you cannot use just a formula. You have to analyze the whole diffraction pattern and have enough information (independent peaks) to be able to consider the anisotropic broadening given by the presence of the dislocation itself.

The paper is a bit old now, but you have all information there. This is consider the state of the art method for line profile analysis

Article Whole Powder Pattern Modelling

You will find the formula in this paper.......

Nuclear Instruments and Methods in Physics Research B 287 (2012) 10–14

http://dx.doi.org/10.1016/j.nimb.2012.07.007

... unfortunately in 2012 you still find people convinced that Scherrer formula (1918) is still the right way to do the calculation. If you read the recent literature on the subject (and I mean literature on powder diffraction) or go to the corresponding conferences (e.g. the EPDIC conference I am attending right in this moment), you find out that Scherrer formula should NOT be used for quantitative domain size analysis.

Moreover stating that dislocation density is equal to 1/L^2 is also total nonsense as there is no such a correlation between the size and the quantity of dislocations you measure (plus size broadening for sphere is isotropic, strain broadening for dislocations is anisotropic)....

Matteo Leoni................ a more appropriate way to measure crystallite size is using Williamson-Hall Method but can you suggest some formula for dislocation density as i have came across this as 1/L^2 as u mentioned

you cannot use just a formula. You have to analyze the whole diffraction pattern and have enough information (independent peaks) to be able to consider the anisotropic broadening given by the presence of the dislocation itself.

The paper is a bit old now, but you have all information there. This is consider the state of the art method for line profile analysis

Article Whole Powder Pattern Modelling

Matteo, it is good to know you have published state of the art paper, but “to calculate the dislocation density and texture coefficient from XRD patterns” using powder specimens is a meaningless work anyway. The question is basic but needs a lot of time and space to answer. However, there are many textbooks describing the method.

Well I totally disagree on this (and I think most of the participants to the conference I am attending, the European Powder Diffraction Conference) would definitely agree with me. Measuring dislocation density from a single powder diffraction pattern is nowadays routine. And powder diffraction means you are working with a specimen that is a powder from the point of view of diffraction (a polycrystalline specimen IS a powder, any metallic part of of a cruise ship is a powder and so on).

Calculating texture coefficients can be meaningless from a single diffraction pattern, but you can even calculate the full ODF if you take a sufficient number of patterns at different tilting angles

Matteo,

Please help me understand why calculating texture coefficients can be 'meaningless' from a single diffraction pattern? I understand one should make sure their measurements/experiments are reproducible. But if one uses a simple Harris Texture Index (HTI):

"Harris, G.B., Quantitative Measurement of Preferred Orientation in Rolled Uranium Bars. Philosophical Magazine, 1952. 43(336): p. 113-123."

then one can correlate material property anisotropy to the quantified HTI. Is this not correct?

Since planes whose normal are parallel to the XRD plane normal generate higher intensities, then a second XRD of the sample at a 90 degree angle orientation to the first should be quite telling. Intense peaks in one orientation should be significantly reduced or 'missing' in the other, and vice versa. I am not a crystallographer, but I have used this simple analysis method before. Have I used it incorrectly?

Jason,

I was talking about extracting texture information from a single pattern and not from multiple ones. In principle to have full texture information you should collect a set of pole figures and then reconstruct the ODF from them. You can, alternatively, collect diffraction patterns at different tilting and try to extract the information from them. Of course the more the information, the more meaningful and accurate the reconstruction. The minimum number of patterns needed to get the information depends on the symmetry of the specimen and of the lattice. I doubt you would be able to get some meaningful texture information from a single pattern of a triclinic material with orthorhombic texture. Rotating the sample 90 deg can give already some indication but you are not guaranteed to get a meaningful answer (the texture axis could be tilted or you could have multiple texture components..)

Matteo,

Ok. Thank you for your clarification.

Dear Aseya,

To calculate dislocation density, I know that, we have to record the rocking curves for symmetric and asymmetric diffraction planes. As in our case of GaN, we record the rocking curves for (002) and (102) to evaluate the screw and edge and then total dislocation density.

For details you have to go some very old literature ~1953 or so.

regards & thanks

Satya

Area under the peaks gives the idea on disorderness of the system,which is a measure of dislocation density and for texture coefficient one has to go for special type of scan the system to collect XRD data.

