Dear Al-Saba
X-Ray diffraction (XRD) technique is widely used in research and development and industry for material characterization and process control, as it can provide detailed information about lattice parameters of single crystals, phase, texture or even stress of polycrystalline materials. Analysis of XRD peak profiles indicated that full-width at half-maximum (FWHM) is sensitive to the variation in microstructure and stress–strain accumulation in the material. Many researchers have successfully attempted the use of FWHM in different manufacturing processes.
Quesnel et al. [1] observed a decrease in FWHM with cyclic softening in a cold rolled high strength low alloy steel. The alloy, in hot rolled condition, exhibited a stable stress response accompanied with an increase in FWHM after fatigue cycling. Goto [2] reported a rapid decrease in FWHM towards the end of the fatigue life in 17-4PH steel tested at stresses higher than the fatigue limit. Decrease in the FWHM response near the end of low cycle fatigue tests in Cr–Mo–V steel has also been observed by Ozdemir and Edwards [3]. FWHM measurement allowed researchers to obtain important information about the surface state of material as this is related to the grain distortion, dislocation density and residual stresses [4]. A handful of researchers have identified various material properties via the FWHM of XRD peaks. An increase in stacking faults and structural disorder widens the XRD peaks [5]. Increases in hardness and density of point defects affect the crystallinity and grain boundary mobility, which in turns causes a linear increase in the FWHM of XRD peak [6]. Presence of tensile stress in the material causes increase in the FWHM while relaxation of tensile stress decreases FWHM [7].
Of course you can always use the Scherrer Equation to estimate the size of the crystallite:
FWHM (2θ) =(Κ λ / L cosθ)
This means that peak width (FWHM) due to crystallite size varies inversely with crystallite size as the crystallite size gets smaller, the peak gets broader
The crystallite size broadening is most pronounced at large angles 2Theta.
[1] D.J. Quesnel, M. Meshii and J.B. Cohen, Mater. Sci. Eng. 36 (1978) p.207.
[2] T. Goto, Advancement in X-ray Analysis, C.S. Barrett, ed., Plenum Press, New York, 1992.
[3] A.T. Ozdemir and L. Edwards, Fatig. Fract. Eng. Mater. Struct. 20 (1997) p.1443.
[4] I.C. Noyan and J.B. Cohen, Residual Stress-Measurement by Diffraction and
Interpretation, Springer-Verlag, New York, 1987.
[5] J.M. Kim and H.T. Chung, J. Power Sourc. 115 (2003) p.125.
[6] H.M. Tung, J.H. Huang, D.G. Tsai, C.F. Ai and G.P. Yu, Mater. Sci. Eng. A 500 (2009) p.104.
[7] S. Rai, B.K. Choudhary, T. Jayakumar, K.B.S. Rao and B. Raj, Int. J. Pres. Ves. Pip. 76 (1999) p.275.
FWHM (not FWHW) is indicative of crystal size and strain. The smaller the size the greater the value of FWHM, and the same holds true for strain.
Debye-Scherrer equation is used to approximate average crystal size from FWHM, but Rietveld refinement is more comprehensive method and includes both crystal size and strain.
Dear Al-Saba
X-Ray diffraction (XRD) technique is widely used in research and development and industry for material characterization and process control, as it can provide detailed information about lattice parameters of single crystals, phase, texture or even stress of polycrystalline materials. Analysis of XRD peak profiles indicated that full-width at half-maximum (FWHM) is sensitive to the variation in microstructure and stress–strain accumulation in the material. Many researchers have successfully attempted the use of FWHM in different manufacturing processes.
Quesnel et al. [1] observed a decrease in FWHM with cyclic softening in a cold rolled high strength low alloy steel. The alloy, in hot rolled condition, exhibited a stable stress response accompanied with an increase in FWHM after fatigue cycling. Goto [2] reported a rapid decrease in FWHM towards the end of the fatigue life in 17-4PH steel tested at stresses higher than the fatigue limit. Decrease in the FWHM response near the end of low cycle fatigue tests in Cr–Mo–V steel has also been observed by Ozdemir and Edwards [3]. FWHM measurement allowed researchers to obtain important information about the surface state of material as this is related to the grain distortion, dislocation density and residual stresses [4]. A handful of researchers have identified various material properties via the FWHM of XRD peaks. An increase in stacking faults and structural disorder widens the XRD peaks [5]. Increases in hardness and density of point defects affect the crystallinity and grain boundary mobility, which in turns causes a linear increase in the FWHM of XRD peak [6]. Presence of tensile stress in the material causes increase in the FWHM while relaxation of tensile stress decreases FWHM [7].
