Geoscience Reference
In-Depth Information
Table 18.6
Dimensionless logarithmic anharmonic derivatives
Substance
K
S
}
T
G
K
S
}
P
G
K
S
}
V
G
{
{
}
T
{
{
}
P
{
{
}
V
Averages
Halides
5.1
2.6
4.1
5.9
0.9
−
3
.
3
Perovskites
∗
4.8
2.7
4.4
5.0
0.3
−
2
.
2
Garnets
∗
4.9
2.6
6.1
4.9
−
1
.
2
−
2
.
3
Fluorites
∗
5.0
2.2
4.8
5.2
0.2
−
2
.
9
Oxides
5.3
2.0
5.7
5.8
−
0
.
4
−
3
.
7
Silicates
5.6
2.8
5.4
5.4
0.2
−
2
.
6
Grand average
5.1
2.5
5.0
5.7
0.1
−
3
.
2
(
±
1
.
0)
(
±
1
.
3)
(
±
1
.
9)
(
±
1
.
9)
(
±
1
.
9)
(
±
1
.
9)
Olivine
5.1
2.9
4.9
6.7
0.2
3
8
−
.
Olivine
4.8
2.9
4.7
6.3
0.2
3
4
−
.
MgAl
2
O
4
-spinel
4.9
0.9
3.8
4.2
0
6
1
0
−
.
+
.
{
}=
∂
/∂
ρ
M
ln
M
ln
∗
Structures.
Table 18.7
Anharmonic parameters for oxides and silicates and predicated
values for some high-pressure phases
Mineral
K
T
}
T
K
S
}
T
G
K
T
}
P
K
S
}
P
G
{
{
{
}
T
{
{
{
}
P
α
-olivine
5.0
4.8
2.9
6.6
4.7
6.5
β
-spinel
∗
4.9
4.8
3.0
6.6
4.7
6.4
γ
-spinel
∗
5.1
5.0
3.1
6.8
4.9
6.5
Garnet
4.8
4.7
2.7
7.9
6.8
4.9
MgSiO
3
(majorite)
∗
4.9
4.7
2.6
7.9
6.0
4.5
Al
2
O
3
-ilmenite
4.4
4.3
2.7
6.8
4.3
7.5
MgSiO
3
-ilmenite
∗
4.7
4.5
2.7
7.0
4.3
6.0
MgSiO
3
-perovskite
∗
4.5
4.5
3.5
7.5
5.5
6.5
∗
4.2
4.1
2.8
6.2
4.0
5.7
SiO
2
-(stishovite)
∗
4.5
4.4
2.4
7.5
6.4
5.0
∗
Predicted.
(
∂
ln
G
/∂
T
)
V
=
α
[(
∂
ln
G
/∂
ln
ρ
)
T
−
(
∂
ln
G
/∂
ln
ρ
)
P
]
K
S
=
K
T
(1
+
αγ
T
)
δ
T
≈
δ
S
+
γ
for many halides, oxides and minerals. Average
values for chemical and structural classes are
extracted in Table 18.6, and parameters for min-
eral phases of the lower mantle are presented in
Table 18.7.
This notation stresses the volume, or den-
sity, dependence of the thermodynamic vari-
ables and is particularly useful in geophysical
discussions.
Values
(
∂
ln
V
P
/∂
ln
ρ
)
3
5
(
1
1
2
2
5
(
=
∂
ln
K
S
/∂
ln
ρ
)
+
∂
ln
G
/∂
ln
ρ
)
−
of
most
of
the
dimensionless
log-
whereIhaveused
K
s
=
2
G
, a value appropriate
arithmic
parameters
are
listed
in
Table
18.5
for the lower mantle.
