X ray diffraction light

X-ray diffraction (XRD) derives from an electromagnetic wave interacting with an array of scatterers. Practically, any wave produces diffraction and to create it, the spacing between the scatterers and the wavelength should be roughy equal. A beam causes each scatterer to re-radiate a portion of its intensity, as a spherical wave. If scatterers are arranged symmetrically with a separation d, these waves will be in sync in directions where their path-length difference 2d sin θ equals a multiple of the wavelength λ. This would result in part of the beam being deflected by an angle 2θ, producing a reflection spot in the pattern. 

 

 

What is X-ray diffraction (XRD)?

Crystals are effectively constructed of repeating, regular arrays of atoms. X-rays are simply waves of electromagnetic radiation and these are scattered through the electrons. An X-ray striking an electron produces secondary spherical waves, which is known as elastic scattering. On occasion, these waves cancel each other out in certain directions through destructive interference. They add constructively in certain directions, determined by Bragg’s law:

d is the spacing between diffracting planes,  is the incident angle, n is an integer, and λ is the wavelength. These specific directions appear as spots on the diffraction pattern called reflections.

 

X-ray diffraction instrumentation

An analyser finds interference patterns reflecting lattice structures by varying the angle of incidence of the beam. Instruments vary by their precision, speed of rotation, and beam size of the x-rays. High resolution instrumentation helps detail the structural analysis of advanced semiconductors, thin film, and nanomaterials. Certain machines can cover wide variety of X-ray scattering methods, including high resolution diffraction, in-plane diffraction, reflectivity, thin film phase analysis, GISAXS, stress and nonambient analysis. Highest resolution machines include a goniometer with Heidenhain encoders for quick positioning, a 5 axis cradle allowing for support and mapping of wafers up to 6 inches in diameter.

 

What is X-ray Crystallography (XRC)?

X-ray crystallography (XRC) determines the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of X-rays to diffract. By measuring the angles and intensities of the beams, you can calculate the density of electrons. The mean positions of the atoms in the crystal can be determined, their chemical bonds and their disorder.

Salts, metals, minerals, semiconductors and biological molecule can all by explained by X-ray crystallography. This method determines the size of atoms, the lengths and types of chemical bonds. It also illustrated the composition of vitamins, drugs and DNA.

X-ray diffraction discovery

In 1912, Ewald proposed experiments that could not be validated using visible light, since the wavelength was much larger than the spacing between the resonators. Von Laue however, proposed that electromagnetic radiation of a shorter wavelength was required. Von Laue created a beam of X-rays through a copper sulphate crystal. The photographic plate showed a large number of spots arranged in a pattern of intersecting circles. He linked the scattering angles, size and orientation of the unit-cell spacings, leading to his Nobel Prize in Physics.

 

X-ray scattering equation

X-ray scattering is determined by the density of electrons, as the energy of an X-ray is much greater than that of an electron, the scattering is the interaction of an electromagnetic ray with a free electron. The intensity of scattering for a particle with mass m and charge q is:

 

 

X-ray scattering techniques

Elastic and Inelastic scattering

X-ray crystallography is elastic scattering. X-rays outgoing have the same energy as incoming X-rays, with different directions. By contrast, inelastic scattering occurs when energy is transferred from the X-ray to the crystal e.g. by exciting an inner-shell electron to a higher energy level. Inelastic scattering is useful for probing excitations of matter, but not in determining the distribution of scatterers.

 

Electron and neutron diffraction

Electrons and neutrons, may be used to produce a diffraction pattern. The electron density within the crystal and the diffraction patterns are related by Fourier transform. However, this works only if the scattering is weak, and the scattered beams are much less intense than the incoming beam. Applications for electron crystallography ranges from bio molecules, like membrane proteins over organic thin films, to the complex structures of inter-metallic compounds.

 

Further X-ray techniques

Other forms of X-ray scattering include Small-Angle X-ray Scattering (SAXS) and X-ray fiber diffraction, used to determine the structure of DNA.

