Dear Henry,

if as you mention only some of the peaks of some of the samples are showing a sharper peak than the LaB6, what you are seen from the aluminum is not representative of your diffractometer and hence it could be sharper (supposing the LaB6 is representative of your instrument broadening).

What is happening in reality?

Some of your aluminum samples have very big grains (strained or not). Than in some cases the diffraction is not coming from the entire volume interested by the beam, but only from few grains in the proper condition (e.g. orientation). The the diffracting volume is much smaller and confined to only the one or few grains in Bragg condition. So it is like for some peaks you are using a very small beam.

To verify if this is the case. Is it your intensity (of the lines) corresponding to a random sample? 

If not, to distinguish between sample graininess (that is causing you these sharper profiles) or texture (not produce the non statistical volume problem): if you take out the same sample and you reposition it in a different way (so you have a different investigated volume), are your intensities changing a lot?

Do you see also strange shapes on certain peaks? This is another indication of extreme graininess.

So the problem is not your LaB6 instrumental function determination or the instrument itself. It is your sample that does not satisfy the minimum requirement for a correct measurement (a sufficient number of grains in the diffracting volume, at least millions, so thousand can diffract at a given orientation).

Give a look on our paper on the instrumental function determination, Powder Diffraction around 1991-1992, if I remember well there was at least one example of graininess for too big grains.

Luca

The answer to the above question is to be found in the following statement (from the attached link, by A. Le Bail):

"Those who have pushed their diffractometer to their limits (for instance using 0.018 scattering slit or so on) know that very low FWHM may be obtained but that correspondingly, at the Rietveld refinement stage, Rp (background subtracted) may be > 20%. In such a case, the figure showing Iobs, Icalc and intensity difference in a manuscript submitted for publication may not be esthetically [sic.] acceptable."

Here "Rp" stands for the quantity Rprofile introduced on p. 70 of the original paper by Rietveld (J. Appl. Cryst. 2, 65 (1969)). For clarity, the "instrumental resolution" in the above question corresponds to FWHM, and this is generally not the all-important parameter from the perspective of the Rietveld method. It is for this reason that instrument makers recommend specific Standard Reference Material, SRM, for calibration.

With reference to "aluminium", the following statement from the same text is relevant (note the "Al2O3"):

"SRM standards were particularly designed for this quest, and particularly LaB6 SRM 660 which is the recommended standard for calibration by the JCPDS-ICDD (Powder Diffraction 3, 209-218, 1988). However, tests were also on Al2O3 SRM 1976, quartz and Na5Cr3F14 choosen [sic.] for medium fluorescence problems with a copper target in the absence of back monochromator."

http://www.cristal.org/powdif/low_fwhm_and_rp.html

Thank you very much for your answer.

In the Rietveld method the crystal must be considered as an infinite crystal, for that reason only the centroids and the intensities of the xrd pattern are included in the refinement, but in microstructural analysis are included the centroids and the fwhm. Is crucial to obtain the fwhm contributed by the instrument. Many authors suggest to use the LaB6 SRM 660, but my problem is that the observed peaks of the deformed aluminum sample (polycrystalline bulk) are less broadened than the observed in the LaB6. I've performed a series of differents configurations for the slits, steps, time per step, point or linear detector, for both, the standard LaB6 and the aluminum samples, but the problem persist.

From your answer I undestand that I don't need to reach the lowest fwhm value for the LaB6, prior to the aluminum measurements, this may be my problem, I've trying to reach this values. I'll measure with other slits configurations.

Thank you.

You are welcome Henry. Perhaps you should contact Armel Le Bail, as I merely quoted him, and he is unequivocal. The relevant e-mail address is to be found in the lower part of the page the link to which I have given above.

Dear Henry,

I have not tried this myself, but there is an example given in the manual of BGMN (see: http://www.bgmn.de/tubetails.html), that states that the SRM LaB6 powder has some size and strain broadening, and I have seen several other papers that confirm that (e.g. http://www.geocities.ws/aang_au/JAC_35_155.pdf). So maybe your sample just has less size/strain broadening?

Pieter

To determine the IRF of your instrument you need to do a measurement, in your diffractometer, a standard as LaB6 or Si or NACALF (this is not standard sample but very good for this procedure).

The conditions for this experiment have to be the best as possible that you can do: 2Theta from 5-140 for example and step about 0.001º or similar. The time will depend about the tube life that you have but try to arrive over 30.000 counts in the maximum peak.

After that, you have to do a correct Rietveld refinement!!!. Values obtained of UVW and other will be your reference for future. In general you will have to create an IRF file and then use it in your future refinements.

A few things come to mind. Regarding the handling and storage of your LaB6 reference. Do you store under Argon to protect against humidity? If not stored correctly LaB6 does readily degrade over time.

