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typically
observed
for
both
dislocations
and
grain
boundaries
(for
example
Atkinson and Taylor 1981 ).
When the diffusion distance is not large compared with the spacing of interfaces
or pipes, the analysis is more complicated because of having to take into account the
lateral diffusion from the high-diffusivity regions into the grains. However, such
analysis is important in the practical determination of the short-circuit diffusion
coefficients, although generally only the value of the product D SC d can be directly
obtained. For details and further references, see Adda and Philibert ( 1966 , Chaps.
12, 13), Le Claire ( 1976 ), Martin and Perraillon ( 1980 ), Peterson ( 1980 , 1983 ).
Owing to the greater degree of disorder in interfaces or pipes, the jump fre-
quency can be expected to be much higher than within the grains due to a lower
value of E. This observation is consistent with the observation of lower values of
Q, typically about one-half to two-thirds that for volume diffusion in case of grain
boundary diffusion in metals and a similar ratio may be expected on nonmetals, for
example, 0.7 in case of NiO (Atkinson and Taylor 1981 ). Consequently, in a given
polycrystal, while the volume diffusion through the grains tends to dominate the
bulk diffusion at high temperatures, short-circuit diffusion through grain bound-
aries and dislocations becomes relatively more important as the temperature is
decreased and may even become predominant at relatively low temperatures (or
when there is a connected network of liquid-filled triple-grain junctions). There is
also some suggestion that diffusion is faster in moving than in static grain
boundaries; see Peterson ( 1983 ) for references and comment. For the influence of
the segregation of solute atoms, see Gupta ( 1977 ), Bernardini et al. ( 1982) ,
Cabané-Brouty and Bernadini ( 1982 ) and Guiraldenq ( 1982 ). The space charge
associated with the impurities may also play an important role (Yan et al. 1977 ).
3.6 Fluid Permeation
The transport of a fluid through a porous solid in response to a pressure gradient in
the fluid has some formal similarity to diffusion but it involves the relative
movement of two phases rather than the relative movement of components within
a single phase. The formal analogy lies in the basic law of Darcy ( 1856 ), com-
monly expressed as
q ¼ Ki
ð 3 : 42 Þ
where q is the flow rate, that is, the volume of fluid passing through unit cross-
sectional area of the porous body in unit time, i is the hydraulic gradient
(qgi ¼ dp = dx where q is the density of the fluid, g the acceleration of gravity,
and p the pressure in the fluid as a function of the coordinate x in the direction
normal to the defined area), and K is a constant called, in engineering usage, the
hydraulic conductivity
or coefficient of permeability and
having
dimensions
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