The refinement of crystal structure using powder XRD pattern can be easy refined using Rietveld Refinement method. The Rietveld refinement can be performed with the help of softwares like FullProf Suite, Jana2006 etc. which are freely available. There are few steps in the process of refinement. For more detail you can contact me by mail on [email protected].
If BiFeO3 has been doped properly with La and Mn (considering La and Mn have substituted some particular atoms in the BiFeO3 lattice) then XRD should give a single phase pattern similar to that of BiFeO3.
Now, with the help of FullProf program (it is a freeware) you can refine it for the changes in lattice parameter, site occupancy etc that have happened due to doping. ( You did not mention what refinement of crystal structure is required by you.)
You can easily find some basic FullProf tutorials on youtube to start with.
Video tutorial for the fullprof suite is attached in the below link. It's quite very helpful in learning the refinement in the initial stages. It has five parts in which I have attached the part 1 link. Other parts will be suggested by YouTube automatically.
You can GSAS/EXPGUI or fullprof package to refine your xrd pattern. if You are new to this field you are suggested to read the following articles carefully