Dear Moncef Triki,

Heusler alloys are cubic, thus it is rather simple to calculate an XRD pattern. You simply have to take the correct lattice constant, put the atoms on the correct places, and calculate the diffraction pattern using suited software. There is freeware for this purpose (I recommend PowderCell, which is rather intuitive to use, it may be downloaded here: https://powdercell-for-windows.software.informer.com/2.4/).

If you do not have any idea about space groups, lattice positions etc. I recommend to check the MaterialsProject home page (https://materialsproject.org/), there you'll find Heusler as well as half Heusler alloys and the related space groups with lattice positions.

Good luck, Dirk

P.S. The crystallography open database is another source of structure data!

http://qiserver.ugr.es/cod/index.php and search for "Heusler" produces 125 entries, maybe there is one suited for you as well?

There are two NiCoMnAl alloy phases presented in our PDF-4+ database that provide the information you asked about, XRD data for comparison to your data. The compositions are similar, both are cubic, space group Pm-3m. The diffraction patterns are almost the same, slight change in lattice constant depending on the NiAl ratio. For you as a student researcher, attached you will find the ICDD Powder Diffraction File entry for one of the phases, including a visual of the simulated XRD pattern. Note carefully the very weak (111) and (210) peaks.

Good luck with you research.

In addition to what Thomas Blanton has posted, you may easily calculate diffractograms - Heusler alloys are composed by 4 fcc-lattices, each element located on one of the 4 sub-lattices, assuming that they are not mixed, which will of course change intensities of certain Bragg peaks. Howver, assuming that this is not the case, you simply have to compose your Heusler alloy structureon a piece of paper, assuming space group (Fm3m, no 225) such as

Ni (0 0 0 & 0.5 0.5 0 & 0 0.5 0.5 & 0.5 0 0.5)

Co (0.5 0 0 & 0 0.5 0 & 0 0 0.5 & 0.5 0.5 0.5)

Mn (0.25 0.25 0.25 & 0.75 0.25 0.25 & 0.75 0.25 0.75 & 0.25 0.75 0.75)

Al (0.75 0.25 0.25 & 0.25 0.75 0.25 & 0.75 0.75 0.75 & 0.25 0.25 0.75)

(Those are all positions, using space group 225 symmetry it would be enough to only consider one of each group, as all other positions are defined by symmetry.)

Then you need to know the cubic lattice constant, which should be of the order of 6 Angstroem, and then you have all you need. Attached find a calculated diffractogram, a model of the structure and the positions of atoms used. By adjusting the site occupancy and the lattice constant you may then also fit your exp. data. Good luck, Dirk

See this link

https://www.icdd.com

Thank you a lot Mr Dirk Luetzenkirchen-Hecht

Thank you a lot Mr Thomas Blanton