Geology Reference
In-Depth Information
merits and limitations. We begin by looking at P-T
The two phase diagrams so far considered
(Figures 1.3a and 2.1) both show the effects of varying
pressure and temperature on a system consisting of
only one component (CaCO 3 or Al 2 SiO 5 ). Other impor-
tant examples of such unary systems are discussed in
Box 2.2.
P-T diagrams can also be used to show the pres-
sure-temperature characteristics of multicomponent
reactions and equilibria. An example is shown in
Figure  2.2. The univariant boundary in this diagram
represents not a phase transition between different
forms of the same compound, but a reaction or equilib-
rium between a number of different compounds:
Jadeite + Quartz
T /ºC
Figure 2.2 P-T diagram showing the experimentally
determined reaction boundary (solid line) for the reaction
NaAlSi O iO
NaAlSi O
a pyroxene
jadeitequartz lbite
+ →
For this reason the term reaction boundary (or equilib-
rium boundary ) is used. It marks the P-T threshold
across which reaction occurs, or the conditions at
which univariant equilibrium can be established.
Two components are sufficient to represent all
possible phases in this system. We can choose them
in a number of equivalent ways; selecting NaAlSi 2 O 6
and SiO 2 is as good a choice as any. Applying the
Phase Rule to point X:
Jadeite (NaAlSi 2 O 6 ) and albite (NaAlSi 3 O 8 ) are both
aluminosilicates of sodium (Na).
this system means that a three-phase assemblage is no
longer invariant, as it was in Figure 2.1.
At first glance one might expect the albite field
(point Z) to be divariant like the jadeite + quartz field,
but here the Phase Rule springs a surprise:
Point Z
(1 phase, albite)
ϕ = 1
Point X
(2 phases, jadeite + quartz)
ϕ = 2
C = 2
(2 components, NaAlSi 2 O 6 and SiO 2 )
C = 2
(2 components, NaAlSi 2 O 6 and SiO 2 )
1 + F = 2 + 2
2 + F = 2 + 2
F = 3
a trivariant equilibrium.
F = 2
signifying a divariant ield.
Analysing the albite field in this way, it appears nec-
essary to specify the values of three variables to
define the state of the system in this condition. P and
T account for two of them, but what can the third
variable be? The answer becomes clear if we ask
what requirements must be met if, in passing from X
to Z, we are to generate albite alone . If the mixture of
jadeite and quartz contains more molecules of SiO 2
than NaAlSi 2 O 6 , a certain amount of quartz will
be  left over after all the jadeite has been used up.
The  resultant assemblage at Z will therefore be
albite + quartz. The presence of two phases leads to a
variance of 2 for this field, as originally expected.
Conversely, if we react SiO 2 with an excess of
NaAlSi 2 O 6 molecules, the resultant assemblage at Z
The jadeite + quartz field is therefore a divariant field
like that of kyanite in Figure  2.1. At point Y on the
phase boundary, however, three phases are in equilib-
rium together:
Point Y
ϕ = 3
(3 phases, jadeite + quartz + albite)
C = 2
(2 components, NaAlSi 2 O 6 and SiO 2 )
3 + F = 2 + 2
F = 1
a univariant equilibrium.
The three-phase assemblage represents a univariant
equilibrium: only one variable, P or T , needs to be
specified to determine completely the physical state of
the system. The value of the other can be read off the
reaction boundary. The existence of two components in
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