Dhkl = 20 nm & Grain Size by SEM of > 1micron
Article Correlation between sintering temperature and properties of ...
This is a question that keeps recurring in RG.
X-ray diffraction does NOT measure grain size (it is possible to do it but in very limited and specific cases): it measures the size of the coherently scattering domains. So for domains of 20 nm it can be used.
Scherrer the first to provide a relationship between the breadth of the diffraction peaks and an average size. However the equation was derived for monodispersed cubes assuming peaks to be approximated by a Gaussian. The theory can be stretched somehow but:
a) the "size" you obtain can be quite far from the mean size (i.e. the first moment of the size distribution), because domains are not monodispersed (you have a size distribution). Furthermore this is a volume weighted size, a quantity that is not always the one sought.
b) there is not just size effects (you have instrument and strain effects that can play a role)
c) you have to consider the whole pattern and not just one peak to be able to extract the information in an accurate and precise way (taking the whole microstructure into account).
It has been already shown in the literature that traditional analysis techniques (including Scherrer equation which is also part of the well known Williamson-Hall method) can lead to serious errors if employed quantitatively (https://www.researchgate.net/publication/200045699_Line_broadening_analysis_using_integral_breadth_methods_a_critical_review).
The suggestion is therefore to use Scherrer equation ONLY for comparison between a uniform set of specimens (i.e. to tell if they are similar or not). If you want to have a quantitative estimation, use more modern techniques that can also help you understanding if the microstructure models you are using are plausible or not. Right now the de facto standard is the WPPM (https://www.researchgate.net/publication/11527348_Whole_powder_pattern_modelling).
Article Line broadening analysis using integral breadth methods: A c...
Article Whole Powder Pattern Modelling
This is a question that keeps recurring in RG.
X-ray diffraction does NOT measure grain size (it is possible to do it but in very limited and specific cases): it measures the size of the coherently scattering domains. So for domains of 20 nm it can be used.
Scherrer the first to provide a relationship between the breadth of the diffraction peaks and an average size. However the equation was derived for monodispersed cubes assuming peaks to be approximated by a Gaussian. The theory can be stretched somehow but:
a) the "size" you obtain can be quite far from the mean size (i.e. the first moment of the size distribution), because domains are not monodispersed (you have a size distribution). Furthermore this is a volume weighted size, a quantity that is not always the one sought.
b) there is not just size effects (you have instrument and strain effects that can play a role)
c) you have to consider the whole pattern and not just one peak to be able to extract the information in an accurate and precise way (taking the whole microstructure into account).
It has been already shown in the literature that traditional analysis techniques (including Scherrer equation which is also part of the well known Williamson-Hall method) can lead to serious errors if employed quantitatively (https://www.researchgate.net/publication/200045699_Line_broadening_analysis_using_integral_breadth_methods_a_critical_review).
The suggestion is therefore to use Scherrer equation ONLY for comparison between a uniform set of specimens (i.e. to tell if they are similar or not). If you want to have a quantitative estimation, use more modern techniques that can also help you understanding if the microstructure models you are using are plausible or not. Right now the de facto standard is the WPPM (https://www.researchgate.net/publication/11527348_Whole_powder_pattern_modelling).
Article Line broadening analysis using integral breadth methods: A c...
Article Whole Powder Pattern Modelling
Matteo Leoni,
Is it right to put the data of Dhkl in the paper of A Sedke et.al. "Correlation between ...."?
There are a few issues in the paper. From the point of view of the X-ray analysis is the refereeing was quite poor (even if it took 1 year):
- Scherrer should be written with two r
- the constant K=0.9 is not tyipcal of a certain ceramic but is a tweak for the model in order to consider more or less spherical domains!
- Dhkl has no meaning if you do not specify the hkl (e.g. D002). And this is a key point: ZnO is hexagonal (wurtzite structure) and therefore the domain size can be anisotropic (it can also have problems of stacking faults). Remember that the value quoted for XRD is in any case volume weighted, whereas the one from SEM is probably the number average. There is no indication whatsoever how the analysis was done!
- a variation in the relative intensity of the epaks has been seen. So why the authors did not try to give some explanation for this? Unexplained data usually means possible problems with the resutls.
- a D from Scherrer equation with 2 decimal places is completely meaningless.
- comparing XRD with SEM just help in understanding if the grains you see are monocrystalline or not. In this case they aren't. The speculation of the authors is in my opinion quite rough. You don't need HR/TEM in this case (as written by the authiors). You need to do things more carefully. XRD line profile analysis is too often abused, especially from non experts. And this is a clear example of this. (actually I can hardly follow the idea of the "polymeric network" here... and perhaps some expert can give some feedback on that).
