X-ray diffraction Talián Csaba Gábor University of Pécs, Medical School Department of Biophysics 2012.10.11.
Outline of the lecture X-ray radiation Interference, diffraction Crystal structure X-ray diffraction on crystals Diffractometer Applications
X-ray radiation 1895: discovery of X-ray radiation (1901: Nobel-prize) Wavelength of X-ray: 0,01-10 nm (10-11 -10-8 m) Energy of radiation: 0,1-100 kev High ionization effect Wilhelm Röntgen (1845-1923, GER)
Spectrum of X-ray Continuous spectrum (Bremsstahlung) Discrete spectrum (Characteristic)
Interference Superposition of coherent waves that results in a new wave pattern Constructive Destructive
Diffraction (bending of the light) double slit experiment Wave nature of the light! Thomas Young (1773-1829, ENG)
How is the diffraction pattern produced? d sin Θ = n λ Condition for constructive interference: diffracted rays are in the same phase! If we increase the distance (d) between the slits, then the intensity maximums are getting closer to each other! d sin Θ = d n λ ~ 1 sin Θ
Optical grating 0,1 mm height 3000 slits/mm Diffraction pattern of square shape slits Diffraction pattern of cross shape slits
Why can the crystal be used as a grating? A crystal is built up of a periodic three-dimensional arrangement of atoms, ions, or groups of atoms. c b a Unit cell: smallest repeating geometrical unit Lattice point: atom, ion, molecule
Theoretical foundations of X-ray crystallography in 1912 he recognized, that spacing between planes of atoms in crystal is comparable to the wavelength of x-rays. Crystal as 3D diffraction (optical) grating! Max von Laue (1879-1960, GER) 1914: Nobel-prize in physics CuSO 4
Diffraction pattern is the result of elastic scattering X-ray beams elastically scatter on the electron cloud of the atoms (Thomson scattering). X-ray scattering is determined by the density of electrons around the atoms!
Laue equations Incident X-ray Path difference: s = AB CD AB α = a cos CD = a cosα n 0 Space between atoms 3 dimension: s s Diffracted X-ray sa = a (cosαn cosα0) = b (cos βn cos β0 = l λ = c (cosγ n cosγ 0 = m λ b ) c ) = Condition for constructive interference: sa = a (cosαn cosα0) k λ k=0,1,2,3.. = Only one dimension! k λ All equations have to be satisfied at the same time!
Bragg s equation William.H Bragg (1862-1942) W. L.Bragg (1890-1971) 1915 Nobel prize in phisycs! Criteria for constructive interference! 2 d sinθ = n λ Bragg s equation The distance between the atomic planes (d) can be calculated from the diffracted angle(θ) of the x-ray beam! Planes of the crystal behave as a mirror!
X-ray diffraction methods Single crystal method - Single crystal (100 μm) - Changing wavelength ( white x-ray ) - Inorganic solids and macromolecules (e.g. proteins, DNA) atomic structure - Goniometer (rotation of the sample) Powder diffraction - Monochromatic X-ray - every possible crystalline orientation is represented in a powdered sample - Identify unknown crystal samples International Centre for Diffraction Data (ICDD) 2Θ Diffractogramm of Zinc-sulphate
Arrangement of X-ray diffraction experiment Source: X-ray tube Goniometer Detector: - photographic plate -CCD (couple-charged device)
Goniométer
Study of protein structure by X-ray diffraction 1958 the first atomic structure of a protein Max Perutz and Sir John Cowdery Kendrew 1962 Nobel Prize in chemistry Sperm whale myoglobin So far ten thousends protein structure were solved by X-ray diffraction. The atomic coordinates of the proteins are freely accesible: www.pdb.org Designing new drugs
DNA X-ray diffraction pattern 1953: DNA model of James D. Watson (1928-, USA) and Francis Crick (1916-2004, ENG)
Thank you for your attention!
Investigation of inorganic materials by X-ray diffraction The earliest structures were simple inorganic crystals (NaCl, ZnSO 4,diamond,graphite) Fundamental laws of physics and chemistry (nature of chemical bonds, radii of atoms). Diamond-tetrahedral arrangement with covalent bonds Graphite: hexagonal arrangement with delocalised electrons Crystal structure of diamond and graphite.