Biomedical Engineering Reference
In-Depth Information
13.6
Theoretical prediction of initial sintering temperature -
T
is
(
) - for selected metals in terms of equation 13.6. The experimental
initial sintering temperature of W, Ni and Ag are also plotted in
for comparison.
37,38
r
General sintering theories hold that a material's sintering temperature is
often correlated with the material's melting point. It has long been known
that the melting temperature of very fine particles decreases with the size of
particles.
19-34
In the case of sintering of nano particles, the decreasing onset
temperature of sintering can be understood, therefore, on the basis of the
lower melting temperature of nano particles. Troitskii et al.
35
studied the
initial sintering temperature of different-sized TiN powders and found the
relationship between initial sintering temperature T
is
and particle size r is:
T
is
r
r
0
ðÞ¼
T
ðÞ
exp
½
c
ð
r
Þ=
r
½
13
:
5
?
where T (
) is the initial sintering temperature of coarse particles, c is a
constant determined by the properties of the material and the energetic state
of the surface layer, and r´ is arbitrary size.
Jiang and Shi
36
ascribed the size-dependent initial sintering temperature
of nanosized particles to the decreased melting temperature of nanosized
particles based on the relationship:
2S
m
ðÞ
3k
1
T
is
r
ðÞ¼
0
:
3T
m
r
ðÞ¼
0
:
3
T
m
ðÞ
exp
½
13
:
6
ð
r
=
r
0
Þ
1
where T
m
(
) is the
bulk melting entropy, r is particle radius, r
0
= 3h (h is atomic diameter) for
nano particles and k is Boltzman constant. Figure 13.6 shows the predicted
size-dependent initial sintering temperature of some metallic powders by
?
) is the melting temperature of the bulk material, S
vib
(
?