In the end you can quote any data in a paper, provided you specify what you do, what is the limit and what you use this value for. For sure you can report a D from Scherrer equation to show that more or less nothing happens to the specimen. But at least say that this is a rough approximation and that details cannot be accounted for. And try to use the values properly, not pretending to have an agreement with the SEM.
At least for the high temperature sintering (calcination was already at 1000°C so I would expect less changes below that temperature) I would have expected to see some variation, as the small domains usually disappear during sintering. You can see this only if you have a size distribution. The fact that the distribution probably changes is clear, even from those poor data (look at the tail of the first peak that increases from the bottom to the top pattern).
Matteo has some good points. I would add that XRD of micron sized domains will have narrow peaks. So narrow it is hard to distinguish 1 micron from 100 micron. I think usually the Scherrer equation can be used to supplement grain/crystallite size for features/domains 500nm and smaller.
Jason is right in saying that large domains would result in narrow peaks.
However I would be very very very very very careful in working with micron sized domains (you can work with micron sized grains containing nano domains). Graininess can be a problem in that case and multiple peaks can easily appear if the specimen is not carefully prepared (this can be easily verified taking the pattern of a badly prepared quartz sample). In any case I would not attach any meaning to a domain size larger than 200 nm unless the experimental conditions and the quality of the pattern are stellar. In fact, in that case most of the broadening is given by the instrument: negligible errors in modelling the instrumental broadening can result in a huge variation in the size values. It's like weighting yourself and then yourself holding a midget in order to weight the midget!
No Scherer's equation is not well suited for microrange,it is well applicable upto 100 nm.(for more details see the book; B.D. Culity, Elements of X-ray Diffraction).
Jason, Mateo and Raghvendra have made very useful coments. From my experience, I can say that Schere's formula works really well when your crystallite size is below 50-60 nm. Because i have seen, using well sintered big grained sample (>10 micron) (even with single crystal Si) that contribution from instrumental broadening itself comes around 200-300 nm. It means, any size bigger than that you can not measure from X-ray line broadening method.
First of all we should be clear that from sherrers formula we are calculating crystallite size and from SEM we are getting particle size. In some cases they may be equal but in most cases particles consist of many coherently scattering domains(crystallites).
From Scherer's equation we can approximately calculate crystallite size upto 100 nm.
Hello
As I understood from the paper:
- block-samples (not grinded) were used for XRD, but the authors did not worry for stress-strain and stacking-fault or dislocation problems; but they mention oxigen vacancies which formed during sintering... which is a good motive to worry about
- I regularly work with ZnO powders, sintered or not, bot those XRD patterns reported in the paper (although, without the type of diffractometer and geometry settings) most certainly are for >100nm or larger crystallites
- by the way: does wurtzite-type structure, SG P6_3mc, show (111) "line"? 'cause its not the case in the crystallography books, databases or structure simulations, at least I could'n achieve such Miller-index for zincite...
I can't resist to express my sincere exasperation over the increasing number of such research papers in "high quality" journals, while papers giving in detail the experimental results are regarded as "too detailed" and "unnecessarily complicated". And I also wish to apology from all those who had been working a lifetime to clear XRD from such spots ( and possibly they are forced to read such papers).
Regards.
Funny, I never thought I would find such valuable comments on this blog !
I very strongly agree with Mateo's comments which pinpoint exactly the source of confusion in the litterature concerning particle size measurements using line profile analysis: XRD provides a measure of the size of the coherently scattering domains. This is also well explained in A. Guinier's books in which, as far as I recall, he mentionned a critical size of ca 30 um below which the Scherrer equation is not applicable. I think this value depends on the system you're looking at.
In fact, if you're looking for a method for particle sise measurement using X-rays, you should look at the scattering at small angles (SAXS), which signal is related to the electron density difference between the particles and surrounding media (provided the particles are sufficiently diluted).
Working with biological nanoparticles, I found a non-linear relation between the size measured by SAXS and using XRD.
There are ways to take into accound strain effects and lattice distortions in XRD line profile analysis, but this goes well beyond Scherrer's equation.
Cheers
Ferenc, the one identified as (111) is the (011), that's for sure. I can't judge the size of Zno domains by eye and believe me you would be surprised to see some pattern where you'd swear domains are around 100 nm and they are actually muc much smaller. The distribution plays a HUGE role, especially if it is wide!
I agree: more and more sh** appears in the literature...
No one savy would drive a car without knowing the traffic signs: well, most people use diffraction without knowing what they are doing...
Dear XRD experts!
Your comments are very detailed and useful.
Is there anyone who would agree to make a trial pre-review of the XRD section of manuscript about ZnO thin films? )
Abil,
I am far from being an expert, I only had to learn "what and how to do" but I can take a look at that manuscript if you wish. Send it over.
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