In order to obtain information about cation distribution of a spinel ferrite, I use Rietveld method using FullProf program. In reference, there is another method by comparing experimental and calculated intensity ratios. So which is a better method to determine cation distribution?
The Rietveld refinement is much better than the intensity ratio as it employs whole pattern not just some peaks in addition it can take into account for preferred orientation, absorption and other effects. In addition the Rietveld method actually refines ratio of 2 ions in one position (site) which provided standard uncertainty for the ion ratio.
In Rietveld method you calculate Structure factor and the corresponding Intensities for each diffraction line which you fit. The fit itself compares observation intensities with the model ones (calculated). So basically - in Fullprof using Rietveld mode you do compare experimental and calculated intensities.
it is the same, the rietveld method confronts experimental and calculated patterns. the problem is: which are the cation in the ferrites?
if are more than two you can not determine it!
if are Fe and another metal, it is very difficult to determine the distribution
I would say that Rietveld method is a method which compare experimental and calculated intensity ratios, so the two methods you propose are basically the same...
Anyway, I would say that it is possible to determine cation distribution from X-ray diffraction if the two cations have "very" different weight (not that it is not possible to distinguish for instance Fe from Mn (Z=26 and Z=25, respectevely, have thus the same weight) with "classical" radiation, while it is possible to distinguish Mg from Fe. (Z=12 compared to Z=26...) Another possibility to distinguish two cloth cations is either to tune the wavelength, at a synchrotron of course, to go to an absoption edge of let me say the iron (this is called DAFS, for details read for instance http://cars9.uchicago.edu/dafs/icas/icas.html) , or to change the radiation type and go to neutron diffraction where the coherence length of the two cations can be very different...
Anyway, it's always some Rietvled refinement, which is, to my knowledge, the best way to do what you want...
Hope it helps....
Konstantin Glazyrin: Thank you for the answer. I do think so. In Fullprof all the peaks were calculated. But the method of comparison intensity ratios only few peaks were chosen. The chosen peaks "vary with the cation distribution". Do you think that choosing some effective peaks is better than covering all?
Davide Levy: Thank you for the answer. My sample is doped spinel ferrite. So there are 3 metals, including Fe. There are 2 site in spinel ferrit, tetrahedral and octahedral. All the metals can come to both sites. I can not determine the distribution of all metals at the same time. I just refine occupancy of one metal and fit that of other const. Why is it difficult to determine the distribution of Fe and another metal? Do you mean that cause of the Rietveld method or cause of Fe properties?
Used to the combination of PXRD and XRF works well unless both instruments are well calibrated. Common industrial task: phase and chemical composition of a mixture. In the case of unknown crystal structure(s) this is direct way to a neutron source.
The method of choice certainly is Rietveld refinement. You will get information from all intensities of your pattern as in principal your struture factor (intensity) is calculate (and compare with your measured intensity) as the sum of ALL atoms in the unit cell. If you pattern is affected by experimental error such as preferred orientation (probably not for the spinels but generally spoken) you have the chance to correct such "errors" and all in all get reliably cation distribution. So you have much more intesity data from which you get your information with much better refinement algorithms. However, be aware that generally you will not be able to discern between cations with similar scattering factors and that is is difficlut if you have more the two differnt cations on one crystallographic position. Best is that you combine Rieteld refinenemt with some quantitative chemical analysis suf as XRF and put the informations together; I would not rely on relative intensity comparison.
a possibility to work with 3 cations is to work with neutron diffraction and XR diffraction. look at my work on MgFeAlO4 https://www.researchgate.net/publication/229430888_In_situ_high-temperature_X-ray_and_neutron_powder_diffraction_study_of_cation_partitioning_in_synthetic_Mg(Fe0.5Al0.5)2O4_spinel?ev=prf_pub
@Artem, if you use only X-ray diffraction you does not resolve the problem
Article In situ high-temperature X-ray and neutron powder diffractio...
