I have a question. I calculate my crystallite size from two peaks and have a crystallite size of 15.98nm and 8.58nm. Can I calculate the average from my values and then is that the crystallite size, as in the example, or do I have to pay attention to something else?
It's a difference of approx. 2X. I have some suggestions for you, i. Do calculate for all peaks and take average after checking all sized, ii. refine your curve selection, iii. check for instrumental refinements. Thanks
@@SAYPhysics So I think I know what my problem is. I want to do a Williamson-Hall analysis for my thesis. I need beta_hkl = beta_size + beta_strain. I have got beta_size from the FWHM of my peaks. But I don't know how to calculate beta_strain. If I neglect beta_strain , my crystallite size, which is calculated with the y-axis, is too large. Can you tell me how to get to beta_strain or how to solve the problem? I haven't found anything useful so far. Thanks for helping :)
I inserted the data of peak position and also FWHM in the file that you have attached. it seems multiple 2 is missing somewhere because using xpert the crystallite size is twice than when I use your file.
Thank you for pointing that out! One key difference is that modern software like Xpert HighScore often uses integral breadth for its calculations, not FWHM. This can lead to some variation in the results compared to methods that rely on FWHM, such as those done manually or in Origin. However, difference of exactly two times is to think over and revisit the formulae.
Sir, I have two questions. 1. 3:43 Why should microstrain follow a decreasing trend as angle increases? Does that mean grains with different orientations have different strains? 2. If the grain size is confirmed to be in the micrometer level, can I directly calculate the microstrain using the equation given in this video, since the effect of grain size is negligible based on Scherrer's equation?
The broadening of XRD peaks (excluding instrumental broadening) may be due to crystallite size or microstrain or maybe both. To calculate microstrain from XRD data, we will have to make sure few parameters, otherwise, microstrain calculation will not be authentic. The very first one, we will have to make sure that XRD peak broadening is only due to strain, that is, crystal imperfection and distortion only. This can be ensured when the microstrain decrease with an increase in 2θ values, while the crystallite size must be consistent over a long range of 2θ values. Then, we can measure the microstrain by using this equation. I'm not very sure about the microstrain following a decreasing trend as the angle increases. It may be due to grains with different orientations have different strains, as you said.
SAYPhysics, at 4:35 you mentioned formula for microstrain in which theta (Bragg's angle) is in degrees while doing calculations you have converted it into radians. According to the formula, it should be in degrees. What do you say?
At 7:30, I have explained it that as Excel calculate by default in Radians, and we need it in Degrees, so we take its Radian before hand to finally get the value in Degrees. Thanks
Unit of microstrain remain the same. However, in the Rietveld refinement, it depends on the nature of microstrain. You may find a detailed analysis here dx.doi.org/10.1524/zkri.2011.1413. Thanks
Negative intercept in Wiliamson-Hall does not make physical sense, as it would imply a peak width below the instrument resolution. So either there are problems with the data treatment, e.g. faulty values for the instrument resolution function. Or the intercept has negative value, but the uncertainty is so high that it is not significantly different from zero. Both effects are very common if the peaks only start at rather high diffraction angles. Or your material shows behaviour that can not be modeled properly within the simple models and assumptions underlying Williamson-Hall, in which case you will have to use more advanced methods. www.researchgate.net/post/What_is_the_meaning_of_negative_intercept_in_Williamson-Hall_Plot_and_Modified_Williamson-Hall_Plot#:~:text=If%20microstrain%20is%20positive%20means%20that%20it%20is%20tensile.
Thanks for your question! Negative microstrain values can sometimes result from instrumental or sample broadening, incorrect baseline corrections, or errors in peak fitting. Make sure that any instrumental broadening is accounted for and that baseline corrections are applied properly during the calculation process. For a more accurate approach, I suggest trying the Williamson-Hall (WH) plot method. In my other video tutorial, I demonstrate how to calculate both microstrain and crystallite size, including considerations for peak broadening due to strain. You can check it out at th-cam.com/video/ipX3iUJ5VcU/w-d-xo.html.
