Geology Reference
In-Depth Information
Grain-boundary diffusion appears to be much more
rapid in most circumstances than volume diffusion.
Grain boundaries provide the main conduit through
which volatile species penetrate the volume of a rock
during metamorphism and hydrothermal alteration.
Open fractures and faults do not occur in the deep crust
owing to the high temperature and confining pressure.
Under these conditions fluid migration is concentrated
along
shear zones
, where deformation has led to a local
reduction of grain size and often to a strong
foliation
,
both of which promote diffusion and fluid movement
because of the increase in grain-boundary area.
Box 3.5 illustrates how diffusion studies can be
applied to estimate the cooling rates experienced by
iron meteorites.
Table 3.1
Illustrative viscosity values (in Pa s) for everyday
liquids and for dry silicate melts
Substance
Viscosity at room
temperature
(~25°C)
Melt viscosity
above liquidus
temperature
Water
0.001
Motor oil Sae 50
0.5
egg white
2.5
treacle
20
Basalt melt (dry)*
7.5-150
Smooth peanut butter
250
Glazier's putty
~10
5
rhyolite melt (dry)*
~10
10
*Melt viscosity increases if suspended crystals or bubbles are present.
The viscosity of an erupted lava affects the style of a
volcanic eruption, and its value depends upon both
melt composition and temperature. Siliceous lavas like
rhyolite have viscosities several orders of magnitude
higher than basalts at their relevant liquidus tempera-
tures (Table 3.1), as explained in Box 8.3. Figure 3.8
shows both this compositional effect and the tempera-
ture variation. By analogy with Figures 3.5 and 3.6b,
viscosity is plotted in a logarithmic form that varies
linearly with inverse temperature. Each of these
straight lines can be described by an equation involv-
ing an activation energy
E
a
:
11
Melt viscosity
The flow of silicate melts is another kind of geological
process where the rate varies strongly with temper-
ature. Like treacle, silicate melts become less viscous as
the temperature is raised.
A liquid flows in response to shear stress applied to
it, which generates a velocity gradient in the liquid.
The velocity of water flowing in a pipe of radius
r
, for
example, increases from zero at the wall to a maximum
v
at the centre, a mean gradient of
v
/
r
. For most liquids
the velocity gradient d
v
/d
z
is proportional to the
applied shear stress σ:
e
E
a
/
RT
=
(3.15)
ηη
0
d
d
v
z
=
σ
η
(3.14)
1
=−
E
RT
1
1
or usingnatural logarithms :ln
a
+
ln
η
η
0
The parameter
η
in Equation 3.14 is called the
viscosity
of the liquid. Because viscosity measures
resistance
to
flow, it is like an inverse rate constant: a
low
viscosity
indicates a runny liquid capable of rapid flow, whereas
a
high
value signifies a 'stiff' or viscous one that flows
only slowly.
As to units of measurement, shear stress
σ
is meas-
ured in Pa = N m
−
2
(Appendix A, Table A2), and d
v
/d
z
is measured in (m s
−
1
) m
−
1
= s
−
1
. Rearranging Equation
3.14 gives η = σ/d
v
/d
z
, so the units in which viscosity
is measured are Pa/(s
−
1
) = Pa s. To provide a feel for
how widely viscosities vary in nature, Table 3.1
provides some illustrative values.
(3.16)
The resemblance of Equation 3.16 to Equation 3.13
tells us that the flow of a silicate melt - like diffu-
sion - requires atoms or molecules to jostle past each
other, surmounting energy hurdles as they do so.
The collective effect of these energy hurdles is
expressed in the flow activation energy
E
a
, the value
of which can be determined by measuring the gradi-
ent of each line (= −
E
a
/
R
). The activation energies
for the flow of silicate melts (which Figure 3.8 shows
to be, like viscosities themselves, higher for siliceous
melts than for low-silica melts) are generally in
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