X-ray crystallography
Mr. Jacob Martin
1st year mpharm
Department of pharmacology
Shree devi college of pharmacy, manglore
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introduction
 X-ray crystallography is a method of determining the
arrangement of atoms within a crystal, in which a beam of Xrays
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 threedimensional
picture of the density of electrons within the
crystal.
 Because X-rays have wavelengths similar to the size of atoms,
they are useful to explore within crystals.
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 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.
 By measuring the angles and intensities of these diffracted beams,
a crystallographer can produce a three-dimensional picture of the density
of electrons within the crystal.
 From this electron density, the mean positions of the atoms in the crystal can be
determined, as well as their chemical bonds, their disorder, and various other
information
 X-ray crystallography is related to several other methods for determining atomic
structures. Similar diffraction patterns can be produced by scattering electrons
or neutrons, which are likewise interpreted by Fourier transformation.
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 X-Ray Crystallography uses the uniformity of light
diffraction of crystals to determine the structure of a
molecule or atom.
 Then they use an X-ray beam to “hit” the crystallized
molecule. The electrons surrounding the molecule
diffract as the X-rays hit them. This forms a pattern,
this type of pattern is called the X-ray diffraction pattern
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Procedure
step-1
 The first-and often most difficult-step is to obtain
an adequate crystal of the material under study.
 The crystal should be sufficiently large (typically
larger than 0.1 mm in all dimensions),
 pure in composition and regular in structure, with no
significant internal imperfections such as cracks
or twinning.
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 Researchers crystallize an atom or molecule,
 because the precise position of each atom in a molecule can only be
determined if the molecule is crystallized.
 If the molecule or atom is not in a crystallized form, the X-rays will
diffract unpredictably and the data retrieved will be too difficult if not
impossible to understand.
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Step -2
 crystal is placed in an intense beam of X-rays,
 usually of a single wavelength (monochromatic X-rays), producing the regular
pattern of reflections.
 As the crystal is gradually rotated, previous reflections disappear and new ones
appear;
 the intensity of every spot is recorded at every orientation of the crystal.
 Multiple data sets may have to be collected, with each set covering slightly more
than half a full rotation of the crystal and typically containing tens of thousands of
reflections.
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STEP -3
 In the third step, these data are combined computationally
with complementary chemical information to produce and
refine a model of the arrangement of atoms within the crystal.
 The final, refined model of the atomic arrangement-now
called a crystal structure-is usually stored in a public database.
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 After the diffraction pattern is obtained, the data is then processed by a computer
and the structure of the atom or molecule is deduced and visualized
 fast Fourier transform (FFT)
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Production of xray
 The x-rays are 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
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cathode anode
Low tension battery
Cooling system
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 Common device used to produce x-rays is called as Coolidge tube
 This tube is designed by Coolidge
 Made up of glass bulb
 Coolidge tube is connected with two electrodes ,
= cathode (tungsten)-filament
=anode – target metal
 Pressure maintained 10-6 mm mercury
 Cathode connected to low tension battery (heating cathode)
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 Two electro magnetic field plates E1 & 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
 Cooling setup to the anode side
 The target metal in 45 degree in path rays
 xrays are produced,
 invisible
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How “X-rays” are created
 Positive voltage (kVp) is applied to anode
 Negative electrons are attracted across the tube to the positive anode.
 Electrons slow down and finally come to rest
 Electron beam is focused from the cathode to the anode target by the focusing
cup
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 The distance between filament and the x-ray tube target is 1 cm.
 Velocity of electron is raised from
zero............half the speed of light
 the speed of light = 299 792 458 m / s
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E- traveling 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
(heat)
and electromagnetic energy in the form of
infrared radiation (also heat) and x-rays.
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X-ray diffraction
 X-rays can be considered waves of electromagnetic radiation
 Atoms scatter X-ray waves, primarily through the atoms' electrons.
 so an X-ray striking an electron produces secondary spherical waves emanating
from the electron. - known as elastic scattering
 A regular array of scatters produces a regular array of spherical waves.
 these waves cancel one another out in most directions through destructive
interference, they add constructively in a few specific directions, determined
by Bragg's law:
2d sin Φ = nπ
where n is a positive integer (order of reflection )and λ is the wavelength of
incident wave
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Bragg Equation
 Bragg 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.