Dr, I have a question, what does it mean if the microstrain data does not decrease as the angle increases, that is, they have a bit of constancy, they decrease and increase at the same time, what conclusion could I draw regarding my material?
Inconsistent microstrain behavior with increasing angle in XRD data may suggest structural complexities or variations within your material. Further analysis and characterization could help identify contributing factors to the observed pattern. Thanks
Consider conducting additional experiments or analyses to explore the structural changes causing the irregular microstrain behavior. This might involve complementary techniques like electron microscopy, TEM, or advanced XRD scans. Additionally, investigate the material's processing conditions and composition to pinpoint factors influencing microstrain variations. Thanks
I calculated the micro strain by your video and also by scherrer calculator in highscore xpert. these data are different. when I searched I found out that xpert is using the william hall method which By plotting FW ( s ) × cos θ on y axis against sin θ on x axis, we get the strain component from the slope and the particle size component from the y intercept.
Thank you for your detailed comment! You're right that different methods, like Scherrer and the Williamson-Hall (WH) plot, can yield varying results when calculating microstrain and crystallite size. The Scherrer equation typically gives an average crystallite size, while the WH method accounts for strain by plotting FW(s)×cosθ on the y-axis and sinθ on the x-axis. The slope provides the strain, and the intercept gives the crystallite size. In my video on the WH method, I’ve also explained when to use which relation for more accurate results. I recommend checking that out if you haven’t already-it might help clarify the differences between the approaches. Thanks again for sharing your experience! th-cam.com/video/ipX3iUJ5VcU/w-d-xo.html
Here are a couple of video tutorials which are addressing this topic. Thanks th-cam.com/video/ipX3iUJ5VcU/w-d-xo.html th-cam.com/video/OG-G6V9X8l0/w-d-xo.html
The crystallite size can be calculated using the same Scherrer equation while Halder Wagner equation is used to calculate the microstrain: ε = (β cos θ) / (4 sin^2 θ) - (β_0 cos θ_0) / (4 sin^2 θ_0) It is important to note that the Halder-Wagner equation assumes that the peak broadening is solely due to microstrain and not to other factors such as instrumental broadening or crystallite size distribution. Therefore, the calculated microstrain may be an overestimate if other broadening effects are present in the XRD data. Thanks
can we calculate microstrain for polymer-metal oxide composite? if yes? then how can we correlate the microstrain consisting material that can be good for any application such as battery or supercapacitor? Thanks in advance
Thanks for the appreciation dear. This tutorial effectively explains the calculation of microstrain from XRD data using Origin irrespective of its compressive or tensile nature, with a focus on crystal imperfections. The emphasis on ensuring XRD peak broadening is solely due to imperfections, demonstrated using LiF XRD data, adds practical insights. A caution about inconsistent trends in crystallite size with increasing angles impacting microstrain authenticity is well noted. Thus, the tutorial provides a concise and comprehensive guide, addressing potential pitfalls and highlighting the importance of data authenticity.
@santanupal7097 Determining the nature of microstrain from XRD data involves analyzing the peak broadening in diffraction patterns. Comprehensive microstrain results in peak broadening, while tensile microstrain typically leads to peak shifting. Advanced techniques like Williamson-Hall analysis or Warren-Averbach method can help quantify microstrain and differentiate between comprehensive and tensile nature. Thanks
SAYPhysics, whenever I recalculate 2theta and FWHM for the same data, it's different. Ultimately, crystallite size, dislocation density, and microstrain are different for the same data. Is it normal?
@Mahwish Sarwar It's not normal for the same data. try to select your peaks positions in zoomed way to clearly locate the peaks. Then do fitting carefully. Every time you'll get the same values, although with fluctuations approx. 0.001. Thanks
sir you did not mention that how to find all things via william son hall plot. Please tell me how to find the size and strain from William son hall plot please.I have been watched your video.
