... follow from statements of the first and second laws of
thermodynamics.
Onsager s principle supplements these postulates and follows from the statisti-
cal theory of reversible fluctuations
[5]. ... balance of forward and backward rates is characteristic of the
equilibrium state, and
detailed balance
exists throughout the system. Microscopic
reversibility therefore requires...
...
Analysis of such diffusion is complex because multiple cross terms and particle-
particle chemical interaction terms appear. The cross terms result in
N2
indepen-
dent interdiffusivities for ...
2. 2 .2.
EXERCISES
129
where
q
=
@,
Using standard tables of transforms to transform back to
(2,
t)
coordinates, the final solutions are
Because erf(z)
=
-erf(-z), the solutio...
... the ratio of strain over stress) is then
El
.E2
-
1-
-_
-
(~1
-
2~ 2)
eiWt
S( W)
=
uo
eiWt
uo
go
(8.71)
Because the strain lags behind the stress, the stress-strain curve for each ... mechanical response of
anelastic materials. Scalar forces in the spring and dashpot model become analogs
for a more complex stress tensor in materials. To enforce this a...
... mean curvature. Such capillary forces are especially influential in fine-scale
microstructures containing interfaces with large curvatures where pressure differ-
ences can become correspondingly ... boundary with isotropic surface energy
yB
intersects a free surface with
isotropic surface energy
ysl
a
grain-boundary groove
forms in order to achieve a
capillary-force balance, as illu...
... the grain center. The pressure due to this
curvature therefore induces growth. Grains with fewer than six sides show the
opposite behavior, whereas grains with six sides possess flat sides and ...
of
grains possessing
N
sides. Figures compare Marder&apos ;s theoretical results with experimental measurements
of
bubble growth
in
soap froths made by Glazier et al.
From Marder
[25...
...
curvature surface regions.
ss.v
Surface Surface Vapor transport Nondensifying
Atoms are transported through the vapor phase from larger-curvature surface
regions to lower-curvature surface regions. ... polycrystalline materials-
those grain boundaries with larger normal tensile loads are sinks for atoms trans-
ported from grain boundaries under lower tensile loads and from those under...
...
association with growth spirals on surfaces,
29 1
climb of,
26 6
379, 478
Bardeen-Herring source/sink for
climb force due
to
stress, 25 5
diffusion-limited kinetics, 26 7
dislocations as sinks for ...
vs.
djscontinuous
free-energy changes during, 428
Landau expansion of free energy, 420
order of a phase transformation, 420
order parameters, 420
conserved vs. non-cons...
...
{fir(Rz
-r2 )sin8+fie
[ (R2
+r2 )cose+2Rr]}
(3.109)
The force on an interstitial lying on a cylinder of radius
R
centered on the origin where
[RZ
+
r2
+
2Rr cos
el2
r
=
R
is then ... absence of stress is proportional to
the exponential factor exp[-Gm/(lcT)], where G" is the free-energy barrier to the
16When the stress is nonuniform and stress gradients exist,...
... diffusion on most surfaces is anisotropic because of their low two-dimensional
symmetry. When the surface structure consists
of
parallel rows of closely spaced
atoms, separated by somewhat larger ... somewhat larger inter-row distances, diffusion is usually easier
parallel to the dense rows than across them. In some cases,
it
appears that the
60ur
discussion follows reviews
by...