2. Content
Introduction
Principle
Types Of Crystal
X-ray Diffraction
Bragg’s Law
Interference
Thomson scattering
Instrumentation & limitation
Different X-ray Methods
Application Of X-ray Crystallography
References
3. Introduction
X-ray crystallography is a technique
used for determining the atomic and
molecular structure of a crystal, In
which the crystalline atoms cause a
beam of incident x-rays to diffract into
many specific directions.
X-ray crystallography is a method of
determining the arrangement of
atoms within a crystal.
4. PRINCIPLE:
Beam of x-ray strikes a crystal
The beam of light to spread
into specific directions
From the angles and
intensities of these diffracted
beams
Crystallographer can produce
a three dimensional picture of
the density of electrons within
the crystals.
From this electron density :
The mean positions of the atoms
in the crystal can be determined,
as well as,
Their chemical bonds and
Their disorder.
5.
6. An electromagnetic wave of high energy and very short
wavelength, which is able to pass through many
materials opaque to light. (wavelength is 0.1 to 100
angstrom)
The wavelength of X-ray photos is on the order of the distance
between atomic nuclei in solids (bonds are roughly 1.5-2.5
angstrom). You can think of it like the waves fit nice between the
atoms and fill the crystal.
7. Researchers crystallize an atom or molecule,
because the precise position of each atom in a
molecule can only be determined if the molecules is
crystallized.
If the molecule or atom not in a crystallized form, the
X-rays will diffract unpredictably and the data retrieved
will be too difficult if not impossible to understand.
9. Diffraction is the slight bending of light as it passes around the edge of
an object.
X-ray crystallography uses the uniformity of light diffraction of crystals
to determine the structure of molecule or atom.
Then X-ray beam is used to hit the crystallized molecule.
The electron surrounding the molecule diffract as the X-rays hit them.
This form a pattern that pattern is known as x-ray diffraction.
11. There is a definite relationship between the angle at which a beam
of x-rays must fall on the parallel planes of atoms in a crystal in
order that there be strong reflection, the wavelength of the X-rays
and the distance between the crystal planes.
Bragg Equation : 2d sin θ = nλ
Here,
d – spacing between diffracting planes
Θ- the incident angle
n – any integer
λ – wavelength
Bragg’s law identifies the angles of the incident radiation relative
to the lattice planes for which diffraction peaks occurs.
Bragg derived the condition for constructive interference of the X-
rays scattered from a set of parallel lattice planes.
12. Bragg considered crystals to made up of parallel planes of atoms.
Incident waves are reflected secularly from parallel planes of atoms
in the crystal, with each plane is reflecting only a very small fraction
of the radiation, like a lightly silvered mirror.
When X-ray strikes a layer of a crystal, some of them will be
reflected. we are interested in X-rays that are in-phase with one
another.
X-rays that add together constructively in x-ray diffraction analysis
in-phase before they are reflected and after they reflected.
13. These two X-ray beams travel slightly different distances. The
difference in the distances traveled is related to the distance
between the adjacent layers.
Connecting the two beams with perpendicular lines shows
difference between the top and the bottom beams.
The length DE is the same as EF, so the total distance traveled
by the bottom wave is expressed by:
14. Constructive interference of the radiation from successive planes
occurs when the path difference is an integral number of
wavelength. This is the Bragg Law.
When X-rays are scattered from a crystal lattice, peak 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.
Bragg reflection can only occur for wavelength:
n λ <= 2d
This is why we cannot use visible light.
The diffracted beams from any set of lattice planes can only occur
at particular angles predicted by the Bragg Law.
15. When an incident x-ray beam hits a scatter x-rays are emitted
in all directions. Most of the scattering wave fronts are out of
phase interfere destructively. Some sets of wave fronts are in
phase and interfere constructively.
A crystal is composed of many repeating unit cells in 3-
dimensions, and therefore, acts like a 3-dimensional diffracting
grating. The constructive interference from a diffracting crystal is
observed as a pattern of points on the detector. The relative
positions of these points are related mathematically to the
crystal’s unit cell dimensions.
16. The x-ray scattering is determined by the
density of electrons within the crystal.
Since the energy of an x-ray is much greater
than that of a valence electron, the scattering may
be modeled as Thomson scattering, the interaction
of an electromagnetic ray with a free electron.
The intensity of Thomson scattering for one
particle with mass m and charge q is:
18. Production of X-ray
Discovered by: ROENTGEN in
1895
The x-rays are produced when
fast moving electrons or cathode
rays hit a heavy metal .
Most x-rays have a wavelength
ranging from 0.01 to 10
nanometers.
Common device used to
produce x-rays is called Coolidge
tube (made up of glass)
Coolidge tube is connected
with two electrodes.
Cathode(tungsten)-
filament
Anode- target metal
Pressure maintained 10-6
mmHg
Cathode connected to low
19. Procedure For X-ray Production:
Two electromagnetic field plates E1 and E2 are arranged on either side of
the cathode, which controls the acceleration of cathode rays (electrons)
emitted by filament.
