Geology Reference
In-Depth Information
Therefore ΔS = +32.4 J K
−
1
mol
−
1
and ΔV = +17.0
10
−
6
m
3
mol
−
1
Thus:
the involvement of a highly compressible phase,
usually a gas (e.g. Figure 2.2.2).
−−
11
d
d
P
T
=
=×
=×
32 4
17 010
19110
19110
.
.
Jmol K
mmol
Jm K
Phase diagrams in
T-X
space
−
63 1
6
−
−−
3
1
.
. Nm K
PaK
Crystallization in systems with no solid solution
6
−−
2
1
5
−
1
=×
19 110
.
P-T
and
P
V
-
T
diagrams make no provision for changes
in the compositions of individual phases during reac-
tions. Such changes are an important feature of igne-
ous processes, and make it necessary to introduce
another type of diagram in which the temperature of
equilibrium is plotted as a function of phase compos-
ition ('X'). An example is shown in Figure 2.4, which
shows the phase relations at atmospheric pressure for
the binary system CaMgSi
2
O
6
-CaAl
2
Si
2
O
8
. Because this
system is relevant to igneous rocks (it includes simple
analogues of basalt), the temperature range extends up
far enough to include melting.
If the temperature is sufficiently high, it is possible
to make a homogeneous melt containing the two com-
ponents CaMgSi
2
O
6
and CaAl
2
Si
2
O
8
in any desired pro-
portion. These compounds are said to be completely
miscible
in the melt phase. Consequently, in the field
marked 'melt', only this single phase is stable. In the
solid state, however, the two components exist as the
separate phases diopside (ideal composition
CaMgSi
2
O
6
) and anorthite (composition CaAlSi
2
O
8
):
there is no stable homogeneous solid of intermediate
composition. The area below 1274 °C is therefore a
two-phase field.
The two areas ABE and ECD are also two-phase
fields, each representing equilibrium between a melt
and one of the crystalline phases. To see how, con-
sider the line
xy
. This is an
isothermal
line at a tem-
perature whose precise value is unimportant (in this
case it is 1400 °C). We call this a
tie-line
, because it
links ('ties') together the compositions of two phases
which can coexist stably at this temperature.
x
repre-
sents the only composition of the melt that can be in
equilibrium with anorthite (composition
y
) at 1400 °C;
it consists of 61% CaAl
2
Si
2
O
8
and 39% CaMgSi
2
O
6
. If
the melt were more CaMgSi
2
O
6
-rich than this (comp-
osition
x
1
for example), it would dissolve anorthite
crystals and thereby increase the CaAl
2
Si
2
O
8
content
until equilibrium was reached or until the anorthite
present had all dissolved. If the liquid had the
The units (10
5
Pa K
−
1
= bar K
−
1
) relate to the gradient of a
line in
P-T
space (Figure 2.2). The sign of the gradient
is positive, consistent with Figure 2.2 (
P
rises with
T
),
and the magnitude (19.1 × 10
5
Pa K
−
1
) agrees well with
the value of about 20 × 10
5
Pa °C
−
1
as measured from
Figure 2.2, noting that kelvins and degrees Celsius are
units of equal size (Appendix A).
The positive slope of Figure 2.2 thus reflects the
observation that both Δ
S
and Δ
V
for this reaction are
positive (or both negative, if we write the reaction the
other way round). A negative slope would signify that
Δ
S
and Δ
V
had opposite signs, as is the case for the
andalusite-sillimanite reaction (Figure 2.1).
The most striking difference between Figures 1.3a,
2.1 and 2.2, on the one hand, and Figure 2.3 on the
other, is that the latter has a curved reaction boundary,
whereas the others are straight. The reaction boundary
is curved because the volume change for such a reac-
tion (and therefore d
P
/d
T
) is very pressure-sensitive:
muscovite anidine orundumvapour
+
+
(2.9)
∆
VV
=
+
V
+
V
−
V
vapour
sanidine
corundum
muscovite
At low pressures the volume of the 'vapour' phase
(actually a supercritical fluid - see Box 2.2) is much
greater than those of the solid phases, and therefore
dominates the value of Δ
V
.
∆
VV
≅
vapour
Because this term is large, the reaction boundary at low
pressure has only a moderate slope. But the vapour,
like any gas, is much more
compressible
than the solid
phases. At higher pressures,
V
vapour
and Δ
V
will get
progressively less, and the slope of the dehydration
boundary will get correspondingly steeper. This gen-
eral shape is a feature of all reactions involving the
generation of a 'vapour' phase (see also Figure 2.1.1).
Curved boundaries in
P-T
diagrams always signify
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