Garrels, R.M. and Christ, C.M. (1965) Solutions, minerals and equilibria, Freeman and Cooper. 450 pages.
Nordstrom D. K. and Munoz J. L. (1985) Geochemical
Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA, Pages 270-281.
Construction of stability diagrams.
Graphical representation of mineral phases and the effect of aqueous fluid composition and temperature on their stability's.
Recall Gibb's phase rule.
f = c - p + 2
variables include; T, P, µi , µj ...
Example: K2O - Na2O - Al2O3 - SiO2 - H2O system
In a five component system at constant T and P, description of a single phase requires 4 degrees of freedom
f = 5 - 1 + 2 = 6 - 2 (T, P) = 4
If the 4 variables are taken to be activities and 2 are held constant then we can make a 2 dimensional coordinate system where any reaction between any two pair of phases will produce univariant curve. It follows then that any reaction between three phases will be invariant.
The specific choice of variables is both dictated and represented by the formulas of the reacting species.
In the above system we might choose the aqueous species:
aK+, aNa+, aH+, aH4SiO4o
This example is simplified for the purpose of demonstration. The Athens Gneiss can be represented by mineral assemblage: Quartz, Muscovite, Albite, Microcline, Kaolinite and Gibbsite.
I. Write reactions for mineral pairs using ions you wish to plot.
Kao + 5 H2O = 2 Gib + 2 H4SiO4o
Qtz + 2 H2O = H4SiO4o
2 Mic + 9 H2O + 2H+ = 2K+ + H4SiO4o + Kao
2 Alb + 9 H2O + 2H+ = 2Na+ + H4SiO4o + Kao
Mus + 9 H2O + H+ = 3 Gib + 3 H4SiO4o + K+
2 Mus + 3 H2O + 2 H+ = 3 Kao + 2 K+
Mic + 7 H2O + H+ = Gib + 3 H4SiO4o + K+
3 Mic + 12 H2O + 2 H+ = Mus + 2 K+ + 6 H4SiO4o
Alb + 7 H2O + H+ = Gib + 3 H4SiO4o + Na
3Alb + K+ + 3H+ + 12 H2O = Mus + 3Na +H + 6H4SiO4o
Alb + K+ + H+ = Mic + Na + H+
Recall: If DG = 0 , then the reaction will not proceed in either direction (at equilibrium state). In this case,
ΔGo = - RT ln K
To calculate the ΔGreaction the ΔGoformation must be obtain from a a data table such as:
Robie R. A., Hemingway B. S., and Fisher J. R. (1984) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (10+e5 pascals) pressure and higher temperature: Bulletin 1452, U.S. Geological Survey, Washington DC.
For the reaction: Kaolinite + 5 H2O = 2 Gibbsite + 2H4SiO4o
ΔGreaction = the products - reactants
ΔGreaction = (2 x -1155) + (2 x-1308) - (-3799) - (5 x -237) = -59 kJ/mol
therefore solve for K,
K = 4.2 x 10-11
K = (aH4SiO4o)2
log K = -10.4
log K = 2 log aH4SiO4o = -10.4
The coordinate system is therefore define by the ratios:
aK+ / aH+
Because kaolinite and gibbsite and quartz do not contain sodium or potassium, their stability's are govern by the silica activity and temperature.
If quartz saturation is always maintained at an activity of aH4SiO4o = 10-3.95 the direction of reactions can be assessed.
For example in step II above, it was shown that for the reaction of kaolinite ---> gibbsite
2 log aH4SiO4o = -10.4
Therefore, under these conditions, the equilibrium activity of silica is 10-5.4.
The reaction will be driven to the left and kaolinite is more stable
than gibbsite under these conditions.
Form of equations is y = mx +b
y = log (aNa+ / aH+)
x = log (aK+ / aH+)
m is the log coefficient
b = zero intercept