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I have a question about Rietveld refinement

The author of this paper claimed that the free refined CN ligand is 1.081. However, they does not show how they got that number. They stated it was based from this table however I am not sure how you can get 1.081 from this table. What is the calculation?

The data

Thank you.

Source:

Reference

  1. Wang, W.; Gang, Y.; Hu, Z.; Yan, Z.; Li, W.; Li, Y.; Gu, Q.-F.; Wang, Z.; Chou, S.-L.; Liu, H.-K.; Dou, S.-X. Reversible Structural Evolution of Sodium-Rich Rhombohedral Prussian Blue for Sodium-Ion Batteries. Nature Communications 2020, 11 (1), 980. DOI: 10.1038/s41467-020-14444-4
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    $\begingroup$ "they does not show how they got that number"—Well, they kinda do, it's just that you don't have raw data to follow it: "All PXRD data analysis was done in TOPAS 5 software. The PXRD data was first indexed to get unit cell, lattice parameters, and crystal symmetry information. Then the indexed unit cell was used for Le Bail fitting the PXRD data to derive the suitable peak profile, and lattice parameters. These derived data was fixed and used for further Rietveld refinement." $\endgroup$ – andselisk Dec 30 '20 at 12:27
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I guess that 1.081 refers to the distance length (in Angstrom) separating the C and N atoms. You obtain this value by applying by using the values listed in the table; this is quite tedious, takes some time and require quite good knowledge about crystallography. Otherwise (and much more easy), you can use the crystallographic data listed in the table to build the structure using a proper crystallographic software (such as Vesta); then the software will calculate bond distances for you.

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    $\begingroup$ I would highly doubt that $d(\ce{C#N})$ can be as small as 1.081 Å (typical nitrile bond is 1.16 Å), that's more likely $d(\ce{C-H}).$ Besides, if you read the paper, it explicitly says that 1.081 is the site occupancy of free refined CN ligand before they fixed occupancies for carbon and nitrogen atoms at 100%. I do agree though regarding your point on VESTA, this is wonderful piece free of software, but here it won't help to get this number. Raw data + TOPAS 5, like authors did, is probably the only way. $\endgroup$ – andselisk Dec 30 '20 at 12:21
  • $\begingroup$ I didn't read the paper. In any case bond length ranges around typical values, but is not fixed. it depends on temperature, pressure and even chemical nature of the surrounding atoms. In the present case 1.081 is not so different than 1.16;if you use the crystallographic data reported in the table you will find that the bond lenth results even smaller than what I supposed, about 0.95 Angstrom. In any case a site occupancy equal to 1.081 is meaningless; an atomic sita cannot be more occupied than 100%. for this reason authors fixed occupancy at 1 (100%). $\endgroup$ – gryphys Dec 30 '20 at 13:12

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