Sir, this is a greatly helpful video! I have a quick question here. As the microstrain will decrease with increased angles, which angle related microstrains should I report, the lowest one or the highest one?
Again I will say that modern software like Xpert HighScore often uses integral breadth for its calculations, not FWHM. What your suggestions based on established literature? Thanks
I have a question. I calculate my crystallite size from two peaks and have a crystallite size of 15.98nm and 8.58nm. Can I calculate the average from my values and then is that the crystallite size, as in the example, or do I have to pay attention to something else?
It's a difference of approx. 2X. I have some suggestions for you, i. Do calculate for all peaks and take average after checking all sized, ii. refine your curve selection, iii. check for instrumental refinements. Thanks
@@SAYPhysics So I think I know what my problem is. I want to do a Williamson-Hall analysis for my thesis. I need beta_hkl = beta_size + beta_strain. I have got beta_size from the FWHM of my peaks. But I don't know how to calculate beta_strain. If I neglect beta_strain , my crystallite size, which is calculated with the y-axis, is too large. Can you tell me how to get to beta_strain or how to solve the problem? I haven't found anything useful so far. Thanks for helping :)
Soon I’ll do a video on the WH plot. Thanks
Wonderful tutorials. Very easy to follow the instructions. Thanks so much!
Thanks for the appreciation dear
Thank you so much for all your tutorials
Thanks for the appreciation dear 😊. Share them please in your circle.
I inserted the data of peak position and also FWHM in the file that you have attached. it seems multiple 2 is missing somewhere because using xpert the crystallite size is twice than when I use your file.
Thank you for pointing that out! One key difference is that modern software like Xpert HighScore often uses integral breadth for its calculations, not FWHM. This can lead to some variation in the results compared to methods that rely on FWHM, such as those done manually or in Origin. However, difference of exactly two times is to think over and revisit the formulae.
Sir, I have two questions.
1. 3:43 Why should microstrain follow a decreasing trend as angle increases? Does that mean grains with different orientations have different strains?
2. If the grain size is confirmed to be in the micrometer level, can I directly calculate the microstrain using the equation given in this video, since the effect of grain size is negligible based on Scherrer's equation?
The broadening of XRD peaks (excluding instrumental broadening) may be due to crystallite size or microstrain or maybe both. To calculate microstrain from XRD data, we will have to make sure few parameters, otherwise, microstrain calculation will not be authentic. The very first one, we will have to make sure that XRD peak broadening is only due to strain, that is, crystal imperfection and distortion only.
This can be ensured when the microstrain decrease with an increase in 2θ values, while the crystallite size must be consistent over a long range of 2θ values.
Then, we can measure the microstrain by using this equation.
I'm not very sure about the microstrain following a decreasing trend as the angle increases. It may be due to grains with different orientations have different strains, as you said.
Thank you very much for these helpful videos
You're welcome dear
@@SAYPhysics the standard deviation of my crystallite size is around 3 nm, can I use the equation you presented for measuring lattice strain?
SAYPhysics, at 4:35 you mentioned formula for microstrain in which theta (Bragg's angle) is in degrees while doing calculations you have converted it into radians. According to the formula, it should be in degrees. What do you say?
At 7:30, I have explained it that as Excel calculate by default in Radians, and we need it in Degrees, so we take its Radian before hand to finally get the value in Degrees. Thanks
What if we do all calculations on origin directly?we will convert angle into radians or not?
As Excel do calculate it in radians by default, we double convert it to get it in degrees. This is what I have already explained. Thanks
Yes, you're right about doing calculations in OriginLab. However, calculations are much easier, traceable, and function-based in The Excel. Thanks
The instrumental broadening is not considered here.Plz suggest how to incorporate the instrumental factor?