Dear Dilip, I have serious problems with your answer: I don't think "disorderness" is a physical measure and disorder is definitely not related to the area of the peaks. The area of the peaks is related to the structure factor and to texture. The only effect of dislocations is to cause anisotropic broadening of the peaks. They introduce also some slight asymmetry but that's a quite high order effect.

Dear Matteo,

Why disorder is not a physical parameter and what do you mean by physical parameter?

I just mean that talking about disorder or saying "disorderness" without specifying what you mean by disorder is like saying a generic "I like food" without specifying what kind of food you refer to!

For instance if you talk about disorder in the occupancy of a specific site, then you can find some "physical parameter" (i.e. the fraction of occupancy by a specific specie) that can quantify that disorder (even if, to be honest, this is not a truly physical parameter).

Dear Matteo,

I don't agree with your answer and every structuralparameter is a physical parameter that changes the roperties of thesystem, So disoredrness can be and should be well studied from XRD.

Dillip, I did nto say that disorder cannot be studied by XRD. However I still don't know (and you still have to explain) what you mean by "disorderness".

Concerning the occupational disorder, physics tells me that in each unit cell the occupancy of one site by a cerain atom MUST be either 1 or 0 (the atom is there or is not there). Putting a non integer occupancy to mimic disorder is just a trick we use and the fractional occupancy can be used to quantify it. That's why I say that it's not a "truly physical parameter". I would just call it a model parameter.

Any disorder can be wel resolved by XRD and that is a physical parameter.

For thin films to estimate the degree of texture strength the rocking curves (θ – scan) around the Bragg peak can be measured. The rocking curves FWHM value may be used as characteristics of texture strength. Small or large values of FWHM indicate strong or weak texture respectively.

Dear Aseya,

Calculation of the density of dislocations depends on the crystal structure of an object. To calculate the density of dislocations from mosaic crystals I want to recommend you to view work:

1. X-ray diffraction peak profiles from threading dislocations in GaN epitaxial films

V.M.Kaganer, O.Brandt, A.Trampert, and K.H.Ploog PHYSICAL REVIEW B 72, 045423 (2005).

2. Substrate effects on the strain relaxation in GaN/AlN short-period superlattices. V.P. Kladko, A.V. Kuchuk, P.M. Lytvyn, O.M. Yefanov, N.V. Safriuk, A.E. Belyaev, Yu.I. Mazur, E.A. DeCuir Jr, M.E. Ware, and G.J. Salamo // Nanoscale Research Letters 2012, 7: 289.

3. Kladko VP, Kolomys AF, Slobodian MV, Strelchuk VV, Raycheva VG,

Belyaev AE, Bukalov SS, Hardtdegen H, Sydoruk VA, Klein N, Vitusevich SA:

Internal strains and crystal structure of the layers in AlGaN/GaN heterostructures grown on a sapphire substrate. J Appl Phys 2009, 105:063515.

4. Heinke H, Kirchner V, Einfeldt S, Hommel D: Analysis of the defect structure of epitaxial GaN. Phys Stat Sol A 1999, 176:391–395.

5. Chierchia R, Bottcher T, Figge S, Diesselberg M, Heinke H, Hommel D: Mosaicity of GaN epitaxial layers: simulation and experiment. Phys Stat Sol B 2001, 228:403–406.

6. Chierchia R, Bottcher T, Heinke H, Einfeldt S, Figge S, Hommel D: Microstructure of heteroepitaxial GaN revealed by x-ray diffraction. J Appl Phys 2003, 93:8918.

7. High resolution synchrotron X-ray studies of phase separation phenomena and the scaling law for the threading dislocation densities reduction in high quality AlGaN heterostructure.

S.Lazarev, S.Bauer, K.Forghani, M.Barchuk, F.Scholz, T.Baumbach Journal of Crystal Growth.

and other references in these papers.

It is tough job to estimate the dislocation density because it is difficult to refine the intensity data to that extent to have the information about the dislocations.

XRD Microscopy: http://www.flickr.com/photos/85210325@N04/8294404556/sizes/h/in/set-72157632729045818/

Come join us and share your erudite opinions:

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[email protected]

Here are example of real time monitoring of texture. We've had the occasion to study several materials including Kevlar, Cotton, Aluminum Foil, Dacron, Ni foil, Brass foil, composite tapes/strips, powders, propellants etc:

Kevlar & Al Foil: http://www.flickr.com/photos/85210325@N04/7975835813/in/set-72157632728981912

Al Foil: http://www.flickr.com/photos/85210325@N04/7944785794/in/set-72157632728981912/

Ni Pattern Ravi.