To your question on Fe: in X-ray diffraction work the intensity is determined among others by the atomic scattering factor which itselfs depends on the electron count of the atom/ ion. So with atoms with very similar electron numbers (Mg and Al, or Fe and Mn) you will have no significant difference between the scattering power of the two metals, so you will not be able to refien e.g. the Al-Si distribution in tetrahedral frameworks of silicates or the Mg-Al distribution in spinels; Neutrons can help here (intenstiy depends on scattering lenghts which are determined by the core) but are less accessible; For Fe-dirstibution you may use other methods such as 57Fe Mössbauer spectroscopy, which (normally) gives you a good estimation of Fe on different crystallographic sites (may be not alwasy in the case of spinels....)
The use of 57Fe Mössbauer can be (in some cases) very helpfull (see Structural and Mössbauer study of the Brownmillerite oxides LaSrMn2-xFexO5 (0 ≤ x ≤ 0.5))
Obviously, Rietveld method is better method for determining cation distribution in ferrites even if there are more than one type of cations. When you substitute octahedral or tetrahedral positions by any cation(s), intensities of some of reflections would be modified depending upon the coordinates of the cations. These changes in intensities can be clearly noticed if you take the step scan XRD data with 5sec or more time of counts for each step, i.e, you need a very precise and accurate XRD pattern. Using Rietveld method (I use MAUD software, freely available on net with demo) you can fit these changes in intensities by positioning the cation in proper positions. If the cation shares both the the octahedral(O) and tetrahedral(T) positions, there is a provision in the software by which you can bound these positions and refine them to make the sum of the fractional occupancies in T and O positions of this cation =1.0. By this way, you can justify whether your ferrite is nornal, mixed or inverse spinel. I've several no. of published article available of net. If you are interested, you may consult these articles where cation distribution in different kinds of ferrites is analyzed with more than one kind of cations.
By Rietveld method (any program) you can obtain the most correct lattice parameters, atoms positions, intensity and others parameters necessary for compare with the theoretical model and calculate the cation distributions.
Rietveld is ok but be aware about fluorescence!! (i mean if you want to determine Fe or Co and your X-ray source is Cu and you dont have a secondary monochromator, you should pay attention).
Besides XRD is quite bad technique if you have metals of similar Z (as stated above) or if one of the cations is much bigger (in electrons number i mean) because it will be responsible of most part of the Intensity so you can fall in a lil error. Combining SXRD and NPD is probably a very good choice and if you have Synchrotron time, spectroscopy techniques may be of big help
A refinement method (last square based method), whatever is the used code) defining statitical standard deviation figures is the most appropriated to deliver the most precise picture of a crystal structure. After (or before) that, the used technique is of prime importance to determine accuratly what you like to see.. (XRD in some cases, neutron diffracrion, spectroscopies such as EXAFS, Mössbauer, XPS....depending on the relative resolution of the technique (form factor, time and stace resolution).
The Rietveld refinement is much better than the intensity ratio as it employs whole pattern not just some peaks in addition it can take into account for preferred orientation, absorption and other effects. In addition the Rietveld method actually refines ratio of 2 ions in one position (site) which provided standard uncertainty for the ion ratio.
There is nothing I could add! But if you just want to have a qualitive stoichiometric ratio, EDX spectroscopy might also be a good choice! Otherwise a rietveld refinement will help you. Nevertheless it depends on the elements you are locking for. If the scattering factor is almost the same, you might need the combination of X-ray and neutron diffraction.
I fully agree with the argument that the Rietveld refinement is a more general and, hence, more accurate approach. I would like, however, to give an example (not relevant to spinel phase) where this could be not fully correct. I am speaking about layered compounds with the so-called intergrowth defects. As I know, standard programs for Rietveld refinement do not contain models for this situation, because the FWHM is in general not a monotonic function of 2Theta. Under such circumstances, comparing areas under the peaks could give more reliable information.
Rietveld refinement .. combining XRD and NPD, you should be able to solve your problem,
Thank you all. It 's really help me a lot. I almost resolve my problem. In conclusion, I will use Rietveld method. And to get accurate information of cation distribution, I'll try to get experiments with better technique like synchrotron source or neutron.
