The strain is a direct cause of crystallite size change or distortion. So if the crystallite is under homogenous pressure, it should be expanded or compressed homogenously, then all the XRD peaks will shift to lower or higher angles. If the pressure is inhomogenous, it should be distorted.

Hi dear Fouzia, Have you repeated the measurement, also, what kind of film you use.

Dear Fozia

Classical and even extremely simple single-line methods for separating “size” and “strain” broadening effects have merit for characterization of the material imperfectness, but it is generally very difficult to interpret the data obtained in terms of microstructure parameters as used in materials science.

The analysis of diffraction-line broadening evolved already shortly after the discovery of diffraction of X-rays by crystals by Friedrich, Knipping and von Laue (1912): Scherrer (1918) found that the breadth of a diffraction line is related to the finite size of the diffracting crystals. Considering that, as follows from differentiating Bragg’s law, lattice-parameter fluctuations are also exhibited by diffraction-line broadening, Dehlinger and Kochendorfer, already as early as 1939, realized that a separation of the diffraction-line broadening in size and strain-related contributions can, in principle, be achieved provided that the diffraction angle dependence of the line breadth is known [1,2].

Unfortunately, straightforward extraction of quantitative information on size and strain from the shape (“width”) data is normally impossible. The least of the problems met is probably the elimination of instrumental broadening effects,

for which more or less reliable approaches exist which depart either from recordings of broadening by standard specimens, or, more recently, from calculation of the instrumental broadening on the basis of the known instrumental/

geometrical details of the diffraction experiment.

Fundamental problems are the unravelling of the various contributions to the observed, broadened diffraction lines due to the various types of microstructural details, as crystallite size, lattice (micro)strain, planar faults ( [3, 4]), etc., and their

interpretation in terms of parameters that are used in materials science, as dislocation densities, faulting probabilities and crystallite size.

On the one hand, more and more advanced methods to extract microstructural parameters from the profile parameters of a single or multiple diffraction lines using more or less realistic, general assumptions on the material imperfection/

line shape are developed: line-profile decomposition. On the other hand, a recent, powerful, yet virginal approach appears to be line-profile synthesis, where the

microstructural parameters are determined by fitting line profiles, calculated on the basis of a model for the microstructure specific for the material investigated, to measured profiles (i.e. no line-shape assumptions are employed).

The length of the diffraction vector (and the correlation of the positions of the scattering atoms) is crucial for the occurrence of incoherency of diffraction, and as a consequence, apart from extreme cases, the so-called crystallitesize

values depend on the reflection considered. Thereby, and this is not often realized, classical methods for line profile analysis, but also recent developments, where all

reflections in the entire diffraction pattern are simultaneously analysed, under simple assumptions as a size broadening independent of the length of the diffraction vector, can become invalidated.

[1] Mittemeijer, E. J.; Scardi, P. (Eds.): Diffraction Analysis of the

Microstructure of Materials. Springer, Germany 2004.

[2] Dehlinger, U.; Kochendo¨rfer, A.: Linienverbreiterung von verformten

Metallen. Z. Kristallogr. 101 (1939) 134–148.

[3] Estevez-Rams, E.; Penton Madrigal, A.; Scardi, P.; Leoni, M.:

Powder diffraction characterization of stacking disorder. Z. Kristallogr.

Suppl. 26 (2007) 99–104.

[4] Leoni, M.: Diffraction analysis of layer disorder. Z. Kristallogr.

223 (2008) 561–568.

thank you Maria  and Shenglong for your replies. This is (001) reflection of a Ti doped ferrite film...I obtained similar kind of distorted peak for Ru doping as well. Although the peak of undoped ferrite film had normal gaussian shape and was quite narrow. the properties of these three are very different. I wanted to some how clarify what structural change is coming. I will go through these references.

