EQUILIBRIUM IN GEOLOGICAL SYSTEMS - Chemical Fundamentals of Geology and Environmental Geoscience

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equilibrium data are available: this one relates to

1220 °C, the temperature of the liquidus at point b in

Figure 2.9b. The area where the liquidus lies below the

temperature of the section (shaded in Figure 2.9d) is a

one-phase field where only melt is stable at 1220˚C.

The rest of the diagram can be regarded as the result of

slicing the top off the solid model at this temperature

(Figure 2.9c), revealing three 2-phase fields, each tra-

versed by a family of tie-lines (summarizing the results

of phase equilibrium experiments at 1220 °C). The

composition of the plagioclase ss in equilibrium with

the melt b at this temperature can be read from the dia-

gram by following the tie-line from b to the NaAlSi 3 O 8 -

CaAl 2 Si 2 O 8 edge of the diagram (point c ).

Tie-line b-c forms one boundary of a three-phase field

representing equilibrium between melt b , plagioclase c

and diopside (composition CaMgSi 2 O 6 ) at this temper-

ature. Any point lying within this field signifies a

physical mixture of these coexisting phases, the pro-

portions of which could be worked out using the Lever

Rule. Because all possible mixtures of diopside and

plagioclase c lie to the right of melt b (along the line

Di- c ), the crystallization of these two minerals with

cooling causes the melt composition to migrate left-

wards, along the boundary - the cotectic - shown in

Figure 2.9b. This direction is indicated by the arrow in

Figure 2.9c. Point d , collinear with the arrow, indicates

the proportion in which diopside and plagioclase (c)

crystallize from the melt b (Exercise 5).

More detailed interpretation of such diagrams lies

beyond the scope of this topic. Further information can

be found in the topics by Morse (1980), Winter (2009)

and Gill (2010).

(Box 2.1) that are familiar to most petrologists, present

phase equilibrium data in an easily understood form.

But many diagrams of this kind refer to experiments

on simple laboratory analogues rather than on the

rocks themselves. The melts in Figure 2.9, for example,

fall short of having true basaltic compositions, owing

to the absence, among other things, of the important

element iron. (One of the many consequences of this

defect is that equilibria in Figure 2.9b are shifted to

higher temperatures than would be found in a real

iron-bearing basalt.) Thus diagrams like Figure 2.9,

although invaluable for analysing general principles of

phase equilibrium, do not reflect in quantitative detail

the behaviour of more complex natural magmas and

rocks. In some circumstances it can be helpful to carry

out experiments on natural rock powders (see, for

example, Gill, 2010, Figure 3.9) or comparable syn-

thetic preparations, but the results cannot be directly

displayed in simple phase diagrams and have less gen-

eral application.

There are also useful applications in petrology for

thermodynamic data (molar enthalpies, entropies and

volumes). Using the Clapeyron equation and Le

Chatelier's principle, we can predict certain features of

phase diagrams without recourse to petrological

experiment. Molar enthalpies and entropies of pure

minerals are measured primarily by a completely dif-

ferent technique called calorimetry , involving the very

accurate measurement of the heat evolved when a

mineral is formed from its constituent elements or

oxides. Such methods and data are less familiar to

most geologists, and their successful application in

solving petrological problems requires a command of

thermodynamic theory beyond the scope of this topic.

Thermodynamics has, however, become one of the

most versatile tools of metamorphic petrologists, ena-

bling them to apply experimental data from simple

synthetic systems to complex natural assemblages.

Review

The great diversity of reactions and assemblages

recorded in natural igneous and metamorphic rocks

provides many avenues for investigating the condi-

tions under which the rocks were formed. We have

seen that, to analyse what such mineral assemblages

mean in terms of pressure and temperature of forma-

tion, we can draw on two sorts of published experi-

mental information. The primary source is the literature

of experimental petrology , in which one can usually track

down a number of phase diagrams relevant to the

assemblages in a particular rock suite. Such diagrams,

derived from well-established laboratory procedures