questions on analysis of domain size from XRD keep recurring on RG. Unfortunately it seems people are not up to date in this field.

With XRD you do NOT obtain the size of the grains, but you obtain information on the size of the coherently scattering domains (those that some people call crystallites). There are several methods to do that and Scherrer formula (proposed in 1918 if you want an idea on the age of it) is the most crude one. There is no "error factor": this is PHYSICS! The instrument, as in any measurement, plays a role. In this case there is an intrinsic broadening of the peaks from the machine due to the presence of real optical elements.

You can measure this effect using a standard (e.g. NIST SRM 660 series). So Adam is partly correct. You cannot use ANY LaB6 specimen to characterize the instrument: the NIST LaB6 standard is made in such a way to give negligible specimen effects.

I would definitely avoid the suggestion of Santonu!!! if you measure a single Si crystal you can kill your detector especially with slow scan (it is like a mirror so the diffracted intensity can be very high!!) . Plus you need the trend with 2theta and with a single crystal this is not possible on a powder machine. Using a "coarse powder" can be good as you avoid problems with absorption, however be careful in preparing this coarse powder: grains should be free from defects, large enough to give no size effect but small enough to give sufficient statistics. Take a silicon wafer, grind it and you will see what I mean: you obtain a powder and the peaks are quite narrow, but it is quite likely that each peak will appear as a multiplet, each of the peaks coming from a slightly different large grain (graininess). This is why hte standard was developed.

You can also try to simulate all optical elements using the Fundamental Parameters Approach but again you need to tune the model parameters to get a proper modelling of the standard.

The effect of the instrument can be little or heavy: it all depends on the broadening caused by your instrument. In any case Scherrer formula is so rough that putting the instrument or leaving it away has practically zero effect on the quality of the number you obtain. Just have a deeper look at the formula and you can clearly see why: it should be valid for monodispersed cubes in the approximation that the diffraction peak is gaussian. It is tweaked to other shapes with a constant that is of the order of 1.

Now how many gaussian peaks have you seen? Is your specimen monodispersed (if it is, then I am VERY interested as so far I always found a clear size distribution)? are you considering all broadening effects (Scherrer considers only size, but any defect in the lattice conditions the broadening)? Do you consider the emission profile in the correct way (Ka1 and Ka2 doublet)?

Scherrer formula should be used ONLY for comparison between specimens. Otherwise hte risk of quoting a nonsense size is quite large!

If you want to have an idea of the risk of using Scherrer formula quantitatively: https://www.researchgate.net/publication/200045699_Line_broadening_analysis_using_integral_breadth_methods_a_critical_review

And if you are interested in the state of the art for microstructure analysis from XRD: 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

Instrumental broadening differs from instrument to instrument. There are couple of ways you can measure the broadening factor. Use a single crystal Si (standard method) and run a very slow scan, from the single highest peak calculate the broadening of your XRD instrument. The second methods is to use dense very coarse grain of the the material you are using and use the broadening of the highest peak as instrumental broadening...

Have a look on one of my papers. Some detals are given:

https://www.researchgate.net/publication/234164424_Microstructural_characterizations_of_plasma_sprayed_hydroxyapatite_coatings?ev=prf_pub

Article Microstructural Characterizations of Plasma Sprayed Hydroxya...

Note that the observed broadening of diffraction lines may stem from different sources. From the purely instrumental point of view the broadening is an effect of interaction of X-ray beam with windows, optics, slits, ambient atmosphere as well as detector errors etc. Second thing is the broadening resulting from finite size of crystals, structural defects and strain. Determining the broadening from a perfect crystal (like Si substrate or a standard) is definitely a good idea. You can also try LaB6 (lanthanum boride). The instrumental broadening should be eliminated by deconvolution.Try this book: http://www.springer.com/chemistry/polymer+science/book/978-3-540-69855-5

questions on analysis of domain size from XRD keep recurring on RG. Unfortunately it seems people are not up to date in this field.

With XRD you do NOT obtain the size of the grains, but you obtain information on the size of the coherently scattering domains (those that some people call crystallites). There are several methods to do that and Scherrer formula (proposed in 1918 if you want an idea on the age of it) is the most crude one. There is no "error factor": this is PHYSICS! The instrument, as in any measurement, plays a role. In this case there is an intrinsic broadening of the peaks from the machine due to the presence of real optical elements.

