Dear Gert and Colleagues,

Let me add a comment that may repeat some other´s but add to the difference between Rietveld and WPPM.

I would say that I applied the Rietveld Method if the fit I made was performed using the Rietveld Formula or Equation. This formula simulates each and every effect that has an influence on the pattern (e.g. structure, microstructure, instrument and sample geometry, background, etc.) and its parameters are adjusted by a least-squares procedure to fit the data.

In my understanding the Pawley and LeBail methods are closely related to the Rietveld method because they model each individual intensity of the pattern using the same factors of the Rietveld method except for those determining the intensities (the structure) that are unknown. Pawley and LeBail methods are used to determine the experimentally observed intensities for a posterior structural determination (by any method that would make use of those intensities).

The Rietveld method use the most physically-accurate model available for the intensities (the structure factor equation including iso or anisotropic thermal parameters, multiplicity, lorentz and polarization factors, preferred orientation, absorption, extinction, anomalous scattering, etc.) but uses a phenomenological description of peak shapes (including both instrumental or micro-structural factors affecting peak-shapes), and a physically sense-less background representation. Some of the corrections of the intensities (e.g. absorption) are not exact, though, they come from approximate models, but perform well when the effect of this factor is not very significant (and some times they are the only available model). Related methods used for determining intensities use the non-intensity-related parameters used in the Rietveld formula, to extract intensities from the fit.

The Rietveld Method, using an accurate representation of the intensities, performs well for structural analysis (refinement of structural model) and also quantitative phase analysis since relative intensities are correctly accounted for, even in the presence of preferred orientation, micro-absorption, etc, that can be reasonably corrected with some physically-sensible models.

The so called "Whole Powder Pattern Modelling" of Prof. Scardi and Leoni, is the physically meaningful representation of background and peak shapes by including accurate models for instrumental, geometrical and micro-structural effects in the data. But the method does not use the structure factors to determine the intensities. The WPPM method is good for determining micro-structural parameters (crystalline size distributions, shape, defect types and densities, etc.) but not atomic parameters (the structure).

In general, if you are dealing with new compounds or mixtures of n components of nicely crystallized phases (no matter if they are simple salts, organics, complex clays, or other) you´ll be able to apply the Rietveld method to fit the pattern (and sometimes combine the Rietveld and LeBail methods to obtain accurate intensities of an unknown phase that is mixed with a known one in the sample). Phenomenological peak shapes used in the Rietveld method will eventually fail to represent the peak shapes in the presence of high concentrations of defects, or very small nanoparticles with complex size distributions or even diffuse scattering by aperiodic portions of the phases present. The Rietveld method is a reciprocal space approach to the analysis, therefore it will be unable to account for the intensities that are far away from the Bragg positions.

If you are dealing with known materials where preparation or processing conditions determine the observed peak shapes, usually very broad or very complex, you would use WPPM to study the microstructure. WPPM comes in both reciprocal and direct space approaches, so you may model many different aspects of your sample in a way that the Rietveld method cannot.

If you have a new material that you can only obtain in very small nanoparticles and the XRD pattern gives funny peak shapes it will probably be impossible to fit with Rietveld-like methods and also impossible to do a meaningful WPPM since you will ignore the kind of defects present (since you ignore the structure). Then you will probably need to use the atomic Pair Distribution Function (PDF) to study the structure (and in some favourable cases the microstructure as it may have an effect in the interatomic distances in the nanoparticles). Some people (Simon Billinge among others) are trying to devise methods to solve structures using the PDF. In this direct-space method, it´s critical to have an accurate determination of the instumental and geometrical components of the background, separate from the diffuse scattering part of the intensity.

In all cases, in my opinion, we are shooting the best bullets we have to the different problems a power diffraction user may encounter. Finding the right method to analyse your particular problem is also part of the analysis process. The book, Diffraction at the nanoscale. Nanocrystals, defective & amorphous materials, edited by A. Guagliardi, N. Masciocchi (Insubria University Press, 2010 ISBN 10: 8895362357 / ISBN 13: 9788895362359) gives a good account of thing that can be done different than the Rietveld method to analyse complex structural or microstructural problems with powder diffraction data.

