X-ray diffraction (XRD) is a technique used to analyze the atomic and molecular structure of materials. It works by directing a beam of X-rays at a crystalline sample; the X-rays cause the atoms in the sample to diffract according to Bragg's law. This allows researchers to determine the sample's crystal structure, including properties like interplanar spacing. XRD is a common non-destructive characterization method in materials science, as it can identify unknown materials and analyze properties like grain size and stress levels. The document provides details on how XRD works, how X-rays are produced, Bragg's law, and experimental techniques like the Laue, rotating crystal, and powder methods.

1. X-RAY DIFFRACTION (XRD)
TARUN MAHAWER
2018UME4013
ABHISHEK MISHRA
2018UME4019
YASH RAJAIN
2018UME4028
COURSE: MATERIAL PHYSICS (EO033)

2. ❏ X-ray diffraction, or XRD, is a technique for analysing the atomic or molecular structure of materials, i.e.,
it is used for crystal structure and inter-planar spacing determinations.
❏ It is non-destructive, and works most effectively with materials that are wholly, or part, crystalline.
❏ A beam of X-rays directed on a crystalline material may experience diffraction (constructive
interference) as a result of its interaction with a series of parallel atomic planes according to Bragg’s
law.
❏ Much of our understanding regarding the atomic and molecular arrangements in solids has resulted
from X-ray diffraction investigations.
What is XRD?

3. ● Measure the average spacings
between layers of rows of atoms in
a substance
● Determine the orientation of an
individual grain or crystal
● Measure the size, shape and
internal stress of small crystalline
areas
● Identify the crystal structure of an
unknown substance.
X-RAY DIFFRACTION
CAN DO THE
FOLLOWING:

4. SCALE OF
STRUCTURE
ORGANIZATION

5. THE 7
CRYSTAL
SYSTEMS
AND THE
14 BRAVAIS
LATTICES

6. X-RAYS
➔ The discovery of X-rays in 1895 enabled scientists to probe crystalline structure at
the atomic level.
➔ X-rays are a form of electromagnetic radiation that have high energies and short
wavelengths- wavelengths of the order of 1 Å (10-10 m), which is about the same size
as the atomic spacings for solids.
➔ It is well known that, for visible electromagnetic radiation to be diffracted, the
spacing between lines in a two-dimensional grating must be of the same order as
the wavelength range for light (3900-7800 Å). The same principle holds good for
diffraction by the three-dimensional grating of the periodic array of atoms in
crystals. The typical interatomic spacing in crystals is 2-3 Å. So, the wavelength of the
radiation used for crystal diffraction should be in the same range. X-rays have
wavelengths in this range and are, therefore, diffracted by crystals.

7. ➔ When a beam of X-rays impinges on a solid material, a portion of this beam will be
scattered in all directions by the electrons associated with each atom or ion that lies
within the beam’s path. The diffraction pattern obtained is then used to determine its
structure, i.e., how the atoms pack together in the crystalline state and what the
interatomic distance and angles are, etc.
➔ X-ray diffraction is one of the most important characterization tools used in solid state
chemistry and materials science. We can determine the size and the shape of the unit
cell for any compound easily using X-ray diffraction.

8. ● X-rays are commonly produced in X-ray tubes by
accelerating electrons through a potential difference (a
voltage drop) and directing them onto a target material
(i.e. tungsten).
● The incoming electrons release X-rays as they slowdown
in the target. The X-ray photons produced in this manner
range in energy from near zero up to the energy of the
electrons. An incoming electron may also collide with an
atom in the target, kicking out an electron and leaving a
vacancy in one of the atom’s electron shells. Another
electron may fill the vacancy and in so doing release an X-
ray photon of a specific energy (a characteristic X-ray).
● X-rays can also be produced by a synchrotron. A
synchrotron is a device that accelerates electrons in an
evacuated ring, steering them with magnets. Manipulating
the electron beam in a controlled way with the magnets
can produce intense beams of X-rays.
PRODUCTION OF X-RAYS
COMMERCIAL
X-RAY TUBE

9. ➢ A diffractive beam is one that is composed of a large number of scattered
waves that mutually reinforce one another.
➢ Diffraction occurs when a wave encounters a series of regularly spaced
obstacles that
1. are capable of scattering the wave, and
2. have spacings that are comparable in magnitude to the wavelength
➢ Furthermore, diffraction is a consequence of specific phase relationships
established between two or more waves that have been scattered by the
obstacles. The phase relationship between these scattered waves, which will
depend upon the difference in path length is important.
➢ When this path length difference is an integral number of wavelengths, the
waves are said to mutually reinforce (or constructively interfere) with one
another.
DIFFRACTED BEAM

