Geology Reference
In-Depth Information
different transfer rates. However, if no compositional change or segregation
occurs, then from a macroscopic or thermodynamic point of view only the
molecular species or an average substance need be considered, to which an
effective diffusion coefficient can be attributed. If, on the other hand, the
deformation accompanies a segregation or differentiation of the body, as may
well happen in geological deformations, then the diffusion of the individual
components has to be considered separately and the flow equations adapted
appropriately.
2. In the expressions (
5.6
-
5.8
) the stress dependence is linear or Newtonian as
long as there is no stress dependence in the other parameters. However, non-
linear stress dependence could, in principle, arise if any of the dimensional
parameters l
;
A
t
;
a
;
A
s
associated with the diffusion path or reaction zones were
to be stress dependent. Also steady state behaviour, or constancy of strain rate
at constant stress, will only appear to the extent that these dimensional
parameters remain constant over the duration of the flow.
3. It is insufficient to discuss only the transfer of material from sources to sinks
without considering how the parts of the body fit together after the transfer, as has
already been indicated in defining the constant C
1
in (
5.1
). We must therefore now
consider the nature and implications of these compatibility constraints.
5.2 Compatibility Considerations
In general, the sources and sinks will need to constitute a more or less continuous
system of interfaces that will define the parts or domains of the body (commonly
the grains of a polycrystal) the fitting together of which will have to be maintained
during the deformation if constancy of volume is to be maintained. In addition,
both a correlation in the relative rates of material removal or emplacement at
different points in the source/sink system and a correlation in the relative motion of
the parts of the body that accompany the material transfer are required to maintain
the fitting together of the parts. These constraints on the geometry of the source/
sink system and on the correlations in the transfer and relative displacement
constitute the compatibility conditions for the deformation mechanism. The gen-
eral framing of appropriate compatibility conditions does not yet seem to have
been set out formally for diffusion creep although the qualitative requirements are
fairly obvious. In the formal framing, generalized dislocation notions may be
useful, involving Burgers vectors with components normal to the source or sink
interfaces, representing the material transfer, and components parallel to the
interfaces, representing sliding at the interfaces required to satisfy the compati-
bility conditions. The details of the consequences of the compatibility constraints
will depend on the specific models but where grain boundaries are the source/sink
system some sliding at grain boundaries will be entailed.
