There are already some good answers. I just have a couple points to add:

First, if the particle shape is determined crystallographically, so that for example the long axis in a rod morphology is always one crystallographic direction, then you have a chance. The Scherrer formula will give you different apparent sizes for different Bragg peaks. For the reasons that have already been discussed, though, I'm not sure how much I'd trust the results.

Second, if you really just want a semiquantitative measure of the typical particle size and shape, just put some particles onto a 3mm lacy-carbon-on-copper-mesh grid and pop it into a TEM. It'll take 30 minutes or less (once you're familiar with the procedure; there's a little bit of a learning curve). In fact you should do this anyway to verify that the Scherrer analysis isn't fooling you. If you want quantitative results, it'll take a little longer in the TEM, but it can definitely be done. But you'd be amazed how often people assume they have a certain morphology and analyze their XRD under that assumption when they could have just looked at the sample for a few minutes in a TEM and seen that their assumptions were completely wrong. Most nanoparticle samples have a pretty wide mix of morphologies that defy simple analysis algorithms.

It doesn't have to be a great TEM. Any functioning TEM has enough resolution to do this measurement. If you're doing this kind of work and you have access to any kind of TEM at all then you really should include it as part of your standard sample characterization. Otherwise you stand a very real chance of adding to the pile of nonsense nanoliterature out there.

The Scherrer formula has a constant K that can be adjusted between 0 and 1 depending on the "sphericity" of the crystallite (e.g. 0.9 is typically used for nearly spherical particles). See https://en.wikipedia.org/wiki/Sphericity

However, experts in the field have been suggesting that the Scherrer method should not be used, as it is not reliable and can be misleading. Despite this fact, many authors still use Scherrer method...

See this paper:

Scardi P, Leoni M and Delhez R 2004 Line broadening analysis using integral breadth methods: a critical review Journal of Applied Crystallography 37 381–90

http://onlinelibrary.wiley.com/doi/10.1107/S0021889804004583/abstract

it seems Claudio has already given you some of the info! I should add just two things:

- the first is the spelling of Scherrer (that should be with the c)

- the second one concerns the result you want to have. If you have rods then you definitely have a distribution with two parameters (you have particles with a diameter and a length). So what "size" do you want? If you want the whole distribution then you need to model the profiles taking the shape AND the double distribution into account.. no doubt there! Just remember also that line profile techniques can't be forced to give you realistic results beyond a 150-200 nm boundary unless you really push your setup and data collection to the limit.. A distribution of cylinders can currently be modeled (even if part of the calculation is numerical) using the WPPM algorithm

- the third one (that should not exist) is that you can certainly succeed publishing "Sherrer" data (misspelled) on most journals (especially those with high impact). You would get  little or no comment on this part as most so-called editors and reviewers have no clue about all this stuff and refuse to combat those bad practices

There are already some good answers. I just have a couple points to add:

First, if the particle shape is determined crystallographically, so that for example the long axis in a rod morphology is always one crystallographic direction, then you have a chance. The Scherrer formula will give you different apparent sizes for different Bragg peaks. For the reasons that have already been discussed, though, I'm not sure how much I'd trust the results.

Second, if you really just want a semiquantitative measure of the typical particle size and shape, just put some particles onto a 3mm lacy-carbon-on-copper-mesh grid and pop it into a TEM. It'll take 30 minutes or less (once you're familiar with the procedure; there's a little bit of a learning curve). In fact you should do this anyway to verify that the Scherrer analysis isn't fooling you. If you want quantitative results, it'll take a little longer in the TEM, but it can definitely be done. But you'd be amazed how often people assume they have a certain morphology and analyze their XRD under that assumption when they could have just looked at the sample for a few minutes in a TEM and seen that their assumptions were completely wrong. Most nanoparticle samples have a pretty wide mix of morphologies that defy simple analysis algorithms.

It doesn't have to be a great TEM. Any functioning TEM has enough resolution to do this measurement. If you're doing this kind of work and you have access to any kind of TEM at all then you really should include it as part of your standard sample characterization. Otherwise you stand a very real chance of adding to the pile of nonsense nanoliterature out there.

