I have two XRD data (before and after treatment). I observed peaks shift to lower diffraction which tells me that the crystal lattice expansion occurs. How can I calculate the lattice parameter for orthorhombic crystal
As far as the XRD is done, use a free suite package, let say FullProf Suite, to calculate the lattice parameters before and after the treatment.
By calculating the parameters and final volume cell, some behavior trends may be deeply clarified, based on the strength of the applied treatment.
Once treated, be sure there is no second phase generated in the treated sample.
Naturally, it is necessary to start from a structure model.
You may get it from CCDC, COD, and JCPDF files; some are available at the Journal of Crystallography, American Mineralogist web site, and some other repositories. If necessary, edit the reference structure, include dopping ions, be sure to obey the site symmetry and multiplicity.
The symmetry and multiplicity are available at the International Crystallographic tables.
Fit the reference CIF file (edited or not) to the treated sample.
Be careful with the sequence of fitting parameters and avoid to fit strongly correlated parameters simultaneously.