B.cosθ= kλ/D+η.sinθ This is Williamson - Hall formula, Read this link:

http://pd.chem.ucl.ac.uk/pdnn/peaks/sizedet.htm

The expression you use for the spacing of the (h,k,l)-planes assumes that your system is cubic. Is it?

Yes my system is Cubic

I guess the first question is "what kind of strain are you trying to measure?"

Dear mm Alsaud,

You want to measure microscopic lengths using XRD. In order to verify your results, you must measure the d without strain and with strain. If there is any resolvable difference, then you can use this method for such measurement and vice verse.

As the strain delta d is much smaller than d, it may not be resolvable.

An alternative way. normally we measure the macroscopic strain delta l by observing the strain of relatively long piece of material whose length is l. Then you can scale delta l to get delta d.

A measuring concept is never measure a small difference between two relatively large quantities. As the error in the measurement will be square root of the sum the square error in the the two quantities and you may not capable to resolve the difference.

Wish you success.

Thank you for all.

i want firstly find d value from d= lambda /(2*sin theta)

But my problem is when i apply this formula on my results i get wrong answer. now how i can find d value like this example.

Dear mm,

If I understood you correctly, in order to calculate d from XRD you have to know lambda of the Xray wave and you must measure 2 theta for certain crystallographic orientation. If you have 100 oriented crystal you can get the lattice constant ,a,. Then you can calculate d and verify it also as given in the table provided that your crystal is cubic.

Wish you success.

Thank you for help me.

Please look at the application in the previous example

lambda is 1.5406 (A) ,2 theta is 33.040 that mean theta is 16.52 (degree) and lattice constant (a) is unkown (crystal is cubic).

Now d= [1.5406/(2*sin(16.52))] =2.7089

This number 2.7089 is wrong is supposed that be 2.7088, and i can't get this number(2.7088).

Dear mm,

If you calculate the error between the two answers E,you find it 0.0001 which makes a relative error Er=0.0001/2.7089=3.6916 x 10^ mince 5 which is a very very small error.

However, it may be caused by the error in calculating the sinusoidal function. To calculate the sinusoidal function by a calculator, one must calculate an infinite series.

Practically one can not calculate the infinite number of terms, rather the calculations are stopped when the terms are smaller than certain error determined by the precision of the computer. Here i assumed that lambda and are the same. Then the error comes from the approximation in the calculations and the error due to finite length representations in the computer.

I raised the error in the numbers in my first comment and it is still valid. Even, this example supports my previous conclusions.

best wishes.

hello dear

for this porpose you can use an special formula Williamson-hall

you can calculate strain of your material

B.cosθ= kλ/D+η.sinθ This is Williamson - Hall formula, Read this link:

http://pd.chem.ucl.ac.uk/pdnn/peaks/sizedet.htm

The value of η is the strain in the crystallites, the value of D represents the size of the crystallites. The constant k is typically close to unity and ranges from 0.8 to 1.39. B width of a diffraction peak

I can recomment to check and perform the X-ray course which is available under the link provided by Amir Zelati (http://pd.chem.ucl.ac.uk/pdnn/pdindex.htm#pubs)

Very useful material to get a good overview and the "how to do"s! Good success, Dirk

Dear Dr. Maryam Al saud 

Peace be upon you,

These research works may help you in your study.

https://www.researchgate.net/publication/277952808_Final_-_Microstructure_and_crystal_imperfections_of_nanosized_CdSxSe1-x_thermally_evaporated_thin_films_-_final_form?ev=prf_pub

https://www.researchgate.net/publication/277010463_Crystal_imperfections_and_Mott_parameters_of_sprayed_nanostructure_IrO2_thin_films?ev=prf_pub

https://www.researchgate.net/publication/300093556_Microstructural_characterization_of_Al-Mg_alloys_by_X-ray_diffraction_line_profile_analysis_------_IJAR-4360_--_9-4-2016?ev=prf_pub

Data Final - Microstructure and crystal imperfections of nanosize...

Article Crystal imperfections and Mott parameters of sprayed nanostr...

Data Microstructural characterization of Al-Mg alloys by X-ray di...

Dear Dr. Amir Zelati,

Sometimes we get negative slope in W-H plot of XRD data. So, what does it mean by a negative slope, i.e., a negative microstrain?

Thank you everyone

The value of strain is calculated using the following equation

ε=βcosθ/4

where β is FWHM in radians and θ is the Bragg angle.

Second you can use the Williamson–Hall plot ( a,UDM, b,USDM and c,UDEDM plots) to calculate the strain.

But was are the dimensions of that strain?

The dimensions of that strain will be similar to β, FWHM in radians and θ, the Bragg angle.

Dear sir,

Please tell me hoe to calculate betaD & BetaS