Currently I'm characterizing the changes of CNTs treated with acid by using XRD. How does FWHM value explain for changes in crystallinity? What are the significant of increasing/decreasing in FWHM value? (comparing the pattern of XRD of pure-CNT and treated-CNT).
Secondly, what the interplanar spacing dhkl value indicate for?
The FWHM derived from the peaks in xrd pattern is inversely related to the crystallite sizes: large fwhm indicates small particles, small fwhm indicates big particles. Difference in d values suggests different values of lattice parameters.
Dear Siti.
I would like to also add that XRD pattern provides a lot of information of a crystalline sample. It is well known that, if the crystal structure is known, the interplanar spacing, d, of a crystalline sample can be calculated via the Bragg's equation and the peak intensity can be calculated by the intensity theory.
About one hundred years ago, Scherrer (Scherrer, 1918) discussed line profile mediated by the finite size of the powder sample, and the famous Scherrer formula provides the relationship between the observed FWHM and the crystallite size of the crystalline sample. Shortly after Scherrerís work, Laue (Laue, 1926) considered the case of crystallites having the form of a parallelepiped and introduced the general form of the integral breadth, and also used Cauchy and Gaussian functions to model line profiles for the first time.
The intensity of a diffraction line can be obtained by superposing of the amplitude of the wave beams. Assume a sample has N+1 crystalline planes with d as its interplanar spacing, which reflects the incidence X-ray. By setting An as the
reflecting amplitude of the X-ray by the níth plane, which may be the function of the
absorption coefficient μ. Letting δln be the path difference between two close beams, and
exp(iφn) be the reflecting phase factor, where φ is the phase angle, which can be obtained
by δl as
φ＝ 2π δl/λ = 2π 2d( sinθ)/λ, where λ is the wave length.
Crystallinity can be monitored with XRD peak profile. Crystalline samples produce sharp diffraction peaks. When nature of sample changes to amorphous, sharp peaks will disappear with a hump (diffused halo) formation. FWHM will be small for sharp peaks and vice versa. Regarding second question, d-values are like fingerprint of a phase and unique for phase identification. Using d-values one can identify various crystalline phases in a sample.
One should additionally notice that there is a difference between dhkl and d(hkl). Whereas the second one describes the distance between lattice planes (hkl), the first uses Laue indices ! d002 does not mean the distance between (002) planes, since they do not exist at all for primitive lattices because there are no lattice point at. It describes the reciprocal distance to the reciprocal lattice point 002.
Braggs equation is therefore either:
n λ = 2 d(hkl) sinθhkl
or
λ = 2 dhkl sinθhkl
i.e. dhkl = d(hkl) / n
FWHM can also tell you about the strain in the material. If the peaks are broad, there is a chance that your material is strained.
Dear all,
Thank you so much for your answers. It really help me a lot.
Siti Aminah Zulkepli
In this video tutorial, I have explained in detail the d-spacing (interplanar spacing) and how to calculate it from the XRD data using OriginLab software. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks
https://youtu.be/0lz3ZMSdbAM
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