How to calculate crystallite size from XRD data using origin 

Thanks dear

I'm happy for you 😊. Thanks for the appreciation dear

Thanks for the appreciation dear. You may share them with others 🙂. Thanks

Thank you for watching the tutorial! Great questions. 1. The Scherrer equation is often considered valid up to 200 nm because it assumes a uniform distribution of crystallites and does not account for factors like strain or defects. Beyond 200 nm, other factors start to become significant, potentially affecting the accuracy of the Scherrer equation. 2. For crystallite sizes larger than 200 nm, alternative methods such as electron microscopy or small-angle X-ray scattering (SAXS) can be more appropriate. These techniques offer higher resolution and can provide more accurate measurements for larger crystallites. Feel free to explore these options based on the size range you're working with.

Thanks for the appreciation dear

Thanks for watching the tutorial! In that specific video, I focused on crystallite size calculation. If you're interested in instrument broadening, check out the complete series at [ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-0PUTB0IhlWw.html&pp=iAQB]. It covers various aspects of XRD data analysis.

Thanks for the appreciation dear. Division by 10 is just the conversion to nm. Thanks

Thanks....your highness

Thanks dear

The value of beta is provided by origin in radian which I have converted into degrees as per requirements of the equation. Please check in the video description the Excel file in which I have done the calculations you can see in the file that when you take radian of a radian value then it is converted into degrees. Thanks

Thanks for the appreciation dear. Theta is the goniometer angle, plotted as 2theta on the x-axis, which is in degrees as we move it around the sample. While beta is the measure of fwhm, which by its equation in radians. These are as per literature, whose references are provided in the video description. Thanks

You're right for β to be in radian, while 𝜽 is to be in degrees. I've confirmed it through literature as well as the modern software (like Highscore etc.) are using the same to calculate the crystallite size. Thanks

Glad to know you liked it. Thanks

Thanks for the appreciation dear. You'll have to purchase it or some universities provide it.

@@SAYPhysics Thank you for the information.

Also , rad to degree conversion is incorrect ..need to multiply with pi and divide with 180

In the vIdeo description, I have attached an Excel file, where all calculations are being done. Thanks

Here, Origin gives the value in radian and in the Scherrer equation we need it in degrees,, so in Excel template, which is available in the video description , we convert it into degrees. Whatever calculations you are saying, Excel is doing it itself. Use the provided template for calculations, please. Thanks

Thanks for the appreciation dear 😊

Thanks for the appreciation dear 😊 In the video description, you will find some relevant references.

@@SAYPhysics Thank you for the reply! Do you know of any book or article that states this?

Thank you for watching my video and for your question regarding the validity of the method for calculating crystallite size using XRD data in Origin. The information about the method's validity for crystallites up to 200 nm comes from various references, for example, as mentioned below. www.nature.com/articles/nnano.2011.145 www.ncbi.nlm.nih.gov/pmc/articles/PMC6459976/ www.sciencedirect.com/topics/chemistry/scherrer-equation prism.mit.edu/XRAY/oldsite/CrystalSizeAnalysis.pdf

Thanks for the appreciation dear ☺️

You're welcome dear

Thanks for the appreciation dear 😊. Share it please with others too.

Thanks for the appreciation dear

I don't know which properties you're interested in. Let me say few things generally. The smaller the crystallite size, the more efficient the sintering (lower possible sintering temperature). However, the drying and firing shrinkage will be very high. The hardness of a material increases as the crystallite size decreases. Thanks

Thanks for the appreciation dear 😊

You're welcome dear. Aameen

The smaller mean particle size from TEM compared to crystal size could be due to differences in measurement techniques, where TEM measures actual particle size, and XRD measures crystallite size. Factors like particle aggregation, polycrystallinity, surface effects, and differences in sample preparation or calibration can also contribute to this discrepancy. If you have more details on the measurements, I can offer more specific insights. Thanks

⁠ I used a pulsed laser in 5 ml of distilled water and deposited the colloidal solution on small pieces of silicon for the purpose of performing an XRD test. I performed a TEM of the solution and the results were as I indicated. There is a difference between the TEM and XRD values ​​with respect to the crystal size and particle size, noting that the targets were silver and gold. @@SAYPhysics

