Biomedical Engineering Reference
In-Depth Information
Reasonable agreement of experimental and calculated temperatures
was found in TiO
2
and Al
2
O
3
assuming certain diffusion mechanisms
[32].
4.2.3 Pore Effects and Grain Growth
The inluence of pores on grain coarsening has been well
documented theoretically and experimentally, mostly in ceramics.
Open pores in nanopowders inhibit grain growth in a similar way
that pores prevent grain coarsening in ordinary grain sized ceramics.
The pinning action of the pores is, however, dificult to predict.
Gupta established an empirical direct relationship between density
and grain size in the intermediate stage sintering [16]. In a pore
controlled grain growth model, Liu and Patterson found a linear
relationship between the inverse of grain size and the pore surface
area per unit volume [29].
A modiied sintering law that directly accounts for pore size
effects on densiication rate was proposed by Mayo [33]:
⎛⎞
1
d
ρ
∝
1 1
-
exp
Q
(4.3)
⎜
⎝⎠
ρρ
(1- )
dt
d
n
r
RT
where
p
is density,
d
is the particle size,
n
is a constant dependent
on the sintering mechanism,
r
is the pore radius,
Q
is the activation
energy,
R
is the gas constant, and
T
is the absolute sintering
temperature. This equation predicts that the highest densiication
rate occurs for the inest pore size. A small pore size is also critical in
controlling the inal grain size based on the pore pinning effect. For
these purposes, a small and uniform pore population is desired in
the green compact.
Based on detailed microstructural studies, the average grain
size can be measured for the sintered samples as a function of
temperature [53]:
n
-
d
o
n
=
kt
(4.4)
where
d
o
is grain size before heat treatment,
t
is time and
k
=
k
o
exp(−
E
/(
kT
)). For ZrO
2
nanopowders experimental coeficient
n
= 3
and activation energy
E
= 4.2 eV.
4.3 Severe Plastic Deformation
Top-down approaches involve the reinement of coarse grains to
ultra-ine grains by severe plastic deformation (SPD) techniques