Of course you can always use the Scherrer Equation to estimate the size of the crystallite:
FWHM (2θ) =(Κ λ / L cosθ)
This means that peak width (FWHM) due to crystallite size varies inversely with crystallite size as the crystallite size gets smaller, the peak gets broader
The crystallite size broadening is most pronounced at large angles 2Theta.
[1] D.J. Quesnel, M. Meshii and J.B. Cohen, Mater. Sci. Eng. 36 (1978) p.207.
[2] T. Goto, Advancement in X-ray Analysis, C.S. Barrett, ed., Plenum Press, New York, 1992.
[3] A.T. Ozdemir and L. Edwards, Fatig. Fract. Eng. Mater. Struct. 20 (1997) p.1443.
[4] I.C. Noyan and J.B. Cohen, Residual Stress-Measurement by Diffraction and
Interpretation, Springer-Verlag, New York, 1987.
[5] J.M. Kim and H.T. Chung, J. Power Sourc. 115 (2003) p.125.
[6] H.M. Tung, J.H. Huang, D.G. Tsai, C.F. Ai and G.P. Yu, Mater. Sci. Eng. A 500 (2009) p.104.
[7] S. Rai, B.K. Choudhary, T. Jayakumar, K.B.S. Rao and B. Raj, Int. J. Pres. Ves. Pip. 76 (1999) p.275.
Dear Al-Saba,
There is small addition to the answers above. Using software like MAUD or PM2K (and a good standard) you can obtain particles size distribution in powder diffraction case.
Another small addition: The theory behind the width of the diffraction peaks is simple: The more lattice planes with identical orientation are contributing to a diffraction peak, the sharper the diffraction pattern will be. It is analogous to the diffraction of visible light from a grating or a slit system of parallel, identical slits: The more slits are illuminated, the sharper the peaks will be. You may cross-check the literature in any optics book!
Hope this illuminates your knowledge, a nice week-end for all of you, Dirk
I agree with all the answers above but there are more useful information has to be taken into consideration : first we have to subtract the broadening due to instumental broadening, second we have to separate the remaining broadening into two parts one which due to strains and the other due to crystallite sise. Reitveld and Maud programs can do that for you.
I might add few more things such as the determination of the stacking faults probability, Alpha in deformed metals and alloys by XRD by just measuring the change in the separation of the two neighboring speaks such as 111 and 200 in FCC structure where these two spectral lines show displacements in opposite directions. Namely:
Del (2Theta 200 - 2Theta 111) =- 45 SQR3 Pi-2 (tan Theta 200 -tan Theta 111) Alpha,
where the term on the left ls the difference in the separation between peaks in a deformed sample and their separation in a well-annealed state.
XRD measurements of stacking fault probability, which is not only proportional with the partial dislocation densities but also their widths, allows us to study segregation kinetics of solute atomic species to the stacking fault areas in alloys having various compositions. The time dependent segregation reaction is here autocatalytic, which means the rate dy/dt is first order with respect to the reactant (1-y); Namely: dy/dt= k y (1-y). Where k may determined by XRD.
Similarity, In deformed samples having various compositions one may study isothermal segregation kinetics at various annealing temperatures, which may result not only intrinsic diffusivity of solute atoms (activation energy etc) and the mobile vacancy densities but also the density of dislocations generated during plastic deformation if one has the knowledge about stacking faults width ( the separation between the partial dislocations enclosing the faults). This information can be easily deduced from TEM observation at room temperature from those thin foil samples exposed to deformation and having the same chemical compositions.