Elena Shishonok
If you want to understand in which crystal positions you cations are, you should make analysis of XRD lines structure of matrix you investigate. I mean symmetry of the positions into which cations are placed in... and no phase analysis.
Rietveld refinement is a proper method to obtain both structure and cationic distribution. I would use Mossbauer spectroscopy as a prime method for identifying cation sites, and compare the results with those obtained by the structural refinement
In modern crystal chemistry, Rietveld method is widely used for powder samples to refine a crystal structure. At the same time, when you have deal with a small crystal (
Rietveld is the easier. Buoild a composite atom using the occupancy fctors. Alternativerly, much more complicated, wold be to collect two patterne t the synchrotron using wavelengts just before and after the k-edge of the atom in consideration
Initial question was: what is better. Comparison of intensity ratios is better. It is faster and easier. Rietveld requires a lot of knowlege, and a lot of time. We have a problem of high level of automation. Today people believe that they can press a button and get a good result in a second. This is wrong. If you are not a specialist in Rietveld or you are not going to become a specialist in Rietveld then do not use it!
Comparison of intensity ratios has a clear physical sence. And often it is quite enough to make conclusions about cations distribution.
It's not that simple for Rietveld refinement even if use a standard sample, U'll always get some deviation in the cationic distribution.
X-ray was diffracted by electron cloud and it's a bit tricky if there's a light elements beside a weight elements. Unless use neutron.
Yet must consider the imperfections, coarse grains, thermal, positions etc. The problematic thing is u must separate between cationic distribution and SH preffered orientation if it present.
The way u refine also can give u different result in lattice parameters as well as cationic distribution. At the end, what is ur Rexp and Rwp? and by visual, how good is the fitting? Last but not least, data quality ???
The measured intensities of a single crystal is the preferred method to determine the cation distribution in the crystalline structure. However currently based methods of powder diffraction data (Rietveld, XLENS, ...) which give results of comparable quality.
It also depends on what elements are being substituted into the ferrite spinel. If you are looking at other transition elements, the scattering factors may not be sufficiently different for you to differentiate them using either the Rietveld method or the RIR method. If you are looking at Mg or Al substitution, then the Rietveld method will give more than satisfactory results.
The best crystallographic methods for determining the cation distribution are based on single crystal data, although at present the data based on data of crystalline materials (Rietveld, XLENS, ...) give very good results. Better if the atomic numbers are quite different.
I would start making a Rietveld refinement, this should give a first idea about the SOF and their correlation with Uij, ODF etc. Small differences in SOF's are expressed mostly at low angles, and some reflections might be particularly sensible. So the idea to use intensity ratios is clever, but make sure you use the right reflections (not just the most intense ones) and correlations can be ruled out.
What is the composition of the ferrite? Check the difference in scattering factors.
What kind of data? X-ray? neutron scattering?
Do you get different results from Rietveld and Intensity ratio?
So first determinate the chemical analyze of spinel then from RX you can determinate the crystallographic parameters from same samples finally you can dressing two points (crystallographic parameters (a or b or c, to chemical composition (zn)) finally via the curve you can determinate the chemical composition from XR analyze as I have doing in my article
The Rietveld refinement seems to be the most informative method, for it renders full structural information.
1. If cations have significantly different X-ray scattering factors, then use X-ray powder diffraction.
2.If cations have close X-ray scattering factors, but significantly different Neutron scattering lengths, then use neutron powder diffraction.
3. If cations have close X-ray scattering factors, and close neutron scattering lengths,
(for example Ti-Mn pair in LiMnTiO4), then look at the Shannon tetrahedral and octahedral ionic radii. The correct model cation distribution should render bond lengths and oxygen parameter which are in good agreement with the observed ones.
For LiMnTiO4, the proposed cation distribution (Li0.66Ti0.34)[Li0.34MnTi0.66]O4 the calculated oxyden parameter (u=0.2571) differs strongly from the observed (u=0.2630) value.
In short, the good profile fit makes sense when it is accompanied by careful analysis and interpretation of the obtained structure data.
Rietveld refinement method is best among the two. You can compare this with Mössbauer spectroscopy which is more appropriate method to determine cation distribution
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