Sphere sintering

Mayoral, R. et al., 3D long-range ordering in an SiOj submicrometer-sphere sintered superstructure, Adv. Mater, 9, 257, 1997. 

For the two-sphere sintering model, derive the equations given in Fig. 8.10 for the neck radius X, the surface area of the neck A, and the volume of material transported into the neck V. 

M. Holgado, A. Blanco 30 long-range ordering in an 3.98 Si02 submicrometer-sphere sintered superstructure,... 

Fig. 1. Contact areas at the neck of zinc oxide spheres sintered to ferric oxide plate at 1128°C for 15.5 hr. Polarized light, 100 x.

Fig. 2. Polycrystalline nickel oxide sphere sintered to polycrystalline ferric oxide sphere plate at 1160 C for 23 hr. Polarized light, 100 x. 

Fig. 5. Time dependence of the neck to sphere diameter ratio x/a for nickel oxide spheres sintered to ferric oxide plates at temperatures indicated.

Fig. 7. Polycrystalline ferric oxide sphere sintered to a single crystal of magnesium oxide at 1090°C for 51 hr. The sphere was held in position by nickel foil visible in the upper part of the photograph. Polarized light, 100 x.

Fig. 14. Polycrystalline ferric oxide spheres sintered to polycrystalline zinc oxide plate at 1136°C for 32.5 hr. Note dark layer of ferrite formed on the surface of ferric oxide particles. Polarized light, 100 X.

Fig. 3. The two-sphere model illustratiag material transport paths I—VII duriag sintering where (a) represents coarsening (b), the two spheres before...

In die operation of die first source, the driving force for sintering is the difference in curvature between the neck and the surface of the sphere. The curvature force A l, is given by... 

Figure 9.8. Sintering of single-crystal copper spheres to a single-crystal copper substrate.

Let us now examine why this mecheuiism might be true. In the case of sintering of spheres, we can define two cases as before, that of no shrinkage and that of shrinkage, both as a function of volume. If we have two spheres in... 

Actual sintering occurs by flow of mass from each sphere to the mutual point of contact, which gradually thickens. We can estimate the volume of mass, V, at the contact area. A, in terms of the foUoAving parameters r, the radius of the spheres p, the thickness of the layer buildup and x, the radius of contact of the built-up layer. If we have shrinkage, then we must also evaluate h, the amount of shrinkage, shown above as the height of interlinking layer. 

This model brings us to an important point, vis If the spheres are too small, there can be little mass flow to the area of joining (sintering) of the spheres. Actually, it is the rate of flow of mass to the joining area that is important and the area of touching of the spheres will determine this. 

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