What I think it is over simplification by experimentist by putting too much emphasis on the FWHM associated with XRD peaks as an useful short cut for the extraction of information sufficient enough for the identifications of the intrinsic and extrinsic structural defects , and then to try hopefully to obtain their densities and distributions in crystalline solids. Like all other spectral peak analysis (NMR, EPR, Internal Friction and Acoustic Attenuation, etc.) one definitely needs powerful physico-mathematical models to assist us not only for the extraction maximum information from the experimental spectral line data, but also to be able to interpret them properly without suffering from any internal inconsistency. BEST REGARDS TO ALL
FWHM (full width at half maximum) can inform us about size of cristallities.
It is addition to the above answer.
According to Debye-Scherrer equation
FWHM (2θ) =(Κ λ / L cosθ); it is readily identify that the materials nature i.e crystalline or amorphous. If the crystal-lite size is smaller, then it more of amorphous nature and there is a wider angle of 2 theta. But it very difficult to identify the combination of two to three compounds having the similar values of 2 theta. The FWHM will not help even to identify the crystal-lite size.
One question arose in my mind. If we are studying epitaxial thin film and the FWHM of a certain peak gives a crystalline size thicker than the film thickness, so what does it mean? By the way, is it possible? or Can we consider this crystalline size as the thickness of our thin film? Which means the higher FWHM corresponds to the thinner film!
Good question! Now imagine using the famous "Scherrer Equation" on a 2D XRD pattern/image :-)
FWHM is just one of the many parameters in reciprocal space that is our focus here. Some of the relevant reciprocal space parameters may include:
- Bragg Peak FWHM. (proportional to the square root of dislocation density)
- Bragg Peak Integrated Breadth.
- Bragg Peak Position.
- Bragg Peak Integrated Intensity.
- Bragg Profile Shape.
These parameters are closely related to the Nano structural morphology as well as stress/strain state of the sampled volume (VOXEL).
Based on the discussion so far, you folks seem to be only considering the FWHM measurements from conventional equatorial scan diffractograms. This technique generally involves convolutions (integration) over large sampling areas and will not be sensitive to individual grain distortion in the polycrystalline alloy. I'd refer you to a huge body of work done by Sigmund Weissmann et al of Rutgers University NJ USA. There are PhD theses aplenty from this group since the 1950's in the study of fatigue using XRD FWHM measurements in polycrystalline materials systems.
I'll add some examples and references soon. I'd also suggest adding up to 15 relevant topics up top to improve the RG member participation and hence enhance feedback. Please review some of the other XRD related topics in the post below:
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
https://www.flickr.com/photos/85210325@N04/11604959265/in/album-72157645018820696/
Thanks Ravi. Now I know that I don't know anything about XRD :)) That's only thing I know :)
Good News! I'm just beginning to learn about XRD myself :-) The potential of XRD is barely tapped yet. Especially, when the majority of folks in XRD are still pacified with archaic conventional methods & tools. Can't grapple with 3D+ reciprocal space data yet!
"I don't know anything about XRD" yet, means that there is a whole lot more to learn.
The more I get to know, makes me realize how much more I need to learn! What I know is a miniscule of that I don't know yet.
https://www.flickr.com/photos/85210325@N04/10242907544/in/album-72157645018820696/
"Of course you can always use the Scherrer Equation to estimate the size of the crystallite". Provided the a correct model is used for the "shape factor" of the CDD (coherently diffracting domain), "K" in "FWHM (2θ) =(Κ λ / L cosθ)". Besides, "FWHM" should be replaced by "Beta, the integral breadth" in Radians. The relationship between FWHM and "Beta" depends on the shape of the Bragg profile in question.
