Chemistry Week 5

Chemistry Week 5 - (4 X-Ray Diffraction How are these...

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(4) X-Ray Diffraction How are these crystal structures determined? To study matter on the length scales found between atoms in unit cells, we need to use light (electromagnetic radiation) with a wavelength that is close to the distances between atoms, i.e., ca. 100 pm = 0.1 nm = 1 Å. This requires X-rays. The nature of the experiment involves generating X-rays, which is done by accelerating electrons at a metal foil (typically Cu, Mo, or Cr, Ag). These electrons excite atoms in these foils and generate characteristic X-rays (Cu: 0.154178 nm; Mo: 0.071069 nm) which are focused (screens, etc.) at the crystal(s). As these X-rays interact with the crystal, they are diffracted (show regions of constructive interference), which is detected by a photographic plate (today, we use CCD detectors – sensitive solid-state detectors used originally for astronomical detection; and image plates – phosphors read by laser light). Information taken from the detector is then converted into deducing the atomic structure in the crystal. There are two types of diffraction experiments: those on (1) single crystals; and (2) powders (several randomly oriented crystals). The information provided by the diffraction experiment includes (a) the position of the diffraction spots on the photographic plate, and (b) the intensity (brightness) of each diffraction spot. The positions give the size and shape of the unit cell; the intensities give details about the electron density and atoms inside the unit cell. Both pieces of information provide the complete crystal structure. Sample Form : 1 Grain (Crystal) 4 Grains 40 Grains 200 Grains (Powder) Diffraction Pattern : The single grain (crystal) gives a discrete pattern to analyze. As more grains become exposed to X-rays, the diffraction patterns superimpose on each other. When there are many grains, the discrete pattern becomes rings, and we measure intensity just along a single direction (powder ).
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Bragg’s Law : When X-rays “illuminate” a crystal, much of the incident X-ray beam travels straight through, but we also observe a collection of X-rays that have been scattered ( diffracted ) by the crystal. Conditions for the positions of these scattered X-rays mean that constructive interference occurs between various X-rays. d Incident X-ray Beam Wavelength = λ Scattered X-rays "Constructive Interference" θ θ θ As electromagnetic radiation, X-rays can be represented by sine/cosine functions with an amplitude and phase. The incident X-ray beam contains rays that are completely in phase. One ray is “reflected” by one plane of atoms; the next ray is “reflected” by the next plane of atoms. For constructive interference, the extra distance traveled by the second ray must be an integral multiple of the wavelength of the X-rays: n λ = 2 d sin θ (Bragg’s Law) n = order of the reflection (an integer : typically chosen as 1, but can take higher values); λ = wavelength of X-radiation; θ = reflection angle (the scattering between the incident and diffracted X-rays is 2 θ ) – “Bragg reflections”; d = distance between adjacent planes in the lattice.
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This note was uploaded on 03/27/2008 for the course CHEM 201 taught by Professor Miller during the Fall '07 term at Iowa State.

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Chemistry Week 5 - (4 X-Ray Diffraction How are these...

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