X-ray crystallography is a technique used to determine the three-dimensional atomic structure of crystals. X-rays are diffracted by the crystal and the diffraction pattern is collected on a detector. By analyzing the diffraction pattern using Bragg's law and Fourier transforms, scientists can construct electron density maps and refine protein structures at high resolution. Key aspects of X-ray crystallography include generating X-rays, collecting diffraction data, solving protein structures, and refining models using computational methods. This technique has provided atomic level insights into protein structure and been instrumental in numerous scientific discoveries through applications like determining unknown material structures.

1. Central University of Bihar
BIS 553: protein modelling and simulation
X-Ray Diffraction
Submitted to:- Submitted by:-
Dr. Durg Vijay Singh Shweta Kumari
Roll no- 21
2nd semester
Central University of South
Bihar, Patna
1

2. CONTENT
Sl. no. Topic
1 what is X-ray
2 Espouser of X-ray in medical science
3 Introduction
4 X-ray Diffraction (XRD)
5 Synchrotron
6 Production of X-rays
7 Hard x-ray and soft X-ray
8 Electron density map
9 Principles of X-Ray diffraction
10 Bragg’s Law
11 Constructive and Destructive
Interference of Waves
12 X-ray Data Collection
13 Structure Solution
14 Refinement of the Structure
15 Crystal Systems and Bravais Lattices
16 Applications
17 Strengths of X-ray Diffraction
18 Limitations of X-ray Diffraction
19 Nobel Prize winners associated with
crystallography
20 Reference
2

3. What is X-ray:
X-rays are a form of electromagnetic radiation, as is visible light, but with
some different characteristics. X rays that makes it different from light is that it
carries much more energy and deposits a part of this energy within the body
as it passes through.
Espouser of X-ray in medical science:
3

4. Introduction:
 The discovery of X-rays in 1895 enabled scientists to probe
crystalline structure at the atomic level. X-ray crystallography was the first
method developed to determine protein structure in atomic detail and still
provides the clearest visualization of protein structure currently available.
 This technique can reveal the precise three-dimensional position of
most atoms in a protein molecule.
 Of all forms of radiation, x-rays provide the best resolution
because
according to optical principles, the uncertainty in location an object is
approximately equal to the wavelengths of the radiation used to observe it
(covalent bond distances and the wavelengths of x-rays used in structural
studies are both ~1.5 A)
 The three components in an x-ray crystallographic analysis are-
1.Protein crystal
2.A source of X-ray
3.A detector
Fig: an x-ray source generates a beam, which is diffracted by a crystal. The resulting diffraction pattern is
collected on a detector.
4

5. X-ray Diffraction (XRD):
 The atomic planes of a crystal cause an incident beam of X-rays to
interfere with one another as they leave the crystal. The phenomenon is
called X-ray diffraction.
Fig: Effect of sample thickness on the absorption of X-
rays
5

6.  X-ray diffraction has been in use in two main areas, for the
fingerprint characterization of crystalline materials and the
determination of their structure.
 Once the material has been identified, X-ray crystallography may be used
to determine its structure, i.e. how the atoms pack together in the
crystalline state and what the interatomic distance and angle are etc.
 X-ray diffraction is one of the most important characterization tools used
in solid state chemistry and materials science.
“The spacing of atoms in a crystal lattice can be determined by
measuring the locations and intensities of spots produced on
photographic film by beam of x-ray of given wavelength, after
the beam has been diffracted by the electroms of the atom.”
Fig: x-ray
diffraction
6

7.  X-rays for chemical analysis are commonly obtained by rotating anode
generators or synchrotron facilities. In rotating anode generators, a
rotating metal target is ombarded with high-energy (10–100 keV)
electrons that knock out core electrons.
 An electron in an outer shell fills the hole in the inner shell and emits the
energy difference between the two states as an X-ray photon. Common
targets are copper, molybdenum and chromium, which have strong
distinct X-ray emission at 1.54 A˚ , 0.71 A˚ and 2.29 A˚ , respectively,
that is superimposed on a continuous spectrum known as
Bremsstrahlung.
 In synchrotrons, electrons are accelerated in a ring, thus producing a
continuous spectrum of X-rays. Monochromators are required to select
a
single wavelength.
 As X-rays are diffracted by electrons, the analysis of X-ray diffraction
data sets produces an electron density map of the crystal.
Note:- “Since hydrogen atoms have very little electron density,
they are not usually determined experimentally by this technique.”
 Unfortunately, the detection of light beams is restricted to recording the
intensity of the beam only. Other properties, such as polarisation, can
only be determined with rather complex measurements.
 The phase of the light waves is even systematically lost in the
measurement.
This phenomenon has thus been termed the phase problem owing to the
essential information contained in the phase in diffraction and
microscopy experiments.
 The X-ray diffraction data can be used to calculate the amplitudes of the
three-dimensional Fourier transform of the electron density. Only
together with the phases can the electron density be calculated, in a
process called Fourier synthesis.
7

