X-RAY
CRYSTALLOGRAPHY
Presented by:-
Akansh Goel
M’Pharm (Sem 1)

CONTENTS
• Introduction
• History
• Principles
• Methods
• Instrumentation
• Applications
• References

Introduction
• X-ray crystallography is a method of determining the
arrangement of atoms within a crystal, in which a
beam of X rays strikes a crystal and causes the beam
of light to spread into many specific directions. From
the angles and intensities of these diffracted beams, a
crystallographer can produce a three dimensional
picture of the density of electrons within the crystal.

Continuation..
• Because X-rays have wavelengths similar to the
size ofatoms , they are useful to explore within
crystals.
• It is a tool used for identifying the atomic and
molecular structure of a crystal.

History
• The English physicist Sir William Henry Bragg
pioneered the determination of crystal structure by X-
ray diffraction methods.
• X-ray crystallography is a complex field that has been
associated with several of science’s major
breakthroughs in the 20th century.

Continuation..
• Using X-ray crystal data, Dr. James Watson and Dr.
Francis Crick were able to determine the helix
structure of DNA in 1953.
• In 1998 Dr. Peter Kim, a scientist, was able to
determine the structure of a key protein responsible
for the HIV infection process.

Principles
• Ray diffraction by crystals is a reflection of the
periodicity of crystal architecture, so that
imperfection in the crystal lattice usually results in
poor diffraction properties.
• A crystal can be described with the aid of grid or
lattice, defined by three axis and angles between
them.

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• Along each axis a point will be repeated as distances
referred to as the unit cell constants, labeled a, b, c.
• Within the crystalline lattice, infinite sets of regularly
spaced planes can be drawn through lattice points.
• These pinlanes can be considered as the source of
diffraction and are designated by a set of three
numbers called the Miller indices(hkl).

DIFFERENT X-RAY METHODS
• X-ray Absorption
• Auger Emission Spectroscopy
• X-ray Flourescence
• X-ray Diffraction

X-RAY ABSORPTION
• The intensity of X-ray is diminished as they pass
through material.
• Wavelength at which a sudden change in absorption
occurs is used to identify an element present in a
sample, and the magnitude of the change determines
the amount of particular element present.
• Used in elemental analysis of barium and iodine in
body.

Fig:- X-ray absorption Fig:-Auger Emission Spectroscopy

AUGER EMISSION SPECTROSCOPY
• The primary X-rays eject electrons from inner energy
levels.
• Just outer level electrons fall into vacant inner levels
by non radiative processes.
• Excess energy ejects electrons from outer levels.

X-ray fluorescence
• The primary X-ray ejects electron from inner energy
levels where the wavelength is equal to absorption
edge.
• But when the wavelength is shorter than absorption
edge it emits secondary X-ray when electrons fall into
inner vacant levels.

Fig:- X-ray fluorescence

X-RAY DIFFRACTION METHODS
• When a beam of monochromatic X radiation is
directed at a crystalline material, one observes
reflection or diffraction of the X-rays at a various
angle with respect to the primary beam.
• The relationship between the X-radiation, angle of
diffraction and distance between each set of atomic
planes of crystal lattice is given by Braggs condition.
nλ= 2dsinθ

METHODS
1. Laue Photographic Method
2. Bragg X-ray Spectrometer Method
3. Rotating Crystal Method
4. Powder Crystal Method

1. LAUE PHOTOGRAPHIC METHOD
• Laue has studied the phenomenon of diffraction of
crystal by two methods:-
o Transmission method
o Back reflection method

Transmission Method
• A is a source of X-rays. This emits beams of
continuous wavelength, known as white radiation
which is obtained from a tungsten target at about
60,000 volts.
• B is a pinhole collimator. When X-rays obtained
from A are allowed to pass through this pinhole
collimator, a fine pencil of x-rays is obtained.

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• This diameter of pinhole is of importance from the
stand point of detail in diffraction pattern. The
smaller is the diameter, the sharper is the interference.
• C is a crystal whose internal structure is to be
investigated. The crystal is set on a holder to adjust its
orientation.

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• D is a fine arranged on a rigid base. This film is
provided with beam stop to prevent direct beam from
causing excessive fogging of the film.
• The x-rays are recorded on photographic plate and
study of diffraction patterns helps to know the
structure of crystal.

Laue transmission
method
Fig:- Laue diagram of
crystal
Fig:-

Back reflection method
• 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.
• This method is similar to Transmission method
however, black-reflection is the only method for the
study of large and thick Specimens.

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• It is very simple and rapid and does not involve the
calculations in solving the patterns obtained.
• The main disadvantage of Laue’s method is that a big
crystal is required and furthermore there is
uncertainty in significance due to unhomogenous
nature of X-rays.

Fig:- Back reflection method

2. Bragg X-ray Spectrometer method
• When x-rays are scattered from a crystal lattice, peaks
of scattered intensity are observed which correspond
to the following conditions:
1. The angle of incidence = angle of scattering.
2. The path length difference is equal to an integer
number of wavelengths.

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• The condition for maximum intensity contained in
Bragg's law above allow us to calculate details about
the crystal structure, or if the crystal structure is
known, to determine the wavelength of the x-rays
incident upon the crystal.

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• The Braggs equation is nλ= 2dsinθ
• where n is a positive integer
• λ is the wavelength of incident wave
• d is the path length
• Θ is the incident angle

3. Rotating Crystal Method
• The rotating crystal method was developed by
Schielbold in 1919.
• The X-ray beam passed to the crystal through
collimating system.
• The rotating shaft hold the crystal and it also rotates.
• This causes the sets of planes coming successively
into their reflecting positions.