I'm sorry for the late response. RU-vid doesn't show for response within another response, which I miss sometime. Please note that crystallite and particle size are not the same. XRD gives you the crystallite size not the particle size. Thanks

@@SAYPhysicsyes sir I know that, my question is (my results appear crystalline size large than particle size)

Please use the Excel template which is provided in the video description. It will do all the calculations for you. Thanks

The one that I did is correct as I confirmed it from an extensive literature. Thanks

I know sem and tem will give me proper result... But any rough idea about size of nanoparticles using XRD data

I'll respond to this in your next question. Thanks

XRD can only give you the crystallite size that can be related with the TEM. The size of NPs can be estimated from uv vis absorption data in case of metal or metal oxide NPs. The following videos can help you estimate the sizes. Thanks 😊 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ktX9ehEvXWQ.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-fQTU-5gtCSQ.html

@@SAYPhysics thank you sir

@lakhichetry3733 you're welcome dear

As you know, different peaks have been taken into account instead of the very intense peak only. The average crystallite size covers many contributing factors. Thanks

XRD, being a technique, is very accurate and reliable. However, calculation of crystallite size depends on accurate measurement of internal parameters like fwhm etc. Thanks for the appreciation dear 😊

Thank you very much,sir.

Thanks for the appreciation dear. Answer will remain the same. If you convert it first from angstrom to nm or later. From the machine specs, we get it in angstrom. Thanks

Thanks for the appreciation dear 😊

Thanks dear

In the data worksheet, there comes two extra sheets after fitting, click the first to see the tables. Thanks

@@SAYPhysics Thank you brother

@aymenfarhi1425 you're welcome dear

Grain is either a single crystalline or polycrystalline material, and is present either in bulk or thin film form. During the processing, smaller crystallites come closer and grow to become larger due to kinetics. Therefore, in the most likely scenario, the grain is larger than a crystallite. Thanks

You are right. In general, it is not recommended to consider a doublet as a single reflection for calculating the crystallite size from XRD data, as this can lead to inaccuracies in the results. This is because a doublet typically indicates the presence of multiple crystallographic domains or twinning, and treating it as a single reflection can result in an overestimation of the crystallite size. However, it is always better to consider all the peaks and then finally take the average of all the calculated crystallite sizes, as explained at 07:50 of the video. As a cross-check, we can compare the calculations from a single reflection and then of the average to confirm these calculations in the video. Thanks for your input.

@@SAYPhysics taking average can help you when consider particular hkl planes , per example 00l. Every reflection indicates/arising from particular hkl plane. Insuch case you can not consider doublet as a singlet. If you want to get quatitateve size then you have to use siglet only. I can not agree singlet can giver over estimation of size. And one more thing origin program not use for quantitative data it's just for rough idea. For more basics kindly read any crystallography text.

Right. Thanks for your input.

Thanks for the appreciation dear 😊

The incident wavelength of X-ray is of the machine, independent of the nature of a material being characterized. Thanks

Thanks for the appreciation dear. There's an upper limit to the Scherrer's equation only. I'm sorry, I don't have any ready reference where calculations have been made for 0.5 nm or less. If I came across one, I'll let you know. Thanks

To find the limit of detection (LOD) and limit of quantification (LOQ) in OriginLab, you can follow these steps: Prepare your data: Ensure that you have experimental data with a series of known concentrations of your analyte or target compound. Create a calibration curve: Plot the signal response (e.g., peak area, intensity, absorbance) against the corresponding concentrations of your standards. You can use regression analysis to fit a curve to your data points. OriginLab provides various regression models such as linear, polynomial, exponential, etc., which you can choose based on your data. Determine the LOD: The LOD is typically defined as the concentration at which the signal-to-noise ratio (S/N) is above a certain threshold (commonly 3:1 or 2:1). To calculate the LOD, you need to estimate the noise level of your data. You can select a region of the baseline or noise in your data and determine its standard deviation (SD) or root mean square (RMS) value. a. Select a region of the baseline or noise in your calibration curve. b. Calculate the SD or RMS value of the selected region. c. Determine the LOD using the formula: LOD = (SD or RMS of noise) × (S/N threshold). Determine the LOQ: The LOQ is typically defined as the concentration at which the S/N is higher than a certain threshold (commonly 10:1 or 3:1). To calculate the LOQ, you can follow similar steps as for LOD: a. Select a region of the baseline or noise in your calibration curve. b. Calculate the SD or RMS value of the selected region. c. Determine the LOQ using the formula: LOQ = (SD or RMS of noise) × (S/N threshold). OriginLab provides various analysis tools to calculate the regression parameters, determine the noise level, and perform the calculations mentioned above. You can refer to the OriginLab documentation or help resources specific to your version of the software for detailed instructions on using these tools and functions. Thanks