When high voltage (20kv) is produced across the electrode, the cathode
rays are emitted and they hit the target which is made up of
molybdenum etc.
Invisible X-rays are produced at 45 degree in path rays.
The distance between filament and the x-ray tube target is 1 cm.
Velocity of electron is raised from zero to half the speed of light.
20. Electron travelling from cathode to anode:
Projectile electron interacts with the orbital electron of the target
atom.
This interaction results in the conversion of electron kinetic
energy
into thermal energy and electromagnetic energy (in the form of
X-rays and infrared radiation).
21. Collimator:
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 narrow beam that passes
between the gap.
Monochromator:
Monochromator is an optical device
that transmit a mechanically selectable
narrow band of wavelength of light or
other radiation chosen from a wider
range of wavelength available at input.
22. Types of Monochromators :
1. Filter
2. Crystal Monochromator
A. Flat Crystal Monochromator
B. Curved Crystal Monochromator
Filter:
X-ray beam may be partly monochromatized by insertion of a
suitable filter.
A filter is a window of material that absorbs undesirable
radiation but allows the radiation of required wavelength to pass.
Crystal Monochromator:
It is made up of suitable crystalline material positioned in the x-
ray beam so that the angle of reflecting planes satisfied the
Bragg's equation for the required wavelength the beam is split
up into component wavelengths.
Material used- Nacl, Lithium fluoride, Quartz, etc.
23. Detectors :
The x-ray intensities can be measured and recorded either by;
1. Photographic method
2. Counter methods
a. Geiger-Muller tube counter
b. Proportional counter
c. Scintillation detector
d. solid state semi-conductor detector
e. Semiconductor detectors
Both these of methods depends upon ability of x-rays to ionize
matter and differ only in the subsequently fate of electrons
produced by the ionizing process.
24. Photographic Method:
To record the position and intensity of x-ray beam a
plane or cylindrical film is used.
The film after exposing to x-ray is developed
The blackening of the developed film is expressed in
terms of density units D given by:
D=log Io/I
Io – incident intensities
I- transmitted intensities
D- total energy that causes blackening of the film
D is measured by densitometer.
The photographic method is mainly used in diffraction
studies since it reveals the entire diffraction pattern on a
single film.
Disadvantage: time consuming and uses exposure of
several hours.
25. Counter Methods:
a.Geiger-Muller tube counter:
Geiger tube is filled with inert gas like Argon.
Central wire anode is maintained at a positive
potential of 800 to 2500 V.
collision with filling gas
production
of anion pair
X-RAY
Electron
central
anode
Positive
ion-
moves to
outer
electrode
The electron is
accelerated by the potential
gradient and causes the
ionization of large number of
argon atoms, resulting in the
production of avalanche of
electron that are travelling
towards central anode.
26. b.Proportional counter:
Construction is similar to Geiger tube counter.
Proportional counter is filled with heavier gas like
xenon and krypton.
Heavier gas is preferred because it is easily ionized
Operated at a voltage below the Geiger plateau.
The dead time is very short (~ 0.2 micros), it can be
used to count high rates without significant error.
27. c. Scintillation Detector:
In a scintillation detector there is large sodium iodide
crystal activated with a small amount of thallium.
When x-ray is incident upon crystal, the pulses of
visible light are emitted which can be detected by a
photo multiplier tube.
Useful for measuring x-ray of short wavelength
Crystal used in scintillation detectors include sodium
iodide, anthracene, naphthalene and p-terphenol.
28. d. Solid State Semi-conductor Detector:
In this type of detector, the electrons produced by x-ray
beam are promoted into conduction bands and the
current which flows is directly proportional to incident x-
ray energy.
Disadvantage: Semi-conductor device should be
maintained at low temperatures to minimize noise and
prevent deterioration.
e. Semi-conductor Detectors:
When x-rays falls on silicon lithium drifted detector an
electron and a hole (+e).
Pure silicon made up of with thin film of lithium metal
plated on to one end.
Under the influence of voltage electrons moves
positive charge and holes towards negative.
29. Voltage generated is measure of the x-ray intensity
falling on crystal.
Upon arriving at lithium pulse is generated.
Voltage of pulse = q/c
Where ,
q- total charge collected on electrode
c- detector capacity.
31. Laue method
The Laue method is mainly
used to determine the
orientation of large single
crystal while radiation is
reflected from or transmitted
through a fixed crystal.
The diffracted beams form
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 d and θ
involved.
Determine the orientation of
single crystals by means of
illuminating the crystal with
32. Transmission Laue Method
In this method, the film is
placed behind the crystal to
record beams which are
transmitted through the crystal.
One side of the cone of Laue
reflections is defined by the
transmitted beam. The film
intersects the cone, with the
diffraction spots generally lying
on an ellipse.
