Sintering evaporation-condensation mechanism

This equation is given in terms of a constant (3Viry Af Po/ (V2A 7 k )), a function of particle size, a, and a time function. This neck size is an important factor in determining the strength of the ceramic and also its conductivity. The radius of the neck, x, will continue to increase until it has become essentially flat. An experimental study of the sintering of spherical NaCl particles [2, p. 472] shows that this relationship for the neck size is indeed followed for this evaporation condensation mechanism. 

A typical example of the evaporation-condensation mechanism is the sintering of NaCl which is affected by growth of contact areas without the particle centres... 

A basic assumption in sintering is that the particles are sintered under a quasiequilibrium state. This means that in the case of diffusion, the diffusion gradient is in a steady state and the time to achieve the steady state is negligible compared with that of a change in particle geometry. Therefore, atoms in any location are locally in equilibrium with a given capillary stress. Under this assumption, sintering kinetics is not controlled by the equilibration reaction and its kinetics at the interface but by atom movement. (This assumption does not apply to the evaporation/condensation mechanism described in Section 4.2.6.)... 

As the evaporation or condensation of material is basically controlled by reactions of atoms at the surface, the kinetics of sintering by the evaporation/ condensation mechanism is also determined by either evaporation or condensation of atoms. The kinetics of neck growth by this mechanism was derived from the Langmuir equation, a gas adsorption equation. The use of the Langmuir equation means that the condensation of atoms controls the neck growth. 

Which process, above all, controls sintering achieved by the evaporation/ condensation mechanism ... 

Consider a system where the sintering occurs by gas phase transport. Explain in detail the change in neck growth rate (dx/dt) with sintering temperature by the evaporation/condensation mechanism in vacuum sintering. Draw schematically and explain the change in neck radius with external Ar gas pressure (from zero to several thousand atm) for the same temperature and the same period of time (log x versus log PAr)-... 

As discussed above, a thermodynamically unstable surface will reduce its total surface energy by forming facets. From the point of view of kinetics, gradients in the chemical potential on a nonequilibrium surface will drive the movement of surface materials toward equilibrium. The transport mechanisms are the same as those that can operate during sintering (47) (a) surface diffusion, (b) bulk diffusion, (c) evaporation-condensation, and (d) plastic or viscous flow. 

For a given powder system, if it is assumed that grain boundary diffusion and vapor transport (evaporation/condensation) are the dominant mass transport mechanisms, the rates of sintering by these two mechanisms vary with the scale of the system with the following relations ... 

From the list of sintering mechanisms given earlier, the evaporation and condensation mechanisms predominate only when the material is volatile at the sintering temperature. The plastic flow will predominate when the compact is highly stressed. This will happen more in metals than in ceramics. In metals, their powders are more ductile, and the compact will hence consist of plastically deformed particles. In all other cases, diffusion is the main mechanism. It was also stated earlier that diffusion in powder compacts can take place through three different pathways. When diffusion of atoms takes place along these three ways to the necks and pores, there is an equivalent flow of vacancies from these sources in the opposite directions. 

In sintering, matter transport by evaporation and condensation is normally treated alongside the solid-state diffusion mechanisms. The rate of transport is taken as proportional to the equilibrium vapor pressure over the surface, which can be related to the value of /Xa - / v beneath the surface. Suppose a number dNa of atoms is removed from the vapor and added to the surface with an accompanying decrease in the number of vacancies beneath the surface. The free energy change for this virtual operation must be zero, so that... 

Figure 3.3. At the beginning of the sintering, the consolidation is done by evaporation of the surfaces and condensation on the neck (on the left) this mechanism is not densifying. If there is a liquid (on the right) the capillary pressure helps the penetration of the liquid in the interstice and the dissolution-reprecipitation effects contribute to the matter transport...

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