Actually the Scherrer' formula doesnt give the particle size but depends on both the coherence length along the hkl direction (temperature, disoreder) and associate size of the scatterer (see e.g. Guinier' book). Differentiation between the different contributions is a difficult task and involves assumptions that should be conforted by TEM analysys.

hi Jasper,

first of all I think that  - for rod shape and wire shape nanoparticles - your approach (using XRD for particle's shape) is not suitable. there are some methods you could approach based on Whole Powder Pattern Fitting or Modelling, but they're complex algorithms and I don't think you could get any useful relevant results.

what I'll recommend you to do is a SAXS analysis for obtaining the particles size distribution function or functions. you can even address a specific analysis algorithm called "separated two-phase Debye model" for particles having no definite shape (they're not sphere, cylinder or spheroid) - just like they are in your case.

TEM can also be used for semiquantitative measurements - just like Bryan said earlier.

best regards and good luck !

DLS, TEM, SEM and...

Dear Dr. Anandhi:

From several contributions steamming of the set of answers consider further focus on the item below.

The Scherrer’s equation is only a proper tool to derive an unidimensional (1D) parameter of length, which is assigned to a specific diffraction lines. In fact, the idea of “size” approaching a 2D or 3D structure is erroneous, as mentioned in two of answers. In fact, area and volume of crystallites can not be extracted in a trivial way from X-ray diffraction.

In this sense, taking in account the dimension of length, for a realistic purpose the Scherrer’s equation exhibits a limit of validity, with relation to the scale of the dimension length.

Due to limitation of application, the Scherre’s equation is only valid for crystallites with length dimension belonging to the range from 150 nm up to 200 nm; or from 1500 angstrons up to 2000 angstrons; or from 0,15 micrometers up to 0,20 micrometers, as mentioned in one of answers.

From this find, the Scherre’s equation is not a proper tool to derives 1D length of crystallites of the order of 10 nm or 1 nm, also is non proper for crystallites scales at around 2000 nm (2 micrometers). By consequence, the Scherre’s equation is inadequate to derive the unidimensional length at nanoparticles.

Kind regards.

Marcos Nobre (M. A. L. Nobre)

TEM, SEM, for semiconductors NCs you can use absorbtion or PL results

good luck !

I am 100% agree with @Bryan W. Reed, use TEM or a FE-SEM. The best way is to use a FE-SEM if you are not planning to measure crystallographic characteristics of your particles because it provides  you a better statistics in terms of covering more number of particles.  

When we work with cellulose nanocrystals, we prefer to use TEM, especially because we have a population of crystals with different sizes. So, we try to measure by TEM at least 100 crystals to measure the lengths and diameters, and calculate the aspect ratio (L/D). We think this is a nice approach because we can have an average value and dispersion parameters (standard deviation, standard error, percentis, etc.).

So, we prepare the grids, send them to the partners, and when we receive the pictures, we use a software as ImageJ or GImp to calculate the dimensions, using the scale bar in the picture for a cross multiplication (nanoparticle dimension (nm) = nanoparticle pixel * scale bar dimension (nm) / scale bar pixel).

I hope you can have success in your work!

Best regards,

JP

thank you mr. S. Abd.El.Aleem - for appreciating my point of view in this matter!

well it seems time to open a good book of physics and start doing some considerations on the various options presented here, right?

- @Denis Negrea:perhaps YOU "could not get useful results" using some advanced line profile analysis methods, but without a proof (and without knowing that this is all about) I would not generalize your assertion. The WPPM algorithm is based on physical models of the microstructure and of the diffraction experiment. Believe it or not, it gives you highly accurate results. You can just generate the grains atomistically, calculate he pattern using the Debye scattering equation and model it with WPPM to judge yourself. And you can refine any size distribution and any shape distribution. The limit is just the physical meaning...My suggestion, before making any recommendation, is to be sure you know what you are talking about (BOTH on WPPM and on SAXS)

