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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.
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
Further reading
Barker, A.J. (1998) An Introduction to Metamorphic Textures and
Microstructures . Abingdon: Routledge.
Best, M.G. (2002) Igneous and Metamorphic Petrology . Oxford:
Gill, R. (2010) Igneous Rocks and Processes - a Practical Guide .
Chichester: Wiley-Blackwell.
Morse, S.A. (1980) Basalts and Phase Diagrams . New York:
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