You can measure this effect using a standard (e.g. NIST SRM 660 series). So Adam is partly correct. You cannot use ANY LaB6 specimen to characterize the instrument: the NIST LaB6 standard is made in such a way to give negligible specimen effects.

I would definitely avoid the suggestion of Santonu!!! if you measure a single Si crystal you can kill your detector especially with slow scan (it is like a mirror so the diffracted intensity can be very high!!) . Plus you need the trend with 2theta and with a single crystal this is not possible on a powder machine. Using a "coarse powder" can be good as you avoid problems with absorption, however be careful in preparing this coarse powder: grains should be free from defects, large enough to give no size effect but small enough to give sufficient statistics. Take a silicon wafer, grind it and you will see what I mean: you obtain a powder and the peaks are quite narrow, but it is quite likely that each peak will appear as a multiplet, each of the peaks coming from a slightly different large grain (graininess). This is why hte standard was developed.

You can also try to simulate all optical elements using the Fundamental Parameters Approach but again you need to tune the model parameters to get a proper modelling of the standard.

The effect of the instrument can be little or heavy: it all depends on the broadening caused by your instrument. In any case Scherrer formula is so rough that putting the instrument or leaving it away has practically zero effect on the quality of the number you obtain. Just have a deeper look at the formula and you can clearly see why: it should be valid for monodispersed cubes in the approximation that the diffraction peak is gaussian. It is tweaked to other shapes with a constant that is of the order of 1.

Now how many gaussian peaks have you seen? Is your specimen monodispersed (if it is, then I am VERY interested as so far I always found a clear size distribution)? are you considering all broadening effects (Scherrer considers only size, but any defect in the lattice conditions the broadening)? Do you consider the emission profile in the correct way (Ka1 and Ka2 doublet)?

Scherrer formula should be used ONLY for comparison between specimens. Otherwise hte risk of quoting a nonsense size is quite large!

If you want to have an idea of the risk of using Scherrer formula quantitatively: https://www.researchgate.net/publication/200045699_Line_broadening_analysis_using_integral_breadth_methods_a_critical_review

And if you are interested in the state of the art for microstructure analysis from XRD: 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

I agree. Mateo's reply is very precise and I think exhaustive. Actually I forgot to write that whatever you do to determine your instrumental parameters, do it with standards. Second, even more important, whenever working with single crystals or crystal-like stuff (like the abovementioned Si substrate) it is necessary to reduce the intensity by either attenuation and/or reducing the generator settings (if applicable) . And third - if you still want to follow the Scherrer approach, do keep in mind the meaning of the Scherrer constant. An brief introduction and example for GID geometry/area detectors is given in the paper by Detlef Smilgies (doi:10.1107/S0021889809040126). Check also the references therein.

Matteo clarify very well the difficulties in obtaining a quantitative data on the "coherent diffraction domains" from XRD. I add another statement: why we need information on "grain size"? What is the macroscopic quantity we want to correlate with the microscopic one? XRD can give useful information on a qualitative trend in e.g. nucleation and growth fenomena, but their results must be supported from other analysis.

Did you mean k in Sherrer's equation?

no, he means the instrumental broadening contribution, that is seldom considered by those still using Scherrer equation for quantitative purposes

Actually, we considered it by applying the Si wafer as Adam and Santonu mentioned. In our work, the Scherrer formula has been also applied as a role for comparisons only. However, the larger the domain size, the greater influence from broadening contribution of XRD (if any). This drives the state into the further order. Sources fro Matteo helps us a lot. Thank you so much for all useful responses!

If you use the archaic 0D point/scintillation counter then you are still in the "DARK AGES" or sometimes I like to call it affectionately "Paleolithic" age. I, myself am a proud dinosaur of the 1970's. Never-the-less, we at Rutgers & JHU broke that mold way back in the early 1980's and moved on to LPDS's (linear position sensitive detectors) and eventually Real Time 2D Area Detectors replacing time consuming film with real time capabilities. The spatial resolution is still being improved.

Mateo is correct about the diffracting domain size. So is Shantonu about the instrumental broadening. The safest way is to always compare to a known calibration standard preferably of the subject material itself. However, any other fully characterized known calibration standard may work as well.

It is possible to estimate the "grain size" or "diffracting domain size" with 2D XRD Image analyses as well.

Requirements:

1. Incident beam must be highly monochromated and collimated.

2. Incident beam must be larger than the largest "particle size" or "grain size" present in the subject sample.

Here is an example of such a highly monochromated (K Alpha 1 only) from a Panalytical X'Pert System (BNL Condensed Matter Group) with a Bartells 4 bounce type beam (2D 3mmH x 25-30mmV) conditioner and a transverse soller slit system to minimize transverse divergence. The smallest FWHM we measured for a GaSb substrate was in the order of 10 Arc Sec or less.

http://www.flickr.com/photos/85210325@N04/8490919402/in/photostream

Limitation:

1. The smallest size measurable is limited by the pixel resolution of the 2D detector.

2. Known calibration standards are required to quantify the estimates obtained through XRD.

Here are some examples using a 1mm diameter point source X-ray incident beam and a 25-30mm 2D Real Time XRD Imaging system with 50-100 um spatial resolution. Due to beam divergence we enjoyed some "magnification" factor and were able to examine sample with particle size in the range of 1-5um as well. Note the incident beam in this case was conditioned only with rudimentary collimator and Ni filter for the Cu K Beta component. The incident X-ray beam thus contained both Cu K Alpha 1 & Alpha 2 components. This would create double topographs for each reflecting particle (diffracting domain). Also note that a particle or grain in our powders may contain multiple single crystallites (poly-crystalline).

Here is an example of particle size ranging from 500um:

http://www.flickr.com/photos/85210325@N04/7920887956/in/set-72157632728981912/

This method works well for large particle sizes with "spotty" Debye-Scherrer rings. See the example of LaB6 NIST standard powder from BNL Beam Line X14A:

http://www.youtube.com/watch?v=acgFl5M7P-I&list=PL7032E2DAF1F3941F

I have the original sample size distribution performed by some optical method by the manufacturer

For fine grained samples with continuous Debye-Scherrer rings, it would be ideal to use a microfocus X-ray source. Using a conventional 0D detector (point/scintillation counter), this would be a time prohibitive task even with modern computers. Besides, there would be scan to scan variations due to sample position relative to the diffractometer axis (alignment). You can actually notice (in the above video for LaB6) how the diffraction pattern changes as the powder (shaped in the form of a wire specimen with epoxy) is rotated about the incident beam. In the case of continuous Debye-Scherrer rings the line broadening analysis would the conventional Reitweld, Warren-Averbach and other techniques very eloquently, earlier in the discussion.

It would be wise to capture and analyze the entire 2D XRD pattern rather than convolute the entire 2D XRD pattern in to one data point as in the case of the ubiquitous conventional diffractometer with a conventional 0D point/scintillation detector in use since the time of the Bragg's. The 2D will give you nearly six orders of magnitude advantage and make spatial mapping a virtual reality. In our case we used 2D devices that were robust enough to look directly at the incident beam to quantify while being sensitive enough to the faint reflections from MBE grown high precision super-lattice structures with periodicities in the 1-10nm range. Further, we are able to resolve strain-field variations in the FEMTOMETER scale using the Rocking Curve Method.

Glad to be under the scrutiny of such erudite and knowledgeable expertise.

Please feel free to join the LinkedIn Group “X-ray Diffraction Imaging for Materials Microstructural QC” and share your expertise, knowledge & skills:

http://www.linkedin.com/groups?displayPolls=&gid=2683600&goback=%2Egde_2683600_member_188581023%2Egna_2683600

Ravi - [email protected]

Typo correction: In the case of continuous Debye-Scherrer rings the line broadening analysis would the conventional Reitweld, Warren-Averbach and other techniques very eloquently stated earlier in the discussion by others.

BTW my fear of burning the detector is completely non-existent now and so is my fear of X-rays. You will not believe the advantage of real time XRD capabilities for sample observations but more so for precise instrument alignment and incident beam characterization.

Here is a YouTube Video Play List with a variety of materials and instuments:

http://www.youtube.com/watch?v=QRcj_t1WgVs&list=PL7032E2DAF1F3941F

Love to get some feed-back!

Chiefly about the choice of music?