- Relation between the chemical and mineralogical composition of a metamorphic rock: The Gibbs phase rule -
During a prograde metamorphic evolution, new minerals are produced while others disappear. However, the number of minerals is not increasing but, on the contrary, remains more or less constant. Thus, at P0-T0 and P1-T1, the rock below has two minerals, even though it goes through an intermediate, transitional stage in which it has three: A, B, C.
There is a very simple mathematical relationship between the number of minerals and the number of chemical constituents in the rock. This is the Gibbs phase rule and is written as follows:
M = C + 2 - F
M is the number of phases that are physically distinct: in the case of rocks, these are the minerals (and the vapour phase).
C is the number of independent chemical constituents. The number 2 refers to the number of intensive parameters of the metamorphism: T and P. If we reason in an isobaric or isothermal system, then this number is 1.
" F " is the degree of freedom or variance of the assemblage of "M" minerals. We consider only values of F equal to 0, 1 and 2. But higher and negative values are possible.
If F=2, the phase rule indicates M=C. This " assemblage " has two degrees of freedom in P-T space. This means that each of the parageneses of "M" minerals is stable when P and/or T vary in a in a DP - DT range. This paragenesis is said to be divariant. In the P-T diagram below, the 2 mineral assemblages A+B and A+C are divariant and are stable in the grey fields.
If F=1, the phase rule indicates M=C+1. But the three-mineral paragenesis A+B+C has only one degree of freedom in P-T space. This means that P can only vary as a function of T (P=f(T)) in order to keep this paragenesis stable. P=f(T) is a curve in P-T space. The mineralogical association A+B+C is qualified as uni (or mono) variant. The coronitic texture corresponds to this situation.
If F= 0, the paragenesis contains M=C+2, but no longer has any degree of freedom: it can only exist at one point, called the invariant point. On the P-T diagram, this point is at the intersection of the univariant curves.
In the P-T diagram, when the rock changes from P0-T0 to P1-T1 conditions, the divariant assemblage of 2 minerals A-B is replaced by another divariant assemblage (A-C or B-C) via the univariant 3-phase assemblage A-B-C. Furthermore, the phase rule dictates that the system contains two independent chemical constituents, since the divariant assemblages are formed by 2 minerals.
An important application of the Rule of Phases is the graphical representation of the parageneses of metamorphic rocks in appropriate diagrams and the construction of petrogenetic grids.
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