The problem (check other threads on the same topic, as suggested also by Kai) is that people still use that equation to get information... without knowing what they get out of it..
Scherrer equation is a dangerous monster!
Before considering strain in Scherrer equation you would have to ask yourself also if you considered the instrumental effects, if your particles are isotropic and if the number you get is really the size you are looking for. You will be surprised to see that in cases where your specimen is well behaving, you get just a correct order of magnitude.. and when you are particularly unlucky you get nonsense (and some people publish that nonsense....)
It can be bigger but if the difference in size is too much you should remeasure the size from the XRD data. Are you using Scherrer equation for this??
The simple answer is "yes". Please do search for existing threads on RG covering the topic. A good search word would be "Scherrer" (for Scherrer equation), you will find discussions on the (in-)adequacy of applying that equation in the first place and elucidating comments on what you may expect from the various ways of measuring "size".
You may also search for contributions of Matteo Leoni (-> answers on his profile) who is one of the competent contributors to this topic.
Errors in determining particle size from TEM can depend on whether the images are formed in bright field or dark field mode, magnification (particle statistics) and host matrix (phase contrast). Also, core/shell particles can exhibit mixed phases (i.e. crystalline core/amorphous shell) for which an image formed by diffraction will always yield an under-estimate. Take care when interpreting the Scherrer equation for XRD analysis. The Phonon Confinement Model has also been employed to determine nano-particle sizes from Raman spectra, although again care is needed when interpreting the length scales for determining your particle sizes.
Yes, XRD is known to underestimate particle size (at least for thin films, in my area of research)
Thanks for your suggestions.........In my TEM images, I have got two region. From one region I have estimated particle size of the order of 5-6 nm and from another region I have got particle size ~50nm. I have also estimated crystallite size from XRD which comes out be of the order of ~50nm and in my XRD pattern of powdered sample I have got only two peaks.What could be the possible reason behind this?
in the XRD pattern each peak contain a VOLUME weighted information on the system... so large particles usually dominate. If you analyse the patterns using e.g. Scherrer equation there is no way you are going to get this information out as you evaluate the width of the peak that will be dominated by the large domains.
TEM is too local so what If you see could be representative of that particular sample, but not of the whole specimen. For sure if you have a bimodal distribution the peaks will have a peculiar shape with a broad base and a sharp tip
Not knowing your compound it's hard to guess why you just see two peaks.. oriented sample? narrow measurement range?
PS thank you Kai
If the particles contain a strain so there is a a different between XRD and TEM analysis. In nanoparticle size the strain is disappeared and the XRD and TEM result is to be identical.
Mukhlis.. I hardly disagree on your answer. If you have "strain" that in any case would be "microstrain" caused by possible defects inside the domains and by the grain boundary (or surface... depends if it is bulk or powder), the variation in size that you expect is close to zero. You have a small effect due to surface relaxation/expansion but it is present in both techniques
As I know the Scherrer's equation is applied only when there is no strain inside particles.
The problem (check other threads on the same topic, as suggested also by Kai) is that people still use that equation to get information... without knowing what they get out of it..
Scherrer equation is a dangerous monster!
Before considering strain in Scherrer equation you would have to ask yourself also if you considered the instrumental effects, if your particles are isotropic and if the number you get is really the size you are looking for. You will be surprised to see that in cases where your specimen is well behaving, you get just a correct order of magnitude.. and when you are particularly unlucky you get nonsense (and some people publish that nonsense....)
Do you notice that the Scherrer's equation can only be used when the peak is single without superposition?
Dear Armin, if you are interrested in average size, isn't it better to make a SAXS/SANS measurement?
You see only two peaks in XRD. Is your sample really cristalline? (This can be answered by two fast small angle scattering measurement below and above the Bragg-edge, for this purpose neutrons are better)
Thanks Sir , I have got only two peaks in XRD and both are corresponding to my system and in my TEM images I got two different region. In one region I have got particle size corresponding to TEM analysis but from another region I have got crystallite size 10 times less than XRD size. So, what is the possible reason?
Volker got a good point.. you need a lot of expertise to be able to get accurate information from a TEM image.
Marton, there are advantages and disadvantages of using SAXS/SANS versus line profile analysis for size estimation. Usually my suggestion is to try using both if you can access them. However (and those that have been involved in the review of synchrotron and neutron proposals know), a lot of people apply for neutron measurements even in cases where they could have the same answer from a 2-hours lab-XRD data acquisition.
If the specimen is diluted and you have enough contrast or you want to characterize the holes or a polymer then I'd go for small angle.. for anything that scatters well and
give some signal on the wide angle, I'd first try some of the modern line profile analysis techniques... you're sensitive to lower order moments of the distribution, you are phase-sensitive and you can easily find information on anisotropy of the domains and of defects. On the other hand with wide angle data you measure domain size and not grain size...
That's why I insist in knowing how/what is the specimen before making any suggestion!
Arvind, the reason can be that you are using the wrong tools to analyze your diffraction data (this happens VERY frequently). If you force all your determination down to the measurement of the width of a peak, you have no way to see a bimodal distribution!
Matteo, you have the truth, I should write a bit more precisely: However I rarely do diffraction, I would not trust in two Bragg-peak if there is no explanation why there are no more.