Sir how we find slope ,R² value , standard deviation in orign.....

The following tutorial is explaining about your queries. There are even more in the playlist. Thanks ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-QESi2dDRnrw.html

k is a dimensionless shape factor (typically around 0.9). The value of k in the Scherrer equation is not dependent on the type of Bravais lattice. It is a constant that depends on the shape of the crystalline domains and the instrument used. In practice, k is often determined experimentally by measuring the size of well-characterized standard samples with known crystallite sizes. Thanks

Thanks for the appreciation dear. It seems that you have fitting issues with your peak(s). I'll suggest you to watch the videos in the playlist to best fit your peaks. Thanks ru-vid.com/group/PLeWSImvDbplc5W0ru6UNKcq6tEJsYxPmY

If all the weights are equal, then the weighted mean is the same as the arithmetic mean. The facts is, as different peaks represent the same crystallites but their different planar orientations, so, both the averages will give the same result. Thanks

It doesn't matter if we use Angstrom or nanometer, provided the dimensions are accurate. Thanks 😊

@@SAYPhysics thank you sir

You're welcome dear

There's a formula for the Vicker's hardness in which you use the diagonal lengths of the microindentation. I'll try to include it in the tutorial series. Thanks

Dear Anisah, This excel file is for the calculations in this video only. You can select peaks of your choice. There's no restriction on the number. Sometimes, some peaks cause a problem in fitting etc., they may be ignored. Thanks

In the description of the video you can find the Excel file. For a hexagonal structure, you may find structural equations in the literature. Thanks for the appreciation dear.

Thanks for the appreciation dear. Yes, but change in symmetry is reflected in the graph shape. These calculations are for simple symmetry. While, when there will be another symmetry, calculations will slightly modify. Thanks

I have explained that crystallite, grain and particle size are different things. Yes, you can calculate the crystallite size. Thanks

Thanks for the appreciation dear 😊

I can't say anything blindly. You may send the screen recorded video at sayphysics@gmail.com. I'll respond to that. Thanks

It seems there might be a misunderstanding in the way Excel is handling the angle measurement. In trigonometry, the angle is typically measured in radians, not degrees. When you calculate cos(44.95887/2) in Excel, it is interpreting the angle as degrees unless you explicitly specify it to be in radians. To get the correct result, you should convert the angle to radians before calculating the cosine. Here's the correct way to do it: Convert 44.95887 degrees to radians: Angle in radians = 44.95887 * (π / 180) Angle in radians ≈ 0.78539816339 radians Now, calculate the cosine of half the angle: cos(44.95887/2) ≈ cos(0.78539816339) Using a calculator or Excel (making sure the mode is set to radians), you should get: cos(44.95887/2) ≈ 0.924016 (rounded to 6 decimal places) So, the correct value for cos(44.95887/2) is approximately 0.924016, not -0.883138. The negative value you obtained might have been a result of using degrees instead of radians. Thanks

This is the DOI of the article. If you can't download it, let me know at sayphysics@gmail.com. Thanks dx .doi.org/10.1107/s0021889878012844

Thanks for the appreciation. Yes, in amorphous, we don't have long range order, so crystallite or grain size calculations are not possible. You're welcome Wafa....

You're welcome dear

Here are the videos ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-tO_frVLxmsg.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-238yM0OgaH8.html

You're welcome dear

Thanks for the appreciation dear 😊

감사합니다.

