wow! Is this real? Perhaps I am using a different technique. I purposely waited for somebody to start shooting some numbers, but did not expect the more experts to be those shooing out of the board. So, let's see what you did not notice: - 0.01 ° what is this number? FWHM? and at which angle? for a copper machine? Are we sure we are talking about 0.01° and not 0.1° ? I doubt you can get down to 0.01° FWHM with a lab instrument and for sure not without cutting most of the intensity - same for Scherrer equation: again what angle? There's a cos involved, so 0.01° at low or at high angle can make a difference...

- on estimating a contribution from the specimen and from the instrument, remember that Scherrer equation works in the Gaussian limit and for Gaussians the breadths are not additive but the square of the combined width is the sum of the squares of the widths... i.e. the broader dominates. So with a more reasonable instrument FWHM of 0.06° (at low angle) and a specimen contribution of 0.03° the measured peak would be 0.067°. So first, what's the accuracy needed here to tell it's 0.03 ° and not 0.031 °. Second, at those sizes the details count so not knowing the multiplying factor of Scherrer equation or the measurement angle, and also knowing that Scherrer equation is qualitative (as peaks are not Gaussian and the specimen is not made of equal cubes) can give an error in the size well beyond 100% so you get a number not a correct one. - reality: it is customary to assume that crystallite sizes above ca. 100 nm in the lab and ca. 200 nm at the synchrotron (on machines with a "clean instrumental function") be considered as "infinite" because there's no way to assess the precision and get a sufficient accuracy of the value. On a general purpose instrument (even worse if without a mono), your analysis relies mostly on a model for the instrumental function (axial divergence is your #1 enemy even using FPA) As a bottom line, with line profile analysis you want to get information about the specimen.. In my school lectures on the topic what I insist on is that you should work in conditions where the dominant contribution is that of the specimen (nano materials). What you want to do here is to take a cruise ship, weight it, disembark the captain, weight it again and calculate the weight of the captain from the difference... good luck with the 300-900 nm.

I cannot answer your question, so just a reminder: bigger particle, less reliable Schrerrer's equation is. Bigger particles can consist of several crystallites, may have more crystal defects, etc. All of this must be taken in consideration which is almost impossible when working close to resolution limit.

the reliability of Scherrer equation does not depend on any size.. If you use it in the conditions for which it is developed and you know the meaning of the result, it gives accurate results. In all other cases the result is always approximate. Bigger monocrystalline particles can give problems of graininess (i.e. the sample is not a powder from the diffraction point of view).

So there is no easy answer to this question for a real specimen. In the specimen you have a distribution of sizes and shapes and each size and shape gives a different profile (shape and width, not just width). If you imagine to start from a very broad profile with a well behaving distribution and then get progressively narrower, you see the mean size increasing until a certain point where it starts flattening out and most likely then giving randomly large values. This is the point you are probably looking for and is dependent not just on your instrumental resolution, but also e.g. on noise and method of analysis. You can try to estimate it from the error in the fitting parameters.. the error on the width gives you what's the variation in width that would give the same result (so larger values can be detected and considered as independent). At that point you use that width in Scherrer equation and get an order of magnitude estimate.

There can be a rough estimation of several 100 nm's according to your base line dedector calibration element. Si or LaB6 can give the most correct line fit by Rietveld and/or Scherrer formula. Debye-Scherrer is very good in the range of 10-100 nm as crystallite size not particle size as estimated from SEM. XRD is more useful than SEM by menas of crystallite sizes which can be seen as polycrystal soft or hard agglomerates in SEM. XRD can measure the size of seeds as crystallite size not the agglomerate sizes.

Some sound advice has been given in the initial 4 answers.

I have assumed -

1) Equivalent of CuKa wavelength - from synchrotron radiation or from a lab monochromator

2) Size-only broadening, not strain or size+strain.

3) You can reliably measure a size-induced broadening at about 0.03 degrees over and above the instrument broadening of 0.01 degrees.

On this basis the Scherrer formula gives an estimate of about 3,000 Ang / 300 nm / 0.3 microns as a notional upper limit.

I would not use Rietveld fitting.

