X-Ray Diffraction Characterization

X-ray diffraction (X-RD) technique has been ever adapted to recognize structural properties of materials and to get information like crystal structure/phase, lattice parameters, crystallite size, orientation of single crystals, preferred orientation of polycrystals, defects, strains and so on. The technique has found to be employed to study the thin films, bulk and nanomaterials [50].

Principle of X-Ray Diffraction

According to the Bragg’s law, diffraction occurs when light is scattered by a periodic array with long-range order, producing constructive interference at specific angles. The atoms in a crystal are arranged in a periodic array and thus can diffract light. The wavelength of X- ray is of the order of interatomic distance of the materials. Consequently, the scattering of X-rays from atoms produces a diffraction pattern, which contains information about the atomic arrangement within the crystal. Amorphous materials like glass do not have a periodic array with long-range order, so they do not produce a diffraction pattern [51].

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A constructive interference occurs only for certain ?’s correlating to those (h k l) planes, where the path difference is an integral multiple (n) of wavelength. Based on this, the Bragg’s condition [52] is given by

2dsin? = n?

Where,

? is the wavelength of the incident X-ray,

D is the inter-planar distance,

‘?’ is the scattering angle and

n is an integer-called order of diffraction.

X- ray analysis is classified into two classes, Single crystal X- ray diffraction and powder X-ray diffraction. Powder X-ray diffraction (XRD) is a rapid analytical technique largely used for phase identification of a crystalline material and can provide details of the unit cell dimensions. The material to be analyzed should be finely ground and homogenized to determine average bulk composition. Powder X- ray diffraction is often easier and more convenient than single crystal diffraction since it avoids the synthesis of individual crystals [53]. A diffraction pattern plots intensity against the angle of the detector, 2?.

In the case of nanostructure, X-rays are diffracted by the oriented crystallites at a particular angle to satisfy the Bragg’s condition. By knowing the value of ? and ?, one can calculate the inter-planar spacing. Since most materials have unique diffraction patterns, compounds can be identified by using a database of diffraction patterns. The purity of a sample can also be determined from its diffraction pattern, as well as the composition of any impurities present. A diffraction pattern can also be used to determine and refine the lattice parameters of a crystal structure. The particle size of the powder can also be determined by using the Scherrer formula, which relates the particle size to the peak width. The Scherrer formula is

D = k ? / ? cos?

Where, k = Scherrer’s Constant ? 0.9,

? = Full Width at Half Maximum (FWHM).

Figure 1Principle of X- ray diffraction: http://www.veqter.co.uk/residual-stress-measurement/x-ray-diffraction

The only disadvantage of XRD is its less sensitivity towards low-Z materials, thus usually high-Z materials can be better characterized. In such cases, electron or neutron diffraction is employed to overcome the low intensity of diffracted X-rays[53].

2.7.1.2 Powder X-Ray Diffraction Instrument

X-ray diffractometer consist of three basic elements: an X-ray tube, a sample holder, and X-ray detector.

Figure 2 Powder XRD Instrument: http://www.mse.engr.uconn.edu/mse-undergraduate-labs-receive-x-ray-diffraction-system.php

2.7.1.3 X- ray tube

The X – ray tube, is nothing but the cathode ray tube in which electrons are generated by heating a filament, accelerated -towards the target by applying high voltage. The accelerated electrons with sufficient energy, when bombarded on target, dislodge inner shell electrons to generate characteristics X- rays, consisting of the K? and K? components. K? consist of two parts, namely K?1 and K?2. K?1 has slightly shorter wavelength and twice the intensity as K?2. Wavelength of generated X- rays is the function of target material.

Out of copper, ferrous, molybdenum and chromium, Copper(Cu) is the most commonly used target material with wavelength equal to 1.5418 Angstrom. The generated X-rays are collimated and filtered through monochromator to bombard onto the sample. The intensity of the reflected X-rays is recorded along different directions by rotating the sample and detector. Constructive interference occurs when the Bragg’s law is satisfied, showing the peaks in the spectrum shown on an output device such as a printer or monitor of dedicated system just like a sample shown in figure 2.6. The arrangement of sample holder and detector is termed as goniometer. The construction of the goniometer is such that, when a sample rotates through an angle ?, the X- ray detector rotates with an angle 2?, with the typical variation of 2? is from 5° to 80° [54]

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