Page 268 - Book Hosokawa Nanoparticle Technology Handbook

4.5 STRUCTURE CONTROL OF NANOPARTICLE COLLECTIVES BY SINTERING AND BONDING FUNDAMENTALS
where, the shape factor, C, is 2 for the material trans-
fer accompanied by densification, and 1 for that with-
Pattern 1
out densification. Considering material transfer
Pattern 2 without densification (C 1), the neck growth rate is
a function of neck radius of curvature as expressed by
the following equation:
Temperarture dX 3 3 4 kT s (4.5.5)

D

dt
2
The equation indicates that sharper the neck is with a
smaller neck radius of curvature, larger the neck
growth rate is; the rate depends on cube of the neck
radius of curvature. In an early sintering step, distri-
bution of neck radius of curvature is related to het-
Time erogeneity in size distribution of raw materials and
packing density. Regarding the neck growth rate in an
Figure 4.5.33 early sintering step (that is, neck growth by surface
Temperature ramping profile for the two-step sintering. diffusion), the sharp neck grows rapidly, while the
neck with large radius of curvature grows slowly, as
indicated by equation (4.5.5). As a result, homoge-
sintering temperature is often necessary for densifica- nization of neck size occurs.
tion, even if nanoparticles are used. By this mechanism in the pre-coarsening at a low
In the two-step sintering of Pattern 1, pre-coarsening temperature, round-shaped microstructure forms,
can dissolve uneven inter-particle network structures neck grows, and neck size is homogenized, while
in a mold, forming homogeneous microstructures. relative density scarcely changes. Holding a sinter-
Since the pre-coarsening proceeds in a low tempera- ing body at a high temperature after this treatment
ture region where material transfer by surface diffu- causes densification by volume diffusion. Sintering
sion predominates, microstructures grow without proceeds more homogeneously in the body that is
densification. In this process, salient features of the pre-coarsened than that not pre-coarsened; this is
microstructures are (1) homogeneous particle size dis- because of the homogenized neck. As a result, par-
tribution with small-sized powder particles decreased, ticle size distribution of bulk products becomes nar-
(2) round microstructures and grown neck structures. row, large particles decrease, and average particle
These structures are confirmed by methods such as size becomes smaller than that of products sintered
direct observation of the microstructures, measure- by the normal method. Since the neck grows at a
ment of specific surface area, measurement of pore- low temperature, sintering speed is low in the mid-
size distribution by a mercury porosimeter and other dle and final sintering periods. With large pores
methods. The homogenization mechanism of scarcely remaining due to the homogeneous
microstructures is related to strong dependence of the microstructure, the density of the final product
neck growth rate on the neck radius of curvature. The becomes high.
neck growth rate by surface diffusion is expressed by In the two-step sintering of Pattern 2, the density
the following equation [4]: increases, with particles hardly growing, during the
period of constant temperature in the 2nd step,
reaching the theoretical value. Figure 4.5.34 shows
4
3
dX 32 r 3 D (4.5.3) the relation between relative density and particle
s size for the ZnO nanoparticle (1st step temperature:
3
dt CX kT 750 C, 2nd step temperature: 650 C). For the heat
6
profile, the temperature of the 1st step is raised to a
where, X is neck radius, r particle radius, . surface temperature such that 75–85% relative density is
energy, atomic volume, D surface diffusion coeffi- obtained. The 1st step temperature, without being
s
cient, C shape factor, k Boltzman’s constant, and T held, is lowered by about 100 C and this tempera-
temperature. The neck radius of curvature, , is ture is held in the 2nd step. If the 2nd step temper-
expressed by the following equation: ature is too low, densification does not proceed.
Since the 2nd sintering temperature is lower than
that of normal sintering, the sintering time is, gen-
CX 2
(4.5.4) erally, more than several tens of hours – a long time
r 4 profile. This method was first proved effective with
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