Dear Noureen Khan,
if you have a diffractogram of a pure CuO phase it is possible to run a indexing program like TREOR or DICVOL (to name only two of them) and to get the lattice parameters.
If you just want to know the lattice parameters of monoclinic CuO it should be also possible to find the data in a data base. For this case I have sent the corresponding cif File wih the lattice parameters.
Best regards,
Wolfgang
The peak position defines you the translation symmetry along an unknown direction in reciprocal space which is equivalent to a distance between an unknown lattice plane (hkl). For a monoclinic phase you need to determine at least 4 different parameters: the length of three basis vectors and one angle (the residual two are 90°). If you know the indexing hkl (Laue indexing) of each peak you can derive from four peak position (which are three not linear dependent) the lattice parameters. If you use 5 you will realize that for each set of 4 you will get 4 slightly different lattice parameters. The reason is that the peak position has some uncertainty. In order to decrease this influence software uses as many as possible reflections.
The lattice parameter calculation formula is an equation system, i.e. there is no single equation, even in case you know hkl. This is only possible for cubic since there you have only one free parameter. For monoclinic this is only possible for 0k0 (in case the crystal has a mineralogic setup with alpha and gamma = 90°).
If you have no idea about the phase (which is not correct in your case) you need to find sets of low-indexed hkl which all describe observed peak positions for an assumed set of lattice parameters. This is not the case since you know the phase. Therefore, you can simply look into a database as proposed by W. Milius already.
However, if you need to refine experimental data since your peak positions do not exactly match the simulations from a database you can refine them using other software like Fullprof.
In addition to Gert's comment please have a look at the equation 5. of the table at the attachment. It is taken from the famous book of Klug and Alexander.
I have to admit that I do not like these formulas since it suggests that the calculations are different from crystal system to crystal system. From my point of view the application of the metric tensor G -- or for the reciprocal lattice G* -- is much better and very straightforward. It works for all crystal system is a very easy procedure since for the calculation of d you only have to multiply G* two times with (hkl). Isn't that easy? G needs to be calculated only once since it is a constant for a phase...and then everything is only matrix multiplication. I have never seen a more simple equation and it can be very easily done in Excel which practically everybody has on his PC. There is even a command to invert G: MINV(...:...). Simple, efficient, and nearly without any potential for errors.
"How to calculate the lattice parameters from XRD peaks for the monoclinic CuO?" Assumed you are new with this mater, go for the easiest -> using software.
"lattice parameters calculation formula" answered by Gert (proper way).
Software: http://www.ccp14.ac.uk/mirror/mirror.htm
Database: www.webmineral.com, www.crystallography.net/, http://crystdb.nims.go.jp/index_en.html, http://rruff.geo.arizona.edu/AMS/amcsd.php, http://database.iem.ac.ru/mincryst/, etc
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