For the mono crystalline substrate and epitaxial film  as in your case, an excellent  X-Ray-ted Lecture by Mauro Sardela of MRL! Featuring Paris Hilton in the bare reciprocal space :-)

"If you find smoke in the reciprocal space then you'll find the cigar in real space" - paraphrasing Andre' Guinier.

https://www.youtube.com/watch?v=lSJc5idl7xc

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_3D_reciprocal_space_data_from_XRD_rocking_curve_analysis2

thanks ravi shall hear these lectures

What is ur instrument settings? Those shape seems familiar.

Please post the whole pattern, raw data if possible.

I have not made these measurements myself. So cant give details of the instrument. I am posting the whole pattern but the shape of this peak will be visible only when you magnify each peak. film peaks are marked by F

Seems as epitaxial film. You may use xrd RSM reciprocal space mapping to get the 2D diffraction pattern, thus you can identify where the strange profile come. IF they come from a tail, may be strain. Come from overLapped peaks, may be several phases seperated. Anyway,you need help to get abetter diffraction pattern

I already have a reciprocal space map of this film. I am attaching it below. RSM doesn't show overlapped peaks as you can see.

I'd like to fully understand the conventional RSM that you have so vividly and appropriately displayed. Excellent question with lots of relevant data. Congratulation Fozia!

I'd also suggest the following:

• Increase the number of topics up top to 15 instead of the present 4.
• Share the experimental and sample details for all to have the same advantage as you in order to help you.
• Post and support parallel discussions in LinkedIn (LI) or other media. Here's an example of how I shared this discussion on LI. Do feel wolcome to join the group and contribute to the knowledge base:  https://www.linkedin.com/groupItem?view=&gid=2683600&type=member&item=5982824735296274434&trk=groups_most_recent-0-b-ttl&goback=%2Egde_2683600_member_5981021407084101633%2Egmr_2683600%2Egde_2683600_member_5981349376998596610%2Egmr_2683600

This will enhance the quality of feedback by increasing the exposure to a larger population of experts.

I'd have to make the following assumptions:

I did gather some literature for STO if it is what I think it is. I'll be glad to share.

We have some interesting XRD reciprocal space images (X/Y-Omega Maps) for a sample consisting of STCO (SrTiCoO) epi film on STO substrate from the diffractometers at MIT. Instead of the 0D detector we've used a real time 2D imaging system. A sample image containing  the NIST2000 standard reference material, LAO-NNO and STCO-STO data is attached. The STO substrate shows a unique reciprocal space image. Please note that our XRD reciprocal space images (X/Y-Omega Maps) are distinctly different from your RSM.

My interest is in understanding the correlation between the conventional 0D RSM images and the 2D real time relative reciprocal space images topographically.

1. https://www.flickr.com/photos/85210325@N04/15703454034/

2. https://www.flickr.com/photos/85210325@N04/16316521660/

In my mind, based on my own experience, I have no doubt that the answer to your question, "If the shape of XRD peak is distorted (as can be seen in the figure attached) then can it point towards a possible structural transition?", is an unequivocal YES! Nanostructural lattice distrotion, inclusive of strain. However, the correct interpretation of the XRD data is really the bottom line! I'm still working on it :-)

As you correctly noted "Broadening of XRD peak is a collective effect of crystallite size, strain and disorder", the challenge is to correctly deconvolute the individual effects from the convolution! Don't forget, shape change as well. For instance we could conclude from this deviation in the experimental (004) symmetric reflection XRD RCP (rocking curve profile) for a GaAs wafer compared with its "strain free state" LEPTOS simulation, that stacking faults with missing smaller Ga atoms sheet was the culprit. Note that the deviation from IDEAL BRAGG CONDITION was below the FWHM on the shoulder and tail area predominantly.

Ref: Nabarro - Dislocations in Solids (something like that). I'll find and post the correct reference details.

https://www.flickr.com/photos/85210325@N04/9430820747/in/set-72157635172219571

Dear Fozia,

Agree with Ravi, please tell ur instrument settings.

It's look like an offcut for the miss-match  and source streak for the spread.

