I can see a lot of information for one specific space group on the 'international table of crystallography'. Say I know the space group of a crystal from XRD analysis, and I want to calculate electronic structure using first principle; but, I would need the positions of the atoms as well which I don't find what and how the authors put in their papers. So, I would be very grateful if someone who is much familiar with the 'international table of crystallography' or the Wyckoff things can help me. Thanks in advance!
Unless you are taking about structures with a very low number of atoms it is impossible derive the full crystal structure only from the tables. The crystal structure is a product of experimental work. Traditionally, you can obtain the crystal structure from X-ray diffraction, but you also can obtain it by nuclear magnetic resonance crystallography, or by first principles. The latter methods fall into your area. Are you able to "calculate" the structure?
Thanks Jose for your response but my question was about how to determine the actual coordinates of the atoms in the unit cell. For e.g., say I fabricated SrTiO3 and XRD reveals it is a good match with rhombohedral phase, say R-3 (space group no. 148). Now, if I want to theoretically analyze it, I need lattice parameter and positions of the individual atoms in the unit cell to start the calculation. So, my question is I know there are three different atoms Sr, Ti and O in the unit cell and I also know the crystal space group. From these information, how can I calculate the tentative positions of these atoms in the unit cell?
I am stuck with this and I have seen the authors don't show these values in their papers when they publish. There must be some way to estimate positions of atoms from the 'international crystallography table'?
By principle you CAN NOT get the structure of a crystal by only knowing the space group, but SrTIO3 is a known compound, It has even an article in wikipedia. Please, see this site:
https://materialsproject.org/materials/mp-5229/
For cartesian coordinates, as the structure is cubic, the conversion is straightforward. The coordinates 0 remain 0 and 0,5 is replaced by 0.5*3.495=1.7475 angstroms. Is this you need?
Thanks Jose and Volker for your time and input.
Your inputs have broadened my understanding quite a bit, however, I am still looking forwards for my specific answers and may be I have quoted my problem in ambiguous way or may be the question was irrelevant itself! Still, thank you guys for answering the query. José A. Fernandes Volker Kahlenberg
I don’t know specifics about your compound, but in general, you need to solve the structure in that space group in order to get the real coordinates of atoms. By solving means, you place atoms in the Asymmetric unit inside the unit cell so that the experimental electron density derived from diffraction matches your atomic assignment. Once you assigned atoms to density, you need to refine and validate you guess assignment and there are many different ways to do this. You can find all these details in any general textbook in crystallography.
If your crystal is known you should get its CIF. Then with help of enCIFer and Mercury programs you will be able to solve your problems.
For your specific question, it is well-known that you can get the unit cell of a crystal from the positions of its diffraction peaks. Hence, as you say above, you can know the unit cell lengths, a,b anc c and the angles alpha, beta and gamma. From those values, you also can typically (but not necessarily unambiguously) determine the space group. However, you need the INTENSITIES of those diffraction peaks. So, as others have said, you cannot get the positions of atoms within the unit cells simply "from first principles" as you have asked - you do need diffraction data.
However, and again as others have said, if you want to study the crystal, many have already been characterized by single crystal diffraction and so you can find databases with the needed atomic positions in them.
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