So Arvind, do you know why you see only two lines? And are you sure that they are from your sample?
Usually particle size from TEM analysis is greater than crystallite size from XRD. TEM analysis gives a good grain size information. The particle size of a grain is normally formed by several crystallites. Crystallite size information is usually obtained by the peak diffraction profile analysis of a X-ray pattern. A known example is the Scherrer equation.
As far as I know, XRD is a long range method, meaning that you will find with Scherrer equation the "mean" particle size of all the sample. Meanwhile TEM can look in more detail some regions and construct an histogram with the frequency versus grain sizes, then later adjust some gaussian distribution to the obtained histogram. The centroid of the gaussian will be the "average" of the grain size of the region analyzed. Depending on the region this value can be greater or smaller than the obtained from XRD. If you analyse the whole sample the result has to be comparable with the XRD but perhaps more accurate (depending on the stastics, the way that the analyser find the size). In general I think you can trust more on TEM because you are actually seeing directly the grain sizes and constructing an histogram of them, meanwhile in XRD you see the broadining of the peak and the extraction of the grain size is indirect and depends on the goodness of the fit, profile function used, if strains of grains also broaden the peaks, etc.
hmm.. Houston we have a problem--. a Gaussian CANNOT represent a size distribution!!!! the distribution function g function should have the properties that dom(g) =[0,inf), g(0)=0, limx->inf(g(x))=0
XRD is not a "long range method". For microstructure it works on the coherent range and that's not that long. For sure diffraction gives an information over a large number of domains with respect to TEM so it is statistically more reliable.
Concerning accuracy I would not be so fast in judging the two. Consider just a couple facts:
- nobody talks about calibration (of TEM) or provides a check for that (you always have the pattern of the standard if you want to analyze XRD data)
- how do you measure the size of a domain using TEM? What do you define as "external surface of the domain"?
- in TEM you see just the projection of the domain shape. Now if you see a rectangle what can you say? is your domain a platelet, a parallelepipedon, a cylinder or simply an inclined cube? and what' can you say about the third dimension?
- how can you be sure that you picked up a set of domains representative of your size distribution? are you sure you did not miss e.g. larger or smaller ones (lost during the specimen preparation or because superimposed)?
So you see that being direct and widely used does not automatically mean being accurate!
Sorry Arvind, I should read more carefully. If the factor is 10 in size and XRD is the winner (it gives the larger size), then there is two possible reasons:
Your sample really contains a small amount of big cristallites (I mean really single crystal particles). And as Matteo said, since the intensity from a 10 times larger particle is 1000 times larger (due to the coherent scattering), you will see them during the diffraction.
On the other hande tt the factor of 10 I do not think calibration would play a role. There is a bigger chance of miscalculation like mixing nm and Anagstroem which happens frequently.
Related to Volker's point above;
Regarding diffraction contrast imaging; whilst the disappearance of those grain boundaries whose rotation axis is parallel to the diffraction vector will certainly provide an under-estimate of the absolute nano-particle density, it is important to state that, unless there is a relationship between particle size and crystal orientation (which I suppose dependes on strain fields in the matrix) then these imaging conditions should (in principle) have no bearing on the 'observable' size distribution. i.e. the size distribution of 'observable' particles in a diffraction contrast image should be representative of the whole population
Thank you all for such a nice discussion. I will gone through all the points suggested by you.
First of all you should pay attention that correct determination of grain size in TEM involves dark-field images analysis. Very often we can find results of bright-field images analysis. In this case, you may not notice for example small-angle boundary and grain size will not correct. Sometimes it is necessary to determine particles mean size in a some matrix (for example presipitates in a steel or in an alloy). In this case investigator do not pays attention to intragranular structure at all. In XRD you determine not grain size, not subgrain size. You determine mean size of crystallites (coherent scattering region). What does it mean? If in one subgrain you observe little misorientation (for example because of wall which consist of several dislocations) in TEM you will see one grain, in XRD you will deal with two coherent scattering regions. I think that this can be a reason of different magnitude of TEM and XRD particle sizes.
Daniel, certainly you are rigth. When I told about grains I meant grains in bulk materials, not powders.
As a rule, always particle size is larger than or equal to the crystallite size :)
For the crystalite size analysis, you can compare the result between scherer and williamson hall equation.
.. this last answer confirms the fact that people do not read. They do not read here (see the various threads about the errors in using using Scherrer equation and the WH plot for quantitative analysis) and they do not read in the literature where the problem of traditional line profile analysis methods has been discussed multiple times
In numerous presentations of this subject it is usually shown that the largest crystallite size to be measured accurately is < 45 and < 90 nm, respectively, for Conventional Diffractometer (FWHM ~ 0.10° at 20° 2θ) and Monochromated lab XRD (Cu Kα FWHM ~ 0.05° at 20° 2θ). In our study the values of crystallite size determined from XRD ( about 200 different samples) were compared with those obtained by imaging in a transmission (TEM) and scanning electron microscopes (SEM). It was found that XRD data are very good coordinated with the real crystallite sizes only for crystallites less than 50-60 nm. According to our results when the XRD method gives the crystallite sizes more than 60-100 nm it must interpreted as a “signal” of need of additional sample investigation by electron microscopy methods.