Please watch my couple of videos on the instrumental broadening th-cam.com/video/238yM0OgaH8/w-d-xo.html
th-cam.com/video/tO_frVLxmsg/w-d-xo.html
Usually, in what units is the micro effort expressed? concerning Rietveld refinement
Unit of microstrain remain the same. However, in the Rietveld refinement, it depends on the nature of microstrain. You may find a detailed analysis here dx.doi.org/10.1524/zkri.2011.1413. Thanks
I would like to know what does it mean a negative (or positive) value in the microstrain value when analyzing a XRD diffractogram?
Negative intercept in Wiliamson-Hall does not make physical sense, as it would imply a peak width below the instrument resolution. So either there are problems with the data treatment, e.g. faulty values for the instrument resolution function. Or the intercept has negative value, but the uncertainty is so high that it is not significantly different from zero. Both effects are very common if the peaks only start at rather high diffraction angles. Or your material shows behaviour that can not be modeled properly within the simple models and assumptions underlying Williamson-Hall, in which case you will have to use more advanced methods.
www.researchgate.net/post/What_is_the_meaning_of_negative_intercept_in_Williamson-Hall_Plot_and_Modified_Williamson-Hall_Plot#:~:text=If%20microstrain%20is%20positive%20means%20that%20it%20is%20tensile.
@@SAYPhysics Thank you so much
I calculated micro strain and the values are negative? what is causing that? how can I fix that ?
Thanks for your question! Negative microstrain values can sometimes result from instrumental or sample broadening, incorrect baseline corrections, or errors in peak fitting. Make sure that any instrumental broadening is accounted for and that baseline corrections are applied properly during the calculation process.
For a more accurate approach, I suggest trying the Williamson-Hall (WH) plot method. In my other video tutorial, I demonstrate how to calculate both microstrain and crystallite size, including considerations for peak broadening due to strain. You can check it out at th-cam.com/video/ipX3iUJ5VcU/w-d-xo.html.
Dr, I have a question, what does it mean if the microstrain data does not decrease as the angle increases, that is, they have a bit of constancy, they decrease and increase at the same time, what conclusion could I draw regarding my material?
Inconsistent microstrain behavior with increasing angle in XRD data may suggest structural complexities or variations within your material. Further analysis and characterization could help identify contributing factors to the observed pattern. Thanks
Consider conducting additional experiments or analyses to explore the structural changes causing the irregular microstrain behavior. This might involve complementary techniques like electron microscopy, TEM, or advanced XRD scans. Additionally, investigate the material's processing conditions and composition to pinpoint factors influencing microstrain variations. Thanks
Thank so much Sir@@SAYPhysics
@antonioculebro8038 you're welcome dear
I calculated the micro strain by your video and also by scherrer calculator in highscore xpert. these data are different. when I searched I found out that xpert is using the william hall method which By plotting FW ( s ) × cos θ on y axis against sin θ on x axis, we get the strain component from the slope and the particle size component from the y intercept.
Thank you for your detailed comment! You're right that different methods, like Scherrer and the Williamson-Hall (WH) plot, can yield varying results when calculating microstrain and crystallite size. The Scherrer equation typically gives an average crystallite size, while the WH method accounts for strain by plotting FW(s)×cosθ on the y-axis and sinθ on the x-axis. The slope provides the strain, and the intercept gives the crystallite size.
In my video on the WH method, I’ve also explained when to use which relation for more accurate results. I recommend checking that out if you haven’t already-it might help clarify the differences between the approaches. Thanks again for sharing your experience! th-cam.com/video/ipX3iUJ5VcU/w-d-xo.html
Respected sir, How we can calculate strain of each hkl plane of our data by using W-H methode
Here are a couple of video tutorials which are addressing this topic. Thanks
th-cam.com/video/ipX3iUJ5VcU/w-d-xo.html
th-cam.com/video/OG-G6V9X8l0/w-d-xo.html
Great Sir G 👍❤️❤️❤️
Thanks
I have a question, how I can get the strain values if my peaks are broader? when I try to click until converge, the plot does not fit with peaks.
