Question

How to calculate lattice parameter from xrd pattern?

Answer 1

The indexing method of X-ray powder diffraction is very simple. It depends on the previous knowledge of your sample. If you already know the symmetry and lattice parameters then you can calculate the d (interplanar spacing) values of possible hkl reflections. For cubic symmetry d = a/sqrt(h^2+k^2+l^2). These are your calculated d values. You can from your X-ray diffraction diagram determine two-theta values of the Bragg reflections. From these values you can calculate the d spacing by using the Bragg law 2d\sin \theta=\lambda. These are your experimental d values. Now compare your calculate d values with the experimental d values and if they match then you have indexed the reflections. For lower symmetries you must look at the formulae for the d values. These can be obtained from the International Tables of Crystallography or from the text books on X-ray crystallography. The procedure of indexing crystals of lower symmetry is similar but is more difficult.

The above method becomes more laborius for low symmetry and large lattice parameters. You are then advised to use programs like FullProf. But I advise you to use the above method for some simple cases before you use any black box program.