Geology Reference
In-Depth Information
Fig. 3.3 Energy E as a
function of distance x in the
presence of a stress
x
Glasstone et al.
1941
; Lasaga
1981
), it is then calculated that the specific rate or
rate coefficient for the forward reaction will be proportional to k
B
T
=
hK
6¼
;
where k
B
is the Boltzmann constant, h the Planck constant, and K
6¼
the equilibrium constant
for the equilibrium between the reactants and the activated complex, which can be
expressed in terms of the partition functions of the participating species including
the activated complex; the proportionality constant contains the activity coeffi-
cients of the participating species. The factor k
B
T
=
h (
¼
2
:
08
10
10
T s
1
)isa
''fundamental frequency'' that determines the dynamics of the process. Thus, apart
from numerical factors generally of the order of unity, we can identify m in (
3.8
)
and (
3.12a
) with k
B
T
=
h and K
6¼
with exp
G
m
=
R
ð Þ:
However, transition state
theory has many limitations and other approaches to a theory of reaction kinetics
have also been attempted (Christian
1975
, Chap. 3; Flynn
1972
, Chap. 7).
3.2.4 Stress-Assisted Thermal Activation
We now consider the rate of thermally activated events that are assisted by the
action of an applied stress on the entity involved. The existence of a mechanical
effect implies that energy can be transferred to the entity by a force acting on it
during a displacement in space. Therefore the appropriate reaction coordinate is a
distance in space. Figure
3.3
depicts the energy E of the entity versus the distance
coordinate x.
We are concerned with an activation event that results in the entity being
displaced from the position 1 to position 3 over the barrier 2. The frequency of
forward jumps will be
m
þ
¼
m
0
exp
DE
Fdx
kT
and reverse jumps