8. Fig. Instrumentation for X-ray diffraction. The most common X-ray sources are (a), particle storage rings
which produce synchrotron radiation, and (b) rotating anode tubes. The schematics of an X-ray diffractometer
are shown in (c).
 Different methods to overcome the phase problem in X-ray
crystallography have been developed, including:
• molecular replacement, where phases from a structurally similar
molecule are used;
• experimental methods that require incorporation of heavy
element salts (multiple isomorphous replacement);
• experimental methods where methionine has been replaced
by seleno-methionine in proteins (multi-wavelength anomalous
diffraction);
• experimental methods using the anomalous diffraction of
the intrinsic sulphur in proteins (single wavelength
anomalous diffraction);
• direct methods, where a statistical approach is used to determine
phases. This approach is limited to very high resolution data sets and
is the main method for small molecule crystals as these provide
high- quality diffraction with relatively few numbers of reflections.
8

9. Synchrotron:
 A synchrotron is a particle acceleration device which, through the use
of bending magnets, causes a charged particle beam to travel in a
circular pattern.
Fig: Synchrotron Light Source
 Advantages of using synchrotron radiation:
•Detecting the presence and quantity of trace elements
•Providing images that show the structure of materials
•Producing X-rays with 108 more brightness than those from normal
X-ray tube (tiny area of sample)
•Having the right energies to interact with elements in light
atoms such as carbon and oxygen
•Producing X-rays with wavelengths (tunable) about the size of
atom, molecule and chemical bonds
9

10. Production of X-rays:
 X- rays are produced by bombarding a metal target (Cu, Mo usually) with
a beam of electrons emitted from a hot filament (often tungsten). The
incident beam will ionize electrons from the K-shell (1s) of the target atom
and X- rays are emitted as the resultant vacancies are filled by electrons
dropping down from the L (2P) or M (3p) levels. This gives rise to Ka and
Kb lines.
Fig: Broad background is called Bremsstrahlung. Electrons are slowed down and loose energy in the form of X-
rays
 As the atomic number Z of the target element increases, the energy of the
characteristic emission increases and the wavelength decreases.
 Moseley’s Law (c/l)1/2 ∝ Z
Cu Ka = 1.54178 Å
Mo Ka = 0.71069 Å
 We can select a monochromatic beam of one wavelength by:
Crystal monochromator Bragg equation
Filter - use element (Z-1) or (Z-2), i.e. Ni for Copper and Zr for
molybdenum.
10

11. Hard x-ray and soft X-ray:
 Hard X-ray are the highest energy X-ray, while the lower energy X-ray are
reffered to as soft X-rays.
 Hard X-ray penetrated more deeply into a substance than soft X-
ray,they require a denser, more massive material to br detected.
Electron density map:
 The electron density map describes the contents of the unit cells averaged
over the whole crystal and not the contents of a single unit cell (a
distinction that is important where structural disorder is present).
 Three-dimensional maps are often evaluated as parallel two-
dimensional contoured sections at different heights in the unit cell.

