Hello Namrata,

Thank you for your indeed interesting question. I myself use more the single crystal XRD and have less experience with the Rietveld method. But the main difference as far as I know is that for a structure determination from powder data an initial model must be known. Structures in which the linkage of the atoms is completely unknown can only be solved by single crystal XRD.

Best wishes, Florian

Hi Namrata,

I would like to elaborate a little bit more on Florian's answer to your questions.

For powder x-ray diffraction, we have to distinguish the Rietveld method from structure determination.

The Rietveld method is sometimes called a Rietveld refinement, because it is used to "refine" and existing model of the crystal structure (or isostructural ones) by making small adjustments to its lattice parameters, atomic positions etc. However, it requires a fairly accurate initial model and does not work without a structural model. If you did powder diffraction on a crystalline material with known crystal structure, a Rietveld refinement could serve the purpose and provide you with lattice parameters, relative quantities (in case of a mixture instead of a pure substance) etc.

If you did powder x-ray diffraction on a material with yet unknown crystal structure, you cannot do a Rietveld refinement. Instead, you would need to do a structure determination based on the powder x-ray diffraction data. A task, that is very difficult, not as accurate as other methods (see below) and that requires exceptionally high-quality data.

Single crystal x-ray diffraction on the other hand won't provide you with information on relative quantities, if you have a mixture of compounds in your sample, but it allows you to determine the crystal structure in the most accurate way.

In particular, it will provide information on atomic positions, anisotropic thermal displacement parameters, and any type of disorder disorder. Also, information on chirality and distinction between enantiomorphic space groups is impossible by powder x-ray diffraction.

In summary, you can use powder x-ray diffraction and Rietveld refinements, if you are working with known crystal structures. If you are dealing with an unkknown crystal structure, single crystal diffraction is the best way to determine the structure. The obtained model can subsequently be used in your Rietveld refinements, but you need the model first.

Nothing is wrong with the aspects mentioned above. But I may add some further aspects:

-Indexing: Single-crystal based diffraction distributes the diffraction information in the reciprocal space in a much more structured way, i.e. on isolated Bragg reflections, whereas in powder diffraction the diffracted intensity is smeared over concentric spheres, which are intersected by the diffraction experiment (everything is projected on a single 2theta scale). Thereby, you lose the 3d information in powder diffraction. Hence, in single crystal diffraction, it can by quite straightforward to index the diffraction pattern, i.e. to identify the unit cell (at least if the crystal is not a twin). Indexing is always a problem and important step upon solving a crystal structure of an unknown material.

-Reflection overlap: For the same reason as above, in single crystal diffraction the peaks are more or less strongly overlapped, for some crystal classes even systematically. The Rietveld refinement is a method to make the best out of it, but when it comes to indexing (see above), determination of Laue symmetry and structure solution this is really a drawback of Powder diffraction. At higher diffraction angle this overlap determines the extractability of the intensities. Hence in single crystal diffraction you typically have more reflections which can be evaluated (better atomic displacement parameters etc).

-Significance of the specimen: This may be regarded as an advantage of powder diffraction, e.g. in materials science. A single crystal is usually a small piece of a large ensemble of not necessarily homogeneous material. Often choice of single crystals to have a sufficient quality leads to a bias for the choice of the crystal for the diffraction experiment. Then you may select growth conditions to get good single crystals which otherwise leave other important parameters (like composition) less controlled. In phase equilibrium studies, we, e.g. have made the experience that single-crystal studies obtained their single crystals under heat-treatment conditions which made it difficult to relate the single crystal structures with actual equilibrium conditions. The much bigger ease to obtain suitable material for a powder diffraction experiment makes it easier to perform systematic studies relating crystallography with prior heat treatment conditions. Moreover, the powder diffraction experiment is designed to monitor multiphase specimens and it is also straightforward analyse microstructural effects on the pattern (e.g. line broadening). The latter information can be (and occasionally is) evaluated from single-crystal like specimens, but the standard single-crystal diffraction is not optimized to do this, but the standard powder diffraction experiment is.

Dear Florian,

Thank you for your time and answer to my question.

Dear Scheifers,

Thank you for your detailed explanation about SC XRD. It was indeed helpful.

Dear Prof. Leineweber,

Thank you for your in-depth explanation. I am new to SCXRD and therefore have to read al lot of basics before understanding your aspects. Could you please suggest me some good hand book on SCXRD other than B D Cullity?