I suspect that the broadening may be caused by stacking faults or twinning, but how do I determine whether this is the case?
There is no software in which you enter the powder data and from which the case of faulting is suggested...
Many cases of faulting in simple metals or mixed-metallic compounds have been already described and some defined laws explaining the broadening of some particular hkl combinations were established (see for instance in the book of Warren - X-ray Diffraction).
But in the case of complex inorganic compounds, you may have to guess from where the phenomenon could come and you will have to test your hypothesis. Good hypothesis may come if you identify easy ways in the structure for connecting blocks of cells through some planar defect in the normal sequence. For instance, in some cubic perovskites, you may imagine an undisturbed cationic subcell, and subtle octahedra tilting inversions on one side and the other of a defect wall. Such hypothesis can be easily tested (by Diffax ?) if you identify the rotations and translations that may transform one part on one side of the wall into the other part on the other side. You may then determine which space group could be used in order to build a supercell : for instance tetragonal, in which the cubic structure is kept unchanged along the c axis on several times the original cubic a axis, then at half the tetragonal c axis, the defect would occur (by a 42 screw axis possibly, or etc). I tried such calculations in the case of HNbO3, cubic, Im-3 space group, showing very special line broadening effects, following a special hypothesis of defects in the perovskite stacking.
The Cauchy-like peaks on the neutron powder pattern plot (see http://sdpd.univ-lemans.fr/powbase/31.gif ) are due only to O and H atoms contributions, not to Nb atoms being at special positions. Selecting a tetragonal supercell with c = 10 a(cubic) or 20a or more, and introducing the suspected defect, made appearing satellite peaks close to some main peaks of the original cubic cell. The more c was large, the more the satellites were close to the main peaks. The problem with this approach is that you impose a periodicity between the defect which is unlikely. But, a distribution of distances between these walls would produce those cauchy-like peaks observed for certain hkl combinations, the broadened peaks, if your hypothesis is correct. You may also add several calculated patterns, produced from different c values of your tetragonal cell, and obtain a final global pattern showing such Cauchy-like large peaks, whereas others peaks would not be modified (no satellites produced). I was quite satisfied by the calculations for HNbO3 - but never published the calculated patterns as compared to the original neutron one... On one side of the imagined defect, the Nb atoms showed no displacement from the original perovskite cell. Only the oxygen and H atoms were slightly displaced by a tilting change.
Observed strange broadening on WO3, HTB (Hexagonal Tunsten Bronze) variety, could also be simulated by introducing some kinds of defects in the octahedra stacking - unpublished too.. (!).
So, my advice is, have an hypothesis for your stacking faults, test this hypothesis by building models, be careful that in the defect zone, you keep all atoms in reasonable environment... Compare your calculated patterns (possibly sum of patterns corresponding to different distances between the defects) to the observed one and try to publish the result - if you are satisfied. Nowadays, it is more easy to make such calculations, and to produce convincing drawings to be inserted in a publication than 15-20 years ago (I never published because of the nightmares in the drawings production).
Best wishes !-).
Armel