10. 10

11. Bragg’s Law states the following:
“When the X-ray is incident onto a crystal surface, its angle of incidence, θ, will
reflect with the same angle of scattering, θ. And, when the path difference, d is equal
to a whole number, n, of wavelength, constructive interference will occur.”
The concluding ideas from Bragg’s law are:
✽ The diffraction has three parameters i.e, the wavelength of X rays, λ
✽ The crystal orientation defined by the angle, θ
✽ The spacing of the crystal planes, d
The diffraction can be conspired to occur for a given wavelength and set of planes.
For instance, changing the orientation continuously, i.e., changing theta until Bragg’s
Law is satisfied.
BRAGG’S LAW

12. Derivation of Bragg’s Law
Constructive interference occurs if Δ=nλ. This gives the criterion for
constructive interference:
Path difference
Δ= 2x => phase
shift
x

13. In practice, to satisfy Bragg's law for X-ray diffraction, it is necessary to vary either the
angle of inclination of the specimen to the beam or the wavelength of radiation.
The three standard techniques of X-ray crystallography allow for this in the following
ways :
1. in the Laue technique, a single crystal is irradiated by a range of X-ray
wavelengths.
2. in the rotating crystal technique, a single crystal specimen is rotated in a beam of
monochromatic X-rays, and
3. in the powder technique, a polycrystalline powder is kept stationary in a beam of
monochromatic radiation.
EXPERIMENTAL CRYSTAL STRUCTURE
DETERMINATION

15. A single crystal is mounted on a goniometer, which enables the crystal to be rotated through known
angles in two perpendicular planes, and maintained stationary in a beam of X-rays ranging in
wavelength from about 0.2 to 2.0 Å. The crystal selects out and diffracts those values of λ for which
planes exist, of spacing d and glancing angle θ, satisfying the Bragg's equation. A flat photographic film
is placed to receive either the transmitted diffracted beam or the reflected diffracted beams.
LAUE METHOD
The resulting Laue pattern consists of
a series of spots. Sharp well-defined
spots on the film are good evidence
of a perfect crystal structure,
whereas diffuse, broken or extended
spots indicate lattice distortion,
defects or other departures from the
perfect crystal lattice.
The Laue pattern reveals the symmetry of the crystal
structure in the orientation used.

16. In this method, a single crystal is rotated about a fixed axis in a beam of
monochromatic X-rays. The rotation brings different atomic planes into
positions for Bragg reflection. An X-ray beam made nearly monochromatic by
a filter or by reflection from an earlier crystal is used to irradiate a single
crystal specimen mounted on a rotating spindle. It is customary to rotate the
crystal about a direction that is normal to the incident beam, and the crystal is
oriented so that one of its crystallographic axes is parallel to the rotation axis.
The dimensions of the crystal are usually less than 1 mm. A photographic film
is mounted in a cylindrical holder concentric with the rotating spindle.
ROTATING CRYSTAL METHOD
Schematic diagram of X-ray diffraction by the
rotating crystal method
The incident beam is diffracted from a given crystal plane
whenever in course of rotation the value of θ satisfies the
Bragg equation. The diffracted beams from all planes parallel
to the vertical rotation axis will be in the horizontal plane and
those from planes having other orientations will be in layers
above and below the horizontal plane.

17. In this method a finely powdered specimen is placed in a
monochromatic beam, often kα radiation, of X-rays. Just by
chance, some of its microcrystals will be oriented at correct
diffraction angle for a particular set of planes and a diffraction
beam will result. The incident radiation, rendered
monochromatic, strikes the finely powdered specimen or
fine-grained polycrystalline specimen contained in a thin-
walled capillary tube. A photographie film strip is wrapped
around the inside of a cylindrical chamber concentric with the
sample. The rays are diffracted from those microcrystals
which happen to be oriented in space with their particular set
of planes making a Bragg angle θ with the beam; the various
diffracted rays lying along the surface of a cone concentric
with the incident beam.
POWDER METHOD
The geometry of the powder method

18. Advantages & Disadvantages of XRD
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
XRD does, however, have certain limitations:
● To best identify an unknown powder
material, the sample should be
homogeneous.
● Typically XRD analysis requires access
to standard reference data
● Preparation of samples often requires
grinding them down to a powder
● If the crystal sample is non-isometric,
then the indexing of patterns can be
complex when determining unit cells
18

19. THANKS!
Any questions?