Sintering

SOLID SOLUTION ADDITIVES AND THE SINTERING OF CERAMICS
The use of solid solution additives provides a very effective approach for the fabrication, by sintering, of ceramics with high density and controlled grain size. The most celebrated example is the small additions of MgO (0.25 wt%) to Al2O3 produced polycrystalline translucent alumina with theoretical density. The effect of the MgO additive. An additive can influence both the kinetic and thermodynamic factors in sintering.
An additive can alter the defect chemistry of the host, thereby changing
the diffusion coefficient for transport of ions through the lattice Dl. segregation of the additive can alter the structure and composition of surfaces and interfaces, thereby altering the grain boundary diffusion coefficient Dgb, the surface diffusion coefficient Ds, and the diffusion coefficient for the vapor phase Dg (i.e., the evaporation/condensation process). Segregation can also alter the interfacial energies, so the additive can also act thermodynamically to change the surface energy ?sv and the grain boundary energy ?gb. Another consequence of segregation, is that the additive can alter the intrinsic grain boundary mobility, Mb.
In a general sense, an effective additive is one that alters many phenomena in a favorable way but few phenomena in an unfavorable one.

VITRIFICATION
Vitrification, is the term used to describe liquid-phase sintering where densification is achieved by the viscous flow of a sufficient amount of liquid to fill up the pore spaces between the solid grains . The driving force for vitrification is the reduction of solid–vapor interfacial energy due to the flow of the liquid to cover the solid surfaces. Vitrification is the common firing method for traditional clay-based ceramics, sometimes referred to as silicate systems. The process involves physical and chemical changes (e.g., liquid formation, dissolution, crystallization) as well as shape changes (e.g., shrinkage and deformation).
A viscous silicate glass forms at the firing temperature and flows into the pores under the action of capillary forces also provides some cohesiveness to the system to prevent significant distortion under the force of gravity. On cooling, a dense solid product is produced, with the glass gluing the solid particles together.






The Controlling Parameters of Vitrification
The amount of liquid formed at the firing temperature and the viscosity of the liquid must be such that the required density (commonly full density) is achieved within a reasonable time without the sample deforming under the force of gravity.
The amount of liquid required to produce full densification by vitrification depends on the packing density achieved by the solid grains after rearrangement. In systems, the use of a particle size distribution to improve the packing density with the occurrence of a limited amount of solution-precipitation means that the amount of liquid required for vitrification is commonly 25–30 vol%. In liquid-phase sintering, the formation of the liquid must be controlled to prevent sudden formation of a large volume of liquid that will lead to distortion of the body under the force of gravity.
We require a high enough densification rate of the system so that vitrification is completed within a reasonable time (less than a few hours) as well as a high ratio of the densification rate to the deformation rate so that densification is achieved without significant deformation of the article. These requirements determine, to a large extent, the firing temperature and the composition of the powder mixture that control the viscosity of the liquid.
The models for viscous sintering of a glass predict that the densification rate depends on three major variables: the surface tension ?sv of the of the glass, the viscosity of the glass, and the pore radius r .
Assuming that r is proportional to the particle radius a, then the dependence of the densification rate on these parameters can be written
?°=(? sv)/(? a)

In many silicate systems, the surface tension of the glassy phase does not change significantly with composition and the change in surface tension within the limited range of firing temperatures is also small. On the other hand, the particle size has a significant effect, with the densification rate increasing inversely as the particle size. However, by far the most important variable is the viscosity. The dependence of the viscosity of a glass on temperature is well described by theVogel-Fulcher equation:
?=?°exp[C/(T-T?)]
The glass viscosity also changes significantly with composition. The rate of densification can therefore be increased significantly by changing the composition or some combination of these to reduce the viscosity.However, the presence of a large volume of liquid during vitrification means that if the viscosity is too low, the sample will deform easily under the force of gravity. Thus the rate of densification relative to the rate of deformation must also be considered. If the ratio of the densification rate to the deformation rate is large, densification without significant deformation will be achieved.
The deformation rate is related to the applied stressand the viscosity
by the expression:
?=?/?