I would not say it´s wrong to call Rietveld analysis a simple QPA of 2 phases, or a fit that confirms a structural model is correct, because they are much simpler than refining a powder pattern of a protein powder or a complex mineral mixture. If both are based on the Rietveld formula then they were both applications of the Rietveld method. I´m kid of very worried of the number of papers published where Rietveld fits are wrong (bad background, bad peak shapes, bad structures, etc) or no analysis is performed other than visual inspection of powder data that supposedly confirms that the structure is as expected, but the trained eye clearly sees that the confirmation is not there. But that is another matter.

Sorry for the long comment...

Dear Gert, from the beginnigs of Rietveld method the aim of some XRD scientists was to use it in quantitative XRD phase analysis. I remember that in some of my articles in this fields in 1986 the referees sugered me to include that method in the references. I was not too much in accord with this because I could not see this application of the Rietveld method, but only the structural application for samples not able to offer good monocrystals. Indeed, I note certain "mistycism" about the structure determination by the RM; many material scientists propose an structure and if the RV gives a low error they ensure that this hypothesis is absolutely true, but it is not really certain because other structures may give also the same good results. In quantitative XRD phase analysis, the RM should be taken with care, because the peak intensities are determined not only by the structure factor, but also by the called granularity effects (see my article). Well Gert, this answer is only for motivating this very interesting question you entered here. I am working since many years in other fields of Material Science, but I shall follow amazingly this discussion between the young diffractionists.

When the email announcing your question dropped to my box a few minutes ago I was doing a quantitative analysis using the full-profile refinement which most of us call the Rietveld method :)) You can refine many different parameters, including relative phase contents, provided the structures are known. Or you can refine atomic coordinates... You may call it a Rietveld method or a full-profile refinement. It is your choice, I guess.

At least on your definition "Rietveld refinement is exclusively a technique describing crystal structure determination using powder diffractograms", you are wrong. You have to replace "determination" by "refinement". Indeed, "determination" is the whole process : indexing, structure solution and refinement. The Rietveld method makes the last step only and needs for a starting model close-enough to the final structure.

As far as I know a full pattern refinement is a full pattern matching. Only the cell parameters, the background, zero shift, profile functions (Gaussian, lorentzian, ...) asymmetry, preferred orientation…are refined. The atomic positions are not included. So you might fit or deconvolute well your powder pattern but you still do not have a structural model for your new compound.

The Rietveld refinement, however is a full pattern matching + atomic positions refinement. At the end you have a structural model for your new compound.

Unfortunately, nowadays many researchers and especially electrochemists just do a full pattern matching and conclude that the phase is isostructural to a known one because the chemical formulas and the powder patterns are similar. However, this not always true and such conclusion should not be made unless a Rietveld refinement has been undertaken.

As an example, Na2NiPO4F has been reported to be isostructural to Na2FePO4F because of the reasons I mentioned above. Recently, the single crystal analysis revealed that the structures are completely different. The cationic frameworks are exactly the same but the ionic frameworks are significantly different.

I always find it useful to start from the notation that Rietveld refinement, full-pattern refinement, Pawley fitting, LeBail fitting ... all do the same thing: fit a diffractogram by refining the parameters of a theoretical model, mostly in the least-squares sense (peak intensities in LeBail fitting being the exception). The theoretical model in all these fitting techniques is the same (bear with me for a second). The only difference is (1) the parameterization and (2) the choice of which parameters to refine and which to keep fixed at a known (or measured) value.

For example, in Pawley fitting and Rietveld refinement, Bragg peak positions are parameterized by unit cell parameters and an instrumental shift. The parameterization of the Bragg peak intensities is done differently however. Peak intensities in Rietveld refinement are described by the Rietveld scaling factor (one for each phase), atomic parameters, preferred orientation parameters, etc. while in Pawley fitting they are refinable parameters themselves. So Pawley fitting is identical to Rietveld refinement, except that you make abstraction of atomic parameters, preferred orientation parameters, etc. and replace them by generic peak intensity parameters. Full-pattern refinement makes further abstraction of physical parameters by considering peak positions as independent parameters (as opposed to being a function of unit cell and instrumental parameters) and keeps peak positions and relative peak intensities fixed, therefore allowing even experimental patterns of pure phases to be used in the fitting model.