Cud u also attach the asymmetric position?

Electrical Properties of Dislocations in Semiconductors, R. Labusch and W. Schroter. From Dislocations in Solids, Editor F. R. N. Nabarro, Volume 5, 1980.

pp. 162.

"8. Dislocations in III-V compounds:

In III-V compounds the two face centered sublattices of the diamond structure are occupied by different kinds of atoms. The (111) slip planes are alternately occupied by atoms of group III and atoms of group V. The core of an edge type dislocation therefore may consist of atoms of group III or group V, depending on the sign of the dislocation. As first pointed out by Hansen [87], the dynamical and electrical properties of the two types should be different on account of their different cores.

This qualitative statement is fully confirmed by velocity measurements of single dislocation half loops in InSb [39, 88-90] and GaAs [90]. So far, the electrical properties of dislocations have been studied in detail only for InSb [6, 91-97].................."

pp. 183.

"Core configuration of dislocations in semiconductors:

The diamond structure has a cubic face-centered space lattice with a basis of two atoms. The stacking of {111}-planes in Si, Ge and many III-V compounds is that of the face-centered cubic structure, except that in the diamond structure each layer consists of two atomic planes. The spacings between adjacent {111}-planes are alternately narrow and wide in the ratio 1:3. Consequently there are two sets of glide planes and two sets of dislocations. If the glide occurs between two widely spaced planes, the dislocations belong to the shuffle set, if between two narrowly spaced planes, it belongs to the glide set. Complete dislocations in the shuffle set are believed to be stable, while those of the glide set are unstable with respect to a dissociation into two Shockley partials with a stacking fault between them; the reaction is of the usual type:

1/2a[110]----->1/6a[211] + 1/6a[121]............................"

sorry for the delayed reply ravi. here are the answers to your questions:

1.How long does the data acquisition take for the RSM?

Ans:- Its depend on samples quality, i.e. peak separations and weakness of peaks (if peak of materials are strong and range is small then we have to take measurements for few Hrs. otherwise for long time.)

2. What angular resolution do you have?

Ans:- Angular resolutions:

Minimum step size 2Theta: 0.0001

Minimum step size Omega: 0.0001

3. What is your beam size at the sample?

Ans:- Focus on Sample:-

Focus type:Line

Length (mm):12.0

Width (mm): 0.4

Take-off angle (°): 2.2

4. What is the smallest slit dimension before the detector?

Ans:- Diffracted beam path

Soller slit

Name:Large Soller slits 0.04 rad.

Opening (rad.):0.04.

5. Can I assume a 0D conventional point counter or 1D?

Ans:- Detector

Name:PIXcel-3D detector

Type: Area detector

Mode:Scanning

No. of active channels:255

Pitch (mm):0.0550

Active length (°):3.347

6. Are the Omega-2Theta coupled scan?

Ans:- Yes.

This is area scans, two axis measurement scans.

Extra Question.

7. What is the smallest slit dimension before scattering to the samples?

Ans:- Incident beam path.

Soller slit

Name: Soller slits 0.04 rad.

Opening (rad.):0.04

Anti-scatter slit

Name:Fixed slit 1/8°

Type:Fixed

Height (mm):0.19

8. Required power for generate the X-ray beam?

Ans:- Voltage (kV):45

Current (mA):40

9. Incident beam optics?

Ans:- X-ray mirror

Name:Inc. Beam Cu W/Si (hybrid MPD)

Crystal:Name:W/Si

Type:Graded

Shape:Parabolic

Acceptance angle (°):0.800

Length (mm):55.3

9. Monochromator?

Ans:- Name:Hybrid monochromator 2-bounce Ge(220) for Cu

Crystal:

Name:Ge

Type:Asymmetric

Shape:Flat

No. of reflections:2

h k l:2 2 0

 yes the substrate is SrTiO3 (001). RSM is about the asymmetric peak (301) and the film thickness is ~200 nm. 

Now, that is a complete question! Thanx & Congradulation!

