The quantitive analysis with XRD is usually done using the Rietveld refinement. In Rietveld refinement you try to minimize the error between the calculate XRD profile and experimental observed profile. The original paper from Rietveld is here: http://www.ccp14.ac.uk/ccp/web-mirrors/hugorietveld/xtal/paper2/paper2.html

There are several software packages which are avaible online for Rietveld refinements:

1. MAUD - http://maud.radiographema.eu

2. FullProf - https://www.ill.eu/sites/fullprof/

3. GSAS - https://subversion.xray.aps.anl.gov/trac/pyGSAS

All of this programs are good, but I think Maud is little more user friendly than the rest, so I think it is good start for first users. However, FullProf and GSAS are programs which have larger user base and often cited in the literature.

I think it is always good practice to do refinement with the two different softwares and see if results compare.

After doing Rietveld refinement you will get the quantitive fraction of the phases in your probe. But you should already know all the phases in your mixture including also crystal structure of all relevant phases. The good starting point for these information is ICSD database: https://en.wikipedia.org/wiki/Inorganic_Crystal_Structure_Database

or open database COD:

http://www.crystallography.net/cod/

I don't know what you mean by internal standard. Before the Rietveld method was established, the standard practice was mixing in different volume percent of well-known substance like quartz/corundum, etc. with your powder sample and then comparing the ratio of peak intensities to the ratio of the fraction of the standard with phase to be determined (equations are here http://epswww.unm.edu/media/pdf/09-Quant-intro.pdf).

However, this method requires the preparation of several samples. It is complicated to use this method when you have a lot of phases. Probably it works only for binary mixtures.

More details on the RM for Quantitive analysis you can find in this paper:

https://www.researchgate.net/profile/David_Bish/publication/200045408_Quantitative_Phase_Analysis_Using_the_Rietveld_Method/links/556de26908aeab7772269c8b.pdf

Probably the best book on the Rietveld method is:

https://global.oup.com/academic/product/the-rietveld-method-9780198559122?cc=ch&lang=en&

Thank you for the answer and the information. Can you also recommned any software that is capable of doing it?

I would suggest you to start with MAUD http://maud.radiographema.eu

https://www.youtube.com/user/MaudRietveldProgram

Contains some videos how to start using the program.