If you just need crystal structure files (.cif) to calculate your spectra, another option would be to search the Crystallography Open Database:
http://www.crystallography.net/index.php
What is the best way to access data from the Joint Committee.... Available from: https://www.researchgate.net/post/What_is_the_best_way_to_access_data_from_the_Joint_Committee_of_Powder_Diffraction_Standards_JCPDS_database [accessed Aug 17, 2017].
It is a commercial product which is not for free as K. Sreenivas already pointed out. However, you don't need them since a simulations is commonly much better especially because you anyway have to compare it with a software which is doing both. So you only need the crystal structure e.g. from COD and you have to calculate the diffraction pattern with software like PowderCell.
I must say Dr. Gert Nolze really gave a very simple practical solution, there are many freely down-loadable XRD pattern analysis programs, which would easily allow you analyse your results, and compare them with the published literature.
Search the compound in which you are interested by putting the names of elements in the search table.
Download the cif file and open it through another free software...Mercury3.2 (Mercury - The Cambridge Crystallographic Data Centre (CCDC))..
On tollbar of this software you find the calculate tab.. under this calculate you have powder pattern option when you will click it XRD pattern will be calculated... you can customize 2theta range and in save option you can save it as xye format.. 3 column file... x is 2theta value y intensity and e column is error.... you can open .xye file in origin or excel.. and plot it with your xrd data ... that will help you a lot...