A broad spectrum of X-rays can also be used to carry out X-ray diffraction, a technique known as the Laue method. This records X-rays scattered backwards from a broad spectrum source. This is useful if the sample is too thick for X-rays.

 

X-ray diffraction applications

Applications for X-ray diffraction are varied across chemical, biochemical, physical and material sciences. X-ray diffraction is analogous to a microscope with atomic-level resolution which shows the atoms and their electron distribution. X-ray diffraction and the other variations all give information on crystalline and non-crystalline, at the atomic and molecular level. 

Drug identification and categorisation

X-ray diffraction has been used for the identification of antibiotic drugs such as: eight β-lactam (ampicillin sodium, benzathine penicillin, cefotaxime sodium, Ceftriaxone sodium). Each of these drugs has a unique X-Ray pattern that makes their identification possible.

Characterisation of textile fibers and polymers

Forensic examination of evidence is based upon Locard’s exchange principle, stating that every contact leaves a trace. Textile fibers are a mixture of crystalline and amorphous substances. The degree of crystalline gives useful data in the characterisation of fibers, using X-ray diffractometry. 

 

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References

  1.  “Resonant X-ray Scattering | Shen Laboratory”arpes.stanford.edu. Retrieved 2019-07-10.
  2. ^ Kepler J (1611). Strena seu de Nive Sexangula. Frankfurt: G. Tampach. ISBN 3-321-00021-0.
  3. ^ Steno N (1669). De solido intra solidum naturaliter contento dissertationis prodromus. Florentiae.
  4. ^ Hessel JFC (1831). Kristallometrie oder Kristallonomie und Kristallographie. Leipzig.
  5. ^ Bravais A (1850). “Mémoire sur les systèmes formés par des points distribués regulièrement sur un plan ou dans l’espace”. Journal de l’École Polytechnique19: 1.
  6. ^ Shafranovskii I I & Belov N V (1962). Paul Ewald (ed.). “E. S. Fedorov”(PDF)50 Years of X-Ray Diffraction. Springer: 351. ISBN 90-277-9029-9.
  7. ^ Schönflies A (1891). Kristallsysteme und Kristallstruktur. Leipzig.
  8. ^ Barlow W (1883). “Probable nature of the internal symmetry of crystals”Nature29 (738): 186. Bibcode:1883Natur..29..186Bdoi:10.1038/029186a0.See also Barlow, William (1883). “Probable Nature of the Internal Symmetry of Crystals”Nature29 (739): 205. Bibcode:1883Natur..29..205Bdoi:10.1038/029205a0. Sohncke, L. (1884). “Probable Nature of the Internal Symmetry of Crystals”Nature29 (747): 383. Bibcode:1884Natur..29..383Sdoi:10.1038/029383a0S2CID 4072817. Barlow, WM. (1884). “Probable Nature of the Internal Symmetry of Crystals”Nature29 (748): 404. Bibcode:1884Natur..29..404Bdoi:10.1038/029404b0S2CID 4016086.
  9. ^ Einstein A (1905). “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” [A Heuristic Model of the Creation and Transformation of Light]. Annalen der Physik (in German). 17 (6): 132. Bibcode:1905AnP…322..132Edoi:10.1002/andp.19053220607.. An English translation is available from Wikisource.
