X-RAY DIFFRACTION SYSTEM: Principles of XRD, Bragg Law, Two-dimensional XRD System and Applications of XRD System


An X-ray diffraction (XRD) system is an ideal method for examining samples of metals, polymers, ceramics, semiconductors, thin films, and coatings. It can also be employed for forensic and archaeological analysis. A 2-D diffraction pattern provides abundant information on the atomic arrangement, microstructure, and defects of a solid or liquid material.

Principles of XRD

X-rays are electromagnetic radiations with wavelengths in the range of 0.01–100 Å. When a monochromatic X-ray beam hits a sample, in addition to absorption and other phenomena, it generates scattered X-rays with the same wavelength as the incident beam. This type of scattering is also known as elastic scattering or coherent scattering. The X-rays scattered from a sample are not evenly distributed in space, but are a function of the electron distribution in the sample. The intensities and spatial distributions of the scattered X-rays form a specific diffraction pattern that is uniquely determined by the structure of the sample. The Bragg law, named after the nobel laureate (1914), Lawrence Bragg, brings out the relationship between the diffraction pattern and the material structure.

Bragg law (a) Incident rays and refracted rays (b) Diffraction peak at Bragg angle

                                                 Bragg law (a) Incident rays and refracted rays

(b) Diffraction peak at Bragg angle

Bragg Law

The Bragg law describes the relationship between the diffraction pattern and the material structure. If the incident X-rays hit the crystal planes with an incident angle q and reflection angle q, as shown in Fig., the diffraction peak is observed when the Bragg condition is satisfied,

 that is, nλ = 2d sin q.

Here, λ is the wavelength, d is the distance between adjacent crystal planes, q is the Bragg angle at which one observes a diffraction peak, and n is an integer number, called the order of reflection. 

This means that the Bragg condition with the same d-spacing and Bragg angle can be satisfied by various X-ray wavelengths. A typical diffraction peak is a broadened peak displayed by the curved line in Fig. The peak broadening can be due to many effects, including imperfect crystal conditions such as strain and mosaic structure. The curved line gives a peak profile, which is the diffracted intensity distribution in the vicinity of the Bragg angle. The highest point on the curve gives the maximum intensity of the peak, Imax. The width of a peak is typically measured by its full width at half maximum (FWHM). The total diffracted energy of a diffracted beam for a peak can be measured by the area under the curve, which is referred to as integrated intensity.

XRD can provide information on the atomic arrangement in materials with long-range order, short-range order, or no order at all, such as gases, liquids, and amorphous solids. Typical diffraction patterns in solids, liquids, and gases are illustrated in Fig. The diffraction pattern from crystals has many sharp peaks corresponding to various crystal planes, based on the Bragg law. Both amorphous solid and liquid materials do not have the long-range order that a crystal does, but the atomic distance has a narrow distribution due to the atoms being tightly packed. The integrated diffraction profiles can be analysed with existing algorithms and methods. Profiling and matching with existing templates in the database enable the identification of variations in atomic structures due to various defects.

Diffraction patterns in solids, liquids, and gases
Diffraction patterns in solids, liquids, and gases

Two-dimensional XRD System

A typical 2-D XRD system, referred to as XRD2, comprises five basic components, as shown in Fig.

X-ray source 

X-rays are produced with the required radiation energy, focal spot size, and intensity.

X-ray optics 

It conditions the primary X-ray beam to the required wavelength, beam focus size, beam profile, and divergence.

Goniometer and sample stage 

Its function is to establish and manoeuvre the geometric relationship between primary beam, sample, and detector.

Sample alignment and monitor 

This component assists users with positioning the sample at the centre of the instrument and monitors the sample state and position.

Area detector 

It intercepts and records the scattering X-rays from a sample, and saves and displays the diffraction pattern into a 2-D frame.

A variety of X-ray sources, from sealed X-ray tube and rotating anode generator to synchrotron radiation, can be used in XRD. The sealed tube generator and rotating anode generator produce X-ray radiation with the same physical principle. Electrons are emitted from the cathode and are accelerated by high voltages between the cathode and the anode.

The anode is made of the selected metal, so it is also called a metal target. When the electron beam hits the target, X-rays are produced and radiate in all directions. Intensity of the X-ray beam depends on X-ray optics, focal spot brightness, and focal spot profile. Cooling water circulation is provided to the X-ray generator to avoid meltdown of the anode. Depending on the cooling efficiency, only limited power can be applied to an X-ray generator.

The total amount of X-rays generated is proportional to the total power load on the anode.

Two-dimensional X-ray diffraction system
Two-dimensional X-ray diffraction system

The function of X-ray optics in XRD is to condition the X-ray beam into a spectrum of desired purity, intensity, and cross section. The space between the focal spot of the X-ray tube and the sample is referred to as the primary beam path. X-rays travelling through this beam path are scattered by the air with two adverse effects. One is the attenuation of the primary beam intensity. The more harmful effect is that the scattered X-rays travel in all directions and some reach the detector. This air scatter introduces a background noise over the diffraction pattern. As a consequence, weak diffraction patterns may be buried under the background. Therefore, the open incident beam path should be kept as small as possible. To reduce air attenuation and air scatter of the incident beam, a helium-purged beam path or a vacuum beam path is sometimes used in an XRD system.

The function of the goniometer and sample positioning stages is to establish and control the geometric relationship between the incident beam, sample, and detector. The goniometer is also the supporting base to many components such as X-ray sources, X-ray optics, sample environment stages, sample-aligning microscopes, and so on. In a 2-D XRD system, the goniometer should facilitate at least three rotation axes in order to cover all the possible orientations of a sample in the diffractometer.

Sample alignment systems are required to position the sample at the centre of the instrument and to monitor the sample state and position before and during data collection. Either optical microscopes or video microscopes can be used for sample alignment and visualization. The optical microscope allows the user to directly observe the sample as a magnified image, with a crosshair to determine the sample position. Video images can be captured more conveniently with the X-ray safety enclosure.

Applications of XRD System

XRD is the ideal, non-destructive, analytical method for examining samples of many types, such as metals, polymers, ceramics, semiconductors, thin films, and coatings. It is increasingly being employed for drug discovery and processing, forensic analysis, archaeological analysis, and many emerging applications. In the long history of powder XRD, data collection and analysis have been based mainly on 1-D diffraction profiles measured with scanning point detectors or linear position-sensitive detectors. Therefore, almost all X-ray powder diffraction applications, such as phase identification, texture, residual stress, crystallite size, and per cent crystallinity, are developed in accord with the diffraction profiles collected by conventional diffractometers. A 2-D diffraction pattern contains abundant information about the atomic arrangement, microstructure, and defects of a solid or liquid material.

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