So I would argue that the naming of XRPD refinement techniques is more related to the parameterization of the fitting model than for what purpose it's being used (and then I didn't even start with the parameterization of peak shapes). After all you could perform quantitative analysis with all the methods mentioned above when used appropriately (and often in different ways as well).

@Wout De Nolf Would that mean that the WPPM of the Dr Leoni is the 'Full-pattern refinement' you're talking about?

and so does that mean that Rietveld refinement is more precise since it has much more parameters to refine?

Dear Gert,

concerning your statements, I think you are mixing up terms. First of all, Rietveld refinement is not a method for crystal structure determination but for crystal structure refinement and analysis. But it is a full-pattern refinement method as the term full-pattern means you are working with the information you get from the whole range of a complete measured spectrum.

Mathematically, the Rietveld refinement is an approach to minimize a residual function using a non-linear least-squares algorithm, as you mentioned. Simplified and concerning the use in crystal structure analysis you are comparing and trying to fit a calculated pattern of a crystal structure to a measured pattern. So the Rietveld method is indeed a full-pattern refinement method as for every point of your measured spectrum a point is calculated due to the information you are willing to input in the applied equation. A classical intensity equation consists of terms for the background (the offset of your measured value), diffraction intensity (determining the "height" of the measured peaks), line broadening (determining the shape of the peaks), number and positions of the peaks (for if there are more than one contributing to the measured intensity at that single point) and so on. All these terms are, for their part, influenced by further effects due to the measured sample (absorption, preferred orientation to name only a few) and it's up to your "experience" and knowledge about your compound if you are taking terms for the refinement of these effects mathematically into account or not.

Based on the fact that you have the powder diffraction pattern of a pure (single phase) material a crystal structure determination is done by the following steps. Indexing of the powder pattern by peak search will give you the unit cell and the crystallographic symmetry of your compound. The crystal structure solution (or determination) yields a proposal for the crystal structure. Depending on your input (structural information of your target compound, applied methods, the used approach and so on) this "guess" is more or less representing the real crystal structure of your compound. At this point the Rietveld method would come into play.

Here the Rietveld method as crystal structure refinement method is a method to check, how close to reality your guess is and to refine it so that the residual functions mentioned above will become as low as possible. To agree with Carlos, a low residual factor (or error, as he called it) does not mean that everything you've done during the refinement is reasonable. But if the resulting crystal structure after the refinement is chemically reasonable, the assumptions you made during your refinement were reasonable and your R-factors are low you can indeed assume, that your crystal structure solution should be representing reality as good as possible.

If your are doing other kinds of analyses with powder diffraction patterns using the Rietveld method , be it quantitative phase analysis, crystallite size and strain analysis or whatever, as you mentioned in your statement, you will vary only certain terms of your refinement, but you will still process your whole measured pattern.

I hope this will help you with with your problem.

@Florent Pessina I don't know WPPM, but just consider what parameters it has in its model: unit cell parameters and several parameters contributing to peak shapes (domain size, dislocations, ....). I couldn't find how it fits the peak intensities, so it is either whole pattern fitting (which is a group name for all fitting techniques similar to Pawley fitting and LeBail fitting) or Rietveld refinement, depending whether it has independent intensity parameters or intensities as a function of atomic parameters etc. Full pattern refinement is basically fitting the diffractogram with a linear combination of pure phase patterns (see http://dx.doi.org/10.4236/ampc.2013.31A007).

To clarify some more, I usually see three levels of complexity in XRPD fitting: Rietveld refinement (the full monty), Pawley fitting (making abstraction of atoms) and full pattern refinement (making abstraction of atoms and structure). Peak shapes are described in the three levels with whatever degree of abstraction you find necessary. I often use the name Pawley fitting instead of whole pattern fitting in order not to confuse with full pattern refinement. You will also find the name "pattern decomposition" which is the same as full pattern refinement (i.e. makes abstraction of atoms and structure).

Thx to all. It really helps defining who's who, even if it seems we all end refining the same critical parameters and checking their validity

Rietveld is not for structure determination! is a refinement method that requieres a starting model of the crystal structure (that was previously determined by any method), then it makes the best fit to the whole powder diffraction pattern (full-pattern refinement)

The question is wrong, Rietveld refinement itself is full pattern refinement.