Another thought is the vastly different linear adsorption coefficients (LAC) present here. I assume you are using Cu radiation. If so LAC of Al is around 130cm-1 while I believe LaB6 is 1138cm-1

I was always taught that you should use materials of comparable LAC to obtain the IRF. Perhaps a highly sintered corundum material is more appropriate?. Another approach is diluting the LaB6 with a light and amorphous material is mentioned in "Two-dimensional X-Ray Diffraction" by B. B. He (Wiley)

It is not possible for deformed Al to have a sharper peak than LaB6. Absolutely impossible. Either you are not measuring deformed Al or you are not measuring LaB6 NIST powder (or perhaps both). Either something is seriously misaligned in your system or the materials you are measuring are not what you think they are. Have you tried Si, Al2O3, CeO2, Y2O3, etc....? All of these MUST have a sharper peak (unless they are nanopowders, in which case they would be very expensive and you would have probably blown yourself up using them) than any metal, deformed or not.

Think about it. It's impossible. Clearly your instrument is misaligned severely.

Henry! Post your data for the best feed-back from the erudite expert membership in RG. Alignment is a key issue ignored by many for expediency. Beware! Trust prior alignment but verify before your own XRD observations. We found many anomalies when we verified for the last Bruker D8 that we worked on. I'll share some examples soon.

Incident Beam Characterization: https://www.flickr.com/photos/85210325@N04/15336978941/

This is what a Si standard powder looked like. Demonstrating the presence of discontinuous Debye-Scherrer rings and operator induced "preferred orientation" due to sample prep: https://www.flickr.com/photos/85210325@N04/15340063112/

I have other examples of highly deformed aluminum foil and LaB6. I'll post..

Henry,

Echoing Ravi it would be good to get an update from you in regard to some the comments posted in reply to your initial question.

"It is not possible for deformed Al to have a sharper peak than LaB6", I agree in principle. However, depending on the XRD tool, technique and detector used it is easy to be beguiled. See below, example of the real time 2D diffractogram for aluminum foil in Laue transmission mode clearly evidencing "preferred orientation". https://www.flickr.com/photos/85210325@N04/7944785794/in/set-72157632728981912 

The conventional diffractograms acquired using a 0D Geiger counter are also displayed side-by-side with two orthogonal orientations of the sample aluminum foil. The peaks do appear to be sharp enough from the most likely "cold rolled" aluminum foil. In fact, I even have the conventional diffractogram from the standard aluminum sample holder, "deformed aluminum sample (polycrystalline bulk)",  for comparison. https://www.flickr.com/photos/85210325@N04/15670218401/

Just for completeness, here is the 2D diffractogram from LaB6 standard powder acquired at BNL Beam Line X14A https://www.flickr.com/photos/85210325@N04/7909734896/in/set-72157632724090465

Both stationary sample and rotating sample diffractograms are shown for the LaB6. As you will observe, depending on the choice of the equatorial plane and "integrating window" (slit sizes) the conventional diffractograms could be significantly different from each other. Both in the case of the aluminum foil as well as the LaB6. The difference vanishes as soon as one rotates the sample and "smudges" the Debye-Scherrer ring.

"Clearly your instrument is misaligned severely". How does misalignment create the difference in FWHMs? I can see it affecting the Bragg peak position. But FWHM, how? I would think not!

Larry is correct! If you are working with aluminum powder, then be cautious. It is a "propellant"! I do note your remark, "deformed aluminum sample (polycrystalline bulk)". Aluminum foil on the other hand, is totally benign. I have used aluminum foil as a convenient "standard" on numerous occasions. More information is better, post it :-)

Henry! You may want to use a simple photographic film exposure to get a better 2D picture of your challenges. Unless, you can scan 2D with the linear detector. Post your current XRD data for a better insight from all!

Note: LaB6 may be a little moisture friendly. It may also be affected by storage condition and age as noted by others before. Watch out!

Lemon to Lemonade Principle: The use of the invariant ubiquitous aluminum sample holder, "deformed aluminum sample (polycrystalline bulk)", as an alignment/calibration tool to ID effects of sample surface displacement w.r.t. the diffractometer axis, We even chose to use the aluminum peak shoulders to align diffractograms rather that the peak positions. Gave us better precision! https://www.flickr.com/photos/85210325@N04/10888339173/in/set-72157645250332687

"How can one determine the instrumental resolution of a X-ray diffractometer better?"

Bottom Line: By using an unequivocal standard as most analyses in XRD are relative!