  10. ^ Compare: Einstein A (1909). “Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung” [The Development of Our Views on the Composition and Essence of Radiation]. Physikalische Zeitschrift (in German). 10: 817.. An English translation is available from Wikisource.
  11. ^ Pais A (1982). Subtle is the Lord: The Science and the Life of Albert EinsteinOxford University PressISBN 0-19-853907-X.
  12. ^ Compton A (1923). “A Quantum Theory of the Scattering of X-rays by Light Elements” (PDF)Phys. Rev21 (5): 483. Bibcode:1923PhRv…21..483Cdoi:10.1103/PhysRev.21.483.
  13. ^ Bragg WH (1907). “The nature of Röntgen rays”. Transactions of the Royal Society of Science of Australia31: 94.
  14. ^ Bragg WH (1908). “The nature of γ- and X-rays”Nature77 (1995): 270. Bibcode:1908Natur..77..270Bdoi:10.1038/077270a0S2CID 4020075.See also Bragg, W. H. (1908). “The Nature of the γ and X-Rays”Nature78(2021): 271. Bibcode:1908Natur..78..271Bdoi:10.1038/078271a0S2CID 4039315. Bragg, W. H. (1908). “The Nature of the γ and X-Rays”. Nature78 (2022): 293. Bibcode:1908Natur..78..293Bdoi:10.1038/078293d0S2CID 3993814. Bragg, W. H. (1908). “The Nature of X-Rays”Nature78 (2035): 665. Bibcode:1908Natur..78R.665Bdoi:10.1038/078665b0S2CID 4024851.
  15. ^ Bragg WH (1910). “The consequences of the corpuscular hypothesis of the γ- and X-rays, and the range of β-rays”Phil. Mag20 (117): 385. doi:10.1080/14786441008636917.
  16. ^ Bragg WH (1912). “On the direct or indirect nature of the ionization by X-rays”. Phil. Mag23 (136): 647. doi:10.1080/14786440408637253.
  17. Jump up to:a b Friedrich W; Knipping P; von Laue M (1912). “Interferenz-Erscheinungen bei Röntgenstrahlen”. Sitzungsberichte der Mathematisch-Physikalischen Classe der Königlich-Bayerischen Akademie der Wissenschaften zu München1912: 303.
  18. ^ von Laue M (1914). “Concerning the detection of x-ray interferences” (PDF)Nobel Lectures, Physics. 1901–1921. Retrieved 2009-02-18.
  19. ^ Dana ES; Ford WE (1932). A Textbook of Mineralogy (fourth ed.). New York: John Wiley & Sons. p. 28.
  20. ^ Andre Guinier (1952). X-ray Crystallographic Technology. London: Hilger and Watts LTD. p. 271.
  21. ^ Bragg WL (1912). “The Specular Reflexion of X-rays”Nature90 (2250): 410. Bibcode:1912Natur..90..410Bdoi:10.1038/090410b0S2CID 3952319.
  22. ^ Bragg WL (1913). “The Diffraction of Short Electromagnetic Waves by a Crystal”. Proceedings of the Cambridge Philosophical Society17: 43.
  23. ^ Bragg (1914). “Die Reflexion der Röntgenstrahlen”. Jahrbuch der Radioaktivität und Elektronik11: 350.
  24. ^ Bragg (1913). “The Structure of Some Crystals as Indicated by their Diffraction of X-rays”Proc. R. Soc. LondA89 (610): 248–277. Bibcode:1913RSPSA..89..248Bdoi:10.1098/rspa.1913.0083JSTOR 93488.
  25. ^ Bragg WL; James RW; Bosanquet CH (1921). “The Intensity of Reflexion of X-rays by Rock-Salt”Phil. Mag41 (243): 309. doi:10.1080/14786442108636225.
  26. ^ Bragg WL; James RW; Bosanquet CH (1921). “The Intensity of Reflexion of X-rays by Rock-Salt. Part II”Phil. Mag42 (247): 1. doi:10.1080/14786442108633730.
