Mac Diff from Rainer Petschick (Frankfurt) is a great program. It is written for Mac, but you can run it on a SheepShaver virtual machine on PC  - I'd recommends to get an old Mac though

Best regards

Michael

http://www.geol-pal.uni-frankfurt.de/Staff/Homepages/Petschick/classicsoftware.html#MacDiff

I think you can do this:

https://departments.icmab.es/crystallography/software/form/6

I used to use CrystalSleuth for powder XRD:

http://rruff.info/about/about_download.php

I think it came with a Raman database but (at the time) it did NOT come with a powder XRD database - instead I just used the old lookup tables and then downloaded the spectra of potential candidates from the rruff.info website. I am not sure if they have since added a database. It was last updated in 2009 and I was using it in 2011 so obviously the havent added an XRD database!! Still - the old school way works well... and I was dealing with powders that contained multiple minerals! It's a great program anyway and I would recommend it. It is also easily installed on Windows.

http://rruff.info/about/about_download.php

With Mac Diff I visualize and interpret diffractograms applied to clay mineralogy and crystalline substances.