X-ray diffraction (XRD) is a non-destructive analytical technique that examines the physical properties of materials through the diffraction of X-rays by crystalline structures. The technique aids in identifying phase composition, determining crystal size, and analyzing crystal orientation, making it vital in fields like geology, material science, and the pharmaceutical industry. Bragg's law governs the principle of diffraction, allowing for the measurement of interatomic distances and the characterization of unknown materials.

1. X- RAY DIFFRACTION
Presented by - Salwa Maryam
170720882007
Pharm D 3rd year
2022-23

2. What is X-ray diffraction?

3. Diffraction occurs as waves interact with a regular structure whose
repeat distance is about the same as the wavelength. The phenomenon is
common in the natural world, and occurs across a broad range of scales.
For example, light can be diffracted by a grating having scribed lines
spaced on the order of a few thousand angstroms, about the wavelength
of light.
It happens that X-rays have wavelengths on the order of a few
angstroms, the same as typical interatomic distances in crystalline
solids. That means X-rays can be diffracted from minerals which, by
definition, are crystalline and have regularly repeating atomic
structures.

5. X-ray diffraction (XRD) is a versatile non-destructive analytical technique
used to analyze physical properties such as phase composition, crystal
structure and orientation of powder, solid and liquid samples.
Many materials are made up of tiny crystallites. The chemical composition
and structural type of these crystals is called their 'phase'. Materials can be
single phase or multiphase mixtures and may contain crystalline and non-
crystalline components. In an X-ray diffractometer, different crystalline
phases give different diffraction patterns. Phase identification can be
performed by comparing X-ray diffraction patterns obtained from unknown
samples to patterns in reference databases. This process is like matching
fingerprints in a crime scene investigation.

6. Principles of X-ray Diffraction
X-Ray Diffraction is the result of constructive interference between X-rays
and a crystalline sample. The wavelength of the X-rays used is of the same
order of magnitude of the distance between the atoms in a crystalline
lattice. This gives rise to a diffraction pattern that can be analysed in a
number of ways, the most popular being applying the famous Bragg’s Law
(nλ=2d sin θ) which is used in the measurement of crystals and their phases.

7. RECIPROCAL LATTICE CONCEPT
The reciprocal lattice represents the Fourier transform of another lattice.
The direct lattice or real lattice is a periodic function in physical space, such
as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in
the mathematical space of spatial frequencies, known as reciprocal space or
k space, where
{k} refers to the wavevector.
The reciprocal lattice plays a fundamental role in most analytic studies of
periodic structures, particularly in the theory of diffraction. In neutron,
helium and X-ray diffraction, due to the Laue conditions, the momentum
difference between incoming and diffracted X-rays of a crystal is a
reciprocal lattice vector. The diffraction pattern of a crystal can be used to
determine the reciprocal vectors of the lattice. Using this process, one can
infer the atomic arrangement of a crystal.
The Brillouin zone is a Wigner-Seitz cell of the reciprocal lattice.

8. THE FOURIER TRANSFORM (FT)
Is a transform that converts a function into a form that describes the frequencies
present in the original function. The output of the transform is a complex-valued
function of frequency. The term Fourier transform refers to both this complex-
valued function and the mathematical operation. When a distinction needs to be
made the Fourier transform is sometimes called the frequency domain
representation of the original function. The Fourier transform is analogous to
decomposing the sound of a musical chord into terms of the intensity of its
constituent pitches.
Reciprocal lattices for the cubic crystal system are as follows.
•Simple cubic lattice
•Face centred cubic lattice (FCC)
•Body centred cubic lattice ( BCC)
•Simple hexagonal lattice

9. BRAVAIS LATTICE
Bravais Lattice refers to the 14 different 3-dimensional configurations
into which atoms can be arranged in crystals. The smallest group of
symmetrically aligned atoms which can be repeated in an array to make
up the entire crystal is called a unit cell.
There are several ways to describe a lattice. The most fundamental
description is known as the Bravais lattice. In words, a Bravais lattice is
an array of discrete points with an arrangement and orientation that
look exactly the same from any of the discrete points, that is the lattice
points are indistinguishable from one another.
Thus, a Bravais lattice can refer to one of the 14 different types of unit
cells that a crystal structure can be made up of. These lattices are
named after the French physicist Auguste Bravais.

