I want to show the influence of changes in unit cell parameters as a function of dopant concentration on the crystallite size changes. I therefore need an excellent equation that correlates the crystallite size with crystal lattice dimensions.
If I understand your question correctly, you would like to study a link between a change in the lattice parameters and a simultaneous change in the crystallites size. The problem is that such a link does not exist: the microstructure of a polycrystalline compound does not depend on its lattice parameters.
When you dope your compound, the lattice parameters will most probably change because of the size difference between the doping element and the substituted one (it could increase, or decrease, depending on this size missmatch), and and the other size the crystallites size may change (it does not necessarily change), because of a pining of the grain boundaries by segregated dopants during the grains growth, or because of a change in the interfacial energy... But there is no direct link between these changes...
Hello sir, Please find some references, hope they help you.
http://umexpert.um.edu.my/file/publication/00003184_81920.pdf
http://www.ias.ac.in/matersci/forthcoming/Feb13/BOMS-D-12-00184.pdf
http://www.is.mpg.de/3474009/review3.pdf
I would believe the Scherrer Eq. would point you in the right direction.
http://en.wikipedia.org/wiki/Scherrer_equation
Hello, for fluorite-type MO2 oxides the change of lattice parameter due to the solid solution formation can be derived by application of empirical equation given by Kim (J. Am. Ceram. Soc. 72-8, 1989 p.1415 or by another expression reported by Hong and Virkar (J. Am Ceram. Soc. 78,1995 p.433), I don't know if this is your case.
Sicerely
Lidia
If I understand your question correctly, you would like to study a link between a change in the lattice parameters and a simultaneous change in the crystallites size. The problem is that such a link does not exist: the microstructure of a polycrystalline compound does not depend on its lattice parameters.
When you dope your compound, the lattice parameters will most probably change because of the size difference between the doping element and the substituted one (it could increase, or decrease, depending on this size missmatch), and and the other size the crystallites size may change (it does not necessarily change), because of a pining of the grain boundaries by segregated dopants during the grains growth, or because of a change in the interfacial energy... But there is no direct link between these changes...
If you know when crystallites become crystals then you know the answer too.
Have you tried Rietveld refinement of your data with and w/o dopants?
From profile analysis you can also try to determine strain. Either by W-H method or double Voigt method. Doping will change the strain in the lattice.
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