When you break symmetry, you also break the degeneracy that causes certain peaks to overlap. For example, in a cubic crystal the d spacings associated with (100), (010), and (001) planes (that is, the a, b, and c lattice parameters) are all the same, but in a tetragonal distortion one would be slightly different from the other two. So, for example, what used to be a single {100} peak becomes two peaks. One is actually the (100) and (010) peaks superposed, and the other is the (001). If your sample is untextured, those two peaks would have a 2:1 intensity ratio. You need sufficient XRD resolution to separate those two peaks. Then you just figure out the d spacings and you're basically done. To check your answer you can calculate the d spacings where you should see all the other peaks you're finding in your measurement.

Now, that said, a lot of crystals have their {100} reflections forbidden by symmetry. You may need to perform a similar trick on {200} or some other peak, depending on your material.

For a more robust analysis, you should curve fit the whole thing using Rietveld refinement. There are lots of software packages out there for that.

When you break symmetry, you also break the degeneracy that causes certain peaks to overlap. For example, in a cubic crystal the d spacings associated with (100), (010), and (001) planes (that is, the a, b, and c lattice parameters) are all the same, but in a tetragonal distortion one would be slightly different from the other two. So, for example, what used to be a single {100} peak becomes two peaks. One is actually the (100) and (010) peaks superposed, and the other is the (001). If your sample is untextured, those two peaks would have a 2:1 intensity ratio. You need sufficient XRD resolution to separate those two peaks. Then you just figure out the d spacings and you're basically done. To check your answer you can calculate the d spacings where you should see all the other peaks you're finding in your measurement.

Now, that said, a lot of crystals have their {100} reflections forbidden by symmetry. You may need to perform a similar trick on {200} or some other peak, depending on your material.

For a more robust analysis, you should curve fit the whole thing using Rietveld refinement. There are lots of software packages out there for that.

Depending on the magnitude of the tetragonal distortion iIn same cases one needs to use an x-ray mirror in combination with a twofold Ge

(4 0 0) crystal collimator for having high-resolution specular

theta/2theta XRD scans.

Yes. It's called Bragg's law. Use it to get a list of d spacings (or for a single crystal, G vectors) and fit your 6 crystal structure parameters. Ideally, if you have enough independent reflections, you should also fit the elastic strain tensor (which could also be considered a distortion of the unit cell). Basically you just fit the parameters assuming a triclinic unit cell.

How can one calculate tetragonal  factor from refined-XRD data?

If it is not yet abundantly clear from all these expert suggestions, then ask Professor Guru Row of IISc Bengaluru or attend one of many of his entertaining lectures on crystallography. This is not to dissuade you from asking questions no matter how basic, but a vociferous (& verbose) encouragement to study and discuss XRD & crystallography even more. I had the good fortune of sitting in on a couple of Dr. Row's classes last August (2014:-). Great refresher! You are fortunate to be among some of the most intellectually gifted, talented and accomplished in the world today, @ IISc Mulualem! A force for the good! Take advantage! Help bring the light of knowledge to wipe out the darkness of ignorance around the world! Creationism or Evolution? A healthy COMBO maybe :-)

Attached are examples of XRD rocking curve analyses (in-plane & out-of-plane) and imaging using XRD reciprocal space data. We have looked at tetragonal Te02 (Paratellurite) using the same method. The attached LinkedIn post will allow you to examine copious details for the (001) symmetric reflection Bragg XRD Microscopy of tetragonal TeO2:  https://www.linkedin.com/grp/post/2683600-266852855

All open-minded RG members are by default pre-approved to join this LI group and post your thoughts freely without "edit" or "moderation" just as in RG. Be prepared for robust intellectual scrutiny as well as vigorous rebuttals just as in RG. An excess supply of intestinal fortitude is recommended in advance :-)

See examples of "incident beam" and distorted (001) diffracted beam (47.75 degrees 2-Theta) due to the step created by surface etching for a TeO2 crystal's longitudinal transverse section from a Czochralski grown boule. I did not have sufficient time to locate and image the other reflections (100) & (010) which would overlap in this case, as mentioned earlier by Bryan. Hope to do so soon :-) Once I have the precise Bragg angle for that, I'll then be able to confirm the "tetragonal distortion factor" for this TeO2 sample at various topographic locations for each VOXEL. The VOXEL size would depend on the 2D detector Pixel size (27.7 um), diffraction geometry and the extinction depth for the (001) reflection which I haven't yet computed :-)

Paratellutire: http://webmineral.com/data/Paratellurite.shtml#.VXVxH9JViko

Jeeva (1st name or last?)! You may increase the number of relevant "Topics" up top to as many as 15. See materials + R&D topic examples in my RG post below. This will unequivocally enhance circulation, participation and hence the quality/quantity of "expert" responses on RG. Leverage to the max!

[email protected]

http://guru.sscu.iisc.ernet.in/biodata.html

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_Omega_2Theta_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses

https://www.linkedin.com/grp/post/2683600-266852855

Thank you Mr.Ravi Anand

Dear Sir

what is the reflection conditions for tetragonal structure ?