Yes Fayroz,

but you have to be sure that the peaks you use for the plot arise from the film.

Please see the dicussion on a similar question from yesterday.

https://www.researchgate.net/post/Hi_everyone_need_suggestion_using_the_XRD_to_find_the_residual_strees

Dear Gerhard, thanks for response

Yes, the peaks belong to the material of the film.

Dear Fayroz Sabah,

You can use Williamson-Hall method for both powder as well as thin film material, for that minimum four diffracted peaks must be needed, in order to get more accurate results.

Dear Ramachandran D

Thanks a lot for your response and interest.

"You can use Williamson-Hall method for both powder as well as thin film material"

Only if one neglects the effect of "preferred orientaion", correct?

https://www.flickr.com/photos/85210325@N04/14348488010/in/album-72157645018820696/

Dear Ravi, thanks for your participate

I read many papers using this method without neglecting the effect of preferred orientation. Do you mean the preferred orientation for instrumental peak broadening (Si (111)), or for thin film?

If you mean preferred orientation for the Si (111), the authors use one peak broadening in their calculations.

Dear Fayroz,

the Si surface may probably induce preferred orientation of the thin film crystallites.

The Williamsen-Hall method works preferably for randomly oriented crystallites.

You will investigate the film. Thus it is advised to have mainly randomly oriented crystallites in the film.

"I read many papers using this method without neglecting the effect of preferred orientation."

That doesn't make them correct, does it?

All conventional powder XRD methods include the "random orientation of diffracting domains" assumption, correct?

https://www.linkedin.com/pulse/real-time-2d-powder-diffraction-revolutionizing-data-ravi-ananth

To my opinion, film texture (preferrend orientation) will contribute to  scatter of the peak widths values in the Williamsen-Hall plot. Thus the reliability of the plot regression will suffer.   

Dear Gerhard and Ravi, what do you mean by "random orientations". I think this term is just for powder, right? I don't use powder in my research I am using thin films, that's why I am asking if it possible to apply Williamson-Hall method on thin films. But regarding to "random orientations", I am not sure that I know what is it mean!!!

"The attached file shows the random orientations are for powder"

And about the "preferred orientations", are they the same available in the JCPDS card? As the peak orientations of the thin films which are identical to this card will emphasized that this material is synthesized on the film.

So the bottom-line is that W-H approach will not work with unknown "preferred orientation" in your film.

Q. "Is Williamson-Hall method applied on powder only or can be applied on thin film also?"

A. Applicable only for random oriented poly crystalline films, substrates and powders.

"random orientations" means that the crystallographic planes (hkl) in each diffracting domain are oriented randomly w.r.t. the diffractometer axis and the incident beam. Meaning, the Debye-Scherrer Arc/Ring has uniform relative intensity along the Arc/Ring (circumferentially).

However, if you have software such as the Bruker LEPTOS or equivalent, you may be able to model and simulate diffraction profiles with various parameters and fit to the observed profiles.

Real Time 2D XRD may be used to quantitatively characterize thin film morphology ranging from amorphous to poly crystalline to oriented poly crystalline to highly oriented poly crystalline to epitaxial.

https://www.linkedin.com/pulse/nist2000srm-resolving-nano-structure-individual-layers-ravi-ananth?trk=pulse_spock-articles

Actually I am still confused about random orientations.

You should find an illustration in most basic books on XRD.

Try this link below, see page 9 of 47:

http://web.pdx.edu/~pmoeck/phy381/Topic5a-XRD.pdf

Ravi,

I am also confused with your statement. 

The W/-H approach in any case works for one direction in the reciprocal lattice. That is why it is applicable for epitaxial films, e.g.,in the c-oriented tetragonal or hexagonal films, a set of 00L reflections is often very well described by the W-H relationship(s). Or I did not get something in your message?

Mark

Hi Fayroz,

do not be confused about 'random' orientation of your crystallites.

If you have an epitaxially grown film, the orientation of the crystallites in the film is not random but governed by the orientation of the lattice structure of the substrate surface.

If you film is not grown epitaxially, then you will have a relative high degree of random orientation of your crystallites like those in an powder sample, but in this case the film is a thin 'powder sample'.

Mark stated in his comment that in special cases  the W/-H method is also applicable in epitaxial films.

Thus nevertheless please try to apply the W/-H method and see what is happening.

Does your series of peak widths follow a 'nice' curve, which can be trusted to be fitted according to W/-H?

Or is the scatter of peak widths so strong that you are not able to fit an W/-H plot?

In the latter case the W/-H method then is not applicable in your case; that's it.

Mark! Do you mean this statement? "Applicable only for random oriented polycrystalline films, substrates and powders."

