World Journal Of Engineering
Nanoscaled Grain Growth
F. Liu, M.M. Gong
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University,
Xi’an, Shaanxi 710072, P.R. China
Email: liufeng@nwpu.edu.cn; Tel : 0086-29-88460374
Owing to the purpose for industrial
of grain growth, the steady solute distribution
application, to suppress grain growth of
can hardly exist. Then, aimed to operate the
nanocrystalline materials and to hold the
nonsteady solute distribution, with the
excellent properties resulted from nano-scale
assumption that the drag exerted by the
appear to be extremely important [1, 2]. As a
segregation is proportional to the difference
promising method to improve stability and to
between solute concentration in bulk and GBs,
inhibit grain growth, solute addition has been
a grain size dependent drag was presented.
demonstrated in various nanocrystalline
Noting that, as shown by J.W. Cahn, the drag
materials, ascribed to the effect from the
force is a complex function of both the grain
segregation of solute in grain boundaries
size and the GB velocity, at the limit of low
(GBs). The role played by GB segregation on
growth velocity, the drag force was found to
grain growth of nanocrystalline materials has
be proportional to the product of grain size
been modeled:
and GB velocity. Furthermore, it could be
I. Thermodynamically, as a mainly part of
deduced that the drag force dependent on
driving force for grain growth, the grain
grain size and on growth velocity can only
boundary energy is regarded as const in
retard but not stop GB migration; see Fig. 2.
common. However, under the condition of
As mentioned above, the reduction of the
solute segregation in GBs, on the basis of the
GB energy and the generation of drag force
Gibbs adsorption theorem the GB energy is
both affect the grain growth of nanocrystalline
thought to be reduced with segregation
materials by the thermodynamic and kinetic
promoting (see Fig. 1) and demonstrated in
ways separately. Thereafter, combining each
Fe-P alloys. Furthermore, a systemic
factor individually with the parabolic equation
metastable state where the GB energy reduces
can provide an insight for grain growth of
to zero with solute segregating has been
nanocrystalline materials. However, the whole
proposed. That is to say, GB segregation
description of growth kinetics requires
reduces the driving force to retard grain
incorporating these two factors into the
growth; and when the GB energy becomes
parabolic equation simultaneously. Applying
zero, the grain growth stops.
these three revised grain growth formulas
II. Kinetically, considering the difference of
which are subjected to the thermodynamic
solute concentration between GBs and the
factor, the kinetic factor and the coupling of
bulk, a drag force on GB migration has been
these two factors to the related experimental
assumed to explain the retardation of grain
data, it shows that the reduction of the GB
growth from the reduction of GB migration. A
energy, i.e. thermodynamic factor plays the
const drag term was firstly proposed to depend
predominated effect on the process of grain
on the final grain size. Nevertheless, only in
growth
for
nanocrystalline
materials
the situation where a steady-state solute
meanwhile the solute drag, i.e. kinetic factor
distribution in GBs has been established, the
only slows down this process; see Fig. 3.
const drag is adaptive. In fact, before the stop
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World Journal Of Engineering
lines are calculated using these three revised
grain growth formulas which are subjected to
the kinetic factor, the thermodynamic factor
and the coupling of these two factors [5].
Reference
[1] H. Gleiter, Prog. Mater. Sci. 33, 233
(1989)
[2] K. Lu, Mat. Sci. Eng. R, 16, 1611 (1996)
[3] R. Kirchheim, Acta Mater. 55, 5129 (2007)
[4] Natter, H., Löffler, M. S., Krill, C. E.,
Hempelmann, R., Scripta Mater. 44, 2321
(2001)
[5] Chen, Z., Liu, F., Wang, H. F., Yang, W.,
Yang, G. C., Zhou, Y. H., Acta Mater. 57, 1466
(2009)
Fig. 1 Schematic illustration of the GB energy,
σb with increasing chemical potential, μB
according to the Gibbs adsorption isotherm
[3].
Fig. 2 Comparison of Burke’ model, Michels’
model, and Rabkin’s model. Assuming an
initial grain size D0 equaling to 0.05Dmax, the
scaled grain size D/Dmax is plotted as function
of the scaled annealing time τ=(k/Dmax2)t.
Fig. 3 Evolutions of average grain size of the
oxygen-doped nickel samples with different
oxygen contents at 673 K [4] with annealing
time. Meanwhile, the dotted, dashed and solid
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