X-ray diffraction (XRD) is a technique used to analyze the crystal structure of materials. It works by firing X-rays at a crystalline sample and measuring the angles and intensities of the diffracted rays. Bragg's law explains why certain crystal structures scatter X-rays at specific angles. There are several methods for XRD including Laue, rotating crystal, and powder methods. XRD is widely used to identify unknown materials and determine structures of molecules, crystals, and thin films. Its applications include material science, mineralogy, and structural biology. Limitations include only being able to detect about 2% of impurities in mixed samples.

1. X-RAYDIFFRACTION
(XRD) Analysis
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2. CONTENTS:
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INTRODUCTION
BRAGG’S LAW
X-RAYDIFFRACTION
METHODS
APPLICATIONS OF XRD
LIMITATIONS OF XRD
REFERENCES

3. INTRODUCTION:
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On 8 Nov, 1895, Wilhelm Conrad Röntgen
(accidentally) discovered an image cast from his
cathode ray generator, projected far beyond the
possible range of the cathode rays (now known as an
electron beam).
In 1912, Max Von Laue, Showed that if a beam of X
rays passed through a crystal, diffraction would take
place and a pattern would be formed on a photographic
plate placed at a right angle to the direction of the rays.
This discovery provided a new method for investigating
the fine structure of matter.

4. BRAGG’S LAW:
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After few months, In 1913, English physicists Sir
William Henry Bragg and his son Sir William
Lawrence Bragg developed a relationship to explain
why the cleavage faces of crystals appear to reflect X-
ray beams at certain angles of incidence (theta, θ).
The variable d is the distance between atomic layers
in a crystal, and the variable lambda λ is the
wavelength of the incident X-ray beam; n is an integer.

5. Although Bragg's law was used to explain the
interference pattern of X-rays scattered by crystals,
diffraction has been developed to study the structure of
all states of matter with any beam.
Bragg carried out a series of experiments, the result of
which he published the Bragg equation –
n λ = 2 d sin θ
where, assume n = 1for the first order reflection
λ = wavelength
θ = X-ray incidence angle
d = distance between atomic layer
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6. X-RAYDIFFRACTION:
X-ray powder diffraction (XRD) is a rapid analytical
technique primarily used for phase identification of a
crystalline material and can provide information on unit
cell dimensions.
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7. To get the diffraction pattern from all parts of crystal,
the primary beam must strike the crystal from many
different directions. This is achieved by rotating the
crystal in the beam during the experiment.
The diffracted spots are recorded either on a film or by
an electronic detector feed the signals directly in a
digitized form into a computer. Several thousand
diffraction spots are collected.
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.
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8. X-RAYDIFFRACTION METHODS:
Generally, there are three methods which is used for
diffraction of X-ray.
I. Laue method
II.Rotating crystal method
III.Powder method
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9. 1)LAUE METHOD:
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The Laue method is mainly used to determine the
orientation of large single crystals while radiation is
reflected from, or transmitted through a fixed crystal.
The diffracted beams from arrays of spots, that lie on
curves on the film.
The Bragg angle is fixed for every set of planes in the
crystal. Each set of planes picks out and diffracts the
particular wavelength from the white radiation that
satisfies the Bragg law for the values of and θ involved.

10. BACK-REFLACTION LAUE METHOD:
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In the back-reflection method, the film is placed between the x-ray
source and the crystal. The beams which are diffracted in a
backward direction are recorded.
One side of the cone of Laue reflection is defined by transmitted
beam. The film intersects the cone, with the diffraction spots
generally lying on an hyperbola.
TRANSMISSION LAUE METHOD:
In the transmission laue method, the film is placed behind the
crystal to recorded beams which are transmitted through the crystal.
One side of the cone of Laue reflection is defined by the transmitted
beam. The film intersects the cone, with the diffraction spots
generally lying on an ellipse.

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12. 2) ROTATING CRYSTAL METHOD:
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In a rotating crystal method, a single crystal is mounted
with an axis normal to a monochromatic X-ray beam. A
cylindrical film is placed around it and the crystal is
rotated about the chosen axis.
As a crystal rotates, sets of lattice will at some point make
the correct Bragg angle for the monochromatic incident
beam, and at that point a diffracted beam will be formed.
Lattice constant of the crystal can be determined by
means of this method; for a given wavelength if the angle
at which are reflection occurs is known, can be
determined.

13. The reflected beams are located on the surface of
imaginary cones. By recording the diffraction patterns(
both angles and intensities) for various crystal
orientations, one can determine the shape and size of
unit cell as well as arrangement of atom inside the cell.
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14. 3) POWDER METHOD:
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If a powdered specimen is used, instead of a single
crystal, then there is the specimen, because there will
always be some crystals at an orientation for which
diffraction is permitted. Here a monochromatic X-ray
beam is incident on a powdered or polycrystalline
sample.
This method is useful for samples that are difficult to
obtaining single crystal form.

15. For every set of crystal planes, by chance, one or more crystals
will be in the correct orientation to give correct Bragg angle to
satisfy Bragg’s equation. Every crystal plane is thus capable of
diffraction. Each diffraction line is made up of a large number
of small spots, each from a separate crystal. Each spot is so
small as to give the appearance of a continuous line.
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16. POWDER DIFFRACTION PATTERN
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17. APPLICATIONS OF X-RAYDIFFRACTION:
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In material sciences, many complicated inorganic and
organometallic systems have been analyzed using single-
crystal and complicated compound methods.
In mineralogy and metallurgy, X-ray diffraction has
been used for determining the arrangement of atoms in
minerals and metals.
X-ray diffraction is used to study the larger molecules,
such as chlorophyll.
XRD is used to solving the structures of various
biological molecules, e.g., penicillin, insulin, cholesterol.

18. Obtain XRD patterns are used to measure d-spacings
of the given compound.
XRD is used to determination of Cis-Trans
isomerism.
X-ray diffraction is used to measure thickness of thin
films and multi-layers.
XRD is used to determine atomic arrangement.
XRD is used to measure the size, shape and internal
stress of small crystalline regions.
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19. LIMITATIONS OF X-RAYDIFFRACTION:
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For mixed material, detection limit is ~2% of sample.
Peak overlay may occur and worsens for high angle
reflections.

20. REFERENCES:
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http://serc.carleton.edu/research_education/geochemsheets/techniques/XRD.h
tml
http://www.authorstream.com/Presentation/venkatkrishna-1155727-x-ray-
diffraction-ppt2003/
http://nptel.ac.in/courses/103103026/13
https://en.wikipedia.org/wiki/XRD
https://www.slideshare.net/NohmanMahmud/xrf-xrd-analysis-
principle?qid=850fd4fd-9a6e-457a-ad1e-20ecc36dc0d6&v=&b=&from_search=1
https://www.slideshare.net/AnuradhaKVerma/xrd-basic?qid=5a442675-29c0-
41c2-944c-d49d7a948fd6&v=&b=&from_search=6