Khadidja Messabih,

There are a few methods to quantification of XRD data. The most common are the Relative Intensity Ratio (RIR) method as well as the Rietveld, LeBail, and Pawley methods.

RIR is notoriously inaccurate due to changes in measurement between your sample and the standard reference material (SRM), assuming all factors are constant except the analyte concentration and the concentration of the SRM is known. This assumes that no peaks of interest between your sample and SRM overlap. This makes the SRM selection critical, as well as expensive if you are using NIST traceable standards. RIR can also be performed using PDF4+ software without the SRMs, due to their data being calculated for many materials. The caveat here is that they have the exact PDF card as well as no structural changes to the sample. Below is a link to the ICDD pdf tutorial on quantification with RIR.

https://www.icdd.com/assets/tutorials/Quantitative-Analysis-RIR.pdf

Rietveld analysis uses some fundamental parameters from *.cif data from PDF4+ to fit the patterns. This is more accurate than other models due to the degrees of freedom in the refinement, i.e. the ability to change lattice parameters, thermal parameters, sample displacement, scale, crystallite size, microstrain, etc. This requires some software (free and paid) as well as *.cif cards found at American Mineralogist database or the Open Crystallographic Database (COD) or the PDF4+ database.

LeBail and Pawley are similar to Rietveld, although there is little information about peak intensity parameters. I've provided a great resource in the link below from former MIT professor and Malvern Panalytical lead application scientist, Dr. Scott Speakman, which details these different methods.

http://prism.mit.edu/xray/oldsite/tutorials.htm

Good luck!

Remark: Mind that by using XRD you only see peaks for phases with a crystal structure. If you use the methods Alec Ladonis mentioned you will get a quantification for crystalline material only. You might have additional amorphous or cryptocrystalline material present that were not quantified.

Tanja Manninger good point and thank you for the clarification, although not totally correct. With Rietveld refinements, you can determine the non-crystalline weight percentage by incorporation of a known SRM standard spiked into the sample. Again, this comes with some caveats, mostly that there are no interferences with the analyte pattern, i.e. peak overlap, SRM stability, etc. I have performed this personally on multiple crystallized glass melts as well as some sintering studies at high temperature, although not with the RIR or other methods mentioned previously.

Alec Ladonis Thank you so much, just a question please, I use HighScore plus software for phases identification and there is a quantification feature in the software it gives us the percentages of the phases but this option is not valid for all the phases if you know the reason?

and are these results (the quantification in the software) accurate?

Khadidja Messabih

HighScore has two versions: HighScore and HighScore+, which the latter is the Rietveld suite. In regards to the phases having different options, this is a little beyond my understanding of the software. My experience is that there are differing file types for your input structures. Without seeing the files and refinement, there isn't much more I can do.

Good luck!