10. There are seven different ways to group the 14 Bravais lattices:
triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral,
hexagonal, and cubic.

11. DIFFRACTION PATTERNS
The light diffracts as it passes through the gaps, and when the two
diffracted waves interact they interfere constructively and destructively.
This leaves regions of high intensity light and other regions where there is
no light at all. If you were to place a screen in front of this, you may see
the following pattern:
The diffracted waves interfere with ones another, leaving the pattern on
the screen on the far right.

12. The areas of light on the diffraction pattern are called maxima, whereas the areas of dark are
called minima. These are labelled from the centre outwards for instance, the central bright
spot is called the central (or zeroth order) maxima, and the ones next to that are called 1st
order maximas, then 2nd order, and so on
Diffraction patterns are obtained by focusing a parallel electron beam on the sample in the
same way as in the imaging mode. A selected area aperture determines the width of the beam
transmitted and the intermediate lens focuses the diffraction pattern onto the screen.
Information in a Diffraction Pattern
• Phase Identification
• Crystal Size
• Crystal Quality
• Texture (to some extent)
• Crystal Structure

21. BRAGG’S LAW
Most methods for determining the atomic structure of crystals are based
of the idea of scattering of radiation. X-rays is one of the types of the
radiation which can be used. The wavelength of the radiation should have a
wavelength comparable to a typical interatomic distance which is in solids
of a few angstroms (10-8 cm). The x-ray wavelength λ can be estimated as
follows

22. X-rays interact with electronic shells of atoms in a solid. Electrons absorb
and re-radiate x-rays which can then be detected. Nuclei are too heavy to
respond. The reflectivity of x-rays is of the order of 10-3-10-5, so that the
penetration in the solid is deep. Therefore, x-rays serve as a bulk probe.
In 1913 Bragg found that crystalline solids have remarkably characteristic
patterns of reflected x-ray radiation. In crystalline materials, for certain
wavelengths and incident directions, intense peaks of scattered radiation
were observed. Bragg accounted for this by regarding a crystal as made out
of parallel planes of atoms, spaced by distance d apart. The conditions for
a sharp peak in the intensity of
the scattered radiation were that:
(1) the x-rays should be specularly reflected by the atoms in one plane;
(2) the reflected rays from the successive planes interfere constructively.

23. Fig shows x-rays which are specularly reflected from adjacent planes. The
path difference between the two x-rays is equal to 2dsinθ. For the x-rays
to interfere constructively this difference must be an integer number of
wavelengths. This leads to the Bragg condition:

24. 2dsinθ = mλ
where lambda is the wavelength,
d is the distance between crystal planes,
theta is the angle of the diffracted wave, and
m is an integer known as the order of the diffracted beam.
Bragg diffraction may be carried out using either electromagnetic radiation
of very short wavelength like X-rays or matter waves like neutrons (and
electrons) whose wavelength is on the order of (or much smaller than) the
atomic spacing. The pattern produced gives information of the separations
of crystallographic planes d, allowing one to deduce the crystal structure.
There are a number of various setups for studying crystal structure using x-
ray diffraction. In mostcases, the wavelength of radiation is fixed, and the
angle is varied to observe diffraction peaks corresponding to reflections
from different crystallographic planes. Using the Bragg law one can then
determine the distance between the planes.

25. The Bragg law is greatly oversimplified
(i) It says nothing about intensity and width of x-ray diffraction
peaks;
(ii) neglects differences in scattering from different atoms;
(iii) neglects distribution of charge around atoms.

27. The main advantages of x-ray diffraction are:
•It is a rapid and powerful technique for identifying unknown minerals and
materials.
•It only requires preparation of a minimal sample for analysis.
•Interpreting the resulting data is relatively straightforward.
•XRD measurement instruments are widely available.

29. APPLICATIONS
•X-ray powder diffraction is most widely used for the identification of
unknown crystalline materials (e.g. minerals, inorganic compounds).
Determination of unknown solids is critical to studies in geology,
environmental science, material science, engineering and biology.
•In the pharmaceutical industry, XRD analysis plays an important role in
the development of new drugs, as it helps to characterize active materials
as well as tests material at different stages of manufacturing so that
quality control is effectively maintained.

30. Thank you.