Neck growth

The differential equations for neck growth by these four titechanisms are (Ashby, 1974)... 

When diree spherical particles are sintered together, die volume between them decreases as the necks increase until a spherical cavity is left. The source of material to promote further neck growth is now removed by die coalescence of... 

Neck Growth between Two Spherical Particles via Surface Diffusion... 

The corresponding neck surface area is approximately p (per neck circumference), and therefore the neck growth rate is approximately... 

Putting Eq. 16.32 into Eq. 16.35 and integrating yields the neck growth law,... 

Equation 16.36 predicts that x(t) oc f1/5 and that the neck growth rate will therefore fall off rapidly with time. The time to produce a neck size that is a given particle-size fraction is a strong function of initial particle size—it increases as R4. Equation 16.36 agrees with the results of a numerical treatment by Nichols and Mullins [11].9... 

Different growth-law exponents are obtained for other dominant transport mechanisms. Coblenz et al. present corresponding neck-growth laws for the vapor transport, grain-boundary diffusion, and crystal-diffusion mechanisms [10]. 

Figure 16.6 Model sintering experiment demonstrating neck growth during sintering...

To show that the rate of two-particle neck growth by surface diffusion in Section 16.1.4 is consistent with the A-4 scaling law, Eq. 16.36 can be written in terms of its fundamental length scales and differentiated ... 

A similar result may be obtained (Exercise 16.6) using the result derived in Eq. 16.16 for the neck growth for a bundle of parallel wires by grain-boundary diffusion. 

The material transport e g. takes by evaporation and condensation. This results in a so-called neck growth between the particles (figure 9.25)... 

Neck growth in polymethylmethacrylate at various temperatures. Data from N. Rosenzweig and M. Narkis, Polymer Sci. Eng. 21 (1981) 1167-70. 

Data for the neck growth of polymethyl methacrylate (PMMA) during sintering is plotted in Figure 14.10. 

The effects of neck shape on the neck growth rate was then predicted by Coblenz et al., assuming that there is conservation of solid volume and the dihedral angle is large. These results are tabvilated in Table... 

TABLE 16.5 Neck Growth Rates for Various Mechanisms with the Initial Stage Geometry Assumed ... 

Mechanism (source sink) Geometry assumption Neck growth rate dx dt... 

The neck growth of the initial stage will be accompanied by interparticle shrinkage of only several percent. After the neck has become... 

For practical purpose, it is convenient to express the neck growth in terms of linear shrinkage A///o ... 

Equations for neck growth in the initial stage have been derived for each mechanism. While the neck growth equations were critical to the early development of sintering theory, their usefulness in practical sintering is limited. The predicted dependence of the... 

Of these, the first two are not capable of moving the centers of particles closer together and, therefore, do not cause densification. They are, however, causing neck growth and strengthening of the initial assembly or compact of particles. The other processes can cause both neck growth and shrinkage. 

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