X-Ray Diffraction
Concepts
Characteristics of electromagnetic waves
X-rays and applications
Visible images
Generation of X-rays and their energies
Image formation
Crystals
Growing crystals
Theory of X-ray diffraction
Bragg’s Law and its application
Crystal morphology
Solving the crystal structure
Molecular Structure and X-ray Diffraction
• The Structures of proteins and nucleic acids
at the atomic level available today come
from X-ray diffraction studies.
• Therefore it is important to understand;
– How the process works
– What kind of sample is needed
– How microscopy works and
– How do you interpret the resulting data.
Structure at the Atomic Level
• Requirements:
– Growing a crystal
– Collecting the x-ray diffraction
pattern
– Constructing and refining a
structure model to fit the x-ray
diffraction pattern.
Concepts
• X-rays - electromagnetic
radiation with short
wavelengths and high
energy.
– X-rays used in structure
studies have ? of ~1 ? or 0.1
nm.
• Like all other
electromagnetic radiation,
X-rays are absorbed,
scattered and diffracted by
matter.
• Scattering and diffraction is
caused by interaction with
electrons.
Concepts
• Atoms in Gases have little or no
interactions.
• Liquids and solids have significant
interactions.
• Liquid molecules “flow,” while solids
are held “rigid” because of their
restricted movements.
• The incident x-rays will simply be
scattered in all directions by the
electrons of atoms in gases and liquids
because of disorder.
• Crystals have ordered array of atoms and
scattering of x-rays is always in certain
directions only.
• The random scattering in all directions is
negligible.
Gases
Liquids
Solids
Concepts
• X-Ray Diffraction: Scattering of x-rays in a few
specific directions by crystals.
• Diffraction patterns: the positions and
intensities of scattered beams produce a diffraction
pattern.
• Incidence of diffraction: Diffraction occurs only
when the ? of the incident radiation is same as or
smaller than the periodicity of atoms in the
crystals.
– The bond lengths in molecules is about 0.12 nm or 1.2
? and ? of x-rays is about 0.1 nm or 1 ? and therefore
diffraction can occur.
Concepts
• Characteristics of a
electromagnetic wave:
electromagnetic radiation
of any ? has two
properties.
– Amplitude
– Phase
• Lenses can be used to
modulate amplitude and
phases of the waves.
– Modulation possible for
visible light.
– Modulation not possible for
x-rays (lenses not
available)
Phase difference = 0
Phase difference = ?/2
Concepts
• If the ?s and phases of the diffracted x-rays can be
measured, then we can calculate the image of a molecule.
• Detectors of x-rays and other electromagnetic radiation
measure the intensity (square of the amplitude) of the
incident radiation but not phase changes.
• The phase information is measured or derived from other
methods.
• The measured diffraction or intensities is sufficient to
determine the type and size of the unit cell.
• Unit cell: the simplest repeating volume element that
produces the crystal.
• To learn about the unit cell or structure of a molecule the
phase information is needed.
• The phase information may be obtained by crystallizing
the molecules in the presence of heavy metals that do not
change the structure of the unit cell.
Applications of X-Ray Diffraction
• X-ray diffraction provides structures of molecules with
atomic resolution.
– Positions of atoms can be determined to 0.001 ? for small
molecules and 0.1 ? for macromolecules.
– Most difficult part of the project is to obtain crystals that have
enough order to diffract the x-rays.
• Structure determination is important to understand
biological function.
– Binding of oxygen to Hb
– Mutations in genes leading to diseases.
– Computational drug design.
– Cell signaling mechanism during cell division, etc.
• Structure of tRNA lead to the understanding of protein
biosynthesis and deciphering of the genetic code.
Visible Images
• Microscopic objects such as bacteria and viruses
can be seen under the microscope by their
ability to scatter visible light. This can be
accomplished for molecules at their atomic
levels.
• Ability to see an object (small or large) is made
possible by three properties.
– Contrast.
– Sensitivity.
– Resolution.
Visible Images
• Contrast: Dependent on the amount of light
scattered by the object and the amount of light
scattered by the objects around it.
– A white fox in snow is not visible because both fox
and the snow scatter light to the same degree.
– Camouflage in war fare and Chameleon on the trees.
• Sensitivity: Depends on the absolute amount of
light scattered by an object.
– A dark adopted eye can detect a pulse of visible
light containing ~50 photons (other devises can
detect smaller amount of light-higher sensitivity).
Visible Images
• Resolution: A measure of special separation of two
sources.
– Average human eye has a resolution of 1 min (there are 60 min
in a degree). (suppose you write the number “11’ on a wall
(1’s 1mm apart) and stand ~3.5 m away from the wall and view
the numbers. The numbers are difficult to see and difficult to
say whether the number is 11 or fuzzy 1. At this distance the
two 1’s subtend an angle of 1 x 10-3 m/3.5 m and it is
equivalent to 3.5 x 10-4 radians (1 min at the eye resolution).
• Resolution can be enhanced using lenses.
• Resolution achieved by lenses is minimal even with the
perfect lenses (less then the wavelength of the