I need some reference or text that explains the body centered and face centered substitutions.
Rietveld refinement using Fullprof-2K,or GSAS, or MAUD software programs of the neutron and x-ray diffraction data of your powder samples is the ways to know the percentage of dopant in your parent composition. In Rietveld refinement your have to refine the occupancy of all the atoms. The Quality of your experimental data and refinement will define the accuracy of the resultant composition.
@ Syed: Can you please highlight some theoretical calculations or any relevant papers? I find some calculations but they're enough.
@Mahmood: Sorry I does not have any good knowledge of theoretical calculation. I belongs to the field of experiment physics. But the doping of any material with some dopent, change the relative intensity of X-ray diffraction peaks , because the relative intensity of any peak depends upon the Crystal structural, Atomic position in that unit cell and electron density of that atom. Since doping means replacing one atom with an atom of different-Z, thus changes the density of electron, which results change in relative peak Intensity.
@ Syed: Suppose I do the doping at some position other than the central location for body centered structure; does this effect the XRD peaks? Do we have elongation of structure also? Do you have any idea about this?
@Mahmood: The structural factor depends upon the atomic factor and the position of atoms in that unit cell (phase factor). Since doping means replacing one atom with an atom of different-Z, it means doing has changes the atomic factor and thus structural factor. So in BCC-lattice replacing atom at any position will change the relative Intensity of peaks. The doping also changes lattice parameters and some time even crystal structural. The unit cell will sustain the crystal structural of parent compound only up to some extent (i.e the difference between ionic radius of the replaced and replacing atom is not different by 10%) this is know as tolerance factor. Thus the doped system will sustain with a unit cell as that of parent, but with some changes in lattice parameters. If the difference between ionic radius of the replaced and replacing atom is more than 10%, then the crystal structural will change.
In general, this depends strongly on the level of doping. Refinement agaist XRD intensity data (assuming the parent structure to be intact) will only work for substitutional replacement, and often be limited to relatively high levels of doping (several %at). Also, it may not be very precise as the refinement by Rietveld methods against experimental data easily suffers from correlations with other effects such as texture, profile shape/instrument resolution, etc. Normally, if you employ XRD, the socalled strain broadening associated with substitutional and interstitial solution of dopants is more accurate. However, you would need a database with known dopant concentrations for comparison. At low concentrations, XRD is not very sensitive at all. If you can afford to waste your sample, Mass spectroscopy would often be much better and easier. You could also consider a fluorescent method, e.g. XPS.
Mass spectrometry is a good analytical technique used for determining the elemental composition of a sample, but before going for this measurement, one should know that during synthesis of a sample, doped element may completely, partially replace the parent element or may remain at gain boundary. In all these condition Mass spectrometry will lead to same results and thus to a wrong conclusion.
Is there any theoretical formula that could calculate the percentage using the number of atoms of the parent and the dopant, and then experimental techniques may verify it?
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