Grain Growth Control

As discussed previously, densification of ceramics is attributed to the flux of matter from the grain boundaries or source to the pores or sinks. When the sintering is governed by diffusion mechanisms, the rate of densification is dependent on grain size G, through the following equation  

As stated before, chemical potential of the atoms under the surface of a sphere 

The smaller the particles, the higher the solute concentration around the particles will be. As a result, there is always a net flux of matter from the smaller particles to the larger ones, i.e., the smaller particles are continuously dissolved, while the particles keep growing, which is driven by the reduction in the interfacial area between the particles and the medium. This process is known as Ostwald ripening. 

The theory of Ostwald ripening is also known as the LSW theory [9-12], The LSW theory is used to describe the coarsening process of idealized systems with three conditions. Firstly, a particle grows at a rate that is the same as the atomic flux at its surface. Secondly, the particles have a continuous size distribution. Lastly, the total volume or mass of the particles follows mass conservation. 

Besides the above three basic conditions, there are also other assumptions (i) the precipitate and the medium are isotropic fluids, (ii) the precipitates are spherical particles, (iii) the number of precipitates is sufficiently large to ensure continuous distribution of radius of the precipitates, (iv) radius of the precipitate is the only factor to determine the solute concentration at the surface of the precipitate, (v) nucleation and precipitate coalescence are neglected, and (vi) the total volume of the system is infinite. 

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Suarez M, Fernandez A, Menendez JL, Tonecillas R (2009) Grain growth control and transparency in spark plasma sintered self-doped alumina materials. Scripta Mater 61 931-934... 

Table 9.1 Examples of Dopants Used for Grain Growth Control in Some Common Ceramics...

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