Rietveld fit :

Both phase and structure information are available.

Peak positions are derived from unit cell and space group. Peak heights are calculated from the structure factors. Peak width and peak shape are constrained by mathematical functions changing slowly with 2Theta.

The scale factor is calculated from the unit cell and from structure data; it can be used for quantitative analysis.

Other method (HS+):

Le Bail fit:

Phase information is available, but no crystal structure (atomic positions) data is present.

Peak positions are derived from unit cell and space group. Observed intensity is redistributed between overlapping peaks in an iterative way. Peak width and peak shape are constrained by mathematical functions changing slowly with 2Theta.

There is no scale factor for quantitative calculations available. Peak intensity is not refined.

Pawley fit:

Phase information is available, but no crystal structure (atomic positions) data is present. Peak positions are derived from unit cell and space group. Each peak height is fitted individually. Peak width and peak shape are constrained by mathematical functions changing slowly with 2Theta. There is no scale factor for quantitative calculations available.

Profile fit (=single peak fit):

No phase information (unit cell, space group) is present.

Each peak is fitted individually. Peak width and peak shape are fitted individually for each peak. For all peaks the peak width and peak shape can be constrained by mathematical functions changing slowly with 2Theta. (This is only useful for peaks from a single phase most of the time.)

There is no scale factor for quantitative calculations available.

HKL-phase fit:

Phase information is available, but no crystal structure (atomic positions) data is present. Relative peak heights are fixed per hkl-phase by a previous Le Bail fit. Peak width and peak shape are constrained by mathematical functions changing slowly with 2Theta. An empirical scale factor for all peaks together is available and can be used for quantitative analysis.

All this fitting method are modeled the data to bell shaped profile function (voigt, pseudo voigt or pearson 7), so called indirect method.

What Prof Metteo did is directly fit the data by the physical aspect (WPPM), so called direct method.

Michael Tem almost got the point, however, "changing slowly with 2Theta" is not really a refinement or fitting algorithm based approach of peak profile parametrization...

The answers above are very helpful and useful, however, I would like to add, if you are working with known structures, use Rietveld refinement (which is also a full pattern refinement based on a physical model and can give a lot of information). If you are working with unknown structures, this is a wholly different story......and a whole lot longer..... :)

All the discussions are very useful. Everything boils down to the fact that Rietveld refinement is a structural refinement and one needs a starting model for it. In fact there is fantastic book published by IUCR edited by R.A. Young on Rietveld Method.

Thanks for the all comments and clarification. I totally agree that I used the wrong term: refinement is definitely correct. Sorry for that. However, what I meant was simply that there should be a difference in terminology between a structure refinement (of an existing model) of a single phase, and the phase fraction determination of a multiphase mixture. We also differentiate between lattice vectors and reciprocal lattice vectors, although both are vectors, and the applied mathematics is practically the same (although the dimension is different).

There is no doubt that both refinement tasks can be very challenging, and there is no doubt as well that both use the same or similar mathematic tools to extract position and intensities of interferences (for finally different reasons). All are based of course an a full-pattern refinement. My irritation is only that many publications use the term Rietveld analysis for a "simple" determination of the phase fraction, what I would in maximum call intensity refinement of the full pattern measured. As I already mentioned above, also this task can be extremely complicated with anincreasing number of or a few "difficult" phases, but the number of free parameters is in many cases much smaller than for a typical Rietveld refinement. The question is: Is it a good idea to mix the name of techniques which are used for multiple phase investigations with techniques used for single phase investigations...even if the mathematical tools applied are nearly identical?

Dear Gert and Colleagues,

Let me add a comment that may repeat some other´s but add to the difference between Rietveld and WPPM.

I would say that I applied the Rietveld Method if the fit I made was performed using the Rietveld Formula or Equation. This formula simulates each and every effect that has an influence on the pattern (e.g. structure, microstructure, instrument and sample geometry, background, etc.) and its parameters are adjusted by a least-squares procedure to fit the data.

In my understanding the Pawley and LeBail methods are closely related to the Rietveld method because they model each individual intensity of the pattern using the same factors of the Rietveld method except for those determining the intensities (the structure) that are unknown. Pawley and LeBail methods are used to determine the experimentally observed intensities for a posterior structural determination (by any method that would make use of those intensities).

