Geoscience Reference
In-Depth Information
temperature and the homologous temperature
are two of these scaled, or dimensionless, tem-
peratures. The ratio
E
∗
/
Table 21.4
Diffusion parameters in silicate
minerals
T
m
is nearly constant for a
variety of materials, though there is some depen-
dence on valency and crystal structure. Thus, the
factor
E
∗
/
Diffusing
D
o
Q
Mineral
Species
(m
2
/s)
(kJ mol
−
1
)
T
in the exponent for activated pro-
cesses can be written
10
−
4
Olivine
Mg
4.1
×
373
is roughly
a constant and
T
m
is the melting temperature.
If this relation is assumed to hold at high pres-
sure, then the effect of pressure on
G
∗
, that is,
the activation volume
V
∗
, can be estimated from
the effect of pressure on the melting point:
λ
T
m
/
T
where
λ
10
−
10
Fe
4.2
×
162
10
−
8
O
5.9
×
378
10
−
13
Si
7.0
×
173
Fe-Mg
6.3
×
10
−
7
239
Garnet
Sm
2.6
×
10
−
12
140
Fe-Mg
6.1
×
10
−
4
344
Ca
2
SiO
4
Ca
2.0
×
10
−
6
230
D
(
P
,
T
)
=
D
o
exp[
−
λ
T
m
(
P
)
/
RT
]
CaSiO
3
Ca
7
468
and
Albite
Na
1.2
×
10
−
7
149
T
m
V
∗
=
E
∗
dT
m
dP
O
1.1
×
10
−
9
140
Orthoclase
Na
8.9
×
10
−
4
220
4.5
×
10
−
12
which, invoking the Lindemann law, becomes
O
107
10
−
6
Nepheline
Na
1.2
142
×
V
∗
=
2
E
∗
(
γ
−
1
/
3)
/
K
T
Glass
Albite
10
−
5
Ca
3.1
193
which is similar to expressions given above. The
temperature
T
, normalized by the 'melting tem-
perature,'
T
m
is known as the
homologous tem-
perature
. It is often assumed that activated
properties depend only on
T
m
/
×
10
−
6
Orthoclase
Ca
2.6
179
×
10
−
5
Basalt
Ca
4.0
209
×
10
−
10
Na
5
41.8
×
T
and that the
effect of pressure on these properties can be
estimated from
T
m
(
P
). Experimentally determined
diffusion
Freer (1981).
parameters
are
given
in
Tables
21.3
V
∗
is about 8--12 cm
3
/mole for oxygen self-
diffusion in olivine and about 2--5 cm
3
/mole in
the lower mantle, decreasing with depth. The
effect of pressure on ionic volumes leads one
to expect that
V
∗
will decrease with depth and,
therefore, that activated processes became less
sensitive to pressure at high pressure. Indeed,
both viscosity and seismic factor
Q
do not appear
to increase rapidly with depth in the lower man-
tle. Pressure also suppresses the role of temper-
ature in the deep mantle. Another way to look
at this is to consider that solids become more
incompressible with depth, and therefore den-
sity, or volume, variations are less, and many
lattice properties vary with volume.
and 21.4.
The melting point of a solid is related to
the equilibrium between the solid and its melt
and not to the properties of the solid alone.
Various theories of melting have been proposed
that involve lattice instabilities, critical vacancy
concentrations or dislocation densities, or ampli-
tudes of atomic motions. These are not true the-
ories of melting since they ignore the properties
of the melt phase, which must be in equilibrium
with the solid at the melting point.
Dislocations
Dislocations are extended imperfections in the
crystal lattice and occur in most natural crystals.
They can result from the crystal growth process
itself or by deformation of the crystal. They can
be partially removed by annealing. Although dis-
locations occur in many complex forms, all can
Homologous temperature
In many processes a scaled temperature is more
useful than an absolute temperature. The Debye