Ravi,

All the images and scans you have shown demonstrate clearly that deformed aluminum peaks are extremely broad, I am talking about the divergence of the actual diffracted rays, not the width measured on a 2D detector which can be dominated by the size of the beam and the width of the sample. I am also assuming that any calibration measurements are done to assure proper powder averaging. If this is not the case then it is impossible to determine anything about the instrumental resolution. I thought this was obvious. If the instrumental resolution is being measured for a point detector (defined either by a slit or analyzer crystal) then misalignment in the geometry, for example not being on the Rowland circle if you are using that geometry, can produce a strange dependence of FWHM versus 2theta. There are many other instrumental alignment problem which can have a dramatic effect on the measured peak widths as a function of angle. It's basically a problem of vignetting  that can occur at the detection point, something which you can see very clearly on a 2D detector due to the larger intersected width at higher angles due to the size of the scattering volume projected onto the flat detector. Just an example for a 2D detector, but I hope you can see just how strange the effects could be if there was a misalignment when using a point detector and slit.

"deformed aluminum peaks are extremely broad". Yes! The incident beam size was about 1mm diameter in the case of the 2D diffractograms. Huge! The "spots" (transmission topographs) are large as the grain intersecting the beam are elongated and large in the rolling direction. I never got a chance to conduct rocking curve measurements to estimate the FWHM of individual grain (spot). This is data from way back in 1984. But, sure would be interesting work, rocking curve analysis of Aluminum foil. I've done this for AL2024 & AL7075 bulk material way back then in the mid 1980's.

You are right, " the width measured on a 2D detector" is "dominated by the size of the beam and the width of the sample". In order to measure the correct FWHM for each pixel one must rock the sample.

These are some of the reasons I recommended an unequivocal "known standard" to best "determine the instrumental resolution of a X-ray diffractometer". Any diffractometer :-)

This is the fwhm from a pseudo voigt fitting for every peak measured by XRD. The error bars are due to measurements from four specimens of each sample. The treatment was: rolling the aluminum, 80% (Al R0), then annealed 15 (Al R15), 30 (Al R30) and 60 (Al R60) min, with 400ºC. Some peaks of the aluminum shows less broadening than those observed from the LaB6 (SRM 660b).

I'm trying to extract the instrumental broadening using the LaB6, but this is not suitable for the aluminum samples due to the broadening problem. I've tryed using differents slits apertures, fixed and varied. This is my best result.

As Lawrence said, It is not possible for deformed Al to have a sharper peak than LaB6. And I've calibrated the diffractometer several times, using the optical wave guide and the Al2O3 powder. May be the LaB6 was contaminated, because it was stored in poor vacuum, but not in argon atmosphere.

Is there another way to determine the instrumental broadening instead of using the LaB6 powder? I've tryed using an aluminum bulk annealed for 50 hours, but the results were not better.

Henry can't see what your problem is. If I have read your plot correctly at each respective 2theta the LaB6 as you would expect has the smallest fwhm value compared with any of the Al materials. Fwhm of 0.06-0.07 for LaB6 between 30 and 90 2theta is generally very good for lab instruments.

Timothy, there are some error bars intersected, that is beacuse some fwhm values of the aluminum are lower than the fwhm values of the LaB6. I've seen fwhm of the LaB6 of 0.05 reported by others, in the same kind of diffractometer. For that reason I expect to obtain lower values for the LaB6. But I'm thinking that the LaB6 was contaminated due to the bad storage conditions.

Dear Henry,

if as you mention only some of the peaks of some of the samples are showing a sharper peak than the LaB6, what you are seen from the aluminum is not representative of your diffractometer and hence it could be sharper (supposing the LaB6 is representative of your instrument broadening).

What is happening in reality?

Some of your aluminum samples have very big grains (strained or not). Than in some cases the diffraction is not coming from the entire volume interested by the beam, but only from few grains in the proper condition (e.g. orientation). The the diffracting volume is much smaller and confined to only the one or few grains in Bragg condition. So it is like for some peaks you are using a very small beam.

To verify if this is the case. Is it your intensity (of the lines) corresponding to a random sample? 

If not, to distinguish between sample graininess (that is causing you these sharper profiles) or texture (not produce the non statistical volume problem): if you take out the same sample and you reposition it in a different way (so you have a different investigated volume), are your intensities changing a lot?

Do you see also strange shapes on certain peaks? This is another indication of extreme graininess.

So the problem is not your LaB6 instrumental function determination or the instrument itself. It is your sample that does not satisfy the minimum requirement for a correct measurement (a sufficient number of grains in the diffracting volume, at least millions, so thousand can diffract at a given orientation).

Give a look on our paper on the instrumental function determination, Powder Diffraction around 1991-1992, if I remember well there was at least one example of graininess for too big grains.

Luca

Finally I've realized that your answer responses the problem we observed, the crystalline domains are too big for the applicability of the methods that we are using. We complemented the study with EBSD measurements, and we observed very large grain sizes, up to 200 micrometers. The measuring of the fwhm is not suitable to determine those sizes, because it exceeds the sensibility of the diffractometer. Some fwhm values are similar to the 2theta-step that we are using.

Thank you very much to all for your support.

Wrong Henry! You are only limited by the archaic 0D detector from the era of the Braggs and not the XRD technique itself. Folks have been working with poly crystalline materials and deconvoluting FWHM from individual crystal/grain topographs since before the mid 1950's with ordinary (now extinct) photographic emulsions (films and nuclear track plates). It is the "spatial blindness" of the 0D point counter (a fancy/expensive Geiger counter) that prompts you to come to such a conclusion temporarily. Shed the blind-fold of antiquity and step forward into the future with real time 2D Bragg XRD Microscopy. You'll be amazed to no end. Imagine a NDE TEM with no sample prep, no vacuum and in situ. That is the potential of Bragg XRD Microscopy. The present detector spatial resolution limit of 1-5um will be overcome soon technologically:-)

Look at this example of grain sizes ranging from 1um to 1000um. With higher spatial resolution, one may rock the sample and record rocking curve profiles for each individual spot (grain/crystal): https://www.flickr.com/photos/85210325@N04/7920887956/in/set-72157632728981912

YouTube video of LaB6 in a real time transmission Laue mode at BNL beam line X14A: https://www.youtube.com/watch?v=acgFl5M7P-I&index=9&list=PL7032E2DAF1F3941F

https://www.youtube.com/watch?v=acgFl5M7P-I&index=9&list=PL7032E2DAF1F3941F

Article Novel Analytical X-Ray Non-Destructive Evaluation (NDE) Tool...

I've used a linear detector. I've aligned it in order to obtain the better resolution. I measured my samples and the LaB6 standard for several line lengths of the detector. And I've used a point detector too, but the results are not better.

If we take the Scherrer equation, only for obtain the order of the crystallite size, a 100um of crystallite size could shows a fwhm of 10e-5 degrees, and the diffractometer reaches 10e-3 degrees of sensibility. So we can't determine those sizes. Are you agreed? Could you help me with some publications about polycrystalline samples with crystallite sizes of 100um or higher?

Thank you very much.

I notice you are not discussing "preferred orientation". How do you intend to account for "preferred orientation" in the deformed aluminum sample? In the Scherrer approach, there is no accommodation for "preferred orientation". Both the 0D and 1D diffractograms would, in my opinion, be "spatially blind". So "diffracting domain size" computation with the Scherrer equation would be erroneous in this case. Big or small grained! If you are using identical orientation for each of the samples, then at best you may use this data only for relative evaluation of the samples w.r.t. the 50hr annealed standard. Not for absolute values!

1. What are the slit sizes that you have used?

2. Have you repeated the diffractograms after rotating the sample about its surface normal? In other words, test effects of any potential preferred orientation.

3. Have you  obtained the diffractogram for the as-received sample? Was the as-received material "rolled" to begin with or was it from a cast ingot?

4. It is my understanding the LaB6 tends to be affected by the moisture and other storage conditions over time, it seems improbable that storage should affect its FWHM unless moisture quenches defects. What is the experience of other members in this regard?

When we were working with fatigue studies @ Rutgers using AL2024 & AL7075, we used a rolled stock that we annealed to get a recrystallized grain size of around 30-80um. This was critical as a "base" standard with minimal preferred orientation effects. We were thus able to use a 2D detector (photo film with slit or LPSD/1D detector but never a 0D fancy Geiger counter) with the XRD rocking curve method to deconvolute the dislocation density in each reflecting grain.

In my opinion, with the conventional method (0D or 1D detector) that you are using, it would be a Herculean task (if at all possible) to deconvolute effects of sampling size, slit size, diffracting domain size, defect density and preferred orientation.

Transmission Laue image from a rolled aluminum foil showing the effects of preferred orientation on the Debye-Scherrer rings and a comparison of the real time 2D data with the conventional linear diffractogram as you have employed:

Hi!

You can refer these papers/books to improve the resolution of your existing diffractometer also.

B. D. Cullity, Elements of X-ray Diffraction, (Addition-Weseley Publishing Company, Inc. London, 1978).

W. R. McIntire, Phys. Rev., B14, (1976), 4386.

N. Shiotani, N. Sakai, F. Itoh, M. Sakurai, H. Kawata, Y. Amemiya and M. Ando, Nucl. Instrum. Methods., A275,(1989), 447.

P. Pattison, P. Suorti and W. Weyrich, J. Appl. Cryst., 19, (1986), 353.

E. Straube, D. Hohlwein and Th. Zeiske, J. Appl. Cryst., 31, (1998), 169.