Geoscience Reference
In-Depth Information
Chapter 21
Nonelastic and transport properties
Shall not every rock be removed out
of his place?
raised. Thus, thermal conduction in solids arises
partly from electronic and partly from atomic
motion and, at high temperature, from radiation
passing through the solid.
Debye theory regards a solid as a system
of coupled oscillators transmitting thermoelas-
tic waves. For an ideal lattice with simple har-
monic motion of the atoms, the conductivity
would be infinite. In a real lattice, anharmonic
motion couples the vibrations, reducing the
mean free path and the lattice conductivity. Ther-
mal conductivity is related to higher-order terms
in the potential and should be correlated with
thermal expansion. Lattice conductivity can be
viewed as the exchange of energy between high-
frequency lattice vibrations -- elastic waves. An
approximate theory for the lattice conductivity,
consistent with the Gruneisen approximation,
gives
Job 18:4
Most of the Earth is solid, and much of it is
at temperatures and pressures that are difficult
to achieve in the laboratory. The Earth deforms
anelastically at small stresses and, over geological
time, this results in large deformations. Most lab-
oratory measurements are made at high stresses,
high strain rates and low total strain. Laboratory
data must therefore be extrapolated in order
to be compared with geophysical data, and this
requires an understanding of solid-state physics.
In this chapter I discuss processes that are related
to rates or time. Some of these are more depen-
dent on temperature than those treated in pre-
vious chapters. These properties give to geology
the 'arrow of time' and an irreversible nature.
2
TK
3
/
2
T
1
/
2
K
L
=
a
/
3
γ
ρ
where
is the
Gruneisen parameter,
T
is temperature,
K
T
is the
isothermal bulk modulus and
a s
the
lattice
parameter,
γ
Thermal conductivity
is density. This is
valid at high temperatures, relative to the Debye
temperature. This relation predicts that the ther-
mal conductivity decreases with depth in the top
part of the upper mantle.
The thermal conductivities of various rock-
forming minerals are given in Table 21.1. Note
that the crust-forming minerals have about one-
half to one-third of the conductivity of man-
tle minerals. This plus the cracks present at
low crustal pressures means that a much higher
thermal
ρ
There are three mechanisms contributing to
thermal conductivity in the crust and mantle.
The lattice part is produced by diffusion of ther-
mal vibrations in a crystalline lattice and is also
called the phonon contribution. The radiative
partisduetothetransferofheatbyinfraredelec-
tromagnetic waves, if the mantle is sufficiently
transparent. The exciton part, is due to the trans-
port of energy by quasiparticles composed of elec-
trons and positive holes; this becomes dominant
in intrinsic semiconductors as the temperature is
gradient
is
maintained
in
the
crust,
