Biomedical Engineering Reference
In-Depth Information
favor of sintering by grain growth. With respect to the densification
mechanisms of nano particles, surface diffusion can cause coarsening of
nano particles which, in turn, contributes to the process of densification.
Therefore, it can be stated that by inducing coarsening, surface diffusion will
contribute indirectly to densification.
Surface pre-melting is another mechanism that could lead to rapid
densification at low temperatures during sintering of nano particles. Due to
a large surface to volume ratio in nano particles, surface pre-melting can
happen at low temperature, and as a result, particle rearrangement is
facilitated by sliding, rotation or viscous flow. Alymov et al.
38
calculated the
dependence of the melting point of a particle as a function of its size using
the following equation:
2Q
1
r
1
s
s
sl
=
s
lg
r
1
1
T
m
=
T
0
¼
1
ð
r
d
Þþ
ð
r
s
=
r
l
Þ
½
13
:
11
where T
0
is the bulk melting point of the solid, Q is its latent heat of fusion,
s
sl
and
s
lg
are the interfacial surface tensions between the solid and the
liquid and between the liquid and its vapor respectively,
r
s
and
r
l
are the
densities of the solid and liquid respectively, r is the radius of particle, and
d
is the thickness of melted layer on a particle surface.
Given that the sintering temperature is proportional to the melting point,
it is generally understood that as the melting point decreases, the sintering
temperature decreases. It has been demonstrated that the melting of a
particle with diameter d will result in coagulation with its neighbors and will
become the center of a new, larger particle. In an independent study of the
sintering of nanometric Fe and Cu, Dominguez et al.
64
attributed the initial
densification to surface melting mechanisms because the activation energies
that were obtained from either constant heating or isothermal experiments
were too small to ascertain lattice diffusion mechanisms. Therefore, it was
reasoned that the presence of a liquid-like layer on the surface of the
nanometric particles during sintering could simultaneously explain such
phenomena as high diffusivity and enhanced grain growth at a narrow
temperature range.
A more generally applicable theory that explains the rapid densification of
nano particles is based on the hypothesis of non-equilibrium high
concentration of vacancies at the inter-particle grain boundaries. In 1974,
Vergnon et al. studied the 'initial stage for the sintering of ultrafine particles
TiO
2
and Al
2
O
3
'.
53
Using flash sintering and isothermal experimental
techniques, he showed that during the first 20 seconds, a fraction of the total
observed shrinkage, up to 95%, was registered.
53
There was an initial loss of
surface area, before the shrinkage starts during the heating of the compact
to the desired temperature, a process which requires only a few seconds. It
was reasoned that this almost instantaneous loss of the surface area
