X-ray diffraction is a technique that uses X-rays to determine the atomic and molecular structure of crystals. When X-rays hit a crystal, they cause the atoms to diffract into specific patterns determined by Bragg's law. By analyzing these diffraction patterns, information about the crystal structure such as lattice parameters and spacing between atomic planes can be determined. Common applications of XRD include identifying materials and determining their purity, structure, and properties.

1. X-ray diffraction (XRD)
Dr. M. Sonia Angeline
ASSISTANT PROFESSOR
Kristu Jayanti College

2. INTRODUCTION
 X-ray diffraction (XRD) is a technique used in materials science for determining the atomic and molecular
structure of a material.
 This is done by irradiating a sample of the material with incident X-rays and then measuring the intensities and
scattering angles of the X-rays that are scattered by the material.

3. INTRODUCTION
 A primary use of XRD analysis is the identification of materials based on their diffraction pattern.
 As well as phase identification, XRD also yields information on how the actual structure deviates
from the ideal one, owing to internal stresses and defects.
 X-ray diffraction, a phenomenon in which the atoms of a crystal, by virtue of their uniform
spacing, cause an interference pattern of the waves present in an incident beam of X rays.
 The atomic planes of the crystal act on the X rays in exactly the same manner as does a uniformly
ruled grating on a beam of light.
 X-ray diffraction (XRD) relies on the dual wave/particle nature of X-rays to obtain information
about the structure of crystalline materials.
 A primary use of the technique is the identification and characterization of compounds based on
their diffraction pattern.

4. PRINCIPLE
 Max von Laue, in 1912, discovered that crystalline substances act as three-dimensional diffraction
gratings for X-ray wavelengths similar to the spacing of planes in a crystal lattice.
 X-ray diffraction is now a common technique for the study of crystal structures and atomic spacing.
 X-ray diffraction is based on constructive interference of monochromatic X-rays and a crystalline
sample.
 These X-rays are generated by a cathode ray tube, filtered to produce monochromatic radiation,
collimated to concentrate, and directed toward the sample.
 The interaction of the incident rays with the sample produces constructive interference (and a
diffracted ray) when conditions satisfy Bragg's Law (nλ=2d sin θ).
 This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice
spacing in a crystalline sample.

5. PRINCIPLE
 These diffracted X-rays are then detected, processed and counted.
 By scanning the sample through a range of 2θangles, all possible diffraction
directions of the lattice should be attained due to the random orientation of the
powdered material.
 All diffraction methods are based on generation of X-rays in an X-ray tube.
 These X-rays are directed at the sample, and the diffracted rays are collected.
A key component of all diffraction is the angle between the incident and
diffracted rays.

6. PRINCIPLE
 The dominant effect that occurs when an incident beam of monochromatic X-rays interacts with a target material is
scattering of those X-rays from atoms within the target material.
 In materials with regular structure (i.e. crystalline), the scattered X-rays undergo constructive and destructive
interference.
 This is the process of diffraction. The diffraction of X-rays by crystals is described by Bragg’s Law, n(lambda) = 2d
sin(theta).
 The directions of possible diffractions depend on the size and shape of the unit cell of the material.
 The intensities of the diffracted waves depend on the kind and arrangement of atoms in the crystal structure.
 However, most materials are not single crystals, but are composed of many tiny crystallites in all possible orientations
called a polycrystalline aggregate or powder.
 When a powder with randomly oriented crystallites is placed in an X-ray beam, the beam will see all possible
interatomic planes. If the experimental angle is systematically changed, all possible diffraction peaks from the powder
will be detected.

7. Why XRD?
 Measure the average spacings between layers or rows of atoms
 Determine the orientation of a single crystal or grain
 Find the crystal structure of an unknown material
 Measure the size, shape and internal stress of small crystalline regions

8. INSTRUMENTATION
 X-ray diffractometers consist of three basic elements: an X-ray tube, a sample holder, and an X-ray detector.
 X-rays are generated in a cathode ray tube by heating a filament to produce electrons, accelerating the electrons
toward a target by applying a voltage, and bombarding the target material with electrons.
 When electrons have sufficient energy to dislodge inner shell electrons of the target material, characteristic X-ray
spectra are produced.
 Filtering, by foils or crystal monochrometers, is required to produce monochromatic X-rays needed for diffraction.
 These X-rays are collimated and directed onto the sample.
 As the sample and detector are rotated, the intensity of the reflected X-rays is recorded.
 When the geometry of the incident X-rays impinging the sample satisfies the Bragg Equation, constructive
interference occurs and a peak in intensity occurs.
 A detector records and processes this X-ray signal and converts the signal to a count rate which is then output to a
device such as a printer or computer monitor.