The Rietveld method use the most physically-accurate model available for the intensities (the structure factor equation including iso or anisotropic thermal parameters, multiplicity, lorentz and polarization factors, preferred orientation, absorption, extinction, anomalous scattering, etc.) but uses a phenomenological description of peak shapes (including both instrumental or micro-structural factors affecting peak-shapes), and a physically sense-less background representation. Some of the corrections of the intensities (e.g. absorption) are not exact, though, they come from approximate models, but perform well when the effect of this factor is not very significant (and some times they are the only available model). Related methods used for determining intensities use the non-intensity-related parameters used in the Rietveld formula, to extract intensities from the fit.

The Rietveld Method, using an accurate representation of the intensities, performs well for structural analysis (refinement of structural model) and also quantitative phase analysis since relative intensities are correctly accounted for, even in the presence of preferred orientation, micro-absorption, etc, that can be reasonably corrected with some physically-sensible models.

The so called "Whole Powder Pattern Modelling" of Prof. Scardi and Leoni, is the physically meaningful representation of background and peak shapes by including accurate models for instrumental, geometrical and micro-structural effects in the data. But the method does not use the structure factors to determine the intensities. The WPPM method is good for determining micro-structural parameters (crystalline size distributions, shape, defect types and densities, etc.) but not atomic parameters (the structure).

In general, if you are dealing with new compounds or mixtures of n components of nicely crystallized phases (no matter if they are simple salts, organics, complex clays, or other) you´ll be able to apply the Rietveld method to fit the pattern (and sometimes combine the Rietveld and LeBail methods to obtain accurate intensities of an unknown phase that is mixed with a known one in the sample). Phenomenological peak shapes used in the Rietveld method will eventually fail to represent the peak shapes in the presence of high concentrations of defects, or very small nanoparticles with complex size distributions or even diffuse scattering by aperiodic portions of the phases present. The Rietveld method is a reciprocal space approach to the analysis, therefore it will be unable to account for the intensities that are far away from the Bragg positions.

If you are dealing with known materials where preparation or processing conditions determine the observed peak shapes, usually very broad or very complex, you would use WPPM to study the microstructure. WPPM comes in both reciprocal and direct space approaches, so you may model many different aspects of your sample in a way that the Rietveld method cannot.

If you have a new material that you can only obtain in very small nanoparticles and the XRD pattern gives funny peak shapes it will probably be impossible to fit with Rietveld-like methods and also impossible to do a meaningful WPPM since you will ignore the kind of defects present (since you ignore the structure). Then you will probably need to use the atomic Pair Distribution Function (PDF) to study the structure (and in some favourable cases the microstructure as it may have an effect in the interatomic distances in the nanoparticles). Some people (Simon Billinge among others) are trying to devise methods to solve structures using the PDF. In this direct-space method, it´s critical to have an accurate determination of the instumental and geometrical components of the background, separate from the diffuse scattering part of the intensity.

In all cases, in my opinion, we are shooting the best bullets we have to the different problems a power diffraction user may encounter. Finding the right method to analyse your particular problem is also part of the analysis process. The book, Diffraction at the nanoscale. Nanocrystals, defective & amorphous materials, edited by A. Guagliardi, N. Masciocchi (Insubria University Press, 2010 ISBN 10: 8895362357 / ISBN 13: 9788895362359) gives a good account of thing that can be done different than the Rietveld method to analyse complex structural or microstructural problems with powder diffraction data.

I would not say it´s wrong to call Rietveld analysis a simple QPA of 2 phases, or a fit that confirms a structural model is correct, because they are much simpler than refining a powder pattern of a protein powder or a complex mineral mixture. If both are based on the Rietveld formula then they were both applications of the Rietveld method. I´m kid of very worried of the number of papers published where Rietveld fits are wrong (bad background, bad peak shapes, bad structures, etc) or no analysis is performed other than visual inspection of powder data that supposedly confirms that the structure is as expected, but the trained eye clearly sees that the confirmation is not there. But that is another matter.

Sorry for the long comment...

Gert, one man may use a microscope to study the natural wonders, while another may use it as a hammer (to brake a glass tube, for example). In both cases it is still a microscope.