  27. ^ Bragg WL; James RW; Bosanquet CH (1922). “The Distribution of Electrons around the Nucleus in the Sodium and Chlorine Atoms”Phil. Mag44 (261): 433. doi:10.1080/14786440908565188.
  28. Jump up to:a b Bragg WH; Bragg WL (1913). “The structure of the diamond”Nature91(2283): 557. Bibcode:1913Natur..91..557Bdoi:10.1038/091557a0S2CID 3987932.
  29. ^ Bragg WH; Bragg WL (1913). “The structure of the diamond”Proc. R. Soc. LondA89 (610): 277. Bibcode:1913RSPSA..89..277Bdoi:10.1098/rspa.1913.0084.
  30. ^ Bragg WL (1914). “The Crystalline Structure of Copper”Phil. Mag28 (165): 355. doi:10.1080/14786440908635219.
  31. Jump up to:a b Bragg WL (1914). “The analysis of crystals by the X-ray spectrometer”Proc. R. Soc. LondA89 (613): 468. Bibcode:1914RSPSA..89..468Bdoi:10.1098/rspa.1914.0015.
  32. ^ Bragg WH (1915). “The structure of the spinel group of crystals”Phil. Mag30 (176): 305. doi:10.1080/14786440808635400.
  33. ^ Nishikawa S (1915). “Structure of some crystals of spinel group”. Proc. Tokyo Math. Phys. Soc8: 199.
  34. ^ Vegard L (1916). “Results of Crystal Analysis”Phil. Mag32 (187): 65. doi:10.1080/14786441608635544.
  35. ^ Aminoff G (1919). “Crystal Structure of Pyrochroite”Stockholm Geol. Fören. Förh41: 407. doi:10.1080/11035891909447000.
  36. ^ Aminoff G (1921). “Über die Struktur des Magnesiumhydroxids”. Z. Kristallogr56: 505.
  37. ^ Bragg WL (1920). “The crystalline structure of zinc oxide”Phil. Mag39(234): 647. doi:10.1080/14786440608636079.
  38. ^ Debije P; Scherrer P (1916). “Interferenz an regellos orientierten Teilchen im Röntgenlicht I”. Physikalische Zeitschrift17: 277.
  39. ^ Friedrich W (1913). “Eine neue Interferenzerscheinung bei Röntgenstrahlen”. Physikalische Zeitschrift14: 317.
  40. ^ Hull AW (1917). “A New Method of X-ray Crystal Analysis”. Phys. Rev10 (6): 661. Bibcode:1917PhRv…10..661Hdoi:10.1103/PhysRev.10.661.
  41. ^ Bernal JD (1924). “The Structure of Graphite”. Proc. R. Soc. LondA106 (740): 749–773. JSTOR 94336.
  42. ^ Hassel O; Mack H (1924). “Über die Kristallstruktur des Graphits”. Zeitschrift für Physik25 (1): 317. Bibcode:1924ZPhy…25..317Hdoi:10.1007/BF01327534S2CID 121157442.
  43. ^ Hull AW (1917). “The Crystal Structure of Iron”. Phys. Rev9 (1): 84. Bibcode:1917PhRv….9…83.doi:10.1103/PhysRev.9.83.
  44. ^ Hull AW (July 1917). “The Crystal Structure of Magnesium”Proceedings of the National Academy of Sciences of the United States of America3 (7): 470–3. Bibcode:1917PNAS….3..470Hdoi:10.1073/pnas.3.7.470PMC 1091290PMID 16576242.
  45. Jump up to:a b “From Atoms To Patterns”. Wellcome Collection. Archived from the original on September 7, 2013. Retrieved 17 October 2013.
  46. ^ Wyckoff RWG; Posnjak E (1921). “The Crystal Structure of Ammonium Chloroplatinate”J. Am. Chem. Soc43 (11): 2292. doi:10.1021/ja01444a002.
  47. Jump up to:a b Bragg WH (1921). “The structure of organic crystals”Proc. R. Soc. Lond34 (1): 33. Bibcode:1921PPSL…34…33Bdoi:10.1088/1478-7814/34/1/306.
  48. ^ Lonsdale K (1928). “The structure of the benzene ring”. Nature122 (3082): 810. Bibcode:1928Natur.122..810Ldoi:10.1038/122810c0S2CID 4105837.