Please post some references for the use of W-H technique for samples with varying range/degree of preferred orientation. How would one accommodate for the presence or absence of preferred orientation? Are you suggesting that the results of W-H would be similar or different comparing poly and epi films?

A far as I know the W-H method is used only with powder diffraction data. In the case of epitaxial film the orientation will be specific and not random. This would mean that the sample (hkl) would have to be optimized with Chi, Omega and Phi adjustments. This happens only for certain specific values of these angles depending on the surface orientation of the epi.

In the case of "random oriented" polycrystalline morphology the (hkl) reflection would be independent of the surface orientation.

It is my understanding that the fundamental premise in the application of W-H method to deconvolute stain and size effect is "random orientation". I'm puzzled with your confusion. I'd be happy to be corrected and schooled better in the subject of the W-H methodology.

I'd think that anisotropic strain will also complicate the W-H analysis, wouldn't it?

I do happen to have studied several epitaxial structures both homoepi and heteroepi using HRXRD rocking curve topography. Generally my objective is to quantify the deviation from IDEAL BRAGG condition and correlate it to material Nanostructure.

Do check out the posts noted below and share your thoughts. My current objective is to be able to correlate XRD rocking curve profiles from various (hkl)'s for the NIST 2000 standard reference material.

https://www.linkedin.com/pulse/nano-structural-meaning-xrd-data-converting-bragg-condition-ananth?trk=pulse_spock-articles

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_o-2TH_o_ph_ch_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses?_tpcectx=profile_questions

It is really so interested subject, I will see all the attached references and posts, also I will check my films and see whether the W/H approach can apply on them or not. I am very gratitude to your response and explanation. Thank you dear Gerhard and Ravi for your big help.

Ravi and Fayroz,

I attach a good review by Scardi et al (2004) on the topic.

Also attached is another paper that implemented W-H approach to YBCO thin films (Fig. 5).

The non-ideal out-of-plane texture (0.5 to 5° FWHM) in coated conductors (CCs) likely makes alignment issues not very relevant.

Mark

Thanks a lot dear Mark for these significant references, I will also read them carefully. Actually I am not deep related to this subject and I want to study a lot about it.

Hi Ilkay,

this is for example what could happen if not a sufficient number of crystallites contribute to your peak(s) in the case of oriental artefacts of the sample, such as a poor  epitaxially grown film. Some peak widths may be too small and thus the W/-H plot accidentally will get a negative slope. Sorry but I havn't got a real  example plot for this; do you have got one?

Remark: in addition the relative peak heights in these cases will significantly  differ from those expected for a powder sample.  This is a hint on orientational artefacts / partly  preferred orientation.

Mark!

Ilkay Demir! "Do you have any idea about negative slope of WH plot?"

Due to the incorrect assumption of "random orientation" when it is clear that most thin films and processed bulk materials have some or a lot of unavoidable preferred orientation. Unless of course, the film or bulk material is amorphous, then the issue becomes moot. XRR would then be the only option to characterize the thickness & surface roughness of such films as well as bulk materials :-)

Dear Ilkay, sorry I don't so familiar with WH method, I just used it recently, that's why I am trying to study it.

Dear Gerhard and Ravi, do you mean the random orientations are poly-crystalline thin film, and epitaxial is the single crystal thin film?

If this is the meanings for "random orientations" and "epitaxial", then there is no problem because I have poly-crystalline thin film with seven peaks.

Your film is most likely oriented polycrystalline film. In order to fully characterize the Nano structure of such films you'd need to quantify the "degree of orientation" besides the thickness and flatness. This can only be done using XRD techniques. Other techniques are neither NDE nor in situ.

The key would be to define:

These may be modeled and computed using software like Bruker LEPTOS etc.

"All samples in these papers have been grown by MOCVD so it means that they have good crystal quality." Meaning, the "random orientation" assumption necessary for the W-H method would be invalid.

This means they are epitaxial and you'd need to establish the degree of epitaxy by quantifying the deviation from IDEAL Bragg Profile.

https://www.researchgate.net/post/What_are_the_potential_Nano_structural_reasons_for_the_difference_in_the_XRD_Bragg_profiles_between_substrate_epitaxial_film

Dear Fayroz,

you are right, having 7 peaks means that  your sample is mainly polycrystalline, but the diffractogram still may suffer from orientational artifacts. Thus I will repeate my  question from above: do these peaks have relative peak heights nearly similar to those from powder sample of same composition as your film?

If yes, I think then you will have enough crystallites contributing to your peak width that the W/-H method is applicable.

If not, then you suffer from orientational artefacts and the W/-H plot  is most likely not applicable.

Dear Gerhard, how can I compare between them? From where could I get the peaks of the powder sample? Do you mean from the database that we can get when do the measurement? or I must do XRD for CuS powder to get its peaks? And why you insert negative sign (W/-H) for the method?

