Geology Reference
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relaxed, we would find that the eutectic was just one
point of a univariant curve in T-X-P space.
A eutectic is always an invariant point in any phase
diagram. On the other hand, the one-phase 'melt' field
has two degrees of freedom:
here begins to crystallize in equilibrium with the melt.
Extraction of anorthite depletes the melt a little in the
CaAl 2 Si 2 O 8 component, causing a shift in composition
to the left in Figure 2.4. But the maintenance of univari-
ant equilibrium demands that the melt composition
should change in conjunction with falling tempera-
ture. As crystallization advances, therefore, the melt
composition migrates steadily down the liquidus
curve towards E, continuously crystallizing anorthite
and changing composition. The phase assemblage here
is shown in the middle roundel on the right, illustrat-
ing what might be seen in a quenched sample under
the microscope.
On reaching the eutectic, the melt begins to crystal-
lize diopside in addition to anorthite, as shown in the
lowermost roundel. At this juncture, the melt composi-
tion becomes fixed, because anorthite and diopside
crystallize in the same proportion as the CaAl 2 Si 2 O 8 :
CaMgSi 2 O 6 ratio of the melt. The temperature also
remains constant, because the eutectic is an invariant
equilibrium (at least within the isobaric framework
being considered): as long as three phases remain in
equilibrium, neither melt composition nor tempera-
ture can change. Continued cooling in this context
merely means the loss of heat (the latent heat of crys-
tallization of diopside and anorthite) from the system
at constant temperature and the formation of crystals
at the expense of melt. Eventually the melt becomes
exhausted, and invariant (Di + An + melt) equilibrium
gives way to univariant (Di + An) equilibrium, allow-
ing the temperature to resume its downward progress.
The total solid assemblage will obviously now consist
of 61% anorthite and 39% diopside ( c in Figure 2.4).
The eutectic therefore represents the lowest projec-
tion of the melt field, the composition and temperature
of the last melt to survive during the cooling of the sys-
tem. Progressive crystallization of any melt in this sys-
tem (with the special exceptions of pure CaMgSi 2 O 6
and pure CaAl 2 Si 2 O 8 ) will lead its composition ulti-
mately to the eutectic. This illustrates an important
general principle of petrology: that the evolving com-
positions of crystallizing magmas of all types tend to
converge upon one or two 'residual magma' composi-
tions (a natural example being granite) at which the
liquidus reaches its lowest temperature.
The eutectic also indicates the composition of the
first melt to appear upon heating any mixture of diop-
side and anorthite (Box 2.4).
Point x 1
(1 phase, melt)
ϕ = 1
C = 2
(2 components, CaMgSi 2 O 6 and
CaAl 2 Si 2 O 8 )
1 + F ʹ = 2 + 1
F ʹ = 2
an isobarically divariant equilibrium
T and X have to be quantified to define fully the state
of the system in this condition.
It would be natural to expect the fields ECD and
ABE to be divariant as well, but the Phase Rule indi-
cates otherwise. Consider the composition represented
by point x 2 . Neither the melt (at this temperature) nor
anorthite can have this composition. The 'composition'
x 2 only has meaning at 1400 °C when interpreted as the
composition of a physical mixture of melt x and anor-
thite y . (The proportions of the two phases in this mix-
ture can be worked out as explained in Box 2.3.) ECD
and ABE are therefore two-phase fields. If ϕ = 2 and
C = 2, we cannot escape the conclusion that F ′ = 1. In
other words, specifying temperature is sufficient to
define the composition of all phases in equilibrium, or
vice versa given that the pressure is already defined.
Thus reaction-boundary lines (cf. Figures 1.3a and 2.1)
are not the only manifestation of univariant equilib-
rium in phase diagrams; areas can also be univariant.
Such fields arise in T-X diagrams whenever two coex-
isting phases have different compositions. One can
imagine them consisting of an infinity of horizontal tie-
lines, as the horizontal ruling in Figure 2.4 is intended
to symbolize.
T-X diagrams are important in igneous petrology
because they allow one to follow the evolution of melt
composition with advancing crystallization in experi-
mental and natural magmatic systems (at constant
pressure). Imagine a melt m cooling from some temp-
erature above the liquidus, say 1450 °C. The phase
assemblage at this point consists of melt alone, as illus-
trated by the top 'microscope view' on the right. At
first there will be no change other than a fall in tem-
perature: we can imagine point m falling vertically
through the 'melt' field. Arrival at the liquidus (point
x ) signals the first appearance of solid anorthite, which
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