What does fwhm physically mean and what information does it reveal about a material being it smaller or relatively larger (when comparing two samples)? Thanks and kind regards
Simply speaking, from the FWHM of the XRD peaks using the Scherrer formula, the crystal size can be estimated.
The Scherrer equation is written as:
τ = kλ/βhklcosθ
where,
- τ be the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size;
- k be a dimension-less number, often called the shape factor, with a value close to unity. Generally its value is taken as 0.9;
- λ be the wavelength of the X-ray used;
- and βhkl be the full width at half the maximum intensity (FWHM) for a particular x-ray diffraction peak, after subtracting the instrumental line broadening, in radians. This quantity is also sometimes denoted as Δ(2θ);
- θ be the Bragg's angle.
(From Wikipedia)
Moreover, the lattice strain can also be calculated from the XRD FWHM using the Williamson–Hall (W-H) method, where the microstrain ε = βhkl/4tanθ
(Karmakar et al., ChemElectroChem 2018, 5, 1147 – 1152)
So, calculating these for each of your materials, you may compare the results.
Simply speaking, from the FWHM of the XRD peaks using the Scherrer formula, the crystal size can be estimated.
The Scherrer equation is written as:
τ = kλ/βhklcosθ
where,
- τ be the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size;
- k be a dimension-less number, often called the shape factor, with a value close to unity. Generally its value is taken as 0.9;
- λ be the wavelength of the X-ray used;
- and βhkl be the full width at half the maximum intensity (FWHM) for a particular x-ray diffraction peak, after subtracting the instrumental line broadening, in radians. This quantity is also sometimes denoted as Δ(2θ);
- θ be the Bragg's angle.
(From Wikipedia)
Moreover, the lattice strain can also be calculated from the XRD FWHM using the Williamson–Hall (W-H) method, where the microstrain ε = βhkl/4tanθ
(Karmakar et al., ChemElectroChem 2018, 5, 1147 – 1152)
So, calculating these for each of your materials, you may compare the results.
you can distaingush your material in the nano scale or nano scale and you will caluclate the crystallite size of your materials using scherrer equation.
The crystallite size is estimated from FWHM using Lorentz fit of the prefertial peak. The enlargement observed can be attributed to the existence of constraints (disorders)
You can calculate crystallite size and lattice strain from FWHM value for a corresponding XRD peak. By knowing both parameters it will be possible to know and understand nano-crystallinity and detects information of a sample.
You can try this online calculator for calculating crystallite size and lattice strain of a sample. Follow the link:https://mahendrakoppolu.blogspot.com/2013/07/xrd-crystallite-size-calculator.html?m=1
Here is a nice introduction into that subject:
http://prism.mit.edu/xray/oldsite/CrystalSizeAnalysis.pdf
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