It is even worse than what I thought! You are actually dumbing down an advanced 2D detector into a 0D "spatially blind" century old tool and technique :-) I'm going to make some hard and tough comments. Are you prepared to share them with your professors and supervisors in the interest of  "improvement"? Obviously, in the same token I'm prepared to take criticism as well.

If you have the PIXcel 3D then why don't you have images like this of the entire sample (size?)?

"A Mouse Scroll Through Reciprocal Space" ZnSe (224) asymmetric reflection: https://www.youtube.com/watch?v=dFCQS8oUyT0&index=37&list=PL7032E2DAF1F3941F 

There is a whole lot more to come once I see how open-minded you are. All I have to talk about is included in the YouTube video playlist attached. I'll illustrate them further with additional images and video to facilitate visualization of the reciprocal space even better. Imagine such a reciprocal space map for and from each of the 256X256 Pixels on the 2D detector with a large wide parallel incident beam. Mind Boggling yet?

Just to get an idea, here is one of my suggestions. Set up the rocking curve for approximately the Bragg condition. Open all vertically limiting slits and expand the beam width to the max. Now affix a dental film with scotch tape in front of the detector and get a topographic exposure. You may do so directly with your PIXcel 3D (misnomer) employing prolonged exposure time. You'll see then! Panalytical does not provide software for this purpose yet. Certainly not in India and certainly not without a hefty price. Hope I'm wrong.

We work with high resolution (

Thank you Ravi for your advice the problem in implementing these suggestions is that we don't have this XRD at our institute. our collaborators take these measurements for us. That is why it took me little long to answer all your questions. I have no idea why they have not used the diffractometer in the efficient way you have described. I am not in a position to suggest these changes from my side. But I do have many other questions to discuss regarding RSM or XRD. So if you still feel like discussing further I will be happy to continue the discussion.

This is your discussion Fozia. So, you may choose to discuss any aspect that you think appropriate. There are many expert members in RG that will guide you through :-)

Please include SDD (Sample to Detector Distance) Bragg angle and the Omega incidence angle used for your RSM. In our case, from figure attached, 2θB=77.17o, ω=19.9o to 20.2o, and estimated penetration depth=15.5µm. I suspect yours would be similar.

Just to clarify, in the RSM displayed, the individual RCP's (rocking curve profiles) are displayed along the ordinate (x) axis while multiple RCP's after delta Omega "nudge" (0.0001o) are "stacked" along the inordinate (y) axis, correct? Please display the pseudo color scale used. I see a "black" area between other colors. Is this a lower relative intensity region in the RSM?

Don't worry I'm as baffled by this conventional RSM as you may be. I'm waiting for someone who actually uses this antiquated monstrosity called the conventional 0D RSM to evaluate Nano structural features. I'll post some more helpful references for the 0D RSM method as I find them.

Here are some of the typical challenges one would face making sense of this data:

1. The data is a gross average of the sampling area, undeterminable yet, until the SDD is known. Roughly 12mm X 0.4mm, your pixel size :-) Wonder how you determined this? Did you use photographic film to record or are you just going by dimensions of the slits? BTW What are your sample dimensions and approximate sample orientation w.r.t. the incident beam after "optimization" for the RCP's?

2. This data does not illustrate the typical spatial variation in sample Nano structure ubiquitously present in every sample to some degree or the other.

Our STO data shown earlier is for the (013) asymmetric reflection as well. Using the coupled Omega-2Theta scan mode in 2D. I notice your nomenclature being (103) for this reflection. What is the convention? The PS (Bragg peak shift), the FWHM (Bragg peak width) and the II (integrated intensity below each RCP) maps clearly illustrate the spatial inhomogeneity in the substrate Nano structure and the 2D incident beam relative intensity. In fact, the images clearly and vividly demonstrate the subgrain structure present in the substrate. The Omega resolution was in the order of 0.5 Arcsec (0.1o/min @ 12fps). The entire data set of 640,000 (800x800 pixels) RCP's took only a few minutes. The Y-Omega and X-Omega maps are a series of RCP's along a cursor line along the Y-axis and X-axis (topographically) respectively for individual 29 um pixels on the 2D detector image (topograph).