Vladimir, can you give us some references about those limits? It can be easily demonstrated that if your machine is not crap you can get up to ca. 100 nm for the average domain size. You could get the same information also from a machine with a beta filter if you would take the filter edge and the correct instrumental profile into account. The major problem (and I always see it), is that people try to compare some average taken from XRD (without knowing what it means) with some average taken from the microscope. To be sure about the result both techniques should be used at their best and the result correctly estimated on the basis of the statistical meaning of the measurement
Matteo, you are absolutely right about the "that people try to compare..." But I would say "some people". Our article on this subject now under reviews. Pay attention to page 6 and page 146 in the next presentations:
1. Line Broadening Analysis, p.9, http://chemistry.osu.edu/~woodward/size_str.pdf
2. Guinuer A, X-ray diffraction in crystals, imperfect crystals, and amorphous bodies. Dover Publications, Inc., New York, 1994, p.146.
My Bruker diffractometer has FWHM = 0.058° at 30° 2θ
Warren Averbach Fourier method is an accurate method of X-ray Line Profile analysis where all aspects are taken care of, as indicated by Dr. Leoni , like Instrumental correction, proper background estimation and effect of lattice strain. This method is based on multiple order of reflection and gives the values of coherently diffracting domain and lattice strain along a particular crystallographic direction. So, this crystallite size value can only be compared with that estimated by Dark Field imaging in TEM. Bright Field imaging in TEM gives more or less an average value of the particle size.
Dear Suchitra Sen, all this is correct when all crystallites have the identical size. Actually we obtain the XRD profile from crystallites different in the size. Therefore XRD method gives the average crystallite size
Dr. Uvarov, you are right in the sense that XRD gives the diffraction profile, not from a single particle, but from a number of particles irradiated by the beam. In that sense, I agree that XRD gives the average crystallite size. But what I wanted to mean is that XRD analysis, whichever method you apply, yields different values of coherently diffracting domain sizes along different crystallographic directions. In that respect, how to obtain the average crystallite size?
Secondly, if by DF imaging in TEM, one analyses a large no. of particles and make a histogram, one can get an idea of average crystallite size along a particular crystallographic direction.
@Suchitra.. not exactly.. as Vladimir already said, the WA gives an average value that is actually a surface weighted average. As we have shown several times, there are techniques such as the WPPM to do the analysis via Fourier methods on the whole pattern in order to provide the full size distribution! of course if you have a distribution of sizes AND of shapes the problem has no solution as you would need to know each individual domain. If you have a "well behaving" shape distribution (it can be one or more shapes) you can extract the whole size distribution "easily". Each directionm, in any case, bear the contribution from instrument AND size (distribution) AND shape AND "microstrain".. the main advantage of XRD over TEM is statistics: with TEM you can surely measure 1000 domains, but I doubt you would get to the grams of powder analysed by XRD and I doubt you can quantify the defects with a good accuracy (you see them but you see hwat you want to see and you miss most of those that are off the zone axis)
@Vladimir, thanks for the references! Finally I have been able also to open the first. For sure the one of Woodward is very outdated (and some numbers sound strange.. as for instance the 233 nm.. why 233 and not 234 or 232?). I have my own copies of the Guinier book but again it is quite obsolete in most parts (including the line profile analysis one). It's amazing to see that most people think XRD development stopped in the 60s, especially in line profile analysis!
Thank you, Dr. Leoni.
Thanks for your briefing. Is WPPM method analogous to Rietveld method? I like to have copy of some of your latest papers.
Can you please elaborate why the WA method gives only surface weighted average?
In TEM analysis, main advantage is the direct observation of the material structure. 'Seeing is believing'! But yes. quantification may be difficult in some cases.
Both XRD and TEM have their own advantages. I would rather say that these two techniques are complementary and it is best to use both of them, wherever possible, to get a complete picture of the material structure.
it can be demonstrated (impossible to do it here) that the WA gives the ratio between the third and the second moment of the (normalised) size distribution p(D). Check the definition of a moment of a distribution to see that this corresponds, in the end, to the ratio of the integrals of [D^3 p(D)] and [D^2 p(D)].
From TEM (and from WPM) you determine p(D) and you usually extract the mean i.e. the integral of [D p(D)]. The "seeing is believing" is good... unless your TEM expert is one of those who like to show you amazing micrographs that are quite often an exception rather than the rule for your powder! Complementing the two is the key: I usually do a quantification via XRD and if I have TEM data I use it to add extra constraints to the XRD models
You can check e.g. my profile for the papers on the WPPM. It is similar to the Rietveld in that you have a model and you refine the parameters on the whole pattern: however it differs as the main focus is microstructure and the pattern is generated starting from physical models of the microstructure (the structure is not needed)
To Suchitra Sen. If you use Rietveld method, then any software gives you single value of crystallite size, and it is an average crystallite size. However, if you are interested in the crystallite size in a certain crystallographic direction, then you need to calculate this size using peak with corresponding Miller indices. For example, TOPAS software is able to calculate the crystallite size for every peak without information about real phase composition. In conclusion I want to say : the more time you are engaged in x-ray methods, the better your understanding that article name "The “state of the art” of the diffraction analysis of crystallite size and lattice strain" (Mittemeijer EJ and Welzel U, Z. Kristallogr. 2008;223:552–560) is very correct:)
Vladimir, most Rietveld software is based on FORCING the peak width to obey the Williamson-Hall approach. The average you obtain is therefore related to it (and forcing the data to behave in a certain way is not physical. With topas you can insert more accurate models but again if you want to extract one value per peak you are still doing something wrong for two reasons:
- DISTRIBUTION: you are not taking into account the presence of a size distribution
- MICROSTRAIN: unless you use the correct model, the risk is that you extract an anisotropic size that in the ed is just a wrongly interpreted strain broadening.
The information from each point in a diffraction pattern MUST be compatible with the information from all other points so unless you process simultaneously the whole pattern you cannot extract something that is physically meaningful!
My only suggestion is to participate to some conference on the topic (e.g. on powder diffraction or on line profile analysis such as the Size-Strain conference series) to see what is the state of the art and to see who is actively doing research in the field... and you will notice that research moves faster than reviews...
My opinion , Crystalline size calculated from XRD is just the estimate value.
...as is "crystal size" calculated by just about any method. What exactly is your point?
@Theerapong: opinions are good, but here we (at least myself) are talking about science. Any scientific method based on the analysis of experimental data gives some "estimate". Unfortunately, nearly anybody can take a ruler and a micrograph and estimate the size of a single nanograin using a microscope (well, at lest in principle), but not many people know exactly what they are doing when they employ diffraction to do such an estimate.
There are a lot of people that think they know how to use TEM and a bunch more that believe diffraction is just getting a pattern and use some formula and software to analyze it (and they never opened a book of crystallography or diffraction). And they publish/write about that and they write things similar to what you wrote (no, I'm not attacking you, don't worry), i.e. opinions, instead of checking the literature and writing something physically meaningful. Believe me, there is so much trash around that I might write an entire book on it....
I do not consider myself an expert in any of the two techniques, but I think my little 20-years or so experience in this field is sufficient to say that, in most cases, you can give an excellent estimate of the DOMAIN size distribution even from lab data. And it can be easily shown that you can extract the input parameters in a virtual experiment.. So it might be an estimate, but if you do things properly (i.e. use the right experimental and modelling tools for the right purpose), this is probably the best estimate you can do for the domain size. It is then just a matter of understanding if the result (the domain size distribution) is the one you need, or if you were looking e.g. for the size of a different class of objects (grains, aggregates, particles etc.).
Thank you, Matteo, I know about these concerns. And I know that there is a vast number of articles (with very contradictory data!) on this topic. I am a practitioner, and therefore I believe that each sample requires an individual approach. For example, if I'm working with nanopowders synthesized by a simple hydrothermal method, I do not think about the impact of microstrain on the calculated crystallite size. And when I work with material, which has the crystallites with flake-like or needle-like morphology, I understand that the crystallite size calculated with using XRD method gives the average thickness of flakes or diameter of needles, and not the real maximum size of the crystal. Other example- You've certainly seen XRD patterns of apatite. (00l) peaks are always narrower than the rest because the apatite crystals have shape of hexagonal prisms stretched-out in this direction. Of course we can specify the presence of preferred orientation in input file and get a good quality of the profile fitting. But what is calculated crystallite size in this case?
Feature size in microstructure strongly depends on several factors and could be different from the actual size due a number of reasons. if you grab a TEM image under kinematical and dynamical conditions, the size varies. Size can be determined close to the real size using kinematical diffraction conditions conditions. however some features may not give a good contrast in bright field, but dark field kinematical conditions, where size appears usually less than bright field conditions.
@ Vladimir. i partly agree with what you say... never assume strain play no role.. I have hydrothermal specimens that show microstrain-type broadening.. Also for the other systems: if you have needles what kind of information do you get if you do not consider the shape, the shape distribution and the size distribution? The average yuo obtain has little meaning. As ofr apatite, I have a nice specimen of HAp rods.. so also in that case there is no general rule. The only rule is, again, to use the proper tools ofr what you want to do: if you want to know if a specimen is better than another you can even superimpose the patterns and evaluate it visually. If you want to have a size distribution for nanoparticles use e.g. the WPPM but definitely NOT a generic Rietveld refinement software. We both agree you can cure headache by cutting the head off.. but perhaps an appropriate medicine (in 2013) might be a more state-of-the-art solution, right?
@ Matteo, of course, all mentioned and taking into consideration (in WPPM) the physical parameters have an influence on the peak shape. But I would not claim that the Rietveld method absolutely does not have a physical basis and I would note that mentioned factors have a very small impact on the calculated size of the crystal (that is about we're talking). I am not ready to compare a traditional Rietveld method to the WPPM method developed by you and P. Scardi. The reason is simple - I didn't work with PM2K software. Of course, your concept based on physical models of the microstructure and lattice defects looks very well, and the results obtained with using WPPM method, which were reported in your articles and presentations, are excellent. However, I think that unfortunately the method will not widely used until the PM2K software have a user-friendly interface (as commercial TOPAS with Fundamental parameter approach or “simple” FullProf and Powder Cell for Windous (PCW ) free software) and until manufacturers of diffractometers use this method in the supplied software. Because today, speaking about the new method, we mean the new software for its application.
P.S. As the topic is interested for many people, I suggest for all comers looking at interesting XRD pattern. I suggest calculating the crystallite size for this material to all people willing to do it. A particular "round robin" will come out of it. I warn that I have TEM and SEM results for this sample. "Everyone is welcome!"
Vladimir, even without doing any analysis, you can clearly see that your specimen has a wide (or a bimodal) distribution. The specimen is cassiterite (SnO2) as you forget to mention that, and there is also some impurity stuff. I add the XY for those that canot read binary proprietary files
If you never used the software why you say it hasn't a user-friendly interface? The WPPM method is not widely used for two main reasons:
* people on average do not read: 99% of the work is usually done by using a method that someone else (perhaps someone known) is using fro similarspecimens. So people keep using Scherrer formula
* it is not (and I want to stress the point here) a push-the-button technique. if the risk of getting bs out of a Rietveld refinement is, on average, 50% (as at least 50% of people use the Rietveld method or a Rietvel drefinemnt software as a black box), with WPPM the chances ramp up to 90%. A fit that look perfect for someone not in the field, might look terrible for someone working daily on microstructure analysis.. and details count here. it is not a matter of getting more or less the shape and the intensity correct. You should get to the point where you are confident that what you are doing is compatible with the data
... as expected we can model the pattern with two distributions... No way you can extract any microstructure information using Scherrer formula here
Vladimir, I wonder how you compare your XRD results with SEM results. SEM will never give you crystallite size values unless each particle is a single crystal and the sample is well-dispersed.
Suchitra, first of all "Never say never". Did I say anything about comparison of XRD and SEM results? I said that I have SEM and TEM results for this sample! Using the SEM images you can estimate the homogeneity of the material. And of course the SEM result gives information about morphology and chemistry of crystallites
Excellent topic/question Arvind Kumar of BHU! I have a lot to read and absorb. I somehow missed this awesome discussion. I'll be back after studying it all. Thanks to all participants. Happy 4th! The Birth-Day of Democracy!
"my two bits" time! Right Matteo? This discussion "stretches a mile". Took me a few minutes just opening them all up. Good stuff!
I see 720 views and 66 answers. You folks ought to at least click the "green arrow" right below the question to indicate that it is an interesting topic. This will circulate the discussion more in the network and get more informed participants. Also feel free to click the "green" & "red" arrows below each response. We are all adults here and none of us will take it as a personal affront if one of us clicks the "red" arrow. I always click the "green" arrow for participation. I choose to contest in content only. I appreciate all points of view. I have a huge appetite for information. Thanx a million!
I agree with Ravi. Maybe we will agree with the following assertion? Traditional XRD methods (along with phase identification, quantitative phase analyses, refinement of unit cell parameters, refinement of atomic positions and site occupancies) allow estimating the average size of crystallites (taking into account features of a diffraction profile and diffractometer configuration). As a rule, the average crystallite size calculated with using XRD method is in a good agreement with results of TEM method at the crystallite sizes less than 50-60 nm. If we want to receive more detailed and exact information on the crystallite sizes (taking into account real physical features of a crystal structure) we can (must?) to use a WPPM or similar methods. P.S. Every can place results of crystallite size calculation for sample 1 here or send me ([email protected]). And sorry for my English:)
Tapas Desai · University of Texas at Arlington - "Yes, XRD is known to underestimate particle size"
XRD doesn't underestimate but it is the interpreters of the data that may skew the analyses. What XRD gives you is the data based on the choice of optics/geometry & incident beam conditioning. Many even now choose to ignore the rich 2D XRD data and convolute/smudge/integrate using the conventional 0D detector to obtain linear diffractograms. I bet you did the same to come to your present opinion.
Iain Crowe · The University of Manchester - "Errors in determining particle size"
Often these errors are due to inaccurate assumptions made regarding shape and other experimental variables. Especially in XRD.
The best practical solution in XRD is having good "known calibration standards".
Arvind Kumar! Could you post your XRD & TEM data when convenient. Your size range implies you should be considering the SAX method to evaluate. What is holding you back?
Both are independent but related. Scherrer equation does not work fine, do Rietveld refinement.
I guess people should carefully read the previous answers ...
@Alexandre: what do you think the Rietveld method is using? if you read one of my previous comments: "most Rietveld software is based on FORCING the peak width to obey the Williamson-Hall approach. " and guess what.. the Williamson-Hall method is just an arbitrary combination of Scherrer equation with the differential of Bragg law. Have a look at the formulas employed to describe the peak width and you can easily find it out yourself.
So my suggestion is at at least to know what you are talking about before suggesting to use some technique (especially a complex one like the Rietveld method).
@Ravi: as you see more or less the hot topics are always the same: David vs Goliath. You know we all appreciate the efforts you put in promoting 2D diffraction
I like your comment "Also feel free to click the "green" & "red" arrows below each response. We are all adults here and none of us will take it as a personal affront if one of us clicks the "red" arrow.". Unfortunately there is no possibility to have any information about why people press the red arrow.. It is meant to "downvote poor content". Well, I do not take it as a personal affront. part from time, I do not lose anything here . However I would definitely like to know on a purely SCIENTIFIC basis the reason of a red arrow. I would gladly accept any number of red ones from someone that can demonstrate that what I write has "poor content", otherwise, I am sorry, but I would consider a red arrow just a sign of ignorance and poor scientific weight of the one who clicked it. Opinions are great when your main field is sociology.. however ours is science and therefore facts and formulas are the only way to demonstrate someone is wrong or he wrote something "poor" or stupid.
@Vladimir: the figure I posted previously is the WPPM result on your data. No Voigt functions and no Scherrer equation. Without using a completely free distribution, the data fit quite well just with a size contribution and a bimodal lognormal. Actually if you use two slightly different cell parameters you get a better fit (expected for the smaller size fraction). You gave no instrumental information (pattern of a standard), so I assumed the instrument effects are totally absent. Values are therefore underestimated and the distribution slightly wrong. From the distributions the mean values (first moment of the distribution) are 3 nm and 49 nm for the main and the other fraction
@Vladimir no roblem but you better post the pattern of the LaB6 as well if you don't mind.. it could be useful as, for instance, the broadening increases with the angle, the shape and intensity of Ka2 depends on your mono etc..
Matteo: "Spherical harmonics expansion" talks to you? No? Then open a book!
the problem is that people are misunderstanding "crystallite size" and "nanoparticle size"...
and sorry if the whole pattern decomposition model lost the war against the Rietveld method. And, talking about complex methods, do not suggest a complete newbie pdf analysis or Debye method!!!
Discussion and answers proposed are very rich and interesting and provide quite all the different aspect of a very complex problem which is always open in the scientific community. Just a small point to keep in mind. XRD diffraction and or Electron beam diffraction can reveal the average coherent domains under Bragg conditionsand so not the real crytal size.
If relaxing equation of Bragg for electron can be considered you cannot calculate the coherent domain average size from the SAED. To get size it is better to extract the information from Dark Field mode and you can get a more realistic size of each hkl planes selected. And thus depending of the crystallinity of your materials. In the article published in European journal of ceramic we discussed of the data issued from XRD and TEM on ceramic fiber Nicalon ("Updating the Behaviour of PCS-based Fibres (Nicalon) during Oxidation") .
@Alexandre: sure I know the spherical harmonic expansion model of Popa (and I know personally both Popa and Balzar)... you don't need to open a book.. you just need to know the authors personally and to have discussed with them the issue some years ago when they were developing the model.... The little problem with the spherical harmonics is that (see the paper of Nicolae) "...the new model of spherical harmonics is, like the old model, a phenomenological one.."
The risk is that you interpret some other effects in terms of size. A different thing is e.g. the model of Popa (reprised by Stephens) where microstrain effects are modelled with a lattice invariant. This has a solid physical basis in establishing the relative breadths of the profiles, even if the shape of the peaks can be, in practical cases where you know the source of microstrain broadening, slightly different (see the recent papers of Leineweber on the subject). Perhaps I don't know all literature, but I think I know most of the works (and I personally know most people working) in the development of models for diffraction line profile analysis (traditional, Rietveld-based, Debye and PDF).
It is not my problem if people keep misinterpreting names (and I still don't like the term "crystallite".. that should be called "coherently diffracting domain"): check again otherthreads on the subject where facts and "opinions" where given on it. It's a lost battle until there will be some official nomenclature (as e.g. in the definition of "crystal" for the crytallographic community).
If I have to suggest anybody a method to extract MICROSTRUCTURE information from their pattern for sure I am going to suggest the Rietveld method as the last resort (there are exceptions if you implement physical microstructure models inside it.. and, believe it or not, the WPPM models are the state of the art fortht purpose). The powder decomposition lost his battle long time ago.. and this is what I keep saying (and people keep using it). WPPM and pattern decomposition are a bit different.
The PDF approach and the Debye are definitely a suggestion for people interested in getting the information on nanoparticles. Even for newbies. I want people to extract physical information, not mathematical one! I think I have said more than once not just here (jhave a look at the various threads in here), but also at most conferences on diffraction and line profile analysis (Size-Strain VII in Oxford will be next one not to miss) that you should use the right method for the right purpose. Using the right method does not mean downloading a software from the net and playing with it: the Rietveld method is unfortunately at that level (and anybody in the field has his own list of literature rubbish containing nonsense parameters extracted from a Rietveld fit. Using the right method means reading first, understainding if physical models are employed fro the purpose and, when this is the case, using it.
A nice exercise for anybody interested: generate a very small domain atomistically (you can do it even by hand), calculate the pattern using the correct Debye equation (at this level it is again something you can do with Mathematica) and then try to model it with any Rietveld software. If the domain is small enough, you can have some really good surprises!
Have fun as this is a real wild world!
Matteo, take a breath. The parameters you extract from any PXRD experiment have anyhow to be taken with caution. The idea behind the spherical harmonics is to have a model where you can change the coherence length in different directions. It is useful for material science if you want to describe you coherent scattering crystal (whatever how puristic you want to call it) and usually people DO understand that the number that are given then are TENDENCIES and INDICATIONS but describes AN AVERAGE number and an AVERAGE structure of the WHOLE sample. For the normal scientist it is a good point to have such "average" small crystal...
