I would like to know why the grain crystal of ZnO is increased when treated with higher annealing temperature. I would prefer a mathematical expression associated with chemical equation between ZnO thin film and annealing temperature processing.
I doubt you can find a simple equation as you would. The factors that can influence the change of size are not completely intrinsic but depend also on your particular case. Got instance think about microstructure and residual stress that might favour the process. If you have growth I'd in any case to minimize the energy and in your case it's done by eliminating grain boundaries
I m agree with Sir Matteo Leoni, I would like to add something else, that is in depends of your deposition and your size particle, but it is possible to use scherrer equation in XRD with SEM image of your particle size, it can take you an estimation of your particle size.
With cats you do not measure the particle size but just the domain size. Depending on the actual domain shape. a film is one of the very very very few cases where Scherrer equation can give a number very close to the actual film thickness as usually domains are elongated, quasi monodispersed and span the thickness of the film. Otherwise read here and in my publications what are the risks of Scherrer equation
In general, the formation of misoriented grains and crystal degradation is expected as you increase the temperature. I think this is due to increased diffusion in the material. Maybe a diffusion equation would help.
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