Geology Reference
In-Depth Information
Fig. 5.1 Schematic
representation of a single
domain consisting of one
source-sink pair undergoing
shape change by atomic
transfer flow
σ
1
d
SINK
AREA
A
SL
σ
3
ALTENATIVE
TRANSFER
PATHS
SOURCE
AREA
A
SD
flow in a solid by a process analogous to that in a viscous fluid is normally
negligible.
As might be expected for a process that involves the relative displacement of
individual atoms rather than large groups of atoms, atomic transfer flow tends to be
more important at relatively low stresses, insufficient to initiate the displacement
of the large groups but sufficient to bias the motion of the individual atoms. It will
be seen later that atomic transfer flow can be of practical importance at high
temperatures when solid-state diffusion is the transport mechanism and at mod-
erate or low temperatures when fluid transfer is involved.
The various types of atomic transfer flow can be classified according to the
nature of the sources and sinks and of the transfer process. Several that may be
relevant for rocks are set out in subsequent sections. However, underlying all is a
common theoretical framework that we first set out.
We consider the macroscopic strain of a body that result from the transfer of
material from source to sink via a well-defined path under uniaxial stress
(Fig.
5.1
). The model is defined in terms of the following elements and symbols:
1. The stress-supporting part of the body is considered, at least for preliminary
discussion, to consist of a single component of molar volume V
m
:
2. The sources and sinks, regarded as surfaces of area A
s
, are characterized by a
rate constant k
s
governing the rate of any reaction required to effect detachment
or re-attachment of material and a numerical parameter a
s
representing the
fraction of surface sites in source or sink at which the detachment or re-
attachment reaction can occur. (The suffixes ''so'' and ''si'' are used to dis-
tinguish source and sink, respectively).
3. The transfer path, of cross-sectional area A
t
;
is assumed to consist of a medium
in which the species being transferred has a diffusion coefficient D and solu-
bility c (c
¼
1
=
V
m
when no other substance exists in the path).