Volker! Excellent question & Segway, "operator error" is the answer. But that brings us right back to "de ja vous". I know the answer lies in the following classic book - X-ray Diffraction, Andre Guinier. I just got my personal copy finally after years. I shall master it. Amazon! I've heard one of my mentors Dr. Thomas Tsakalakos (Rutgers) paraphrase his teacher Andre Guinier - "If you find smoke in the reciprocal space then you will find the cigar in real space". The real question is "how do you measure it?" I believe the solution is in 2D XRD Image Acquisition & Analyses! What seems obvious is that ambiguities exist in both XRD & TEM quantifications. The user needs to be very vigilant regarding the assumptions and experimental conditions.
You folks are discussing thoughts I've been wrestling with for decades. I'm glad to be in a forum erudite enough to boldly discuss it in real time. I'm a bit lost with all the acronyms (e.g., PXRD) and some model specific jargon flying around. I request you use expansions when possible for us "little folk, laymen" among stalwarts. Please post or send PDF files and certainly detailed references when possible and convenient.
I shall closely follow this line of thought and further encourage discourse. I'm sure even the "flat earthers" thought that to be "devine truth" ("purely scientific basis") up until recent history. For me that sounds like yesterday (pun intended).
We shall all be magnanimous enough to look at the "pure facts" past the back-ground of arrogance, conceit, humor, personality & opinion that each of us brings to this discussion. A little forethought, courtesy & sense of humor would serve as excellent lubricants to the often rambunctious and contentious exchange of "informed opinion" that I love to participate in.
Good to intellectually spar with each of you.
BraggXRD [email protected]
Philippe! "XRD diffraction and or Electron beam diffraction can reveal the average coherent domains under Bragg conditions and so not the real crystal size." Are you suggesting these two aren't related or that their relationship is not yet established? Do you mean the unknown "shape factor"?
Since you are at it. Please go forward and define your "crystal size" as you interpret it and distinguish it from the "diffracting domain size" as you see it.
"Scherrer equation is a dangerous monster!" Maybe, maybe not! It seems to be the knee-jerk panacea for "grain/particle/crystallite? size" measurements. Just the definition of "size" alone has so many connotations and is so nebulous/subjective that it causes confusion among many XRD users. Especially, when you consider the fact that XRD is applicable over so many varied fields of materials.
The fear of the "unknown" usually creates the appearance of the "monster". We are all gathered here to exorcise that "demon". Let us all shed light on the "darkness" of XRD analyses.
Millions of crystallites take part in forming the powder X-ray diffraction pattern. These crystallites are not absolutely identical (by shape, size, presence of defects, chemistry, etc). We attempt to extract maximum information from acquired XRD pattern. I think that we always obtain the average value for any parameter regardless of the used approach. It is inherent property and feature of powder diffraction. Theoreticians, I have a simple question: Why we have to consider comprehensive physical model for a crystal if his neighbors in investigated sample can be different??? Maybe I'm missing something?
I see 864 views and 89 answers and only 2 like the discussion. I know there are more than 2 contributors here. So, why the apathy? You ought to at least like what you say. Make your opinion count. Click it!
I'm posting this link on our LinkedIn group (all of you are invited & pre-approved), "X-ray Diffraction Imaging for Materials Microstructural QC", discussion board in order to invite others to join in this discussion on RG:
http://www.linkedin.com/groups?viewMembers=&gid=2683600&sik=1373056802552
http://www.linkedin.com/groupItem?view=&gid=2683600&type=member&item=255546873&qid=e6cc088a-52f5-4971-aa48-8049c9f58a09&trk=group_most_popular-0-b-cmp&goback=%2Eanp_2683600_1373056802552_1
@Ravi - perhaps the reason is that the question, and most of the answers, are neither "interesting" nor "poor", but lie somewhere in between.
Just the fact that there is so much "ambivalence" with XRD & TEM should be cause to make it exciting. After nearly a century of experience we ought to be a little more certain in our conclusions from the data. Which leads me to believe there is much opportunity to explore. That excites me!
I agree absolutely that there are tremendous opportunities in what at first glance is a very old topic that was adequately covered decades ago. The new literature clearly shows that this is the case. There are a number of very good researchers working in this area, driven in part by the new tools we have available.
Edward, if you consider the number of journals, the poor refereeing work, the fact that people do not read and prefer to get a result in zero time, you can understand that there is no solution to this problem. The majority will keep citing (and mostly in the wrong way) the paper of Scherrer and the majority of referees will ask for "TEM validation" of XRD data but never for the opposite (more obvious from a statistical point of view!).
In most cases the real problem is whether to look for the most physically plausible solution according to the state of the art methods (from a statistical, physical and mathematical point of view) or the one that most people are able to obtain (and this is also the big question mark for the new NIST X-ray domain size standard, that is taking ages to be set up and fully characterized). One value is useful if you want to start building theories based on the data, the other just for comparison purposes... and most people will not follow this policy!