  49. ^ Pauling L (1960). The Nature of the Chemical Bond (3rd ed.). Ithaca, NY: Cornell University PressISBN 0-8014-0333-2.
  50. ^ Bragg WH (1922). “The crystalline structure of anthracene”Proc. R. Soc. Lond35 (1): 167. Bibcode:1922PPSL…35..167Bdoi:10.1088/1478-7814/35/1/320.
  51. ^ Powell HM; Ewens RVG (1939). “The crystal structure of iron enneacarbonyl”. J. Chem. Soc.: 286. doi:10.1039/jr9390000286.
  52. ^ Bertrand JA; Cotton; Dollase (1963). “The Metal-Metal Bonded, Polynuclear Complex Anion in CsReCl4“. J. Am. Chem. Soc85 (9): 1349. doi:10.1021/ja00892a029.
  53. ^ Robinson WT; Fergusson JE; Penfold BR (1963). “Configuration of Anion in CsReCl4“. Proceedings of the Chemical Society of London: 116.
  54. ^ Cotton FA, Curtis NF, Harris CB, Johnson BF, Lippard SJ, Mague JT, et al. (September 1964). “Mononuclear and Polynuclear Chemistry of Rhenium (III): Its Pronounced Homophilicity”. Science145 (3638): 1305–7. Bibcode:1964Sci…145.1305Cdoi:10.1126/science.145.3638.1305PMID 17802015S2CID 29700317.
  55. ^ Cotton FA; Harris (1965). “The Crystal and Molecular Structure of Dipotassium Octachlorodirhenate(III) Dihydrate”. Inorganic Chemistry4 (3): 330. doi:10.1021/ic50025a015.
  56. ^ Cotton FA (1965). “Metal-Metal Bonding in [Re2X8]2− Ions and Other Metal Atom Clusters”. Inorganic Chemistry4 (3): 334. doi:10.1021/ic50025a016.
  57. ^ Eberhardt WH; Crawford W Jr.; Lipscomb WN (1954). “The valence structure of the boron hydrides”. J. Chem. Phys22 (6): 989. Bibcode:1954JChPh..22..989Edoi:10.1063/1.1740320.
  58. ^ Martin TW, Derewenda ZS (May 1999). “The name is bond–H bond”. Nature Structural Biology6 (5): 403–6. doi:10.1038/8195PMID 10331860S2CID 27195273.
  59. ^ Dunitz JD; Orgel LE; Rich A (1956). “The crystal structure of ferrocene”Acta Crystallographica9 (4): 373. doi:10.1107/S0365110X56001091.
  60. ^ Seiler P; Dunitz JD (1979). “A new interpretation of the disordered crystal structure of ferrocene”. Acta Crystallographica B35 (5): 1068. doi:10.1107/S0567740879005598.
  61. ^ Wunderlich JA; Mellor DP (1954). “A note on the crystal structure of Zeise’s salt”Acta Crystallographica7: 130. doi:10.1107/S0365110X5400028X.
  62. ^ Jarvis JAJ; Kilbourn BT; Owston PG (1970). “A re-determination of the crystal and molecular structure of Zeise’s salt, KPtCl3.C2H4.H2O. A correction”. Acta Crystallographica B26 (6): 876. doi:10.1107/S056774087000328X.
  63. ^ Jarvis JAJ; Kilbourn BT; Owston PG (1971). “A re-determination of the crystal and molecular structure of Zeise’s salt, KPtCl3.C2H4.H2O”Acta Crystallographica B27 (2): 366. doi:10.1107/S0567740871002231.
  64. ^ Love RA; Koetzle TF; Williams GJB; Andrews LC; Bau R (1975). “Neutron diffraction study of the structure of Zeise’s salt, KPtCl3(C2H4).H2O”. Inorganic Chemistry14 (11): 2653. doi:10.1021/ic50153a012.
  65. ^ Hävecker, Michael; Wrabetz, Sabine; Kröhnert, Jutta; Csepei, Lenard-Istvan; Naumann d’Alnoncourt, Raoul; Kolen’Ko, Yury V.; Girgsdies, Frank; Schlögl, Robert; Trunschke, Annette (2012). “Surface chemistry of phase-pure M1 MoVTeNb oxide during operation in selective oxidation of propane to acrylic acid”Journal of Catalysis285: 48–60. doi:10.1016/j.jcat.2011.09.012hdl:11858/00-001M-0000-0013-FB1F-C.