@Brian:

I agree with such robust estimation, but I would extend the size to L=1.54/(0.01pi/180)=9000Å to answer the original question.

Anything beyond this limit is non-sense, and a crystallite size approaching the limit (say, 3000-9000Å) would need special care to be meaningful, such as standards, deconvolution, size-strain separation, sample preparation, error estimation etc.

Regarding Rietveld refinement (I would recommand using the LeBail (structureless) method), results are based on multiple, instead of one only, peaks and the separation of instrument-size-strain is straightforward. Also, anisotropic line broadening, due to domain shape anisotropy or other phenomena, is easily detected in this way. This may give more insight in the microstructure of a material then single peak analysis.

In this case, work with standards is of course mandatory to get a correct description of the instrument resolution.

All major Rietveld software (fullprof, gsas, maud, topas etc) can do the job.

I disagree. I posed a lower-limit of 0.03 deg (due to specimen broadening) over and above the instrument value of 0.01 degree, not 0.01 degree over and above above the instrument value of 0.01 deg. That is why gave my estimate.

wow! Is this real? Perhaps I am using a different technique. I purposely waited for somebody to start shooting some numbers, but did not expect the more experts to be those shooing out of the board. So, let's see what you did not notice: - 0.01 ° what is this number? FWHM? and at which angle? for a copper machine? Are we sure we are talking about 0.01° and not 0.1° ? I doubt you can get down to 0.01° FWHM with a lab instrument and for sure not without cutting most of the intensity - same for Scherrer equation: again what angle? There's a cos involved, so 0.01° at low or at high angle can make a difference...

- on estimating a contribution from the specimen and from the instrument, remember that Scherrer equation works in the Gaussian limit and for Gaussians the breadths are not additive but the square of the combined width is the sum of the squares of the widths... i.e. the broader dominates. So with a more reasonable instrument FWHM of 0.06° (at low angle) and a specimen contribution of 0.03° the measured peak would be 0.067°. So first, what's the accuracy needed here to tell it's 0.03 ° and not 0.031 °. Second, at those sizes the details count so not knowing the multiplying factor of Scherrer equation or the measurement angle, and also knowing that Scherrer equation is qualitative (as peaks are not Gaussian and the specimen is not made of equal cubes) can give an error in the size well beyond 100% so you get a number not a correct one. - reality: it is customary to assume that crystallite sizes above ca. 100 nm in the lab and ca. 200 nm at the synchrotron (on machines with a "clean instrumental function") be considered as "infinite" because there's no way to assess the precision and get a sufficient accuracy of the value. On a general purpose instrument (even worse if without a mono), your analysis relies mostly on a model for the instrumental function (axial divergence is your #1 enemy even using FPA) As a bottom line, with line profile analysis you want to get information about the specimen.. In my school lectures on the topic what I insist on is that you should work in conditions where the dominant contribution is that of the specimen (nano materials). What you want to do here is to take a cruise ship, weight it, disembark the captain, weight it again and calculate the weight of the captain from the difference... good luck with the 300-900 nm.

Seems we've forgotten about instrumental broadening as well as strain and crystallite (Scherrer equation) broadening.

Matteo Leoni I disagree with your statement 'the reliability of Scherrer equation does not depend on any size.. If you use it in the conditions for which it is developed and you know the meaning of the result, it gives accurate results'. To my knowledge there are no internationally (e.g. NIST certified) material standards for XRD line broadening, so accuracy cannot be defined or assessed.

I do not consider an instrumental resolution of FWHM of 0.01° to be unreasonable. Already ten years ago our laboratory machine managed an overall FWHM of (marginally) less than 0.03° for the low-angle peaks of silicon and LaB6. There was anisotropic broadening, so this resolution was affected by the sample; the instrumental contribution must have been smaller. This was already with a Mythen detector, but still using an old-fashioned tube. With a modern tube and more intensity, one can close the slits even more, going for even higher resolution.

I agree with Matteo Leoni , however, in that the uncertainty of the instrumental contribution starts to become an issue at this level. An instrumental contribution of 0.010° or 0.015° will make a huge difference if the sample contribution is also small. You would either need a reliable calibration measurement or a very good simulation of your instrument to make this work reliably.