Back Reflection Laue
Method
In this 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 reflections is defined by
the transmitted beam. The film
intersects the cone, with the
diffraction spots generally lying
on hyperbola.
33. Rotating crystal method
In the 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 the crystal rotates, set of lattice planes will at
some point make the correct Bragg angle for the
monochromatic incident beam, and at that point a
diffracted beam will be formed.
34. Lattice constant of the crystal can be determined by
means of this method; for a given wavelength if the
angle θ at which a reflection occurs is known, can be
determined.
The reflected beams are located on the surface of
imaginary cones. By recording the diffraction patterns
(both angles and intensities0 for various crystal
orientations, one can determine the shape and size of
unit cell as well as arrangement of atoms inside the
cell.
35. Photographs can be taken by:
1. Complete rotation method:
• In this method series of complete revolutions occur.
• Each set of a plane in a crystal diffracts four times during
rotation.
• Four diffracted beams are distributed into a rectangular pattern
in the central point of photograph.
2. Oscillation method:
• The crystal is oscillated at an angle of 15 or 20 degree.
• The photographic plate is also moved back and forth with the
crystal.
• The position of the spot on the plate indicates the orientation of
the crystal at which the spot was formed.
36. Powder method (debye-scherrer)
X-ray powder diffraction is a rapid analytical technique primarily
used for phase identification of a crystalline material and can
provide information on unit cell dimensions (lattice parameter).
Types of material to be determined: finely ground,
homogenized and average bulk composition.
37. Procedure of Powder method:
A very small amount of powdered materials is sealed into a fine
capillary tube made from glass that does not diffract x-rays(fine
powder is struck on a hair with a gum).
The specimen is placed in the Debye-Scherrer camera and is
accurately aligned to be in the center of the camera.
X-rays enter the camera through a collimator
The powder diffracts the x-rays in accordance with Braggs law
to produce cones of diffracted beams. These cones intersect a strip
of photographic film located in the cylinder camera to produce a
characteristics set of arcs on the film.
When the film is removed from the camera, flattened and
processed, it shows the diffraction lines and the holes for the
incident and transmitted beams.
38. If the angle of incidence = θ then, the angle of reflection = 2 θ
If the radius = r, the circumference = 2 π r correspond to a
scattering angle of 360 degree.
θ= 360 * 1/ π r
From the above equation the value of θ can be calculated and
substituted in Bragg’s equation to get value of d.
There is no need to rotate the specimen.
Applications:
Useful for determining the complex structures of
metals and alloys.
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.
39. Application f XrD
XRD is a nondestructive technique. Some of the uses of x-ray
diffraction are:
1. Differentiation between crystalline and amorphous materials
2. Determination of the structure of crystalline materials
3. Determination of electron distribution within the atoms, and
throughout the unit cell.
4. Determination of the orientation of single crystals
5. Determination of the texture of polygrained materials
6. Measurement of strain and small grain size, etc.
Miscellaneous application
1. Soil classification based on crystallinity
2. Analysis of industrial dusts
3. Assessment of weathering & degradation of minerals &
polymers
4. Study of corrosion products
5. Examination of tooth enamel & dentine
6. Examination of bone state & tissue state
7. Structure of DNA & RNA
40. Advantages of x-ray:
X-ray is the cheapest, the most convenient and
widely used method.
X-rays are not absorbed very much by air , so the
specimen need not be in an evacuated chamber.
Disadvantage of x-ray:
They do not interact very strongly with lighter
elements
Limitation:
Cannot identify amorphous materials.
No depth profile information.
Minimum spot size of 50 micrometer.
41. 1. HIV: scientists also determined the x-ray crystallographic
structure of HIV protease, a viral enzyme critical in HIV’s
infection. Pharmaceutical scientists hoped that by blocking this
enzyme, they could prevent the virus from spreading in the
body.
2. Arthritis: to create an effective painkiller in case of arthritis
that doesn’t cause ulcers, scientists realized they needed to
develop new medicines that shut down COX-2 but not COX-1.
3. In Dairy Science: this technique has been a widely used
tool for elucidation of compounds present in milk and other
types of information obtained through structure function
relationship. The mineral constituents and lactose are the only
true crystalline constituents in dairy products that can be
analyzed.
4. Analysis Of Milkstones: this technique also applied for
analyzing the chemical composition of milk stones. Since each
chemical compound gives a definite pattern on a photographic
42. 5. Differentiation Of Sugar: since each crystalline
compound gives a definite pattern according to the atomic
arrangement, the identification of the common sugars (sucrose,
dextrose and lactose)is made simple by x-rays.
6. In Case Of New Material: x-ray crystallography is till the chief
method for characterizing the atomic structure of new materials
and in discerning materials that appear similar by other
experiments.
7. X-rays Analysis Of Milk Powder: this technique has
also been used in study of milk powder. Most work has been
confined to determine the effect of different milk powdering
processes upon structural group spacing's within the milk proteins.