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• Each plane will produce a spot on photographic plate.
• One can take photographs
in two ways;
• Complete rotation
method
• Oscillation method
Rotating Crystal
Method
Fig:-

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• Complete rotation method: In this method there
occurs a series of complete revolutions. It is observed
that each set of planes in crystal diffracts four times
during the rotation. These four diffracted beams are
distributed into a rectangular pattern about the central
point of photograph.

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• Oscillation method: In this method, the crystal is
oscillated through an angle of 15º or 20°. The
photographic plate is also moved back and forth with
a same period as that of rotation of the crystal. The
position of spot on the plate indicates the orientation
of crystal at which the spot was formed.

4. Powder Crystal Method
• 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.
• The analyzed material is finely ground and
homogenized.

• A is a source of X-rays which can be made
monochromatic by a filter.
• Allow the X-ray beam to fall on the powdered
specimen P through the slits S1 and S2.
• Fine powder, p, struck on a hair by means of gum is
suspended vertically in the axis of a cylindrical
camera. This enables sharp lines to be obtained on the
photographic film which is surrounding the powder
crystal in the form of a circular arc.

Fig:-Powder Crystal Method

Continuation..
Theory:
When a monochromatic beam of X-rays is allowed to
fall on the powder of a crystal, then following
possibilities may happen:-
• There will be some particles out of the random
orientation of small crystal in the fine powder, which
lie within a given set of lattice planes for reflection to
occur.

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• While another fraction of the grains will have another
set of planes in the correct position for the reflections
to occur and so on.
• Also, reflections are also possible in the different
order for each set.

Instrumentation
• This includes,
1. Production of X-rays
2. Collimator
3. Monochromator
4. Detectors

1. Production of X-ray
• X-rays are produced inside the x-ray tube when high
energy projectile electrons from the filament interact
with the atoms of the anode .
• Conditions necessary:
 Source of electrons
 Target (anode)
 High potential difference
 Cooling facility

Production of X-ray
Fig :- Coolidge X-ray Tube

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• There is a cathode which is a filament of tungsten
metal heated by a battery to emit the thermionic
electrons.
• This beam of electrons moves towards anode and
attain the kinetic energy and 99% of energy is
converted into heat via collision and remaining 0.5-
1% is converted to X-rays via strong coulomb
interactions ( Bremsstrahlung process).

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• Generally the target gets very hot in use.
This problem has been solved to some extent by
cooling the tube with water.

2. Collimator

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• The X-rays produced by the target material are randomly
directed.
• They form a hemisphere with a target at the centre. In
order to get a narrow beam of X-rays, the X-rays
generated by the target material are allowed to pass
through a collimator which consists of two sets of closely
packed metal plates separated by a small gap.
• The collimator absorbs all the X-rays except the narrow
beam that passes between the gaps.

3. Monochromator
They are two types;
A. Filter monochromator:
• A filter is a window of material that absorbs
undesirable radiation but allows the radiation of
required wavelength to pass.
• An interesting example is use of zirconium filter which
is used for molybdenum radiation.

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• When X-rays emitted from molybdenum are allowed
to pass through a Zirconium filter, the Zirconium
strongly absorbs the radiation of molybdenum at
short wavelengths but weakly absorbs the K alpha
lines of molybdenum.
• Thus, zirconium allows the K beta lines to pass.

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B. Crystal monochromator:
• A crystal monochromator is made up of a suitable
crystalline material positioned in the X-ray beam so
that the angle of reflecting planes satisfied Bragg’s
equation for the required wavelength.

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• The beam is split up by the crystalline material into the
component wavelengths in the same way as a prism
splits up the white light into rainbow.
• Such a crystalline substance is called an analysing
crystal.

Continuation..

4. Detectors
A. Photographic methods:
• In order to record the position and intensity of X-ray
beam a plane or cylindrical film is used.
• The film after exposing to X-rays is developed. The
blackening of the developed film is expressed in
terms of density units D given by
D = log I˳/I

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• Where, I˳ and I refer to the incident and transmittance
intensities of X-rays.
• The quantity D is related to the total X-ray energy that
causes the blackening of photographic film.
• The value of D is measured by densitometer.
• This is used in diffraction studies since it reveals the
entire diffraction pattern on single film but this
method is time consuming and uses several hours

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B. Counter methods:
• The Geiger tube is filled with an inert gas like argon
and the central wire anode is maintained at a positive
potential of 800 to 2500V.
• When an X-ray is entering the Geiger tube, this ray
undergoes collision with the filling gas, resulting in
the production of an ion pair: the electron produced
moves towards the central anode while the positive
ions move towards outer electrode.

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• The electron is accelerated by the potential gradient
and causes the ionisation of large number of argon
atoms, resulting production of an avalanche of
electrons that are travelling towards the central anode.

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Fig:- Gieger Tube

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• The Geiger tube is in expensive and is relatively
trouble free detector. This tube gives the highest
signal for given X-ray intensity.
• The disadvantages are:-
The efficiency of Geiger tube falls rapidly at
wavelength below 1 Aº.

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 As the magnitude of the output pulse does not
depend upon the energy of the X-ray which causes
ionisation, a Geiger tube cannot be used to measure
the energy of ionising radiation.

Application of X-ray Diffraction
• 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.
• Determination of Cis- trans isomerism.

Continuation..
• Differentiation of sugar.
• X-ray analysis of milk powder.

REFERENCES
• Instrumental method of analysis-Willards, 7th edition,
CBS Publishers
• Instrumental method of chemical analysis- Chatwal ,
Himalayan Publishing House