Lattice parameters (a, b , c, and inter-axial angles), as well as space group, can be obtained from peak position in the X-ray diffraction pattern of the solid. For determination of the atomic coordinates (position of every atom within the unit cell) the relative intensity of each diffraction line has to be taken into account as well. When dealing with powder XRD, that is usually done by using the Rietveld method, in which the crystal structure is refined by fitting the entire profile of the diffraction pattern to a calculated profile, using a least-squares approach.

Lattice parameters (a, b , c, and inter-axial angles), as well as space group, can be obtained from peak position in the X-ray diffraction pattern of the solid. For determination of the atomic coordinates (position of every atom within the unit cell) the relative intensity of each diffraction line has to be taken into account as well. When dealing with powder XRD, that is usually done by using the Rietveld method, in which the crystal structure is refined by fitting the entire profile of the diffraction pattern to a calculated profile, using a least-squares approach.

Thank you @ Carlo Otero Arean, can you please elaborate or can you help me out by sending the relevant paper.

Hope the enclosed articles (and cited references) can help.

Best regards,

C O Arean

Yes. You can determine atoms position from the diffraction peaks intensity. You need some chemical information to solve the structure. 1) material density 2) unit cell parameter and 3) chemical composition. If you know it, you can calculate how many atoms are in each unit cell. To solve the atom position, you guess the position of heavest atoms and calculating the intensity of peaks from the atomic scattering factor. After you know the position of heavy atoms, you refine the structure finding position of light atoms. There are commercial and free softwares to calculate it for you., Please check http://www.ccp14.ac.uk/ website for good softwares.

Dear Sai Pranav

Yes You can. I concur with Prof. Carlos Otero Areán and Prof. Emerson Camargo with their suggestions and opinions.

Good luck

Dear Sai,

XRD is the method of choice for determining atom positions but the practice is more subtle. You have to adapt the technique according to the crystallinity of your material, the size of the domains in case of a polycrystalline material or the depth of the layer in case of single crystalline TiO2. In case of a powder, lab facilities will perform what is called a powder diffraction pattern from which can be determined the structure of the material (rutile and anatase are the most common for TiO2) as well as the position of the atoms through the positions in the reciprocal space of Bragg reflections. In case the surface of a single crystal the incidence angle of the incoming X ray beam will determine the depth at which the sample is probed with best sensitivity to the surface at total reflection angle (grazing incidence of about 0.2° at 18 keV). Wide angle x ray scattering will give you full information about the position of the atoms in the lattice which can be further refined by doing the crystal truncation rod analysis. This will give you access to relaxation of every atoms of the surface lattice and under layers.

The bible for TiO2 is "The surface science of titanium dioxide", U. Diebold, Surface Science Reports, 48 (2003) 53±229. Hope it helps, best.

If possible, to most accurately determine the position of atoms in the crystal lattice using the Rietveld method, it is necessary to use the diffraction of neutrons.

Quantum mechanics asserts that we may speak only about average value of position of vibrating atoms which cannot be immobile even in solid state.

I agree with the answer given by Carlos, Emerson and Axel.

There are tens of monographies dealing with XRD. XRD was usually invented (discovered) to prove the concept of a crystal structure as three-dimensional periodic atomic arrangement, so that one of the first topics was crystal structure analysis. Here a specific question arises: for what do you need the positions of To and O? a) I would hardly suggest that all relevant Ti-O structures are already determined, i.e. you only need to visit COD (Crystallographic Open Database) in order to get them. And b): Nobody seriously claims that the given atomic positions are absolutely "exact". Call it movement, vibrations, average position...you always have to ask yourself if any of these concepts will help you or simply make everything more complex and finally won't help you. All comments are correct, but we have to admit that crystal structure data derived from x-ray diffraction are sufficient for the majority of applications and quantum mechanics as well as neutron diffraction may improve the precision of a certain data set but considering other sources of errors they are (in nearly all cases) irrelevant. There are more serious (absolute) errors in crystal structure databases which are not the result of not taking neutrons or  quantum mechanics into account.

As last comment: for crystal structure analysis single crystal are preferred. ONLY in case there are no single crystals available, people are that "crazy" to use a data set reduced from 2D to 1D to solve a problem which is already complex and erroneous with an entire 2D data set. Also therefore the procedure for powder samples is called REFINEMENT and not DETERMINATION. Some answers suggest that you only have to download a software, import your diffraction data and everything is solved. This is certainly not the case, and one should be serious enough to point this out first. It is a damn difficult job, even for people who are doing this for years already and have a lot of experience. A software practically always will give a result. Unfortunately no software can tell you how probable the result is. This always scientists have to decide who are experienced enough. R values (R from reliability?) in maximum can tell you a tendency. A solution with a bad R value can be closer to the correct solution than one with a remarkably smaller R value.