Geology Reference
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the  same range as for diffusion (see captions to
Figures 3.6 and 3.8).
The deformation of crystalline rocks, although a
much more complicated process, shows a similar
dependence on temperature:
T /°C
2000
1500
1000
Basalt
-5
strain rate = (
)
Ae ERT
a /
N
σ
(3.17)
Rhyolites
where σ is again shear stress, and N is a constant
depending on details of the deformation process (its
value is typically about 8). The factor in brackets is
analogous to inverse viscosity. It is not given that name
because σ , instead of appearing in linear form, is raised
to the power N . Activation energies are nonetheless in
the same range as those for viscous flow of melts.
-10
1
η
In ( )
-15
Silica
-20
Persistence of metastable minerals:
closure temperature
0.4
0.5
0.6
0.7
0.8
0.9
10 3 /K -1
T
An equilibrium Earth would be extremely boring (e.g. there would
be no life, no O 2 in the air, no plate tectonics, etc.). Disequilibrium is
what makes the Earth so diverse and interesting. Without kinetic
barriers there would be no geochemists to study kinetics or science,
because all human beings, and in fact all life forms, 'should burst
into flames'! (Zhang, 2008)
Figure 3.8 Arrhenius plot of viscosities (in N s m −2 ) for some
silicate melts; Viscosity is the inverse of the flow rate-constant
so it has been plotted here in reciprocal form. Temperature
is expressed in kelvins (K). The slope of the graphs increases
with silica content, reflecting an increase in activation
energy as follows:
Paradoxically, chemical equilibrium in geological pro-
cesses would be of less interest to the petrologist were it
not for the intervention of disequilibrium. Consider an
argillaceous rock undergoing metamorphic recrystalli-
zation in conditions corresponding to the kyanite-sill-
imanite phase boundary (Figure 2.1). Once equilibrium
is achieved, kyanite and sillimanite will coexist stably
in the rock. If, following uplift and erosion, the rock is
found at the surface still containing kyanite and sill-
imanite, their coexistence and textural relationship will
testify to the high-temperature conditions under which
the rock crystallized and will give the petrologist an
indication of the conditions of metamorphism. Yet the
current state of the rock is plainly one of disequilib-
rium, as sillimanite is now well outside its stability
field; it remains only as a metastable relic of a former
state of equilibrium.
Metamorphic equilibrium seems generally to keep
pace with changing conditions more effectively in pro-
grade reactions (those involving a temperature increase)
than during the waning stages of regional metamor-
phism. One reason is that volatile constituents such as
Basalt melt: 230 kJ mol 1
Rhyolite melt: 350 kJ mol 1
Pure silica melt: 500 kJ mol 1
(Source: data from Scarfe (1978) and other authors cited
therein).
water vapour, whose presence accelerates recrystalliza-
tion, will be more abundant during the prograde stage
owing to the dehydration reactions taking place. Once
volatiles have been lost from the system, they are no
longer available to facilitate the retrograde (falling-tem-
perature) stages of metamorphism that follow. In the
absence of volatiles it is likely that temperature asserts
the dominating influence on metamorphic reaction rates.
As metamorphic or igneous rocks cool, they pass
into a temperature range of increasing kinetic paraly-
sis, in which reaction rates fall behind changing cir-
cumstances (as illustrated in Box  3.5). Eventually a
temperature is reached (depending on the reaction
being considered) at which diffusion rates become
substantially slower that the cooling rate of the rock,
 
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