I'm not an expert in this area but I wonder about one thing. You don't considered in your equation a fact that chitin is famous for its preferred orientation. The intensity of 110 reflection can easily be affected by this effect while the amorphous part remains the same...
In addition to previous answer, I think you need run other experiment such as FTIR or C-13 Solid State NMR or Rietveld program to make sure all the peaks as representative peaks shown clearly....
This is the equation of Focher, B., Beltranme, P.L., Naggi, A., Torri, G. Alkaline Ndeacetylation of chitin enhanced by flash treatments: reaction kinetics and structure modifications. Carbohydr. Polym. 1990, 12, 405–418.
There is a discussion of it in the link below.
What is your question?
http://dx.doi.org/10.3390/md8051567
Just another quick comment form me. I see some lack of understanding what texture can do to this or similar equation. It does not matter how or with what program you fit your Bragg peaks. The integrated field will not work . Nor the raw intensity. In order to better understand what texture of chitin may look like check the following paper:
https://www.researchgate.net/publication/27560555_Kristallographische_Texturen_und_richtungsabhngige_mechanische_Eigenschaften_des_Exoskeletts_des_amerikanischen_Hummers_sowie_Texturen_weiterer_Biomaterialien
Here is some other example how strongly textured bio materials are (the paper is about calcite but should give you some idea)
https://www.researchgate.net/publication/267679865_The_application_of_EBSD_analysis_to_biomaterials_microstructural_and_crystallographic_texture_variations_in_marine_carbonate_shells
The only way to escape from the texture problem would be a powder diffraction on a large, very finely ground powder sample. Synhrotron quality beam would certainly be the best but some of the brighter lab sources with nearly parallel beam will do the job.
Article Kristallographische Texturen und richtungsabhängige mechanis...
Article The application of EBSD analysis to biomaterials: microstruc...
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