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Two phases A and B may react together to produce a third phase C.

A + B = C

The reactants A and B are shown in an xy or binary system along which all the inter-mediate compositions between A and B are represented (Fig. 9); x and y are the constitu-ents of the system. Each composition of the system is characterized by a concentration X:

(x and y are generally expressed in mols). In the particular case where A and B represent the two extremities of the system, the compositions are defined by the concentration

or In a closed system the composition of phase C is obligato-rily located on the segment AB between A and B. Figure 9 is therefore a TX diagram which represents the mineralogical evolution of the system as a function of temperature at con-stant pressure, TX(P). It is also possible to construct PX(T) or GX(T,P) diagrams.

At low temperature (below the temperature of reaction the association, or mineral assemblage, A + B is the most stable of the possible assemblages. Above phase C is more stable than the association A + B, it therefore should crystallize at the expense of

Metamorphism: Factors and mechanisms 19

B. The exact nature of the mineral assemblage depends on the initial composition of the system on the AB segment; the critical composition is that of phase for 0.6 the stable assemblage above is A + C, in effect, for at that composition all of phase B is consumed by the reaction and phase A remains “in excess”; for the stable assemblage is B + C where B is the excess phase; for only phase C is present. At temperature the stable assemblage is A + B + C for all values of different from 0.2 (composition of A) and 0.9 (composition of B).

This reaction is represented on a P-T diagram (Fig. 10) analogous to that of Figure 7.

The nature of the mineral assemblages in relation to the reactions is clarified using segment AB which defines the composition of the system. As in the case of the polymorphic changes the reaction curve is the projection on the P-T plane, of the intersection of the free energy surfaces. The difference in free energy of the reaction is:

in taking into account the stoichiometric coefficients of the phases participating in the reac-tion.

The graphical representation of free energy of a mixture of two phases is shown in Figure 11.

The slope of the equilibrium curve is given by:

The diagram TX (Fig. 9) shows that at temperature an instability develops between B and C:

This reaction, naturally, only applies to those compositions of the system falling be-tween and and the assemblage A + C does not react above under the pressure conditions considered (P).

Reactions in a binary system of the type A + B = C involve more important ionic displacements than those which result from polymorphic changes. The recombination of elements between different phases involves, in effect, migrations which are on the order of magnitude of the size of the crystals in the mineral assemblage (several mm to several cm).

The time parameters which control the diffusion rate of atoms within the assemblage must therefore be taken into account to determine the kinetics of the reaction, the time required to achieve equilibrium. These kinetics are slower at lower temperature, so that equilibrium is never attained under conditions of low grade metamorphism. It is thanks to these ex-tremely low reaction kinetics at low temperatures that high grade metamorphic assem-blages are observed at all, and may be studied at the low temperature and pressure condi-tions of present-day outcrops.

1.9.2 Ternary Systems

The composition of the system is defined by three chemical components (or ingredients) x, y and z, which form the three points of a triangular diagram. Each point located within the triangle represents a particular composition of the system characterized by a concentration

Metamorphism: Factors and mechanisms

composition, and it is not possible to use T-X or P-X projections as before. It is possible, however, to show the mineral reactions and resultant stable assemblages in a simple fashion in P-T space (Fig. 12).

Consider a system which is widespread in nature, that of the quartz-bearing carbonate rocks. This system is represented by the triangle on the understanding that sufficient water and carbon dioxide are always present in order for a reaction to pro-ceed (it is said that and are “in excess”). The compositions of such carbonate rocks are shown in the diagram (hachured field). Under low temperature and pressure conditions (diagenesis) all of these rocks display the same mineral assemblage.

The right part of the diagram is unoccupied; the mineral assemblages which are theo-retically possible under these conditions are unrealistic, lacking material of a suitable com-position.

At moderate P and T (about 380 °C) quartz and dolomite become unstable together.

The following mineral reaction takes place:

The appearance of the assemblage talc + quartz signifies that

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The reaction curve (Fig. 12) represents, as in the previous cases, the projection of the intersection of the free energy surfaces of the two associations onto the P-T plane. The carbonate rocks display two different mineral assemblages depending on their initial com-position:

quartz + calcite + talc dolomite + calcite + talc

or

A part of the calcite and talc are reaction products, quartz or dolomite are “excess”

phases which can no longer coexist.

Different possible mineral reactions in this system are also shown in Figure 12. The following points should be noted:

1) certain theoretically possible reactions (for example tremolite) do not concern the composition under consideration; they do not take place, therefore, in the topochemical system under scrutiny, lacking the presence of an appropriate composition.

2) certain mineral assemblages are never practical for the composition under scrutiny (for example qtz + tlc + tr; also tlc + tr + dol).

3) all the postulated reactions must be geometrically feasible; the tie line between the products must necessarily cut the tie line between the reactants (qtz + dol = cal + tlc is a possible reaction; cal + dol = tlc + qtz is incorrect). Or else the triangle defined by the reactants contains the product of the reaction (cal + tlc + qtz = tr is a possible reaction; dol + tlc + cal = tr is incorrect). If these conditions are not respected, it is not possible to balance the reaction.

The arrangement of the reactions and mineral assemblages as shown in Figure 12 obeys the phase rule and the strict geometrical constraints which are outlined in Chapter 3.