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mechanism. Coble creep is dominant at very fi ne grain sizes whereas N-H
creep is rate controlling at larger grain sizes. Also at relatively low homolo-
gous temperatures Coble creep is rate controlling and N-H creep takes pre-
cedence at high homologous temperatures. This approach to understanding
diffusion creep is quite valid for metals and alloys. Similar phenomena in
ceramics become complex due to ambipolar diffusion and stoichiometry.
The diffusion fl ux of both cations and anions constituting the ceramic must
be considered to estimate the net diffusion rate. In monovalent materials
the vacancies in diffusion creep regime can get transported along the grain
boundaries or the lattice and the total strain rate of deformation is given
by the sum of N-H and Coble creep mechanisms. But in a ceramic of the
type
A
p
B
q
, where
A
is the cation and
B
the anion, both the anions and cat-
ions participate in the diffusion process and might adopt different transport
paths. In this case the total strain rate of deformation in the Coble creep
model is given by
ε
∝
D
D
composite
D
omposite
⎣
(
)
⎤
(
)
+
(
+
+
p
)
⎡
D
L
+
1
Dd
+
+
2
δ
[3.61 ]
L
D
b
p
=
(
)
(
)
(
)
.
+
(
)
D
+
1
)
(
+
+
qp
+
(
(
)
+
(
The transport path of the anions and cations was originally considered by
Gordon
100
who suggested that the total transport of vacancies from the hor-
izontal to the vertical boundaries should be in the appropriate stoichiomet-
ric ratio. This leads to the prediction that creep would be controlled by the
diffusion of the slower moving species along the faster diffusion path. In this
scenario, it is possible for the cations and anions to be transported predom-
inantly along different paths as depicted in Fig. 3.25a.
However the transport paths suggested by Gordon might lead to the
development of local non-stoichiometry
101
which has not been observed in
ceramics. Hence Chokshi
102
suggested that it would be appropriate to con-
strain diffusion fl uxes along each path to be in the appropriate stoichiometric
ratio, as depicted schematically in Fig. 3.25b. In this scenario, it is necessary
to fi nd the slower moving species along each path, and the rate controlling
process is then determined from the faster diffusion path. The difference in
transport paths suggested by Gordon
100
and Chokshi
102
has implications for
the transitions in diffusion creep mechanisms. Plots of strain rate against
T
m
/
T
, for a fi xed grain size are shown in Fig 3.26a and 3.26b. The symbols C
and N, in these fi gures, represent Coble and N-H creep, and the superscripts
+ and − represent cation and anion, respectively. Figure 3.26a, correspond-
ing to transport paths suggested by Gordon, indicates that there will be
transitions with an increase in temperature from diffusion creep controlled
by cation grain boundary diffusion (
C
+) to cation lattice diffusion (
N
+
) to
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