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Lecture 1 X-Ray Diffraction I GG 711: Advanced Techniques in Geophysics and Materials Science X-Ray Diffraction: Lecture 1 X-ray Diffraction I: Powder Diffraction Pavel Zinin, Li Chung HIGP, University of Hawaii, Honolulu, USA www.soest.hawaii.edu\~zinin Why X-Rays Best possible resolution of : OM > 0.2 µm. AFM > 1.0 nm SEM > 1.0 nm TEM > 0.2 nm 0.61 0.61 0.61 r ; Airy sin NA nNA TEM AFM OM eye 1 Å 1 nm 1 µm 1 mm 1 cm Red Blood Atoms Molecules Viruses Computer Hair Circuits Cells Why X-rays Definition: X-radiation (composed of X-rays) is a form of electromagnetic radiation. X-rays have a wavelength in the range of 10 to 0.01 nm, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3 × 1016 Hz to 3 × 1019 Hz) and energies in the range 120 eV to 120 keV (Wikipedia, 2009). c E h f h hc E 1240 ()nm E() eV 1 eVt is 1 volt (1 joule divided by 1 coulomb) E is the energy of the photon, h is multiplied by the electron charge (1.6021×10-19 the Plank’s constant, f is the coulomb). One electron volt is equal to 1.6021 ×10-19 frequency, is the wavelength. joules. EM Spectrum Lines Produced by Electron Shell Ionization K X-ray is produced due to removal of K shell electron, with L shell electron taking its place. K occurs in the case where K shell electron is replaced by electron from the M shell. L X-ray is produced due to removal of L shell electron, replaced by M shell electron. M X-ray is produced due to removal of M shell electron, replaced by N shell electron. X - Ray In 1895 at the University of Wurzburg, Wilhelm Roentgen (1845-1923) was studying electrical discharges in low-pressure gases when he noted that a fluorescent screen glowed even when placed several meters from the gas discharge tube and even when black cardboard was placed between the tube and the screen. He concluded that the effect was caused by a mysterious type of radiation, which he called x-rays because of their unknown nature. Nucleus of target atom Copper Tungsten rod target Typical x-ray wavelengths are about 0.1 nm, which is of the order of the atomic spacing in a solid. X-rays are produced when high-speed electrons are suddenly decelerated, for example, when a metal target is struck by electrons that have been accelerated through a potential difference of several thousand volts. X-ray generation Spectrum of the X-rays emitted by an X-ray tube with a rhodium target, operated at 60 kV. The smooth, continuous curve is due to bremsstrahlung, and the spikes are characteristic K lines for rhodium atoms. Historical Background He wrote an initial report "On a new kind of ray: A preliminary communication" and on December 28, 1895 submitted it to the Wurzburg's Physical- Medical Society journal. This was the first paper http://www.nobel.se/physics/laureates/1901/rontgen-bio.html written on X-rays. On November 8, 1895, Roentgen referred to the German physics professor radiation as "X", to indicate that it was an Wilhelm Conrad Roetgen Print of Wilhelm Rontgen's first x- stumbled on X-rays while unknown type of ray, the hand of his wife Anna taken experimenting with Lenard radiation. on 1895-12-22, presented to and Crookes tubes and Professor Ludwig Zehnder of the began studying them (1901 Physik Institut, University of Nobel prize in Physics). Freiburg, on 1 January 1896. History of X-ray and XRD •The first kind of scatter process to be recognised was discovered by Max von Laue who was awarded the Nobel prize for physics in 1914 "for his discovery of the diffraction of X-rays by crystals". His collaborators Walter Friedrich and Paul Knipping took the picture on the bottom left in 1912. It shows how a beam of X-rays is scattered Max von Laue (1897-1960) into a characteristic pattern by a crystal. In this case it is copper sulphate. •The X-ray diffraction pattern of a pure substance is like a fingerprint of the substance. The powder diffraction method is thus ideally suited for characterization and identification of polycrystalline phases. X-ray generation X-ray spectrograph of lysozyme, the second protein to have its molecular structure determined by x-ray (From L. Bragg’s Nobel Prise lecture.. X-ray generation Ionizing spectrometer was the instrument used by W.H. Bragg to conduct x-ray spectra collection Wave interference Wave diffraction can cause complex patterns of destructive and constructive interference. X-ray generation Diffraction of the parallel rays from two parallel surfaces. Historical Background He wrote an initial report "On a new kind of ray: A preliminary communication" and on December 28, 1895 submitted it to the Wurzburg's Physical- Medical Society