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Say I want to solve the crystal structure of barium sulfate, and I want to not only determine crystal type and the lattice parameter, but also the orientation of the oxygen atoms on the sulfate anion. How do I proceed? All I have is the powder X-ray diffractogram (i.e. intensity vs $2\theta$ for the compound).

I don't want to use any existing software as this is more about learning how crystal structures are solved. I have looked at books and they seem to be incredibly difficult to follow.

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    $\begingroup$ This is rather a big question, the only way is to work through some examples, there are several in McKie & McKie ' Essentials of Crystallography' (publ Blackwell Scientific), chapter 7 is all about power photographs and their analysis. $\endgroup$
    – porphyrin
    Mar 11, 2017 at 9:06
  • $\begingroup$ Thank you. I will go through the book suggested and get back on this comment thread. $\endgroup$
    – gluco
    Mar 11, 2017 at 15:26
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    $\begingroup$ This is ...probably possible - in some cases. I sat 2 years interpreting XRD data with EVA and Rietveld curve-fitting software (TOPAS) - and I am certain I would not be able to do so. You would have to be very experienced, because interpretation of a crystallogram, if you do not know the rotation nor lattice parameters at all, is tricky. You would have to be able to - in your mind - picture the different planes and their diffraction peaks - as you rotate the crystal - and recognize them in the diagram. If anyone could do that, and were female, I would very politely ask her to have my babies. $\endgroup$
    – Stian Yttervik
    May 11, 2017 at 13:50

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The lattice constants and the symmetry of the lattice determine the position of the diffraction peaks observed along the $2\theta$-scale. The intensity of the diffracton peaks, leaving out increase by accidental or systematic superposition of them, is due to the arrangement within the asymmetric unit, i.e. the motif which -- after application of the symmetry operators (centres of inversion, proper axes, rotoinversion axes, glide planes, mirror planes) -- builds the unit cell.

So you face the phase problem (as single crystal diffraction analysis does, too). If you do not want to rely on already existing software (like DASH, MAUD, Jana, or FOX to mention a few), you will look up the Rietveld refinement. Beside by the comment by @porphyrin, as shown in this lecture briefly providing some background, the numerous properties of sample and experiment (including their statistics) equally lead me to the recommendation to use software already proven to work. The International Union of Crystallography maintains a software directory, along with -- under their educational umbrella -- the notes of a dedicated workshop about powder diffraction.

Perhaps contacting a local crystallographer may be helpful, too; like via the American Crystallographic Association ACA.

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    $\begingroup$ Would it not be easier to calculate the patterson function and then just brute force the phases? $\endgroup$
    – Jeppe Nielsen
    Apr 1, 2017 at 11:27
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I found a rather good reference on the internet that answers my question in some detail, without going into the jargon. The section on diffraction theory and indexing methods is especially good. http://pd.chem.ucl.ac.uk/pdnn/pdindex.htm#unit2

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  • $\begingroup$ An interesting site; and maybe more suitable for your specific needs than more general introductions into the field than the detailed IUCr primer by Trueblood. $\endgroup$
    – Buttonwood
    Mar 12, 2017 at 22:05

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