Please see my other videos on advanced fittings. Thanks
How to calculate microstrain and the crystallite size using Halder Wagner equation
The crystallite size can be calculated using the same Scherrer equation while Halder Wagner equation is used to calculate the microstrain:
ε = (β cos θ) / (4 sin^2 θ) - (β_0 cos θ_0) / (4 sin^2 θ_0)
It is important to note that the Halder-Wagner equation assumes that the peak broadening is solely due to microstrain and not to other factors such as instrumental broadening or crystallite size distribution. Therefore, the calculated microstrain may be an overestimate if other broadening effects are present in the XRD data. Thanks
Can you give me the theory part for better undertstanding?
Please check the video description where I have mentioned some valid references for an extended study. Thanks
can we calculate microstrain for polymer-metal oxide composite? if yes? then how can we correlate the microstrain consisting material that can be good for any application such as battery or supercapacitor? Thanks in advance
Please review some literature as for a polymer or stainless steel, calculations are slightly different. Thanks
@@SAYPhysics thank you so much sir
You're welcome dear
It is a nice video. Can you please explain what is the nature of the calculated micro-strain? Is it compressive or tensile?
Thanks for the appreciation dear. This tutorial effectively explains the calculation of microstrain from XRD data using Origin irrespective of its compressive or tensile nature, with a focus on crystal imperfections. The emphasis on ensuring XRD peak broadening is solely due to imperfections, demonstrated using LiF XRD data, adds practical insights. A caution about inconsistent trends in crystallite size with increasing angles impacting microstrain authenticity is well noted. Thus, the tutorial provides a concise and comprehensive guide, addressing potential pitfalls and highlighting the importance of data authenticity.
Thank you for your kind reply. Can you comment on how to find out the nature of the micro-strain?
@santanupal7097 Determining the nature of microstrain from XRD data involves analyzing the peak broadening in diffraction patterns. Comprehensive microstrain results in peak broadening, while tensile microstrain typically leads to peak shifting. Advanced techniques like Williamson-Hall analysis or Warren-Averbach method can help quantify microstrain and differentiate between comprehensive and tensile nature. Thanks
if the microstrain is showing irregular trend then what to do sir?
In that case, we’ll go for the W-H plot, which I’ll cover soon, IA. Thanks
SAYPhysics, whenever I recalculate 2theta and FWHM for the same data, it's different. Ultimately, crystallite size, dislocation density, and microstrain are different for the same data. Is it normal?
@Mahwish Sarwar It's not normal for the same data. try to select your peaks positions in zoomed way to clearly locate the peaks. Then do fitting carefully. Every time you'll get the same values, although with fluctuations approx. 0.001. Thanks
@@SAYPhysics Thank you so much.
Sir please tell me how to find lattice strain
In this playlist you will find some tutorials on it. Thanks
OriginLab Tutorials: th-cam.com/play/PLeWSImvDbpleVJEkXIwSkWpRiA0_sX42z.html
sir you did not mention that how to find all things via william son hall plot. Please tell me how to find the size and strain from William son hall plot please.I have been watched your video.
I told you earlier that WH plot video I'll cover soon. It's awaited. Thanks
sir how to find strain from William son hall plot please upload the video.
Soon a video on the WH plot will be uploaded. Thanks
Sir, this is a greatly helpful video! I have a quick question here. As the microstrain will decrease with increased angles, which angle related microstrains should I report, the lowest one or the highest one?
An average microstrain is usually reported. Thanks for the appreciation.
@@SAYPhysics Thank you so much for the reply.
is micro strain and lattice strain same thing??
Yes dear
I guess the FWHM that you use from origin is half of FWHM calculated by xpert
Again I will say that modern software like Xpert HighScore often uses integral breadth for its calculations, not FWHM. What your suggestions based on established literature? Thanks