Controlled Crystal Growth and Microstructural Evolution

the value of the CSL-E value is obtained for symmetric tilt boundaries between cubic crystals as follows  

For asymmetric tilt boundaries between cubic crystals, E is calculated from (Randle, 1993) 

In polycrystals, misorientation angles rarely correspond to exact CSL configurations. There are ways of dealing with this deviation, which set criteria for the proximity to an exact CSL orientation that an interface must have to be classified as belonging to the class E=n. The Brandon criterion (Brandon et al., 1964) asserts that the maximum deviation permitted is voE-1/2. For example, the maximum deviation that a E3 CSL configuration with a misorientation angle of 15° is allowed to have and still be classified as E3 is 15°(3)-1 2 = 8.7°. The coarsest lattice characterizing the deviation from an exact CSL orientation, which contains the lattice points for each of the adjacent crystals, is referred to as the displacement shift complete (DSL) lattice. 

Consistently reliable approaches for the de novo prediction of a material s crystal structure (unit cell shape, size, and space group), morphology (external symmetry), microstructure, as well as its physical properties, remain elusive for 

A very important industrial crystallization process, which is the most common method used for the production of high-purity oriented single-crystalline semiconductor ingots, is the Czochralski method (Czochralski, 1918), named 

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In crystalline systems, we have shown that microstructural evolution is dominated by phase transformations that accompany gel dehydration or that result from phase metastability. Both phase transformations and crystallization of amorphous systems may involve changes in the coordination numbers of the network-forming species (e.g., Al or Ti). In transformations that occur by nucleation and growth, the addition of seeds that serve as multiple nucleation sites appears to be a viable approach to microstructural control. 

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