Vasyl. that's always my though... and this is what happens also in Yuriy's publication.... this is why I keep insisting in using full pattern methods where you can see that each measured point (the information) matches the model.. versus Scherrer formula where one number matches one extracted parameter (the "width").
You can measure the size along any direction.. remember that if you impose a certain average shape you can calculate the whole diffraction pattern. The distribution effects can be somehow decoupled but must always be considered as they are the responsible for the smooth shape of the peak.
For the less expert.. the diffraction peaks from a sphere in reciprocal space are the Fourier transform of 1-3L/(2D)+L^3/(2D^3) where L is the variable to be transformed and D is the diameter of the sphere. Try plotting it and you'll see some ripples appearing. They cancel out if you have a distribution. Plus you can test Scherrer formula ;)

PS to add a note to Kai's: believe me when I say that Scherrer equation is one of the most ABUSED equation in the field of X-ray diffraction....

Youssef, this is a rather dangerous recommendation. There are several threads here on RG where the inadequateness of the Scherrer equation is discussed at length. Please search and consult these discussions.
Selvalakshmi, it is honourable that you ask the way you do unlike many others. For simplicity, I'd recommend you to to the same as to Youssef. I am sure you will readily find those threads.

I am giving you some idea about Particle
Particle is minut object with a cetain size and shape. Macroscopically it is very small but microscopically it ontains number of olecules and atoms.
Particle size:It is size of individual Particle, determining absolute particle size is very difficult.
The crystallite size is the average size of a coherent scattering domain (perfect arrangement of unit cells or perfect crystal). The following Scherrer's formulae is using for crystallite size,
Crystallite size (nm) = kl / FWHM (cos q)
The term crystallite have been usually used by physicists and chemists, while grain size is mostly used by metallurgists.
You can easily findout the above by XRD, SEM, AFM , Particle size analyser(Horiba Company Japan)etc.
Better you refer the book Element of X-ray diffraction by W.D. Cullity.

I agree with Nagbasavanna, that the crystallite size may be considered as the average size of coherent scattering domain (CSD). Use of Scherrer's formula does not allow to calculate the correct value of CSD size. This It is shown in our paper which attached.

Youssef, this is a rather dangerous recommendation. There are several threads here on RG where the inadequateness of the Scherrer equation is discussed at length. Please search and consult these discussions.
Selvalakshmi, it is honourable that you ask the way you do unlike many others. For simplicity, I'd recommend you to to the same as to Youssef. I am sure you will readily find those threads.

Here anyone knows what is the relation between particle size and surface area? let me i ask a posed question clearly: for example in 1gram of the powder sample, higher surface area shows higher number of particles or higher size of the particles or lower particle or.....

This is a philosophical question. There is no standard definition for the word "crystallites". Many people incorrectly interpret it and abusing the term "cruystallite size"). Diffraction pattern carries information about the size of the regions of coherent scattering. This is called by some people "crystallites." But crystallites are called amorphous nanoclusters and what is not crystalline at all!.
That is the size and shape of the object does not define its internal (atomic) structure.
In addition, you can measure the size of the coherent domain using XRD only in a certain direction. In addition there is the size distribution. Most people are probably using Scherrer formula for estimating the "average crystallite size" for crystalline material, do not understand what they receive value is not the average size distribution areas.

Vasyl. that's always my though... and this is what happens also in Yuriy's publication.... this is why I keep insisting in using full pattern methods where you can see that each measured point (the information) matches the model.. versus Scherrer formula where one number matches one extracted parameter (the "width").
You can measure the size along any direction.. remember that if you impose a certain average shape you can calculate the whole diffraction pattern. The distribution effects can be somehow decoupled but must always be considered as they are the responsible for the smooth shape of the peak.
For the less expert.. the diffraction peaks from a sphere in reciprocal space are the Fourier transform of 1-3L/(2D)+L^3/(2D^3) where L is the variable to be transformed and D is the diameter of the sphere. Try plotting it and you'll see some ripples appearing. They cancel out if you have a distribution. Plus you can test Scherrer formula ;)

PS to add a note to Kai's: believe me when I say that Scherrer equation is one of the most ABUSED equation in the field of X-ray diffraction....

Yuriy, thin films as you know show extra issues. You can have two very different cases: random grained and columnar film and in most cases a residual stress (with possible gradient). This is why films are still the bad beast! If you have negligible stress or if you have a negligible stress gradient, then things are simpler (as you don't have extra broadening due to the depth-dependent strain effects). In that cases for the "equiaxed" all discussions on the Scherrer equation done so far apply. For the columnar case, the Scherrer result is much closer to the "true one" as usually the size distribution in much narrower and is more closer to the cube approximation.

