x-ray diffraction dr. t. ramlochan march 2010. public service announcement… radiation warning...

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  • X-Ray DiffractionDr. T. Ramlochan March 2010

  • Public service announcement

    Radiation warning symbolNew IAEA Radiation warning symbolRadiation is dangerous, so run away!

  • CrystalsA crystal is a solid material where the constituent atoms are arranged in an orderly repeating pattern extending in all three spatial dimensionsSrTiO3CaSO42H2O

  • CrystallographyCrystals are divided into 7 lattice systems all crystalline materials must fit in one of these unit cellslengths of edges (a, b, c) of unit cell and the angles (, , ) 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

  • CrystallographyThe atoms in a crystal lattice form planes (described by Miller indices) that repeat

  • X-rays and diffractionX-rays were discovered in 1895 by Rntgen

    X-rays are electromagnetic radiation with wavelengths in the range of 0.5-2.5

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

  • X-rays and diffractionDifferences 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-raysAtoms (or their electrons) will scatter X-rays in all directionsIf 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 beamsDiffraction is essentially reinforced scattering

  • Braggs LawFor a particular condition of scattering where the angle () 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

    n = 2d sin

    This was first identified by W.L. Bragg and is called Braggs Law

  • Braggs LawFor a fixed wavelength () and value of d, there will be an angle theta () where diffraction (complete reinforcement) occurs

    Diffractogram is a plot of the intensity of the diffracted X-rays vs. 2 over a range of anglesEach peak represents a plane in the crystal lattice with a given d-spacingBasis for powder diffraction

  • X-ray productionX-ray are produced when electrically charged particles (e.g., electrons) with sufficient kinetic energy give up some energyNon-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 productionX-rays named according to shell being filled and number of shells changed (e.g., K shell filled by L shell (K radiation) or M shell (K radiation))Each peak represents a transition; more than one peak (family of X-rays); K (highest probability) is ~5 times stronger than KK is a doublet (K1 and K2) different spin statesK1 always about twice the intensity of K2For Cu K1 1.540598 K2 1.544426 K 1.541874 K 1.392250

  • X-ray productionFor 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 K and K wavelengthsFor Cu radiation use Ni filter K reduced to 1/500; K reduced by 1/2

  • X-ray generationTo generate X-rays a) source of electrons, b) high accelerating voltage, and c) a metal targetUse a water-cooled X-ray tubeEvacuated glass tube with an anode (Cu target) and cathode maintained at high negative potential (HT transformer)Filament is heated to emit electrons accelerated towards targetX-rays emitted through (X-ray-transparent) beryllium windows

  • X-ray diffractometerDiffractometer has two parts:Generator to generate X-raysGoniometer to scan sample through a range of angles

  • Diffraction optics/geometryX-rays diverge from source pass through Soller slits and divergence slits to define and collimate incident beamIncident beam diffracted by flat powder specimenDiffracted beam passed through receiving slitsSecondary monochromator reduces background radiation from sampleX-rays collected by detector (proportional, Geiger, scintillation, semiconductor)

  • DiffractogramsGives information about peak positions, intensity, and shape

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