journal. This was the first paper http://www.nobel.se/physics/laureates/1901/rontgen-bio.html written on X-rays. On November 8, 1895, Roentgen referred to the German physics professor radiation as "X", to indicate that it was an Wilhelm Conrad Roetgen Print of Wilhelm Rontgen's first x- stumbled on X-rays while unknown type of ray, the hand of his wife Anna taken experimenting with Lenard radiation. on 1895-12-22, presented to and Crookes tubes and Professor Ludwig Zehnder of the began studying them (1901 Physik Institut, University of Nobel prize in Physics). Freiburg, on 1 January 1896. History of X-ray and XRD •The first kind of scatter process to be recognised was discovered by Max von Laue who was awarded the Nobel prize for physics in 1914 "for his discovery of the diffraction of X-rays by crystals". His collaborators Walter Friedrich and Paul Knipping took the picture on the bottom left in 1912. It shows how a beam of X-rays is scattered Max von Laue (1897-1960) into a characteristic pattern by a crystal. In this case it is copper sulphate. •The X-ray diffraction pattern of a pure substance is like a fingerprint of the substance. The powder diffraction method is thus ideally suited for characterization and identification of polycrystalline phases. Analysis of crystal structure by means of X-rays Bragg's law was an extremely important discovery and formed the basis for the whole of what is now known as crystallography. This technique is one of the most widely used structural analysis Sir William Henry William Lawrence techniques and plays a major role in fields Bragg (1862-1942) Bragg (1890-1971) as diverse as structural biology and materials science. The father and son team of Sir William Henry and William Lawrence Bragg were awarded Wikipedia. 2009 the Nobel prize for physics "for their services in the analysis of crystal structure by means of Xrays“ in 1915. X-ray Diffraction In physics, Bragg's law states that when X-rays hit an atom, they make the electronic cloud move as does any electromagnetic wave. The movement of these charges re- radiates waves with the same (or elastic scattering). These re-emitted wave fields interfere with each other either constructively or destructively (overlapping waves either add together to produce stronger peaks or subtract from each other to some degree), producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. X-ray wavelength is comparable with inter-atomic distances (~1.5 Å) and thus are an excellent probe for this length scale (Wikipedia, 2009). nd 2 sin X-ray Diffraction Plane wave Plane and spherical waves X-ray Diffraction In physics, Bragg's law states that when X-rays hit an atom, they make the electronic cloud move as does any electromagnetic wave. The movement of these charges re- radiates waves with the same (or elastic scattering). These re-emitted wave fields interfere with each other either constructively or destructively (overlapping waves either add together to produce stronger peaks or subtract from each other to some degree), producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. X-ray wavelength is comparable with inter-atomic distances (~1.5 Å) and thus are an excellent probe for this length scale (Wikipedia, 2009). nd 2 sin Inter-Planar Spacing, dhkl, and Miller Indices The (200) planes The (220) planes of atoms in NaCl of atoms in NaCl • The unit cell is the basic repeating unit that defines a crystal. • Parallel planes of atoms intersecting the unit cell are used to define directions and distances in the crystal. – These crystallographic planes are identified by Miller indices. X-ray Diffraction Adding up phases at the detector of the wavelets scattered from all the scattering centers in the sample: The crystallographer’s world view Diamond Atomic structure of diamond Definition: A crystal consists of atoms arranged in a pattern that repeats periodically in three dimensions. There are two aspects to this pattern: Periodicity; Symmetry Ideal Crystal: • An ideal crystal is a periodic array of structural units, such as atoms or molecules. • It can be constructed by the infinite repetition of these identical structural units in space. • Structure can be described in terms of a lattice, with a group of atoms attached to each lattice point. The group of atoms is the basis. Periodicity and a Crystal Lattice A Primitive Cubic Lattice of Diamond To describe the periodicity, we superimpose (mentally) on the crystal structure a lattice. A lattice is a regular array of geometrical points, each of which has the same environment (they are all equivalent).
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