Peter Debye – 1936 Nobel Prize in Chemistry Max von Laue – 1914 Nobel Prize in Physics William Henry Bragg, William Lawrence Bragg – 1915 Nobel Prize in Physics The cubic lattices include planes that have 1, 2, 3, or 4-fold rotational symmetry, but quasicrystals displaying 5-fold structures have been observed in experiments on Al-Mn alloys and generated mathematically as Penrose tiles. Another method, Laue diffraction, uses x-rays of multiple wavelengths and a fixed target, producing a pattern reflective of the symmetry present in the crystal structure. One popular method of determining crystal structure, x-ray diffractometry, involves monochromatic x-rays bouncing off a rotating target the resulting peaks indicate the identity and spacing of the close-packed planes, which are different for FCC and BCC. X-rays reflect off each atomic plane in a crystal, producing patterns of destructive and constructive interference according to Braggs’ law. Lecture Slides (PDF - 5.3MB) Lecture Summary 12.3, “Structures of Simple Binary Compounds.”Ĭommon structures of binary compounds, x-ray diffractionĭiffraction, Braggs’ law and reflection rules single-crystal, polycrystal, and powder diffraction techniques Determine the types of symmetry present in a given tiling pattern.Īrchived Lecture Notes #5 (PDF), Sections 4-6.Explain the difference between x-ray diffractometry and Laue diffraction.angle, or the 2θ values of the diffraction peaks, determine the crystal structure and lattice constant of the sample. Identify which planes produce x-ray diffraction peaks in FCC and BCC crystals.Sketch the reflection of incident radiation off atomic planes, and derive Braggs’ law for this geometry.Learning ObjectivesĪfter completing this session, you should be able to: It is also used to determine the degree of long-range order and symmetry present in a crystal, or lacking in a glass, which is the topic of the next module ( Session 21: Introduction to Glasses). X-ray diffraction is a popular technique to discover the structures of organic molecules such as proteins ( Session 31) and, most famously, DNA ( Session 32), as well as inorganic crystals. X-ray production methods and characteristic emission lines (Cu K α, etc.).Miller indices for crystal directions and planes.Growth of single-crystal Si, identification of planes and symmetry in crystals, Penrose tilesīefore starting this session, you should be familiar with the prior topics in this module ( Session 15 through Session 17), especially: X-ray diffraction, Braggs’ law, angle of incidence, angle of reflection, constructive interference, destructive interference, crest, trough, amplitude, wavelength, phase, monochromatic, coherent light, incoherent light, order of reflection, index of refraction, collimator, diffraction peak, rotational symmetry, Laue diffraction, quasicrystal, translational symmetry, long-range order, x-ray crystallography, Penrose tiles, William Henry Bragg, William Lawrence Bragg, Max von Laue, Roger Penrose, Peter Debye, Peter Scherrer, Dan ShechtmanĬopper (Cu), nickel (Ni), silicon (Si), aluminum-manganese alloy (Al-Mn) X-Ray Diffraction Techniquesīraggs’ law, x-ray diffraction of crystals: diffractometry, Laue, and Debye-Scherrer, crystal symmetry and selection rules
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