Biomedical Engineering Reference
In-Depth Information
Shi
60
showed that equation 13.13 becomes
1
X
1
r
m
n
¼
D
g
s
O
g
b
fr
ð
;
f
;
f
e
Þ
½
13
:
15
where
g
b
is boundary energy,
f
is the contact angle and
f
e
is the equilibrium
dihedral angle. From a thermodynamic point of view, when
f
=
f
e
, the
driving force for the neck growth is zero. Intuitively, it is possible under
certain conditions when
f
f
e
, driving force for coarsening may equal that
for neck growth. Hence, coarsening by inter-particle mass transport may
take place significantly prior to the achievement of the equilibrium dihedral
angle and the beginning of grain boundary migrations.
Considering the coarsening mechanisms described above, the initial grain
growth can, therefore, be described by a two-step qualitative growth
model.
95
When particles of different sizes are in contact, the first step in
grain growth is coarsening due to inter-particle mass transport via the
growth of larger particles into smaller particles, which results in the increase
of the material's average grain size regardless of whether the size ratio r
1
/r
2
is larger or smaller than R
c
. During the coarsening and sintering progress,
the size ratio between particles can increase. When the condition of size ratio
r
1
/r
2
>
<
R
c
is reached, grain boundary migration will occur, leading to the
second step of grain growth by the grain boundary migration. Figure 13.16
and 13.17 schematically illustrate the two-step process.
13.4.3 Initial grain growth mechanisms
From the very porous structure at the start of sintering, several possible
mechanisms for grain growth during sintering of nano particles exist,
including: 1) coarsening as the result of inter-particle diffusion; 2) grain
boundary migration; 3) solution and reprecipitation (two-phase system);
and 4) coalescence.
Generally, the initial grain growth during sintering is attributed to the
coarsening of nano particles due to inter-particle diffusions. Surface
diffusion especially plays a major role for inter-particle mass transport. In
a study of the sintering of BaTiO
3
, Shi et al. observed that the contacting
particles become one particle via surface diffusion, as shown in Fig 13.18.
58
Surface diffusion transported the atoms from the dissolving small particle to
be re-deposited on the surface of the larger particle. This is a direct evidence
of the role of surface diffusion in the coarsening of nano particles at the
beginning of sintering. It is noted that surface diffusion causes coarsening of
larger particles by consuming small particles, i.e. grain growth without
requiring either grain boundary migration and rotation, or grain boundary
diffusion.
