Geology Reference
In-Depth Information
1600
Melt
Melt
D
1500
m
Melt
x
2
y
x
1
x
A
1
400
An
n
An + melt
Di + melt
1
300
E
X
B
C
(12
74)
Melt
An
Di + An
1
200
Di
0
20
40
c
80
100
Pure
CaMgSi
2
O
6
Pure
CaAl
2
Si
2
O
8
Percentage of CaAl
2
Si
2
O
8
by mass
Figure 2.4
Melting relations in the
pseudo-binary
system CaMgSi
2
O
6
-CaAl
2
Si
2
O
8
at atmospheric pressure. The horizontal
ruling represents two-phase fields: the solid-solid field is ruled more heavily than the solid-melt fields. 'Di' and 'An' refer to
the phases diopside (composition CaMgSi
2
O
6
) and anorthite (composition CaAI
2
Si
2
O
8
). This phase diagram is not strictly
binary because small amounts of aluminium enter the pyroxene phase (see Morse, 1980, pp. 53-7, for details). The circular
cartoons on the right illustrate what an experimental 'magma' might look like under the microscope at each stage.
composition
x
2
, it would precipitate anorthite, so
reducing the CaAl
2
Si
2
O
8
content.
As the line DE shows, the composition of melt that
can exist in equilibrium with anorthite (An) depends
on the temperature. The corresponding line A-E shows
that the same is true of the melts that can coexist with
diopside (Di). The curve AED, the locus of the melt
compositions that can coexist in equilibrium with
either diopside or anorthite at different temperatures,
is called the
liquidus
. All states of the system lying
above it in Figure 2.4 consist entirely of the melt phase.
The one point common to both limbs of the liquidus is
E, which therefore represents the unique combination
of melt composition and temperature at which all three
phases are simultaneously at equilibrium. This condi-
tion is called a
eutectic
.
In applying the Phase Rule to Figure 2.4, we must
recognize that a
T-X
diagram like this is no more than
the end-view of more complex phase relations encoun-
tered in
P-T-X
space (cf. Figure 2.6a). By considering
melting relations only at a single - in this case atmos-
pheric - pressure, we are in fact artificially restricting
the variance of each equilibrium. Any statements we
make about variance in this diagram relate only to an
apparent variance
F
′ where:
FF
'=−1
(2.10)
One may write the Phase Rule in terms of
F'
as follows:
(
)
=+
φ
+=++
F
φ
F
'1
C
2
Therefore
φ+=+
FC
'
1
(2.11)
This form of the Phase Rule, applicable to
isobaric
T-X
(and, incidentally,
isothermal
P-X
) phase diagrams, is
sometimes known as the
Condensed Phase Rule
.
Point E
ϕ
= 3
(3 phases, Di + An + melt)
C
= 2
(2 components, CaMgSi
2
O
6
and
CaAl
2
Si
2
O
8
)
3 +
F
ʹ
= 2 + 1
Therefore
F
ʹ
= 0
an isobarically
invariant
equilibrium
The term
isobarically invariant
is jargon that reminds us
that this equilibrium is invariant only so long as the
pressure is held constant; if this constraint were to be
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