Biomedical Engineering Reference
In-Depth Information
13.16
A linear array of two spheres of initial radii of
r
1
and
r
2
(
r
> r
2
):
1
(a) just in touch without the formation of interface, (b) when
r
1
/
r
R
c
, (c)
2
> R
c
.
60
r
1
/
r
2
=
R
c
, and (d)
r
1
/
r
2
13.17 Particle configuration change after the formation of a dihedral
angle shown in Fig. 13.20: (a) the configuration when
r
2
R
c
(boundary
cannot move); (b) the configuration resulted from the mass transport
between particles before boundary motion; (c) the transient
configuration after boundary motion where
r
1
/
> R
c
; (d) final
configuration either directly by mass transport or by combined mass
transport and boundary motion.
r
1
/
r
2
becomes
Neck formation and coarsening of contacting nano particles
To understand initial grain growth, the key issue is the interaction between
ultrafine particles at the start of sintering. According to classical sintering
theories by Kuczynski,
91
Kingery,
92
Coble
93
and Johnson,
94
necks will form
and grow between adjacent particles, which are assumed to have equal
diameter. Densification is modeled as the approach of the centers of the two
particles. In this situation, no grain growth occurs at the beginning of
sintering. In practice, however, there are always wide particle size
distributions. The densification and grain growth behavior will be markedly
different from two-sphere models. Figure 13.16 illustrates that when very
fine particles are in contact, where the particle sizes are not uniform, inter-
particle diffusion will lead to coarsening of particles, in addition to
formation of the neck. Large particles will grow at the expense of small
particles. The coarsening of particles can be understood using the criteria
shown by equation 13.12, which was first expressed by Lange
1
based on
