EQUILIBRIUM IN GEOLOGICAL SYSTEMS - Chemical Fundamentals of Geology and Environmental Geoscience - page 39

Ternary phase diagram with solid solution

When the temperature falls to meet the liquidus
(about 1430 °C at point y ), the variance of the equilib-
rium changes as olivine begins to crystallize:

Figure 2.9 shows another example of a ternary phase
diagram relevant to magma crystallization. It incorp-
orates along its edges two binary phase diagrams
we have already discussed, Figures 2.4 and 2.5. The
involvement of the plagioclase series (Figure 2.5)
introduces solid solution, giving this diagram a dif-
ferent appearance to Figure 2.8. The gross features of
the system can again be appreciated from a perspec-
tive sketch (Figure 2.9a) showing the topography of
the liquidus surfaces as in Figure 2.8. In this diagram,
however, these liquidus surfaces meet in a V-shaped
low-temperature trough running out of the binary
eutectic in the system CaMgSi 2 O 6 -CaAl 2 Si 2 O 8 . The
phase relations in this and the companion binary
systems (CaMgSi 2 O 6 -NaAlSi 3 O 8 and CaAl 2 Si 2 O 8 -
NaAlSi 3 O 8 ) can be indicated on the vertical faces of
the 'model'.
The main diagram (Figure 2.9b) is invaluable for
examining the evolution of melt composition during
crystallization, and considering the parallel magmatic
evolution in real igneous rocks. The V-shaped valley
divides the diagram into two fields, each labelled with
the name of the solid phase that crystallizes first from
melts whose compositions lie within that field. For
example, a melt of composition a at 1300 °C will init-
ially crystallize diopside. A line drawn from the
CaMgSi 2 O 6 apex to a , if extended beyond a , indicates
the changes in melt composition caused by diopside
crystallization. If the temperature continues to fall, the
melt composition will eventually reach the boundary
between the diopside and plagioclase ss fields (at point
b ), and here crystals of plagioclase begin to crystallize
together with diopside. The boundary indicates the
restricted series of melt compositions that can coexist
with both diopside and plagioclase at the temperatures
shown.
To work out the composition of the plagioclase that
crystallizes from melt b requires the use of tie-lines. But
one must remember that tie-lines are isothermal lines
(since two phases in equilibrium must have the same
temperature), and for this purpose it is appropriate to
use a second type of diagram derived from the three-
dimensional model. This is the isothermal section shown
in Figure 2.9d. One can visualize this section as a horiz-
ontal slice through Figure 2.9a at a specified tempera-
ture (see Figure 2.9c). In principle an isothermal section
can be drawn for any temperature for which phase

Point y
( T = T liquidus )

melt + forsterite

ϕ = 2

C = 3

CaAl 2 Si 2 O 8 + Mg 2 SiO 4 + CaMgSi 2 O 6

2 + F ʹ = 3 + 1

Therefore a divariant equilibrium

F ʹ = 2

Melt composition y can coexist with olivine only at the
liquidus temperature, so temperature (now dictated by
that of the liquidus surface) ceases to be an independ-
ent variable and the variance decreases to 2.
When the melt evolves to point z , plagioclase begins
to crystallize too:

Point z ϕ = 3 melt + forsterite + anorthite

C = 3

CaAl 2 Si 2 O 8 + Mg 2 SiO 4 + CaMgSi 2 O 6

3 + F ʹ = 3 + 1

Therefore F ʹ = 1 a univariant equilibrium

For this equilibrium to be maintained, the two compo-
sitional parameters can only vary in an interdependent
way that confines z to the cotectic line, making this a
univariant equilibrium.
When crystallization of forsterite and anorthite has
driven the residual melt composition to point E:

Point E melt + forsterite + anorthite + diopside

ϕ = 4

C = 3 CaAl 2 Si 2 O 8 + Mg 2 SiO 4 + CaMgSi 2 O 6

4 + F ʹ = 3 + 1

Therefore F ʹ = 0 an isobarically invariant equilibrium

Here, with the melt in equilibrium with forsterite,
anorthite and diopside, we have reached an invariant
situation, the ternary analogue of the binary eutectic in
Figure 2.4. Melt composition and temperature now
remain fixed, and only the proportions of the various
phases can vary: as heat is lost at a constant tempera-
ture of 1270 °C, melt crystallizes into forsterite, anor-
thite and diopside until no melt remains. This removes
one of the four phases (melt) from consideration, leav-
ing the three solid phases to continue cooling in a
solid-state, univariant equilibrium.
A second invariant point R exists in this diagram,
a reaction point similar to that discussed in Box 2.6.
In the present context this complication can be
ignored.