- SAXS vs WPPM vs TEM. This is the major point of the whole discussion and again it seems everybody here is forgetting physics and statistics. TEM is sensitive to the number of grains, XRD to the volume (third moment of the size distribution), and SAXS to the sixth moment of the size distribution. With the TEM you see a 2D "section" of your specimen, with XRD you analyze a large volume and separate the single crystallographic directions, with SAXS the directional information is lost. With TEM and SAXS the phase information is completely absent (try doing a size analysis of two polymorphs), with XRD a multiphase specimen is not more difficult than a single phase one and you have independent size distributions. With XRD you can measure the size distribution in a nano polycrystalline aggregate, in a suspension, in situ inside a reactor, on a large quantity of powder. SAXS can work in some of those cases. Good luck with the TEM. Yes, there are also weak points, I have no doubts there: the WPPM works only for crystalline domains and for sizes that are below ca. 150-200 nm and of course it measures the coherently scattering domains (see my previous comment for grain size). But there are no limits about shapes or size distributions. The assumptions you make when analyzing the SAXS data are much more than those with XRD. Both are based on the analysis of the shape function (or form factor) but while in XRD this is separated per direction (hkl) and far from the direct beam, in SAXS it is integrated for all directions (over the shape and size distributions). With SAXS you can go beyond the size that you can access from XRD because you don't have the limit of the instrument resolution affecting the Bragg peaks. However how many times do you fit the whole SAXS region and how many times do you simple limit the analysis to just one of the two regions where simplified laws are valid? Plus you need enough electron density contrast to see some meaningful effects.

With the TEM you can see the shapes (actually not really, unless you tilt), but what's the meaning of what you see? You are trying to obtain an information about the whole specimen by observing a few grains. Actually (and nobody does this), it is possible to simulate the diffraction pattern starting from the TEM result and compare it with the diffraction pattern obtained for the whole specimen. You would be amazed to see how many times the two don't agree. Sorry but it's a problem of statistics of the TEM. I would love to see some papers where people did an accurate XRD analysis and completely missed the information. Yes, you miss it for sure using Scherrer formula. It would be like measuring the diameter of a spot of a SAED pattern to get information on the size of the grains from which the SAED has been determined. Saying that the TEM result do not agree with the Scherrer result and thus XRD analysis is not accurate is also absurd: it's like comparing pears with apples. The two MUST NOT agree. Physics says that TEM gives the number average on a few grains and Scherrer formula (in the few rare cases where it is sufficiently accurate) gives the volume weighted average. The two are definitely not the same unless your distribution is a delta or a Gaussian (sorry but none of those cases can be found in a real specimen). Try comparing the size distribution obtained from WPPM with that obtained from the TEM and then find the physical causes for the differences (if you see significant ones).

So I agree about stopping the nonsense literature. Then just tell the editors and the reviewers of most journals dealing with nanoparticles to ask for BOTH for the TEM and XRD analysis, ALWAYS when presenting data on nanostructured materials. Most of those people have their brain fossilized to 1918 (Scherrer) formula and are so coward that they refuse publishing any work showing that the stuff they published so far (based on comparing macroscopic properties with data from a few TEM micrographs) is in most cases nonsense. Just open any journal starting from those with the highest IF...

Simple is not synonym of accurate, dear Denis and appreciation is not synonym of correctness. Ask those that keep using Sherrer equation (misspelled) quoting some paper in the literature that used it... this increases the impact factor but that's not science!

dear mr. M. Leoni - my remark : "thank you mr. S. Abd.El.Aleem - for appreciating my point of view in this matter!" was a funny-sarcastic one, based on the fact that mr. S. Abd.El.Aleem just copy-pasted my previous answer to mr. Jasper topic question. anyway...I've worked with Rietveld analysis and I know how powerful this XRD model is, but ...since mr. Jasper is not interested (or that's what I've understood) in crystallite's size or strain but in particle's size (although at the nanometric scale these might be the same), it was my humble opinion that best approach is SAXS. In the end, allow me to say that I very much appreciate yours and mr. Scardi's work especially on WPPM methods and I'm honored by you presence on this topic.