/3 (5)

and

V = nn_n (6)

where:

V = Volume of the crystal

b = geometric shape factor

n_n = volume of an atom or ion in crystal

Equation 4 can be written so as the express the free energy of formation of a single crystal from a supersaturated solution as a function of supersaturation of the solution and the number of atoms in the crystal n.

DG_n = -nk_BTlnW + s_n^2/3n_n^2/3 b (7)

Above is a plot of the free energy of formation of a single crystal as a function of the number of atoms in a crystal. The parameter values to the right represent an abrbitrary choice of numbers and when used in equation 7 they function is plotted as black squares. The different colored plots are sensitivity tests to show the effect of changing parameter values on the critical nucleation size.

For example, note that at higher degrees of supersaturation both the amount of free energy and the size of the crystal are smaller.

Note the free energy maximum necessary for nucleation. Formation of a crystal form in solution requires an increase in free energy.

It can also be shown that there is a strong dependence upon the rate of nucleation and the degree of supersaturation (W). There is even a stronger dependence upon of nucleation rate upon Temperature, shape factor and specific interfacial free energy (T,b, s)