Geology Reference
In-Depth Information
where the numerical constant C
NH
now contains also the proportionality constants
relating V
;
A
t
and l to the powers of d and D
V
is the bulk or volume diffusion
coefficient. Values of C
NH
of around 12-14 have been calculated for particular
grain geometrics by Herring (
1950
), Raj and Ashby (
1971
) and others; for a
summary, see Poirier (
1976
,
1985
) who also discusses the alternative presentation
of the theory in terms of shear strain rate and shear stress, in which case C
NH
is
multiplied by 3.
As an illustration of the typical application of (
5.9
), e
D
V
=
d
2
if we assume V
m
¼
10
4
m
3
;
T
¼
1200 K and r
1
r
3
¼
10 MPa
:
If, further, D
V
¼
10
18
m
2
s
1
;
then
e
¼
10
6
s
1
for d
¼
1lm and e
¼
10
12
s
1
for d
¼
1mm
:
For metals it is common to formulate the theory in terms of vacancy diffusion
(Poirier
1976
,
1985
), which presumes a vacancy diffusion mechanism for the
atomic transfer process. In the case of compound substances, however, as in
minerals and rocks, it would seem more appropriate to discuss the transfer process
directly in terms of the compound itself. Several atomic species may be involved
but, except where chemical segregation or differentiation is occurring, the creep
rate is to be related to the total molecular flux. The relevant diffusion coefficient
and molar volume in (
5.9
) will then be those of the molecular species of which the
material consists. In the case of ionic compounds of form A
a
B
b
;
and since for a
pure substance it is the self-diffusion that is involved, the diffusion coefficient of
the molecular species will be given by the expression (
3.40
), that is, by
D
A
D
B
bD
A
þ
aD
B
D
¼
ð
5
:
10
Þ
where D
A
and D
B
are the self-diffusion coefficients of the cation and anion,
respectively; thus, if D
B
\\D
A
, then D
D
B
=
b and the creep rate will be
determined essentially by the self-diffusion coefficient of the anion. In the case of
ceramics, such as beryllium oxide, it has been deduced that the anion diffusion
tends, in fact, to be rate-controlling in Nabarro-Herring creep (Gordon
1973
,
1975
).
In more complex systems, where more than one component is to be recognized, it
is possible that a certain amount of creep can occur by selective diffusion of the more
mobile components, leading to a differentiation or segregation. However, more
complicated compatibility requirements will arise in such cases in connection with
accommodating the immobility of the more sluggish components and the selective
transport of the others. Such segregation effects have long been used to aid in
recognizing diffusion creep, the classic case being that of magnesium -1/2 % zir-
conium alloy in which the re-deposited material is relatively devoid of the slower-
diffusing zirconium, as shown by the distribution of zirconium hydride precipitates
after hydrogen treatment (Squires et al
1963
); also see Poirier (
1976
,
1985
) for this
and other examples.
