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X-Ray Diffraction. Dr. T. Ramlochan March 2010. Public service announcement…. Radiation warning symbol. New IAEA Radiation warning symbol. Radiation is dangerous, so run away!. Crystals.

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X-Ray Diffraction

Dr. T. Ramlochan

March 2010

public service announcement
Public service announcement…

Radiation warning symbol

New IAEA Radiation warning symbol

Radiation is dangerous, so run away!

  • A crystal is a solid material where the constituent atoms are arranged in an orderly repeating pattern extending in all three spatial dimensions



  • Crystals are divided into 7 lattice systems → all crystalline materials must fit in one of these unit cells
    • lengths of edges (a, b, c) of unit cell and the angles (α, β, γ) between them are the lattice parameters
  • The space group of a crystal is a description of the symmetry of the crystal → the unit cells do not just repeat side-by-side
  • Space groups in three dimensions are made from combinations of different symmetry operations (reflection, rotation and improper rotation, the screw axis and glide plane)
    • 230 unique space groups
  • The atoms in a crystal lattice form planes (described by Miller indices) that repeat
x rays and diffraction
X-rays and diffraction
  • X-rays were discovered in 1895 by Röntgen
  • X-rays are electromagnetic radiation with wavelengths in the range of 0.5-2.5 Å
  • As with visible light X-rays will undergo diffraction when they encounter an obstacle
    • If the diffracting obstacle is on the order of the size of the wavelength, the propagating waves will have interference due to different waves having travelled different path lengths

X-ray diffraction image of DNA by Rosalind Franklin (1952)

x rays and diffraction1
X-rays and diffraction
  • Differences in the length of the path travelled lead to differences in phase
  • The introduction of phase differences produces a change in amplitude → summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes
scattering of x rays
Scattering of X-rays
  • Atoms (or their electrons) will scatter X-rays in all directions
  • If atoms are arranged in space in a regular periodic fashion, as a crystal, some of the scattered X-rays will undergo reinforcement in certain directions and cancellation in other directions producing diffracted beams
  • Diffraction is essentially reinforced scattering
bragg s law
Bragg’s Law
  • For a particular condition of scattering where the angle (θ) of the incident beam and the ‘reflected’ X-rays are the same, the scattered X-rays will be completely in phase and undergo reinforcement if the path difference is equal to a whole number of n wavelengths, such that

nλ = 2d sin θ

  • This was first identified by W.L. Bragg and is called Bragg’s Law
bragg s law1
Bragg’s Law
  • For a fixed wavelength (λ) and value of d, there will be an angle theta (θ) where diffraction (complete reinforcement) occurs
  • Diffractogram is a plot of the intensity of the diffracted X-rays vs. 2θ over a range of angles
    • Each peak represents a plane in the crystal lattice with a given ‘d-spacing’
    • Basis for powder diffraction
x ray production
X-ray production
  • X-ray are produced when electrically charged particles (e.g., electrons) with sufficient kinetic energy give up some energy
    • Non-characteristic (continuous) X-rays → electrons decelerated in an electromagnetic field (Bremsstrahlung)
    • Characteristic X-rays → if electrons have high enough kinetic energy can knock electrons out of their shells

→ when an electron moves from an outer shell to an inner one it is ‘excited’ and releases excess energy directly as X-rays with eV/wavelength characteristic of the atom released from

x ray production1
X-ray production
  • X-rays named according to shell being filled and number of shells changed (e.g., K shell filled by L shell (Kα radiation) or M shell (Kß radiation))
    • Each peak represents a transition; more than one peak (‘family of X-rays’); Kα(highest probability) is ~5 times stronger than Kß
  • Kα is a doublet (Kα1 and Kα2) → different spin states
  • Kα1 always about twice the intensity of Kα2
  • For Cu

Kα1 1.540598 Å

Kα2 1.544426 Å

Kα1.541874 Å

Kß1.392250 Å

x ray production2
X-ray production
  • For XRD we want monochromatic X-rays (i.e., X-rays of a single wavelength travelling in the same direction/plane)
    • Can filter the beam by passing through a material with an absorption edge between Kα and Kß wavelengths
    • For Cu radiation use Ni filter → Kß reduced to 1/500; Kα reduced by 1/2
x ray generation
X-ray generation
  • To generate X-rays → a) source of electrons, b) high accelerating voltage, and c) a metal target
  • Use a water-cooled X-ray tube
    • Evacuated glass tube with an anode (Cu target) and cathode maintained at high negative potential (HT transformer)
    • Filament is heated to emit electrons → accelerated towards target
    • X-rays emitted through (X-ray-transparent) beryllium windows
x ray diffractometer
X-ray diffractometer
  • Diffractometer has two parts:
    • Generator → to generate X-rays
    • Goniometer → to scan sample through a range of angles
diffraction optics geometry
Diffraction optics/geometry
  • X-rays diverge from source → pass through Soller slits and divergence slits to define and collimate incident beam
  • Incident beam diffracted by ‘flat’ powder specimen
  • Diffracted beam passed through receiving slits
  • Secondary monochromator reduces background radiation from sample
  • X-rays collected by detector (proportional, Geiger, scintillation, semiconductor)
  • Gives information about peak positions, intensity, and shape