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Diffraction Methods 1 Diffraction methods Diffraction Methods 1 Diffraction Methods . Diffraction methods are the most important approach to the analysis of crystalline solids . both phase and structural information . Continuous solids usually can not be purified . elemental analysis not much use on its own . Solid state NMR is a powerful technique . but does not provide a detailed picture Types of diffraction experiment . X-ray . Routinely used to provide structural information on compounds and to . identify samples . Used with both powder and single crystal samples . X-rays produced in the home lab or using synchrotrons . Can also be used to examine liquids and glasses . Electron diffraction . primarily used for phase identification, and unit cell determination on . small crystallites in the electron microscope . also used for gas phase samples . Neutrons . useful source of structural information on crystalline materials, but . expensive . Also useful for spectroscopy and structure of liquids/glasses 2 A comparison of X-rays and neutrons X-rays Neutrons Atomic scattering power varies Atomic scattering power varies smoothly with atomic number erratically with atomic number Atomic scattering power Atomic scattering power is decreases as the scattering constant as the scattering angle angle increases chanages Insensitive to magnetic Scattered by magnetic moments moments Readily available as intense Low intensity beams beams Typically, strongly absorbed by Weakly absorbed by most all but low Z elements materials The scattering of X-rays by electrons . The charge on an electron interacts with electromagnetic radiation and can give rise to elastic scattering . If the source, electron and detector lie in a plane perpendicular to the X-rays electric vector the scattering probability is isotropic . If the electric vector lies in the plane the scattering is not isotropic 3 The scattering of unpolarized X-rays . For an unpolarized beam of X-rays being scattered by an electron I α 0.5 x (1+ cos22θ) . This is the physical origin of the polarization correction used in crystallography Scattering of X-rays and neutrons by atoms . X-rays are scattered electrons in atoms . the electron cloud is about the same size as the wavelength of the X-rays . Neutrons are scattered by nuclei . nuclei are much smaller than the neutron wavelength . for magnetic materials electron spin interacts with neutron spin and gives scattering 4 X-ray scattering by atoms X-ray and neutron form factor . The form factor is related to the envelope function for an atom 5 Neutron scattering lengths Neutron scattering lengths 6 Diffraction Methods . X-rays are scattered from the atoms in the sample. The x-rays scattered from the different atoms interfere with one another either constructively or destructively . For crystalline solids this interference pattern has sharp well defined peaks . The positions of the peaks are determined by the lattice for crystalline solid Scattering patterns for different substances 7 Interference between waves Double slit experiment 8 Bragg’s law 2d sinθ = λ . Can consider crystal to contain repeating ‘reflecting’ planes (lattice planes) . Interference between x-rays scattered from different planes leads to peaks in the diffraction pattern d-spacing formulae . For a unit cell with orthogonal axes 2 2 2 2 2 2 2 – (1 / d hkl) = (h /a ) + (k /b ) + (l /c ) . Hexagonal unit cells 2 2 2 2 2 2 – (1 / d hkl) = (4/3)([h + k + hk]/ a ) + (l /c ) 9 Powder diffraction Energy and angle dispersive diffraction . An X-ray diffraction pattern is a measurement of X-ray intensity versus d-spacing . d-spacing, scattering angle and λ are related by Bragg’s law » 2d sinθ = λ Energy dispersive diffraction Angle dispersive diffraction Fix 2θ and vary λ Fix λ and vary 2θ Quick experiment with fixed sampling High resolution but slow and volume, but low resolution sampling volume varies 10 Instrument geometries . There are several different ways of collecting powder diffraction patterns . Debye Scherrer . Bragg-Brentano (flat plate) . Guinier etc. The Bragg-Brentano geometry is the most commonly used The Debye-Sherrer camera 11 Bragg-Brentano diffractometer Powder X-ray diffraction . Powder XRD is used routinely to assess the purity and crystallinity of materials . Each crystalline phase has a unique powder diffraction pattern . Measured powder patterns can be compared to a database for identification 12 Powder patterns for different substances . Can distinguish between the same compound with different structures and different compounds with the same structure Information from powder XRD . Phase purity . both qualitative and quantitative . Crystallinity . amorphous content, particle size and strain . Unit cell size and shape . from peak positions . Crystal structure in simple cases 13 Indexing a powder pattern . The process of figuring out what Miller indices belong to each peak or “d-spacing” in a powder pattern is called indexing . During the indexing process the unit cell constants are also determined . Indexing can be done by hand or by computer . indexing by hand is only sensible for materials that are thought to have high symmetry Indexing the powder pattern of NaBr 14 Systematic absences and centering . The presence of a centered lattice leads to the systematic absence of certain types of peak in the diffraction pattern . For I centered lattices: . h + k + l = 2n for a line to be present . For an F centered lattice: . h + k =2n, k + l = 2n and h + l = 2n . For a C centered lattice: . h + k = 2n 15 .
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