I know that I need to calculate lattice mismatch to determine which substrate a particular material can grow on. However, no matter how much I searched, I could not find a way to calculate the lattice mismatch of materials with different lattice parameters (a, b, c). All I've found is a way to calculate lattice mismatch through XRD measurements. Is there a way to calculate the lattice mismatch of materials with different lattice parameters (a,b,c) before XRD measurement?
for example
Sapphire substrate (0.4760, 0.4760, 1.2991), Epitaxial direction [0001] and
GaN (0.3189, 0.3189, 0.5185), Epitaxial direction[0001]
Jun Park
Read the possible way of theoretical calculation in the article.
Article The structure and magnetic properties of cobalt ferrite nano...
If you have the lattice parameters, you do not need to do an XRD measurement. The formula for lattice mismatch is simply the lattice parameter of one material minus the lattice parameter of the other divided by one of those parameters. For your example the mismatch would be (0.4760 - 0.3189)/0.4760 = 33% - which is huge; however, there are other sapphire and GaN orientations that are somewhat better matched (for which you would use the appropriate plane spacing for the R-cut or whatever it is), although the figure I see is about 16% (not sure what orientation) which is still very large. For the case of GaN and sapphire, people have successfully grown films with a buffer layer of some kind such as AlN (see J. Cryst. Growth vol. 178 pp 168 - 173 (1997) for ex.)
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