"If we are studying epitaxial thin film and the FWHM of a certain peak gives a crystalline size thicker than the film thickness, so what does it mean?" Now you have mixed up the "polycrystalline" Scherrer Equation with a "monocrystalline" epitaxy :-)
Thickness/thinness/flatness may be evaluated using XRR, X-ray Reflectivity. Watch this video of typical XRR data and analyses!
https://www.youtube.com/watch?v=nSEkBv6VKXc&list=FL7-u3nABX4YMdHDugoPsYcA
https://www.youtube.com/watch?v=nSEkBv6VKXc&list=FL7-u3nABX4YMdHDugoPsYcA
https://www.researchgate.net/post/Is_it_possible_to_precisely_estimate_the_epitaxial_film_thickness_with_XRD_rocking_curve_analysis_2kW_Power_Sealed_Tube_Source?_tpcectx=profile_questions
Thank you sooooo much :)
I will study as much as possible :) But I have some other questions. Can I have your email or skype? Thanks. :)
Post them as questions on RG. You'll get excellent selfless advise from many experts simultaneously. Send me the link through in-mail on RG.
I think if you wish to build a theory to calculate the crystalline size from the so-called line width or much better to say the line width broadening then you will end up with the second moment of the peak of under consideration. İf you go to the higher moments because asymmetry on the peak profile, which may be closely related to the stacking fault defects then you may hopely obtained stacking fault probability. But I think XRR is most promising technique to study not only single layer on top of the substrate but also the multi layer structures. I have seen some where that they go up to few angstrom in thickness. Best regards.
Note: Problem with line width broadening measurement is that ; the dislocation can also cause the line broadening, which is superimposed on the crystalline size broadening effect. Similarly domain walls or dislocation cell structure produce similar effect on the line broadening, which should be extracted by convolution analysis.
I should also thank to Dr. Ravi Anant who he has given us an excellent disposition of the XRR and its applications on the characterization of the material structures.
Typical examination depth with XRR appears to be 200-500nm depending on the material system.
https://www.researchgate.net/post/What_depths_can_one_typically_probe_with_XRR_X-ray_Reflectivity_Reflectometery?_tpcectx=profile_questions
Hello again,
in a heteroepitaxial film, due to relaxation, the lattice constant should go to the theoretical value. Now if I deposit a material with a lattice constant larger than substrate. while relaxation what will happen for 002-peak of this material in XRD pattern? (both have rocksalt structure). my results show that with increasing thickness of film the 002-peak goes to lower values to reach the theoretical value. but if we have in-plane compression we should have out-of-plane expansion. So with relaxation we will go to lower values of lattice constant. but why does the 002-peak decrease?! It should increase!
Which lattice constant is achieved by using of 002-peak?!
Hi Hadi
FWHW can help you to calculate the crystal size of your matearials where the broad XRD peak (big FWHW value) means the cystal in nanosize
Hello Sir, what is the formula to use predict crystal size from FWHW ?
Hi Radhakrishnan,
Particles size is calculated from XRD using Scherrer equation. Please see the details in the web
https://en.wikipedia.org/wiki/Scherrer_equation
Hi,
FWHM is a good sense to the existence of defects formed in the semiconductor layer grown on a substrate. Regardless of the defects in the substrate rested from wafer fabrication, the magnitude of FWHM of the peak layer is often compare to the substrate peak of the same material. Usually, the existence of high density crystalline defects, such as dislocations, causes broaden the peak, and vice-versa.
I think you guys are too shy to use more sophisticated mathematical techniques such as ''FFA in connection with convolution method'' to analyze the complete XRD peak to get not only the particle size and its distribution but also the residual strain distributions.
FWHW has a very limited applications for the severely deformed metals and alloys. It has no use for the detection of stacking faults and twin fault boundaries etc.
The grain size is calculated from XRD using Scherrer equation for above experts mention the formula
A very simple logic to determine the particle size
whenever the FWHM value is increased the particle size decreased
Scherrer equation may be applicable only in poly crystalline materials with certain "particle size range" and "random orientation". The "particle shape" and "preferred orientation" are not included in such estimation of size. These two factors will distort the results using the conventional powder diffractogram.
By the way, the use of the "integrated breadth squared" has much better sensitivity than the FWHM. This parameter shown as "beta" in the Scherrer equation would be more sensitive to Bragg profile changes below the "half height". Generally, most of the action, in terms of defects, can be seen along the "shoulder & tail" of the Bragg profile (below the FWHM).
To calculate FWHM in XRD analysis. See it here http://bit.ly/2qvW3ZZ
I hope it will help you.
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