My personal objective is to understand the correlation between the conventional 0D RSM (as you show it) and the 2D images as we observe. So, I appreciate you asking this question!

Please download the original size (3944x3040 pixels) image from Flicker.com to make actual measurements using MS Paint. Each pixel on the image is calibrated!

https://www.flickr.com/photos/85210325@N04/15703454034/

I compute your SDD to be around 240mm, which is typical for Panalytical. I also surmise you are using a Panalytical diffractometer because their detector will not work otherwise. You cannot mount a PIXcel 3D on a Bruker D8 and vice versa with the VANTEK 2000 detectors. They can't be mounted on a X'Pert either. They are all protecting their turf at the expense of science. No wonder folks like you are still stuck in the past about a century with conventional tools and techniques in XRD.

Glad RG allows me to edit this stuff, just in case I be proven wrong sometime soon :-)

After 3 decades of exposure to 2D real time XRD imaging, I feel like Rip Van Winkle rudely awakened from the past every time I see modern high resolution, high precision tools used like sledge hammers.

https://www.flickr.com/photos/85210325@N04/11343736043/in/set-72157645018820696

Assuming little or no beam divergence along the diffractometer equatorial plane, a 0.4mm (400µm) wide window on the detector would subtend nearly 172 Arcsec at the diffractometer axis with 240mm SDD. An integrating window significantly larger than the 0.0001o (0.36 Arcsec) angular resolution that you think you have :-)

Alternatively, a 55µm pixel would subtend 47 Arcsec while a 29µm pixel would subtend about 25 Arcsec at the same SDD. The smaller the better!

Despite all these drawbacks, the conventional RSM is a widely used and well understood method for characterizing the Nanostructure of thin films and substrates non destructively! I'd encourage you to review the LinkedIn profile of  Dr. Iuliana Cernatescu (ex-Panalytical) who has done prolific work with conventional RSM's.

https://www.linkedin.com/profile/view?trk=contacts-contacts-list-contact_name-0&id=9935585

Distance between Sample to Detector (or X-ray tube to sample) is 240.0 mm (Radius of Goniometre is 240.0 mm).

I figured it out from your data namely, 0.055mm per pixel & 256 pixels=3.347o! 

It is also typical of Panalytical diffractometers. Anyone know what the magical 240mm is all about?

I think with any thin film on a monocrystalline substrate it would be relevant to quantify the following parameters through real time XRD imaging:

• Estimate film thickness using XRR. 
• Estimate relative misorientation between substrate and film. Both in-plane and out-of-plane by using appropriate (hkl)'s for analyses.
• Estimate the epitaxy of the film.
• Estimate defect density and distribution in both substrate and epi.
• Perform NDE depth analyses using different wavelengths and various (hkl)'s - Topotomography?
• Did I miss anything?

The prerequisites for precise XRD analyses are "optically flat" sample surface and a reasonable estimate of overall penetration depth in the sample. For the (013) reflection and the geometry we used our estimate of sampling depth was 15.5um for STO.

The conventional RSM is somehow supposed to provide all these parameters from reciprocal space for the single large averaged "pixel", in your case 0.4mm X 12 mm. Which implies that you are integrating nearly 7 pixels x 220 pixels (1540 Pixels). BTW what was the max CPS on the Bragg peak with the 1.8kW power that you used? What was the "dwell time" at each angular increment for each RCP in your RSM? Just trying to estimate the dynamic range and data collection time in your case :-)

In general,

Q. "How can we quantify lattice disorder in thin films through X-Ray diffraction peaks?"

A. It would be through a thorough understanding of the Fourier Transform of the XRD data.

https://www.flickr.com/photos/85210325@N04/10515372183/in/set-72157645018820696