W-H analysis is the INCORRECT technique to "force fit" your experiment, as it requires "random orientation" of the diffracting domains for validity, precision and accuracy.

If you have free access to XRD equipment, then run fast scans to understand the effect of "non-random orientation" before you decide the analytical tools to employ.

Suggestions:

There are no short cuts with XRD in order to be unambiguous! Especially, with the spatially "blind" tool, the ubiquitous 0D point/scintillation/proportional counter, that most XRD practitioners still employ!

https://www.flickr.com/photos/85210325@N04/10242907544/in/album-72157645018820696/

Dear Fayroz

a)  the  ' -' is not a minus but  a hyphen ; sorry I should type 'W-H' for 'Williamsen-Hall'

b) CuJ powder XRD spectrum: the best way is to measure a powder spectrum by your own, so all experimental influences are the same for your film and for the powder; but

c) the suggestion of Ravi  on performing XRD measurements of your film on different angular orientations  is excellent. So you might easily see  artefacts on preferred orientation. No powder spectrum will be necessary. Good idea Ravi !!! 

Dear Ravi and Gerhard, thanks a lot for the clarification. 

I have made my comment a few days ago and now would like to add some more detailed considerations.

The W-H approach describes the line broadening effects due to finite crystallite size L0 and presence of micro strain, e, i e variation in interatomic spacing whatever its reason.

The different forms of W-H expression (linear or quadratic) stem from assumptions upon the line profiles (Lorenzian or Gaussian) with L0 and e as parameters. There are modifications of these relationships as described by Scardi et al (2004), but in any case L0 and e serve as model parameters.

The effect of finite crystallite size on the line width is usually illustrated for the case of one-dimensional diffraction by summing up the scattering factors for N identical layers, which gives the structure factor

F ~ sin(Nx/2)/sin(x/2)

where x is the deviation from Bragg position in dimensionless units.

The FWHM of this function FWHM ~ 1/N ~ 1/L0.

The strain e is in general direction dependent. However for the reflections of the same family, e.g., 00L, e is certainly the same.

Thus, the W-H relationship is fully applicable for the layered systems and perfectly works for epitaxial films.

Ok Mark! So how do I test this with the NIST 2000 wafer. I have computed the layer thicknesses with XRR using LEPTOS simulation and would like to verify the results with the W-H method, if doable. I then wonder what the effect of sub-grain structure and defect density would be on the W-H analyses besides the degree of epitaxy (preferred orientation) :-). My objective is to be able to perform such analyses for individual pixel data in the 2D diffraction image. Intuitively, I'd think that the relative twist, tilt and defect density in each diffracting VOXEL on the sample surface would effect the W-H results significantly. I'm open-minded to learn.

I have (004)s, (224)- and (113)- so far for the NIST sample. What else do I need to move forward into the W-H analysis?

Do I need the (002) or (008) for the layers to complete the W-H analysis? The individual layer signals were clearly visible with the Rigaku Smartlab rotating anode instrument for the (004)s reflection with approximately parallel to the diffractometer axis. See below.

https://farm2.staticflickr.com/1539/25763957534_b40a69acd3_b.jpg

Ravi,

I think you should try to analyze 002, 004 and 008.

I am not clear what do you mean you need the analysis for an individual pixel.

That means, unlike the conventional diffractogram where all the signal coming into the 0D point counter is counted as one relative intensity value we have the ability to consider the entire 2D pixelated image (27.5x27.5um) of the diffracted beam. Generally, this would be controlled by the "source slits" and is typically a "line source" of dimensions 1x10mm. The longer dimension is generally parallel to the diffractometer axis (aka rocking axis). Using parallel beam geometry, each 2D pixel signal may be considered coming simultaneous from multiple parallel point sources. Basically boils down to the rocking curve technique (coupled 2Th-Om or Om-2Th scans).

When the film has "extreme" preferred orientation as in epitaxial films, then one would need to probe the reciprocal space in the Phi (relative angle about the surface normal) and Chi (relative tilt angle of the sample surface w.r.t. the diffractometer axis) directions as well to find and optimize the (004)s reflection, for instance. It doesn't show up for random position of Phi and Chi like in a powder with random orientation of diffracting domains. Once you find the (004)s then it would be relatively easy to find the higher or lower order reflections. Meanwhile, the rest of the reflections that come from planes non-parallel to (004) would have diminished relative intensities, if any. BTW optimizing the reflection with a "point source" instead of a "line source" would be a nightmare as well :-) That is why, my intuition is that the W-H approach may find challenges.

Check out these attached posts for additional info:

https://www.linkedin.com/pulse/real-time-2d-powder-diffraction-revolutionizing-data-ravi-ananth?trk=mp-reader-card

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_o-2TH_o_ph_ch_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses