Neck/sphere diameter ratio

Fig. 8. Plot of experimental values of mean neck/grain diameter ratios shown in Table II against 0. Continuous line shows predicted relationship for equal spheres.

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.

Run Sintering temp. (°C) Sintering time (hr) Sample number External load (g) Sphere diameter a (mm) Neck diameter x (mm) Ratio (x/a)... 

The ratio of neck diameter to sphere diameter for samples 8C and 8D, with a sphere diameter of 1.63 mm, is greater than for samples 8A and 8B with a sphere diameter of 2.54 mm. This would be expected because of the higher surface tension stress in the samples with the smaller sphere diameter. 

This physical picture is reasonably consistent with the TEM micrograph shown in Fig. 11, although the estimate of the particle size is somewhat high. An overestimate of the particle size, based on Eq. 1, means that the surface area is less than that expected for particles of the equivalent spherical diameter observed by TEM. This indicates that the interparticle contacts are necked or deformed. According to Meissner et at. [14] the ratio of cavity radius to throat radius should equal about 1.4 for spheres compacted to a coordination number of about 8. The ratio obtained from values of the average pore sizes derived from the adsorption and desorption branches of the nitrogen isotherm was closer to 1.3, consistent with some interparticle neck formation. 

Stokes law is the basis of the falling sphere Auscometer shbwn in figure (5). The viscometer consists of a vertical cylindrical tube filled temperature. A steel ball, of density D and a diameter suitable to give a slow rate of fall, is now dropped through the neck of the tube, and the time of fall between two marks is determined with a stop watch. If the process is repeated with a liquid of known density and viscosity, then equation (5) gives the ratio of the two viscosities as. 

We know that the model of the tangential spheres applies for small fractional extents. We initially calculate the relation that exists between the variation of the area and the diameter of the neck, then, we deduce a method to determine the power of the x/r ratio. 

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