Introduction
This post here will basically focus on the calculation of the size of nanomaterials synthesized by chemical, physical or biological method. There are different methods of calculating the size of nanomaterials.
However, below I will narrow my discussion to determination of the size of nanomaterials from the characterization of nanomaterials using Xray Diffractometer. From the X-ray Diffraction analysis we can determine if a nanomaterial is crystalline or amorphous. This is because we have nanomaterials as amorphous or crystalline sample.
In the analysis of XRD measurements of nanomaterials, Debye Scherrer equation is mostly used to determine the size.
Debye Scherrer Equation:
source
Definition of terms:
D = the average crystallite size (nm),
k = Scherrer constant,
λ = X-ray wavelength,
β= full width at the half maximum of the peak (FWHM). This has to be converted to radians
θ = angle of diffraction.
A standard sample of an XRD result will indicate the following constants, K, and λ. The θ, and β are also obtainable from the results.
From the data in the picture, the range of the XRD is shown, also the λ is recorded in Armstrong.
Also, the peaks obtained from XRD results are indicated in the data file. This makes it easier to get the needed parameters.
The data under the FWHM column are then used to make appropriate calculations.
Below is a typical XRD pattern of a crystalline nanomaterial
[1]
Converting β to radians,
K = 0.9
and λ =1.54060 Armstrong = 0.154060 nm
Note:
I will not be using the exact values of the graph above. I will make assumptions to illustrate how the calculation of the nanomaterial can be used.
In the graph, 2Theta value at 38.5∘, 44.5∘, 65∘, 77.8∘, and 82∘ were indexed to (1 1 1), (2 0 0), (2 1 1), (2 2 0), and (2 2 2)
(hkl) can be obtained from corresponding reference sample by searching the JCPDS file database
2Theta can be obtained from the results of the XRD analysis.
FWHM is also given from the result obtained from the XRD machine.
β is calculated in radian
The result of the calculation is placed in the column shaded as yellow below
The size is determined using this method
Table showing the size of the nanomaterials
Conclusion
This method is useful in determining the size of the nanomaterials using XRD patterns.
Reference
[1]. Adesuji, E. T., Oluwaniyi, O. O., Adegoke, H. I., Moodley, R., Labulo, A. H., Bodede, O. S., & Oseghale, C. O. (2016). Investigation of the larvicidal potential of silver nanoparticles against Culex quinquefasciatus: a case of a ubiquitous weed as a useful bioresource. Journal of Nanomaterials, 2016.
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What's the difference between crystalline and amorphous particles? That's my first question.
Simply, crystalline particles have well ordered microscopic atomic arrangement, and they are always held by intermolecular forces whereas amorphous particles do not have an ordered internal arrangement instead they have disordered or random pattern.
Oh I get it. Like maybe salt for crystalline and water for amorphous? Or do you have to tell at the atomic level?
At the atomic level, we get the right information to classify them as either crystalline or amorphous.
Thanks for sharing this educative post @turpsy my friend
You welcome @adigsbeauty my friend.
I stumbled on this write-up. It is nice and will be helpful except that the topic should have read "the size of crystallite (crystallite size)" as you can't use XRD to determine nanoparticle size.
XRD (Crystallite size)
TEM (Nanoparticle size)
SEM (Grain size).
well done prof. I hope I will be able to follow this trend. so much to do, so little time