Geoscience Reference
In-Depth Information
be obtained by the superposition of two basic
types: the edge dislocation and the screw dislo-
cation. These can be visualized by imagining a
cut made along the axis of a cylinder, extending
from the edge to the center and then shearing
the cylinder so the material on the cut slides radi-
ally (edge dislocation) or longitudinally (screw
dislocation). In the latter case the cylinder is sub-
jected to a torque. Dislocation theory has
been applied to the creep and melting of
solids, and to the attenuation of seis-
mic waves.
interface depends on the mineralogy and the
amount of the lower-melting-point phase. The
Earth is slowly cooling with time and therefore
melting was more extensive in the past and prob-
ably extended, on average, to both shallower and
greater depths than at present. Eclogitic por-
tions of the mantle can also have long melting
columns and low melting temperatures.
The dependence of melting point T m on
pressure is governed by the Clausius--Clapeyron
equation
d T m / d P
= V / S = T V / L
where
S are the changes in volume and
entropy due to melting and L is the latent heat
of melting.
V and
Melting and origin of magmas
V can be
either positive or negative. Therefore the slope of
the melting curve can be either negative or posi-
tive but is generally positive. Although this equa-
tion is thermodynamically rigorous, it does not
provide us with much physical insight and is not
suitable for extrapolation since the parameters
all depend on pressure. Because of the high com-
pressibility of liquids,
S is always positive, but
There are several ways to generate melts in the
mantle; raise the absolute temperature, lower
the pressure, change the composition or raise
the homologous temperature. Melting can occur
in situ if the temperature is increasing with depth
and eventually exceeds the solidus. The main
source of heating in the mantle is the slow pro-
cess of radioactive decay. Heating also leads to
buoyancy and convection, a relatively rapid pro-
cess that serves to bring heated material toward
the surface where it cools. The rapid ascent of
warm material leads to decompression, another
mechanism for melting due to the relative slopes
of the adiabat and the melting curve. Extensive in
situ melting, without adiabatic ascent, is unlikely
except in layers or blobs that are intrinsically
denser than the overlying mantle. In this case
melting can progress to a point where the intrin-
sic density contrast is overcome by the elimina-
tion of a dense phase such as garnet. Below about
100 km the effect of pressure on the melting
point is much greater than the adiabatic gradi-
ent or the geothermal gradient in homogenous
regions of the mantle. The melting curve of peri-
dotite levels off at pressures greater than about
100 kb. This combined with chemical boundary
layers at depth makes it possible to envisage the
onset of melting at depths between about 300
and 400 km or deeper. Because of the high tem-
perature gradient at the interface between chem-
ically distinct layers, melting is most likely to
initiate in chemical boundary layers. Whether
melting is most extensive above or below the
V decreases rapidly with
pressure, and
S probably approach
limiting values at high pressure.
The Lindemann melting equation states
that melting occurs when the thermal oscillation
of atoms reaches a critical amplitude,
V / V and
2 V 2 / 3
T m =
Am
where m is the mass of the atoms, V is the vol-
ume,
is the Debye temperature and A is a
constant. Gilvarry (1956) rewrote this in terms of
the bulk modulus and volume of the solid at the
melting point,
T m / T o = ( V o / V m ) 2( γ 1 / 3)
and obtained
c
=
(6
γ +
1)
/
(6
γ
2)
Other theories of melting assume that some criti-
cal density of dislocations or vacancies causes the
crystal to melt or that a crystal becomes unsta-
ble when one of the shear moduli vanishes. All of
the above theories can be criticized because they
do not involve the properties of the melt or con-
siderations of solid--melt equilibrium. They cor-
respond rather to an absolute stability limit of a
Search WWH ::




Custom Search