Sintering Equations
Lattice Diffusion
The cylindrical pores along the edges enclose each face of the structure. Because the vacancy flux from the pores terminates on the boundary faces assumed radial diffusion from a circular vacancy source and neglected the shape effects on the corner of the structure.
For the boundary to remain flat, the vacancy flux per unit area of the boundary must be the same over the whole boundary.
The flux per unit length of the cylinder is given by:
J/l= 4?Dv?C
where Dv is the vacancy diffusion coefficient and C is the difference in vacancy concentration between the pore (source) and the boundary (sink).
used a procedure similar to that outlined earlier equation was approximated to that corresponding to diffusion between concentric spherical shells. The final result is
Ps= 6?/2[(Dl ?sv)/(l K T)] (tf-t)
where Ps is the porosity at a time t, Dl is the lattice diffusion coefficient, ?sv is the specific energy of the solid–vapor interface, lp is the edge length of the structure (taken as approximately equal to the grain size), k is the Boltzmann constant, T is the absolute temperature, and tf is the time when the pore vanishes.
Grain Boundary Diffusion
A final stage sintering equation for grain boundary diffusion was not derived but apart from a difference in the numerical constant, later developed models for diffusional sintering with an applied pressure from which sintering equations for both the intermediate and final stages can be extracted.
(?sv N)/? (t-t°)=F(?)-F(?°)
Effect of microstructure and grain boundary chemistry on boundary mobility
Assumption that the grain boundaries were pore-, inclusion-, and essentially solute-free a very rare occurrence, indeed was made, predicts the so-called intrinsic grain growth kinetics. The presence of "second phases" or solutes at the boundaries can have a dramatic effect on their mobility, the mobility of these phases that is rate-limiting. To illustrate consider just a few possible rate-limiting processes:
Intrinsic grain boundary mobility.
2. Extrinsic or solute drag. If the diffusion of the solute segregated at the
grain boundaries is slower than the intrinsic grain boundary mobility,
it becomes rate-limiting. grain boundary must drag the solute along, that tends to slow it down.
3. The presence of inclusions (basically second phases) at the grain boundaries. It can be shown that larger inclusions have lower mobilities and that the higher volume fraction of a given inclusion, the larger the resistance to boundary mobilities.
4. The interactions, between pores and grain boundaries can occur, pores cannot enhance boundary mobility; they only reduce it. During the final stages of sintering as the pores shrink, the mobility of the boundaries will increase.
As the grains get larger and the pores fewer, the grain mobility increases
accordingly.
Factors Affecting Solid State Sintering
Typically a solid-state sintered ceramic is an opaque material containing
some residual porosity and grains that are much larger than the starting
particle sizes. the more important factors that control sintering in the following arguments .
1. Temperature. Since diffusion is responsible for sintering, clearly
increasing temperature will greatly enhance the sintering kinetics,
because D is thermally activated. As noted earlier, the activation
energies for bulk diffusion are usually higher than those for surface and
grain boundary diffusion. Therefore, increasing the temperature usually
enhances the bulk diffusion mechanisms which lead to densification.
2. Green density. Usually a correlation exists between the green (prior to
sintering) density and the final density, since the higher the green
density, less pore volume has to be eliminated.
3. Uniformity of green microstructure. More important than the green
density is the uniformity of the green microstructure and the lack of agglomerates. The importance of eliminating agglomerates.
4. Atmosphere. The effect of atmosphere can be critical to the densification of a powder compact. In some cases, the atmosphere can enhance the diffusivity of a rate.
5. Impurities. The role of impurities cannot be overemphasized. The key
to many successful commercial .
6. Size distribution. Narrow grain size distributions will decrease the
propensity for abnormal grain growth.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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