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of compounds, will be the effective diffusion coefficient for the molecular species
(
Sect. 3.5.3
). The activation energy obtained from an Arrhenius plot for the steady-
state creep rate would in this case be expected to coincide with that for self-
diffusion. Such an equality has indeed been widely observed at high temperature in
pure metals (Poirier
1985
, p. 44; Weertman and Weertman
1983b
) as well as in
various other materials, but it is not always found. For example, in olivine the
experimental activation energy for high-temperature creep is higher than that
found for the diffusion of any of its atomic components (Jaoul et al.
1981
).
Thus, insofar as high temperature, steady-state creep by dislocation glide is
recovery controlled, which it probably almost always is in some sense, the rate-
controlling process may often be the volume self-diffusion involved in climb, as
assumed for (
6.45
), but it is evidently not always so. Several alternatives may be
mentioned. Thus, at intermediate temperatures it is possible that pipe diffusion
along dislocation cores may be important, leading to a lower activation energy.
Alternatively, and again at intermediate temperatures, the recovery process may be
cross-slip controlled, for which the activation energy would probably also be lower
than that for self-diffusion; the possible importance of cross-slip control has been
the subject of controversy (Poirier
1976
,
1978
,
1979
; Sherby and Weertman
1979
).
The observed tendency for the experimental activation energy for steady-state
creep to decrease as the temperature decreases could thus correspond to a tran-
sition to either of these two situations; in the case of pipe diffusion the stress
exponent n might also be expected to increase by 2 {Evans 1979}. Even if the
recovery is climb controlled, the climb process itself may not be entirely diffusion
controlled, but may depend also on the rate at which the diffusing material can
be attached or removed at the dislocation core. The attachment/removal can be
expected to occur mainly at jogs in the dislocation and so the climb rate could be
limited by the jog nucleation rate if the latter were relatively low. Since the climb
rate will be proportional to the product of the probability of an atom arriving/
departing by diffusion at the dislocation and the probability of a jog being present
at which to attach/detach the atom, the activation energy for climb will be the sum
of the activation energies for diffusion and for job nucleation. A negligible value of
the activation energy for jog nucleation is thus a prerequisite for the activation
energies of steady state climb-controlled creep and diffusion to be equal. However,
even with zero jog nucleation energy, a further source of inequality of the acti-
vation energies could arise in the case of compounds through there being a
chemical reaction type of barrier involved in the attachment/detachment of atoms
at the dislocation core; this barrier would derive from there being transitory higher
energy configurations at the jog as individual atomic components of the compound
are attached/detached.
Further theoretical development thus requires more specific assumptions about
mechanisms at the microstructural scale, where many possibilities arise and where
further developments in the future could follow from new understanding of mutual
dislocation interaction mechanisms (
Sect. 6.6.3
). The archetype of climb-
controlled recovery models is that of Weertman (Weertman
1955
,
1957
,
1968
; see
also Weertman and Weertman
1983b
) but many variants of such a model have
