Instead of Rietveld refinement, you can use Diffax code to simulate the xrd patterns with different probabilities and then match with yours.. It will give you an idea regarding quantitative phase fraction determination ..

The questions you put are clear and important for the characterization of your zeolite beta samples and, in general, of zeolites,

The zeolite beta is a complex structure deriving from the intergrowth of two (somebody says more, even six but it is another story) different but structurally related polymorphs A and B. Consequently, the XRD pattern of zeolite beta contains sharp reflections (common to both polymorphs) and broad reflections corresponding to the directions in which the disorder occurs. In general, in standard zeolite beta samples the probability of stacking A and B is roughly 50% (and if you read the original paper by John M. Neasam et al. (Nature 1988) you can easily understand why) and that produces a well-defined XRD pattern that you can find in the literature for comparison with your samples.

The disordered nature of zeolite beta structure implies that the approach for its structural characterization is different respect to those employed for a 3D ordered structure. In fact, the CIF file you refer contains all the structural information related to a given phase and can be used for preparing the input file for , e.g., a program for simulating the XRD pattern, for the Rietveld refinement method or for the representation of the structure. In the case of zeolite beta, the Database of Zeolites contains the data for the polymorph A (*BEA, which is still hypothetical, since this polymorph has never been prepared in the pure form) and for polymorph C (BEC) but not for polymorph B. if you want to simulate (not refine) the XRD pattern of a standard zeolite beta, you need special programs, specifically developed for this purpose. The most popular is DIFFaX but it is not for beginners, since it requires a deep knowledge of crystallography and powder diffraction. Moreover, it is not a program for the refinement but just for calculating the XRD pattern on the basis of the disordered model you have in mind and the comparison between the exp. And simul. Patterns is usually not straightforward. Better would be to visit the database of the disordered zeolite structures in which the evolution of the XRD pattern of zeolite beta with varying stacking probabilities (from pure polymorph A to pure polymorph B) is reported. You can compare your data with those reported in the database for verifying if you have any enrichment of one or the other polymorph.

The structural data reported by IZA refer to the topological structures (optimized under the geometrical point of view), which often do not correspond to those reported in the literature. They are useful because provide a general view of the structure, which, as you know, can undergo modifications, distorsions, etc. depending on the chemical composition of the real sample, on the conditions applied during the data collection, etc.

You ask how to take into account the Si/Al ratio in you sample. Well, in first approximation, the Si/Al ratio has no dramatic effect on the XRD pattern because the scattering coefficients of Al and Si (which differ for 1 electron only) are very similar. This is particularly true in the case of high-silica zeolites in which only a small fraction of Si atoms are replaced by Al (or by other tri- or tetravalent elements). In these cases, it is common practice to consider the Al atoms homogeneously distributed over all the crystallographically independent tetrahedral sites (this is the reason why in many papers the positions of the tetrahedral sites are defined as T and not as Si or Al). In reality, there is the possibility that the heteroatom (i.e. atom different from Si) prefers some specific sites over the others. How can assess that? In some cases, you can examine in details the geometry of the different tetrahedra and see how the average T-O distance for each of them differs from the typical Si-O (1.61 Å) and Al-O (1.76 Å) ones. For example, if the experimental average T-O distance for a given tetrahedron is 1.68 Å, you can conclude the site is populated with 50% of Si and 50% of Al (for this case you can see the papers from Prof. Alberto Alberti, University of Ferrara, Italy). There is another possibility, i.e. an ordering of the Al atoms. This is quite uncommon and refers only to the structure with Si/Al = 1 in which, according to the Loewenstein’s rule, for avoiding any Al-O-Al kinkage, each Al atom is surrounded by 4 SiO4 tetrahedra and each Si atom is surrounded by 4 AlO4 tetrahedra (i.e. perfect alternation of Si and Al in the structure). Look at the low-silica zeolites, e.g. the differences between zeolite X and Y.

Coming to you zeolite beta samples: if you change the Si/Al ratio, you will not see any difference in the XRD pattern of the calcined forms unless a shift of the positions of the sharp reflections (to lower angles upon increasing the Al content). This is due to substitution of Si by a bigger element (see above). For high-silica zeolites, a linear variation of the unit cell parameters and volume is observed upon increasing the heteroatom content. This was verified in several cases (expansion with Si/Al, Si/Ga, Si/Ti and contraction with Si/B) and even in the case of zeolite beta it occurs. The problem is that the shifts are very small and very careful and accurate data collections are necessary for having reliable results. In the case of zeolite beta, you can accurately measure the positions of the few sharp reflections indexed according to the tetragonal model of *BEA (you can also index them according to the monoclinic system of polymorph B, but in this case you have to determine 4 parameters (a,b,c and β) while with the tetragonal only 2 (a and c) and you have only a few data i.e. 5 – 7 interlayer distances of the sharp reflections) and determine the parameters by least-squares fitting.

This is what I can say with a very short reply to your questions. My suggestion is to start from this information to study the different issues in details.

I am just at the beginning studying zeolites, thanks very much for your exhaustive and also very interesting reply!