This is the doi of the article. If you can't download it, let me know at sayphysics@gmail.com. Thanks dx.doi.org/10.1107/s0021889878012844

The Excel template is provided in the video description where all calculations are clearly mentioned. Thanks

For a single crystal, they're the same only. Thanks

@@SAYPhysics an other question please, when the crystallite size increase ,the grain size also increase? And vice versa, that it's true or not?

Principally, yes. Thanks

@@SAYPhysics thanks sir

Thanks for the appreciation. You're right. We have the value from machine specs in the Angstroms, but you can convert as per your ease.

@@SAYPhysics Thanks man. Keep up the good work.

Sure. Thanks

Thanks for the appreciation dear 😊 Aameen

Thanks 😊

Good suggestion. Noted with thanks 👍

@@SAYPhysics yes sir..thanks...sir please work on it and share yours efforts ....

Sure. Thanks

As per formula, beta should be in rad and cos must be degrees to make the equation dimensionally correct. Thanks

In the video description, I have attached an Excel file in which all these calculations are being done. Please note that Excel calculate the value by default in radian, so to have it in degrees, we take its radian again. Thanks

@@SAYPhysics Thank you very much!

Somehow you're right Oliveira. Let me elaborate what do you mean actually. The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. Now, if all the weights are equal, then the weighted mean is the same as the arithmetic mean. The facts is, as different peaks represent the same crystallites but their different planar orientations, so, both the averages will give the same result. Thanks

Thanks for the appreciation 🙂 dear

Thanks for the appreciation dear 😊

Glad it helped! Thanks 👍

You're welcome dear

In my case, it is not an outlier. However, sample to sample it may not be the case. Thanks

Thanks dear 🙂

It's a diameter of a crystallite not length. Thanks

Thanks for the appreciation dear

One radian = 180/ PI degrees and one degree = PI /180 radians. Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90º = 90 × PI /180 radians = PI /2). Thanks

The statement cannot be generalized. However, depending on the nature of grain (material), it is affected by the calcination/sintering temperatures. Thanks

I didn't get your question what exactly you want to ask. Thanks

At time stamp 05:55 in this video, I have explained how to select a given peak. Thanks

Excel calculate the value in radian by default. So if we take its double radian, we'll get our required value in degrees. Thanks

In the Scherrer equation, the angle is to be in degrees. The value we get form OriginPro is in radians. As we know that Excel by default calculates angle in radians so we apply radian again to eventually get the value in degrees. Thanks

@@SAYPhysics thanks for the explanation

@manashjyotidas3748 you're welcome dear

You're most welcome

Glad you liked it

This is crystallite size only and can't be applied to NPs. How to calculate size of NPs, I'll do another video based on UV-Vis technique for metal NPs..Thanks

You're welcome dear

Okay Sir..I got it now thanks

Great. Thanks

Thanks

In degrees. I have explained it in this and other relevant videos about it, please watch carefully. Thanks

@@SAYPhysics Hi Sir, seems you use radians for cos theta calculation in attached excel file. And when I calculated COS[Radian(44.95887/2)], only then got same value as 0.924016 (as same as 7:28 in video)

Excel by default calculates in rad, so where we need it in degrees, we'll have to take it's double radian. Thanks

Clay mineral XRD is a separate field. You may watch my video tutorial on XRD via the following link. Thanks ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-r1EKRfV4ZRg.html

Thanks for your input dear. I haven't calculated grain size but the crystallite size. I have explained the difference between crystallite and grain size clearly. I'll appreciate to watch the tutorial carefully and thoroughly instead of jumping to a wrong conclusion. Thanks

I’m glad and honoured to know. Thanks Brhane

Thanks dear

You're welcome dear

Thanks for the appreciation dear 😊

In the start of the tutorial while discussing about K, I have provided a reference in which K values are given for different structures. Thanks

You're welcome dear

I rechecked. It's OK. If you mention specifically what is wrong with it, I'll address that. Thanks

I’m using 2018 version. However, OriginLab fitting isn’t version dependent, way of utilisation is. Thanks

Yes, if you know the exact size from other means like TEM etc. Thanks

Here, I have explained microstrain in details. Thanks ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oUwJpGtwOVk.html

Thanks dear