Electron density is measured in electrons per cubic ångström, e Å-3.
11

12. Fig: electron density map
12

13. Principles of X-Ray diffraction:
 The interaction of electromagnetic radiation with matter causes the electrons
in the exposed sample to oscillate. The accelerated electrons, in turn, will emit
radiation of the same frequency as the incident radiation, called the secondary
waves.
 The superposition of waves gives rise to the phenomenon of interference.
Depending on the displacement (phase difference) between two waves, their
amplitudes either reinforce or cancel each other out.
The maximum reinforcement is called constructive interference, the
cancelling is called destructive interference.
 The interference gives rise to dark and bright rings, lines or spots, depending
on the geometry of the object causing the diffraction. Diffraction effects
increase as the physical dimension of the diffracting object (aperture)
approaches the wavelength of the radiation. When the aperture has a
periodic structure, for example in a diffraction grating, repetitive layers or
crystal lattices, the features generally become sharper.
 Bragg’s law describes the condition that waves of a certain wavelength will
constructively interfere upon partial reflection between surfaces that produce a
path difference only when that path difference is equal to an integral number
of wavelengths.
 From the constructive interferences, i.e. diffraction spots or rings, one can
determine dimensions in solid materials. Since the distances between atoms
or ions are on the order of 10_10m (1A˚ ), diffraction methods used to
determine structures at the atomic level require radiation in the X-ray region
of the electromagnetic spectrum, or beams of electrons or neutrons with a
similar wavelength. While electrons and neutrons are particles, they also
possess wave properties with the wavelength depending on their energy (de
Broglie hypothesis).
 Accordingly, diffraction can also be observed using electron and neutron
beams. However, each method also has distinct features, including the
penetration depth which increases in the series electrons – X-rays –
neutrons.
13

14.  Diffraction occurs only when Bragg’s Law is satisfied Condition
for constructive
 interference (X-rays 1 & 2) from planes with spacing d.
Bragg’s Law:
“The Braggs were awarded the Nobel Prize inphysics in 1915 for their work in
determiningcrystal structures beginning with NaCl, ZnS and diamond.”
 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, e.g., ions, electrons,
neutrons, and protons, with a wavelength similar to the distance between
the atomic or molecular structures of interest.
14

15. The Bragg Equation:
Fig:Bragg’s law. Interference effects are observable only when radiation interacts with physical dimensions that
are approximately the same size as the wavelength of the radiation. Only diffracted beams that satisfy the Bragg
condition are observable (constructive interference). Diffraction can thus be treated as selective reflection. n is an
integer (‘order’), is the wavelength of the radiation, d is the spacing between the lattice planes and  is the angle
between the incident/reflected beam and the lattice plane.
Reflection of X-rays from two planes of atoms in a solid x = dsinθ
The path difference between two waves: 2 x wavelength = 2dsinθ
Bragg Equation: nλ = 2dsinθ
15

16. Constructive and Destructive Interference
of Waves:
XRD instruments:
16

17. X-ray Data Collection:
The process of collecting a complete set of X-ray diffraction data from a crystal
consists of measuring the intensity of the diffracted beam from each set of planes.
The experimental set up consists
of an X-ray source, a goniometer on which to mount the crystal, and a detector
to measure the intensity of the reflected X-ray beam.
Fig: a schematic sketch of the experimental setup for X-ray diffraction
The outcome of the data collection process is a list of angles, indicating the orien-
tation of the crystal and the detector and the intensity of the reflection from the
ori- ented lattice plane at this position.
Instead of the angles, it is usual to identify the set of planes that give rise to
each diffracted spot by the Miller indices hkl and associate with each value of
hkl the appropriate value of the intensity.
17

18. Structure Solution:
The structure of the molecule is obtained by a Fourier transform of the
observed amplitudes hkl.
Structural Analysis
 X-ray diffraction provides most definitive structural information
 Interatomic distances and bond angles
 Measure the average spacing between layers of row of atom
 Determine the orientation of a single crystal or grain
 Find the crystal structure of unknown materials
 Measure the size, shape and internal stress of small crystalline regions
Fig: The Fourier decomposition of a complex periodic function (thick line) into its sine and cosine
components (thin lines). As more component waves at different frequencies (wave length) are added, the
resulting wave approaches a square wave more and more closely. The furrier decomposition of a square
wave itself would result in components of all possible frequencies.
18

19. Refinement of the Structure:
Once the approximate value of the phases are determined the next step is to refine
them. This usually more conveniently done by performing the Fourier transform
and refining the approximate positions of the atoms obtained by including other
known data such as stereochemistry.
Crystal Systems and Bravais Lattices:
• The seven crystal systems are a method of classifying crystals according to
their atomic lattice or structure.
• The atomic lattice is a three dimensional network of atoms that are arranged in a
symmetrical pattern.
• The shape of the lattice determines not only which crystal system the stone belongs to,
but all of its physical properties and appearance. In some crystal healing ractices the
axial symmetry of a crystal is believed to directly influence its metaphysical properties.
In 3D there are 7 crystal systems:
 Triclinic
 Monoclinic
 Orthorhombic
 Trigonal (Rhombohedral)
 Hexagonal
 Tetragonal
 Cubic
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20. Applications:
 Single-crystal diffraction-
A crystal is a solid in which atoms or molecules are packed in a particular
arrange- ment within the unit cell which is repeated indefinitely along three
principal direc- tions in space. Crystals can be formed by a wide variety of
materials, such as salts, metals, minerals and semiconductors, as well as various
inorganic, organic and bio- logical molecules.
 Fibre diffraction-
Certain biological macromolecules, such as DNA and cytoskeletal components,
cannot be crystallised, but form fibres. In fibres, the axes of the long polymeric
structures are parallel to each other. While this can be an intrinsic property, for
ex- ample in muscle fibres, in some cases the parallel alignment needs to be
induced.
 Powder diffraction-
Powder diffraction is a rapid method to analyse multicomponent mixtures
without the need for extensive sample preparation. Instead of using single
crystals, the solid material is analysed in the form of a powder where, ideally, all
possible crys- talline orientations are equally represented.
20