 Bragg considered crystals to be made up of parallel planes of atoms. Incident
waves are reflected specularly 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.
 In mirror like reflection the angle of incidence is equal to the angle of reflection.
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 When the X-rays strike 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 xray diffraction analysis in-phase before
they are reflected and after they reflected.
𝜽 =Incident angle
Λ=Wavelength of X-ray
2 θ =Total Diffracted
Angle
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 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 the
difference between the top and the bottom beams.
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 The length DE is the same as EF, so the total distance
traveled by the bottom wave is expressed by:
 Constructive interference of the radiation from successive
planes occurs when the path difference is an integral
number of wavelenghts. This is the Bragg Law.
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Braggs law
 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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2d sinq =nl
 where, d is the spacing of the planes and n is the order of diffraction.
 Bragg reflection can only occur for wavelength
nl 2d
 This is why we cannot use visible light. No diffraction occurs when the above
condition is not satisfied.
 The diffracted beams (reflections) from any set of lattice planes can only occur at
particular angles predicted by the Bragg law.
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Different x-ray methods
 Laue photograph
 Rotating crystal method
 Powder photograph
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Laue method
 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.
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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.
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 Based on how the film is positioned there are two types in Laue method,
1. Transmission Laue method
2. Back reflection Laue method
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1. Transmission Laue method
 The film is placed in the forward direction (behind the crystal) so that forward
scattered radiation is detected.
 The film is at and perpendicular to the incident beam and the diffracted beams are
partially transmitted through the sample before striking the film.
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 Single crystal
 Continuous spectrum of x-rays
 Symmetry of the crystal; orientation
 Several wavelengths can reflect in different orders from the same set of planes
 with the different order reflections superimposed on the same spot in
the film.
This makes crystal structure determination by spot intensity difficult
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2. Back reflection Laue 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.
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 the back reflected rays are used to form the image.
 The incident beam passes through a hole in the film and falls on the crystal.
 Zone axis represents the common direction for a set of planes, the direction is said
to lie in all the planes belonging to that zone axis.
 Laue reflections from a single crystal lie on the surface of a cone whose axis is the
zone axis.
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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, sets 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.
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 The crystal is rotated about its axes and as it rotates different
sets of planes will form the correct Bragg angle for direction
and produce spots.
 The reflected beams are located on the cones with the zone
axis as the axis of the cone.
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 This coincides with the axis of rotation.
 The diffracted spots on the films, when it is unrolled will then
lie of horizontal lines, each corresponding to diffraction
from a set of planes corresponding to a particular
zone axis.
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 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
atoms inside the cell.
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THE POWDER METHOD
 similar to the rotating crystal method
 monochromatic x-rays are used to generate the diffraction pattern.
 This method is useful for samples that are difficult to obtain in single
crystal form
 Here, the angle is varied not by rotating the sample but by having small
crystallites with all possible orientations (all possible θ).
 Usually a powder sample is used, where the individual 'grains' can be
considered as individual crystals .
 Thus, some grains will have 100 orientation, some will have 111
orientation and so on.
 Each of these will diffract at certain Bragg angle so that we can consider a
the diffracted rays as forming a cone, with the crystal as the apex.
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 The film is usually wrapped around the sample, in the form of a cylinder.
 When the cones intersect with the film they leave traces (lines which are actually
arcs of circles) with the central spot corresponding to the zero or 180 position.
 This type of arrangement is called Debye-Scherrer method
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 If a monochromatic x-ray beam is directed at a single crystal, then only one or two
diffracted beams may result.
 the sample consists of some tens of randomly orientated single crystals, they are
seen to lie on the surface of several cones.
 The cones may emerge in all directions, forwards and backwards.
 A sample of some hundreds of crystals (i.e. a powdered sample) show that the
form continuous cones.
 A circle of film is used to record the diffraction pattern as shown. Each cone
intersects the film giving diffraction lines. The lines are seen as arcs on the film.
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Debye Scherrer Camera
 A very small amount of powdered material is sealed into a fine capillary tube made from
glass that does not diffract x-rays.
 The specimen is placed in the Debye Scherrer
camera and is accurately aligned to be in the centre 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 cylindrical camera to
produce a characteristic set of arcs on the film.
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Powder diffraction 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.
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Application of 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
7.Polymer characterization
8. Identification of impurities
9. Particle size analysis …..etc
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