Grain size density trajectories

It is useful to plot the resultant behavior in what is known as grain size versus density trajectories, such as those shown in Fig. 10.5a and b. Typically, a material will follow the path denoted by curve v, where both densification... 

Figure 10.5 (a) Grain size versus density trajectories for densification (curve z) and coarsening (curve x). Curve y shows a powder for which both coarsening and densification are occurring simultaneously, (h) Alternate scheme to represent data in terms of grain and pore size trajectories. 

In Fig. 10.6a-/, the time dependence of the microstructural development of an MgO-doped AI2O3 compact sintered in air at 1600°C is shown. Note that as time progresses, the average grain size increases whereas the average pore size decreases. The corresponding grain size versus density trajectory is shown in Fig. 10.6g which is typical for many ceramics that sinter to full density. 

There are essentially two strategies that can be employed to prevent pore breakaway, namely, reduce grain boundary mobility and/or enhance pore mobility. An example of how slowing grain boundary mobility enhances the final density is shown in Fig. 10.6g, where the grain size versus density trajectories for two aluminas, one pure and the other doped with 250 ppm MgO, are compared. It is obvious from the results that the doped alumina achieves higher density — the reason is believed to be the result of impurity drag on the boundary by the MgO. 

Sintering trajectories, i.e., grain size (G) versus relative density (p), of the undoped and silica-doped samples sintered for 2 h at 1450-1800 °C, are shown in Fig. 7.5 [11]. It was observed that grain size increased at a very slow rate until the... 

Figure 16.14. Relative density-grain size trajectories for compacts in atmospheres of...

Figure 9.51 Experimental results for microstructural development in AI2O3 doped with 200 ppm MgO, showing the grain size versus density trajectories for fabrication by hot pressing, conventional sintering, and fast firing. (From Ref. 90.)...

Separation in these devices known as winnowing machines [3], is achieved due to the difference between trajectories of coarse and fine particles in the separation zone (Fig. lb). Their operation and efficiency are strongly affected by the stochastic factors of the process, in particular by uncertainties in feeding and particles aerodynamic interactions. In most cases coarse particles prevent proper classification of fines. Separation efficiency of these devices is usually low. They are normally used for separation of solid particles according to densities (e.g. grain from peel), rather than by size. Sometimes crossflow separation in horizontal streams is used in combination with other separation principles. 

Draw schematically the G—p trajectories and explain for two powder compacts (a) with different green densities (low and high) and (b) with the same green density but with different pore size distributions (narrow and broad). Assume that the compacts were made from the same starting powder and that densification occurs by lattice diffusion and grain growth by surface diffusion. 

After defining the structural representation of the coarse-grained system and interaction terms, a simulation protocol has to be devised. This protocol involves an equilibration or thermalization phase, as well as production runs. In a production run, the system trajectory is simulated under well-defined thermodynamic conditions, over a specified period of time, in order to generate a statistically meaningful ensemble of uncorrelated system configurations. In the final step, these configurations are analyzed using RDF, and density maps that provide direct information on size, shape, and distribution of phase domains in the composite medium. 

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