21. Strengths of X-ray Diffraction:
• Non-destructive – small amount of sample
• Relatively rapid
• Identification of compounds / phases – not just elements
• Quantification of concentration of phases – (sometimes)
• Classically for powders, but solids possible too
• Gives information regarding crystallinity, size/strain, crystallite size, and
orienta- tion
Limitations of X-ray Diffraction:
• Not a “stand-alone” technique – often need chemical data
• Complicated spectra – multiphase materials – identification / quantification
can be difficult.
Nobel Prize winners associated with
crystallography:
• The Nobel Prize is an international award administered by the Nobel
Foundation in Stockholm, Sweden. It has been awarded every year since
1901 for achievements in physics, chemistry, physiology or medicine,
literature and for peace. Over the course of its history, many awards have
been made for scientific achievements directly related to, or involving the
use of, crystallographic methods and techniques.
21

22. Sl. No Scientist name Year of prize Subject Work
1 R. J. Lefkowitz and
B. K. Kobilka
2012 Chemistry For studies of G-
protein- coupled
receptors
2 V. Ramakrishnan, T.
A. Steitz and A. E.
Yonath
2009 Chemistry Studies of the
structure and function
of the ribosome
3 R. D. Kornberg 2006 Chemistry Studies of the
molecular basis of
eukaryotic
transcription
4 P. Agre and R.
MacKinnon
2003 Chemistry Discoveries
concerning channels
in cell membranes
5 P. D. Boyer, J. E.
Walker and J.C.Skou
1997 Chemistry Elucidation of the
enzymatic mechanism
underlying
thesynthesis of
adenosinetriphosphate
(ATP) and discovery
of an ion- transporting
enzyme
6 J. Deisenhofer, R.
Huber and H. Michel
1988 Chemistry For the determination
of the three-
dimensional structure
of a photosynthetic
reaction centre
7 A. Klug 1982 Chemistry Development of
crystallographic
electron microscopy
and discovery of the
structure of
biologically important
nucleic acid- protein
complexes
8 C. B. Anfinsen 1972 Chemistry Folding of protein
chains
9 D. Hodgkin 1964 Chemistry Structure of many
22

23. biochemical
substances
including Vitamin
B12
10 F. Crick, J.
Watson and M.
Wilkins
1962 Physiology
or Medicine
The helical structure
of DNA
11 J. C. Kendrew
and M. Perutz
1962 Chemistry For their studies of the
structures of globular
protein
12 L. C. Pauling 1954 Chemistry For his research into
the nature of the
chemical bond
13 J. B. Sumner 1946 Chemistry For his discovery that
enzymes can be
crystallised
14 C. J. Davisson
and G.
Thompson
1937 Physics Diffraction of
electrons by
crystals
15 P. J. W. Debye 1936 Chemistry For his contributions
to our knowledge of
molecular structure
through
hisinvestigations on
dipole moments and
on thediffraction of X-
rays and
electrons in gases
16 W. C. Röntgen 1901 Physics Discovery of X-rays
23

24. Reference:
• WilsonWalkerPrinciplesandTechniquesofBiochemistryandMolecularBiology
7thEd
• Biophysics Vasantha Pattabhi, N. Gautham
• http://www.chem.sc.edu/faculty/zurloye/xrdtutorial_2013.pdf
• http://www.wileyvch.de/books/sample/3527310525_c01.pdf
• http://web.pdx.edu/~pmoeck/phy381/Topic5aXRD.pdf
• http://www.genesis.net.au/~ajs/projects/medical_physics/xrays/
• http:/ /ww w.iucr .org/peo ple /nob elprize
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