10. How Does it Work?
 Crystals are regular arrays of atoms, whilst X-rays can be considered as waves of electromagnetic radiation.
 Crystal atoms scatter incident X-rays, primarily through interaction with the atoms’ electrons.
 This phenomenon is known as elastic scattering; the electron is known as the scatterer.
 A regular array of scatterers produces a regular array of spherical waves.
 In the majority of directions, these waves cancel each other out through destructive interference, however,
they add constructively in a few specific directions, as determined by Bragg’s law: 2dsinθ = nλ
 Where d is the spacing between diffracting planes, θ{display style theta } is the incident angle, n is an
integer, and λ is the beam wavelength.
 The specific directions appear as spots on the diffraction pattern called reflections. Consequently, X-ray
diffraction patterns result from electromagnetic waves impinging on a regular array of scatterers.
 X-rays are used to produce the diffraction pattern because their wavelength, λ, is often the same order of
magnitude as the spacing, d, between the crystal planes (1-100 angstroms).

11. APPLICATIONS
 Determination of unknown solids is critical to studies in geology, environmental science, material science, engineering and
biology.Other applications include:
 characterization of crystalline materials
 identification of fine-grained minerals such as clays and mixed layer clays that are difficult to determine optically
 determination of unit cell dimensions
 measurement of sample purity
 With specialized techniques, XRD can be used to:determine crystal structures using Rietveld refinement
 determine of modal amounts of minerals (quantitative analysis)
 characterize thin films samples by:
 determining lattice mismatch between film and substrate and to inferring stress and strain
 determining dislocation density and quality of the film by rocking curve measurements
 measuring superlattices in multilayered epitaxial structures
 determining the thickness, roughness and density of the film using glancing incidence X-ray reflectivity measurements

12. XRD Benefits and Applications
 XRD is a non-destructive technique used to [2]:
 Identify crystalline phases and orientation
 Determine structural properties:
- Lattice parameters
- Strain
- Grain size
- Epitaxy- type of crystal growth or material deposition in which new crystalline layers
- Phase composition
- Preferred orientation
 Measure thickness of thin films and multi-layers
 Determine atomic arrangement

13. Crystallography

14. INTRODUCTION
 A crystal consists of a periodic arrangement of the unit cell into a lattice.
 The unit cell can contain a single atom or atoms in a fixed arrangement.
 Crystals consist of planes of atoms that are spaced a distance d apart, but can be resolved into many atomic
planes, each with a different d spacing.
 a,b and c (length) and α, β and γ angles between a,b and c are lattice constants or parameters which can be
determined by XRD.
 Crystallography is the science that examines crystals, which can be found everywhere in nature—from salt to
snowflakes to gemstones.
 Crystallographers use the properties and inner structures of crystals to determine the arrangement of atoms
and generate knowledge that is used by chemists, physicists, biologists, and others.

15. WORKING
 X-ray crystallography (XRC) is the experimental science determining the atomic and molecular structure of a crystal, in
which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions.
 By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional
picture of the density of electrons within the crystal.
 From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical
bonds, their crystallographic disorder, and various other information.
 X-ray crystallography is still the primary method for characterizing the atomic structure of new materials and in
discerning materials that appear similar by other experiments.
 X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical
interactions and processes, or serve as the basis for designing pharmaceuticals against diseases.
 In a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer. The goniometer is used to
position the crystal at selected orientations.

16.  The crystal is illuminated with a finely focused monochromatic beam of X-rays, producing a diffraction pattern of
regularly spaced spots known as reflections.
 The two-dimensional images taken at different orientations are converted into a three-dimensional model of the
density of electrons within the crystal using the mathematical method of Fourier transforms, combined with
chemical data known for the sample.
 Poor resolution (fuzziness) or even errors may result if the crystals are too small, or not uniform enough in their
internal makeup.
 Crystallographers use X-ray, neutron, and electron diffraction techniques to identify and characterize solid
materials.
 They commonly bring in information from other analytical techniques, including X-ray fluorescence, spectroscopic
techniques, microscopic imaging, and computer modeling and visualization to construct detailed models of the
atomic arrangements in solids.

17. APPLICATIONS
 The pharmaceutical and biochemical fields rely extensively on crystallographic studies.
 Proteins and other biological materials (including viruses) may be crystallized to aid in studying their
structures and composition.
 Many important pharmaceuticals are administered in crystalline form, and detailed descriptions of
their crystal structures provide evidence to verify claims in patents.
 This provides valuable information on a material's chemical makeup, polymorphic form, defects or
disorder, and electronic properties.
 It also sheds light on how solids perform under temperature, pressure, and stress conditions.
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