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X Ray Diffraction (XRD)
X-ray diffraction is a method of characterization of nano-crystals. The spacing in diffraction grating is equivalent to the wavelength of an X-ray. Since this spacing and wavelength are equivalent, an X-ray is used for diffraction. Basically, X-ray is used as a source of radiation.
The main theory behind XRD is-
X ray is applied on crystals. This X ray has both electric and magnetic field. The electrons of atoms interact with the electric field of the radiation. Since the wavelength of X ray is similar to the inter-atomic distance, the electrons of the atom get energy from the radiation. Now these electrons oscillate in EM field and it behaves like secondary source of EM radiation.
This radiation which is coming from the secondary source has the same frequency as the X-ray frequency. So the atoms in crystals work as a coherent source and this emission goes in all directions. This radiation causes constructive or destructive interference.
Measuring the Interlayer Distance -
To measure the distance between the atomic layers, we use Bragg’s Law nλ= 2d sinθ where n is an integer, λ is the wavelength of X-ray and θ is the angle of incidence. Now to get the diffraction pattern, we have to see whether there is constructive interference of reflected X rays or not. In this case, we are considering d as the spacing between planes. An intense reflected X-ray can be produced if the reflected beams satisfy the conditions for constructive interference. Since constructive interference is happening here, the path difference has to be an integer multiple of the used wavelength.
Diffraction is caused by different planes. The diffraction pattern helps to know about the atomic arrangement in the crystal.
A single crystal produces a spot pattern on the detector. On the other hand, powdered samples are analyzed from the plot of the intensity of the scattered X-ray & different angles of a sample. The intensity is proportional to the square of the structure factor.
Intensity (Ihkl) |Fhkl|2 where Fhkl = is the structure factor. The plane normal [hkl] must be parallel to the diffraction vector ‘s’. The ‘s’ vector bisects the angle between the incident and diffracted beam.
For XRPD XRD, we use 2θ angle as this is the angle between incident beam and the detector.
XRD method is applicable to determine-
1. As the diffraction pattern for every phase is unique, even samples with the same chemical composition may have different phases. Phase combination determination is very significant for a sample. Using position and relative intensity, the samples are compared with experimental and reference data.
2. Unit lattice parameter and Bravais lattice symmetry can be determined by the XRD method. Accurately measuring the peak position over a long 2θ range, the lattice parameters can be determined. Using this property, the impact of doping, alloying, temperature, and pressure on lattice parameters can be observed.
3. Epitaxy: The orientations of crystallites can affect the diffraction peak intensities. Using pole figures we can measure the tilt and rotation of peaks.
4. Crystallite size:
The crystallites which are smaller than 120 nm, broaden the diffraction peak. By using Scherrer’s equation we can determine the average size of nanoparticles. From the calibration curve of instruments, we can observe the contribution of peak width.
5. Microstrain.
The microstrain is the root mean square of the variations in the lattice parameters across the sample. The microstrain depends on non-uniform rapid distortion, grain surface relaxation, and dislocation.
The diffracted X rays are detected by photographic films by the Debye-Scherrer camera. In a powdered sample, many crystals are present. These crystals form continuous cones. Each cone makes a diffraction line on the film.
References:
1. https://serc.carleton.edu/research_education/geochemsheets/BraggsLaw.html
2. https://www.researchgate.net/post/Microstrain-what-does-it-mean
3. https://www.iitk.ac.in/che/pdf/resources/XRD-reading-material.pdf
4. Wikipedia.
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