Matteo - a good start might be the journal editors (a smaller pool than the referees) of the relevant journals. If we can gain consensus there as to what is and is not acceptable for publication, then we stand a chance of getting to a solution. But the odds of this are not so good. Frankly the discussions on this forum alone serve to illustrate the magnitude of the problem.
Even given all the usual issues with the Scherrer equation, I frequently find myself reviewing papers where the authors have failed to consider the instrumental broadening, so that their crystallite size estimates are an order of magnitude or more smaller than what is the truth.
For what it is worth, I like your description "the most physically plausible solution according to the state of the art methods". That should be the target, no?
Come join us and share in the wealth of knowledge. Free Webinar, July 12 at 11am EST on X-ray Diffraction Techniques in Transmission Geometry
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"Scherrer equation is a dangerous monster!"......what kind of information is being extracted from this equation? how is it related to TEM?
From the Scherrer Equation you can get in very limited conditions of validity a "coherence length". This coherence length can be estimated to be the diameter of a nanocrystal d. These crystals may bind together and we end up with larger nanoparticles with a diameter D, and this you measure in TEM. There is a number relating both, so D=k.d but k has not a specific meaning, just that your nanoobjects are polycrystalline...
I share your opinion Edward, but we should act starting with ourselves as reviewer and simply reject what is nonsense and that could not be. It may sound hard but it saves our time and will help increase the quality of the papers!
well, let's similar discussion on reviewing is going on on the Rietveld mailing list and on several exchanges of emails between members of the X-ray community. There is no easy way out: I reviewed a lot of junk (complete nonsense from a mathematical or physical point of view) and I have seen the very same paper published in another journal with no corrections (not even the typos !). Trash literature is the result of the growth in the number of journals and the growth of a class of Editors that use this title just as a further entry in their CV. Take any journal and check the Editorial boards. And I mean seriously check who they are, how they are related each other, what is their field of expertise vs that of the journal and you will understand what I mean.
We should start having again (as was in the past) someone putting their face, name and reputation attached to a published paper: How many would review a paper on a subject they're not strong in, if the risk is that the whole community will laugh at them?
Next year will be the International Year of Crystallography (for those interested, look for www.IYCr2014.org) and we hope a lot of people will spend some time learning what crystallography and modern diffraction methods are.
So back to my friend Scherrer and to Dinesh. Scherrer equation is a typical example of easy= popular and the most striking example of a formula that everybody knows but nobody knows what's about. Moreover there are several versions of the same equation with different constants and with different parameters (e.g. FWHM vs integral breadth). I defined it as a "dangerous monster" in one of my previous posts and you can easily understand why. Start from the equation describing the intensity for a single cuboid (analytical but hard to manage without a computer), replace it with a Gaussian (e.g. with same maximum and area) and then calculate the powder average. The resulting intensity equation will still be a Gaussian: calculate its FWHM et voilà you have Scherrer equation. Now:
- people use it for peaks that are not Gaussian
- people use it for shapes that are not cubes (you can actually do an analogous calculation for a sphere and for other shapes and you can obtain a similar equation)
- people use it for real specimens where you don't have monodispersed domains
- people compare the resulting value directly with other sizes. Actually they compare Scherrer value with a "mean" (ror quote it as such) i.e. the FIRST moment of a size distribution.
So the first lesson is: use it as a QUALITATIVE comparison tool among homogeneous patterns.
The second one is harder: if your specimen is polydispersed (i.e. ALWAYS), then Scherrer equation provides a ratio between higher moments of the column length distribution (the ratio of the fourth to the third moment). Now, unless your specimen is monodispersed (if you have one, I am interested in buying it), or the size distribution is Gaussian (impossible as the Gaussian cannot represent a size distribution) this ratio does not correspond to the mean.
Now you can do whatever you want with this number: I would definitely not try to compare it with any TEM data.
To avoid silly replies (that I have already heard): yes you can work out the same ratio starting from the TEM distribution of the corresponding objects (the coherently diffracting domains) and compare them if you like. Beware of a few things that you might have overlooked though:
- you did not consider the effect of the instrument
- you did not consider other sources of broadening (impossible to rule out from a single-peak analysis)
- you did not consider the actual shape of the peak (I see a lot of answers here but how many of you took the data of Vladimir and actually tried to calculate the size?)
- you did not prove that your domain shape is correct (you need multiple peaks)
- the moments of a distribution are intimately related to its shape & skewness that, in turn, define the shape of the peak, information that you don't use!
- there is no direct relationship between result and data (and the risk of fitting the data on your model and not viceversa is always there!)
- with TEM how many domains did you survey? How did you select them? Well with one XRD measurement you analyze more material than that seen by a TEM in its whole working life...
In the first lecture of my Nanstructured Materials class I tell my students that "size matters" and a nanoparticles of 4 nm can behave totally different from one of 8 nm or 16 nm... so if you work with nanoparticles, think twice (and perhaps more, and maybe have a deep search in the literature) before using one or another technique to estimate their size. And if you can, use the whole information you collect (the data), refine your models on the data and take all physics you know into account. As already said several times, in 2013 there are alternatives to Scherrer equation that can take the microstructure properly into account!
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