To determine crystalite size, you can use the scherrer equation,it true, it can gives you an estimation of the crystallite size, if you want to have more accurate, you must use the SEM or TEM

Youssef it seems you are not reading the answers that have been posted here and in other similar threads. Talking about "crystallite size" and increase in accuracy by using SEM (that measure grain size when you are lucky) or TEM (where you measure the cross section of just a few domains) is complete nonsense. My suggestion is to participate to "Accuracy in Powder Diffraction IV" (http://www.nist.gov/mml/apdiv_conference_2013.cfm it is done once every TEN years) and see what people think about accuracy in domain size estimation. I know the speaker ;) so I know what he will say...

some few additonal things here:
- light scattering: this gives you the size of diffusing objects then most often it is related to particle size
- XRD: this gives you the coherent scattering domain size. This can be hkl dependent and can be strongly affected by stacking faults or other defects.
Sherrer is a rough method but can be used in case of non strained nanoparticles.
(Warren-Averbach is an old method that in principle allows you separating size-strain effects). Now, most of rietvled codes include different models/approaches to treat size-strain effects, in which the convolution between instrumental resolution and size-strain effects is done directly (contrarily to sherrer approach).
- TEM : this gives you a picture of coherent domain (by perfomring filtered Back FT). so the size is that of coherent domain.
- SEM: this would give you the particle/grain size in powders or the grain size in ceramics (after thermal teching or fracture). Some methods exist to extrapolate the 2D grain size as obtained from images to 3D images. (interception method)
...

## Popular Answers

Matteo Leoni· Università degli Studi di TrentoYou can measure the size along any direction.. remember that if you impose a certain average shape you can calculate the whole diffraction pattern. The distribution effects can be somehow decoupled but must always be considered as they are the responsible for the smooth shape of the peak.

For the less expert.. the diffraction peaks from a sphere in reciprocal space are the Fourier transform of 1-3L/(2D)+L^3/(2D^3) where L is the variable to be transformed and D is the diameter of the sphere. Try plotting it and you'll see some ripples appearing. They cancel out if you have a distribution. Plus you can test Scherrer formula ;)

PS to add a note to Kai's: believe me when I say that Scherrer equation is one of the most ABUSED equation in the field of X-ray diffraction....

Kai Fauth· University of WuerzburgSelvalakshmi, it is honourable that you ask the way you do unlike many others. For simplicity, I'd recommend you to to the same as to Youssef. I am sure you will readily find those threads.

## All Answers (14)

Nagbasavanna Sharanappa· Gulbarga UniversityParticle is minut object with a cetain size and shape. Macroscopically it is very small but microscopically it ontains number of olecules and atoms.

Particle size:It is size of individual Particle, determining absolute particle size is very difficult.

The crystallite size is the average size of a coherent scattering domain (perfect arrangement of unit cells or perfect crystal). The following Scherrer's formulae is using for crystallite size,

Crystallite size (nm) = kl / FWHM (cos q)

The term crystallite have been usually used by physicists and chemists, while grain size is mostly used by metallurgists.

You can easily findout the above by XRD, SEM, AFM , Particle size analyser(Horiba Company Japan)etc.

Better you refer the book Element of X-ray diffraction by W.D. Cullity.

Selvalakshmi Thangaraj· National Institute of Technology TiruchirappalliGrain size has grain boundary to define the size. similarly does particle size have any boundary?

Yuriy P. Gnatenko· National Academy of Sciences of UkraineAucun Jwane· University of StrasbourgKai Fauth· University of WuerzburgSelvalakshmi, it is honourable that you ask the way you do unlike many others. For simplicity, I'd recommend you to to the same as to Youssef. I am sure you will readily find those threads.

Hamid Farahani· Putra University, MalaysiaVasyl Peter Kladko· National Academy of Sciences of UkraineThat is the size and shape of the object does not define its internal (atomic) structure.

In addition, you can measure the size of the coherent domain using XRD only in a certain direction. In addition there is the size distribution. Most people are probably using Scherrer formula for estimating the "average crystallite size" for crystalline material, do not understand what they receive value is not the average size distribution areas.

Matteo Leoni· Università degli Studi di TrentoYou can measure the size along any direction.. remember that if you impose a certain average shape you can calculate the whole diffraction pattern. The distribution effects can be somehow decoupled but must always be considered as they are the responsible for the smooth shape of the peak.

For the less expert.. the diffraction peaks from a sphere in reciprocal space are the Fourier transform of 1-3L/(2D)+L^3/(2D^3) where L is the variable to be transformed and D is the diameter of the sphere. Try plotting it and you'll see some ripples appearing. They cancel out if you have a distribution. Plus you can test Scherrer formula ;)

PS to add a note to Kai's: believe me when I say that Scherrer equation is one of the most ABUSED equation in the field of X-ray diffraction....

Yuriy P. Gnatenko· National Academy of Sciences of UkraineVasyl Peter Kladko· National Academy of Sciences of UkraineMatteo Leoni· Università degli Studi di TrentoAucun Jwane· University of StrasbourgMatteo Leoni· Università degli Studi di TrentoG. Dezanneau· Ecole Centrale Parissome few additonal things here:

- light scattering: this gives you the size of diffusing objects then most often it is related to particle size

- XRD: this gives you the coherent scattering domain size. This can be hkl dependent and can be strongly affected by stacking faults or other defects.

Sherrer is a rough method but can be used in case of non strained nanoparticles.

(Warren-Averbach is an old method that in principle allows you separating size-strain effects). Now, most of rietvled codes include different models/approaches to treat size-strain effects, in which the convolution between instrumental resolution and size-strain effects is done directly (contrarily to sherrer approach).

- TEM : this gives you a picture of coherent domain (by perfomring filtered Back FT). so the size is that of coherent domain.

- SEM: this would give you the particle/grain size in powders or the grain size in ceramics (after thermal teching or fracture). Some methods exist to extrapolate the 2D grain size as obtained from images to 3D images. (interception method)

...

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