Dillip! Ni pattern too: http://www.flickr.com/photos/85210325@N04/8008714677/in/set-72157632728981912/

Ravi,

Really both the patterns are not only nice but also informative so for as the structures are concerned.

Thanks a lot for your support and understanding my views.

When you measure rocking curves to get the dislocation density by using formula ((FWHM)^2) / (9*b^2)

Where b is Burger's vector,

If you do in you will and up in quantity with unit deg^2 / cm^2, but in the unit of dislocation density is /cm^2.

I am bit confused about this. Do anyone have an answer?

Thought of it a lot before but never asked yet as you, Nagaraja! I mean, the "((FWHM)^2) / (9*b^2)" formula itself. I'll start looking. Very important question. There's got to be a simple answer. I ought to know. I'll post some publications that have used the formula that may give us the references and the clue. Matteo Leoni would be able to shed light on this matter as well.

Same as Scherrer formula... angles are in rad not in deg. Remember the anisotropy due to dislocations here is not considered...

I agree Matt! Unless, we use the XRD Rocking Curve Technique, where we can deconvolute the effects of "anisotropy due to dislocations" by monitoring multiple (hkl)'s while isolating & separating Bragg Peak Shift & FWHM for each (hkl). I'm not yet sure of all the mechanics & modeling involved.

BTW Matt! How does the Radian replacing the Degree change the final dimension of Dislocation Density? A little puzzled. I apologize if I "stuck my big foot in my mouth". Pardon the temporary ignorance.

Matteo,

The angles are not in Radian.

Why not Dillip? They ought to be in Radian always, never in Degree. My understanding is that we use Degree just for convenience (decimation is easier & linear scale perhaps?). It is mostly converted to the reciprocal space parameter through "Lambda/Sin(Theta)" transform and we never notice or pay heed to Radians or Degrees. Maybe? Here it comes "scalpel" or "sword"? I submit.

Aseya Akbar! It would serve your interest best if you were to describe your sample better. This will help you leverage the incredible knowledge available through RG members much more effectively.

1. Is it bulk material with "preferred orientation"?

2. Is it a powder composite with texture?

3. Polymer with texture?

What is your sample morphology?

1. Thick Bulk sample amenable only to XRD reflection mode measurements.

2. Thin film amenable to XRD transmission mode measurements.

3. Other. Sample dimensions?

What XRD instrumentation? Geometry/Optics? Dimensions?

Ravi,

The data collected from the machine are in degrees.

Yes the one collected can be in deg but in the formula it must be in rad. I doubt there are formulae that work with deg. The missing conversion is a quite frequent error in the use of Scherrer formula

Dear Leoni,

I did not get how the dislocation density will have the unit of /cm2,

If at all you keep the FWHM in radians the final result would be in rad/cm^2

Can you put some light on it??

rad is a conventional way to identify the angles.Fortunately or Unfortunately is one of those cases where the unit of measurement (rad) it is a dimensionless quantity. After all what's the ArcSin(0.5) ? you usually say Pi/6 rad or 30 deg... but coming from a trigfunction it should be dimensionless

Please remember this awesome Panalytical training session for: Introduction to quantitative X-ray texture analysis

Almost all physical properties of crystalline materials strongly depend on the crystal orientation. In practice, most commonly used artificial and natural solid materials are polycrystalline and show a texture, a non-random orientation distribution of the crystallites. Therefore the materials properties can only be determined if the texture of a sample is known.

X-ray diffraction is a widely used technique to determine preferred orientations from pole figures. The webinar gives a short introduction to quantitative texture analysis for the materials scientist.

Webinar details

Date: December 3, 2013

Time: 10:00 AM - 11:00 AM EST (4:00 PM - 5:00 PM CET)

Panelist information:

Hans te Nijenhuis studied Applied Physics at the Delft University of Technology in the Netherlands, with a focus on the field of physical crystallography. He obtained a PhD degree in Solid State Physics at the University of Nijmegen with a thesis on gas phase deposition of epitaxial layers. Afterwards he joined PANalytical (Almelo, the Netherlands) and is now working in the department Product Management X-ray diffraction.

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If we are measuring say a "line" in a "volume" perhaps, then it would need to be mm/mm^3=mm^(-2). Yes? I may be plagiarizing myself. I still can't grasp the "Radian" bit, though. Radian, dimensionless? (Matteo) It is after all, only a relative direction. Yes?