X- ray crystallography

Submitted to:
Dr. Prema Kumari . K. B.
Assistant Professor,
Department of Pharmaceutics,
COPS, DSU
Banglore.
Presented by:
Arpitha B M
M Pharm (I SEM),
Department of Pharmaceutics,
COPS, DSU
Banglore .
X- RAY
CRYSTALLOGRAPHY

Contents
• Introduction
• Production of x- ray
• Bragg’s law
• Types of crystal
• Reference
COPS DSU Department of Pharmaceutics 2

Introduction
• X-rays were discovered in
1895 by the German
physicist W. C Roentgen
• He was awarded the
Nobel prize for physics in
1901.
Wilhelm Conrad Röntgen
(1845-1923)

X-RAY PROPERTIES
• X – ray invisible, highly penetrating ER of much
shorter wavelength (higher frequency) than
visible light.
• The wavelength range for x rays is from about 10-8
m to about 10-11 m, the corresponding frequency
range is from about 3 × 1016 Hz to about 3 × 1019
Hz.

GENERATION OF X-RAYS
X- rays are generated by following methods :
• By bombarding target element with a beam of
high energy electrons.
• By irradiating metal target with primary beam
of x- rays.
• By using a radioactive source whose decay
causes emission of x rays.

Absorption of X-rays
• A larger atom is more likely to absorb an X-ray
photon, because larger atoms have greater energy
differences between orbitals -- the energy level more
closely matches the energy of the photon.
• Smaller atoms, where the electron orbitals are
separated by relatively low jumps in energy, are less
likely to absorb X-ray photons.
• The soft tissue in our body is composed of smaller
atoms, and so does not absorb X-ray photons
particularly well. The calcium atoms that make up
our bones are much larger, so they are better at
absorbing X-ray photons.

X-RAY CRYSTALLOGRAPHY
• X-ray crystallography is a technique in crystallography
in which the pattern produced by the diffraction of x-
rays through the closely spaced lattice of atoms in a
crystal is recorded and then analyzed to reveal the
nature of that lattice.
• The wavelength of X-rays is typically 1 A°, comparable
to the interatomic spacing (distance between atoms or
ions) in solids.
• We need X-rays:
eVx
mx
hchc
hE rayx
3
10
103.12
101
 



Crystal Structure Determination
A crystal behaves as a 3-D diffraction grating for x-rays
• The, measurement of the separation of the X-
ray diffraction maxima from a crystal allows us
to determine the size of the unit cell and from
the intensities of diffracted beams one can
obtain information about the arrangement of
atoms within the cell.

Bragg’s law
•English physicists Sir W.H. Bragg
and his son Sir W.L. Bragg
developed a relationship in 1913.
•To explain why the cleavage faces
of crystals appear to reflect X-ray
beams at certain angles of
incidence (theta,θ).
•This observation is an example of
X-ray wave interference.
9
Sir William Henry Bragg (1862-1942),
William Lawrence Bragg (1890-1971)
• In 1915, the father and son were awarded the Nobel
prize for physics "for their services in the analysis of
crystal structure by means of Xrays".

Bragg’s Law Theory
• When a beam of x- ray is incident upon the crystal, it gets
scattered by the electrons constituiting the crystal atoms.
• If the scattered x rays undergo constructive interference, they
are said to be diffracted by the crystal plane.
• Each crystalline matterial scatters the x- rays in a specific
diffraction pattern and thus produce a fingerprint of its
internal structure.
• The diffracted beams are called reflection. X- rays are
difffracted only if Bragg’s law is satisfied which is given by the
equation.
• Sin θ = n λ /2d
Where n= integer θ=angle of incidence
λ= wavelength d= the interplanar distance of the crystal

Bragg’s equation
• When an x ray beam strikes a crystal surface at an
angle θ, electrons constituiting the atoms of crystal
surface to oscillate at the same frequency as that of
incident x ray beam and emits fraction of ER.
• Rest of the rays penetrate to the second layer. Again
in second layer some of the rays gets scattered while
rest of them penetrate to the third layer and so on.
• Every crystalline substance scatters the rays in a
unique diffraction pattern thus producing finger
prints which is characteristic to its atomic and
molecular structure.

• The scattered rays may give constructive and
destructive interference.
• Constructive interference are obtained only if the
pathlength or distance between two planes is
equal to a whole number of wavelength.
Basic requirements for the x- ray diffraction are,
• A) path lengths or difference between layers of
atoms should be same as that of wavelength of
radiation.
• B) scattering centers should be spatially
distributed.

• Bragg’s law governs the condition for diffraction and the
diffracted beam reffered to as reflection, obeys bragg’s
equation
• When an x- ray beam strikes the crystal surface making an
angle θ, fraction of the incident radiation gets scattered owing
to the interaction with atoms located at O,P and R as shown in
the figure below.

• As mentioned above,
pathlengths or distance
between the planes l,m,n
is identical and
represented as ‘d’.
• When an x- ray beam
strikes the top crystal
plane at O and the x-ray
strikes the second crystal
plane at P, pathlength
between the parallel x rays
is equal to AP+PC .

• But for constructive interference,
AP + PC = n λ --------(1)
When n= integer
λ = wavelength of scattered radiation

• Now consider the two
triangle OAP &OCP
shown in the figure. From
the two triangles
ΔAOP=ΔCOP
ΔOAP=ΔOCP=90⁰
• According to ASA( angle
side angle) rule, ΔOAP
are similar because two
angles and one of their
sides are equal

• Therefore ΔOAP= ΔOCP
• Since side AP=PC substituting AP=PC in eq 1 we
get,
• PC+ PC= n λ
2PC= n λ
PC= n λ /2-------(3)
• Now consider the Δ OPC
In ΔOPC, Sinθ= PC/OP
PC=OP Sinθ
PC= d Sinθ (distance between two
parallel lines l and m is d)

Therefore PC=d Sinθ
But from eq 3 PC= n λ /2-----(4)
Therefore by substituting eq 3 in eq 4
n λ /2= dSinθ----Bragg’s equation
By rearranging , we get
Sinθ= n λ /2d (to get constructive interference)

COPS DSU
Department of Pharmaceutics
19
Constructive & Destructive Waves
• Constructive interference is the
result of synchronized light
waves that add together to
increase the light intensity.
• Destructive İnterference .
results when two out-of-phase
light waves cancel each other out,
resulting in darkness.
19

Reference
• Textbook of pharmacetical analysis vol 2
• Instrumental methods of chemical analsis, Dr.
G. R. Chatwal and Sham Anand

X- ray crystallography

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