  66. ^ Kinetic studies of propane oxidation on Mo and V based mixed oxide catalysts. 2011.
  67. ^ Naumann d’Alnoncourt, Raoul; Csepei, Lénárd-István; Hävecker, Michael; Girgsdies, Frank; Schuster, Manfred E.; Schlögl, Robert; Trunschke, Annette (2014). “The reaction network in propane oxidation over phase-pure MoVTeNb M1 oxide catalysts”Journal of Catalysis311: 369–385. doi:10.1016/j.jcat.2013.12.008hdl:11858/00-001M-0000-0014-F436-1.
  68. Jump up to:a b Brown, Dwayne (October 30, 2012). “NASA Rover’s First Soil Studies Help Fingerprint Martian Minerals”NASA. Retrieved October 31, 2012.
  69. ^ Westgren A; Phragmén G (1925). “X-ray Analysis of the Cu-Zn, Ag-Zn and Au-Zn Alloys”. Phil. Mag50: 311. doi:10.1080/14786442508634742.
  70. ^ Bradley AJ; Thewlis J (1926). “The structure of γ-Brass”Proc. R. Soc. Lond112 (762): 678. Bibcode:1926RSPSA.112..678Bdoi:10.1098/rspa.1926.0134.
  71. ^ Hume-Rothery W (1926). “Researches on the Nature, Properties and Conditions of Formation of Intermetallic Compounds (with special Reference to certain Compounds of Tin)”. Journal of the Institute of Metals35: 295.
  72. ^ Bradley AJ; Gregory CH (1927). “The Structure of certain Ternary Alloys”Nature120 (3027): 678. Bibcode:1927Natur.120..678.doi:10.1038/120678a0.
  73. ^ Westgren A (1932). “Zur Chemie der Legierungen”. Angewandte Chemie45(2): 33. doi:10.1002/ange.19320450202.
  74. ^ Bernal JD (1935). “The Electron Theory of Metals”. Annual Reports on the Progress of Chemistry32: 181. doi:10.1039/AR9353200181.
  75. ^ Pauling L (1923). “The Crystal Structure of Magnesium Stannide”. J. Am. Chem. Soc45 (12): 2777. doi:10.1021/ja01665a001.
  76. ^ Pauling L (1929). “The Principles Determining the Structure of Complex Ionic Crystals”. J. Am. Chem. Soc51 (4): 1010. doi:10.1021/ja01379a006.
  77. ^ Dickinson RG; Raymond AL (1923). “The Crystal Structure of Hexamethylene-Tetramine” (PDF)J. Am. Chem. Soc. 45: 22. doi:10.1021/ja01654a003.
  78. ^ Müller A (1923). “The X-ray Investigation of Fatty Acids”. Journal of the Chemical Society123: 2043. doi:10.1039/ct9232302043.
  79. ^ Saville WB; Shearer G (1925). “An X-ray Investigation of Saturated Aliphatic Ketones”. Journal of the Chemical Society127: 591. doi:10.1039/ct9252700591.
  80. ^ Bragg WH (1925). “The Investigation of thin Films by Means of X-rays”Nature115 (2886): 266. Bibcode:1925Natur.115..266Bdoi:10.1038/115266a0.
  81. ^ de Broglie M; Trillat JJ (1925). “Sur l’interprétation physique des spectres X d’acides gras”. Comptes rendus hebdomadaires des séances de l’Académie des sciences180: 1485.
  82. ^ Trillat JJ (1926). “Rayons X et Composeés organiques à longe chaine. Recherches spectrographiques sue leurs structures et leurs orientations”. Annales de Physique6: 5. doi:10.1051/anphys/192610060005.
  83. ^ Caspari WA (1928). “Crystallography of the Aliphatic Dicarboxylic Acids”. Journal of the Chemical Society?: 3235. doi:10.1039/jr9280003235.
  84. ^ Müller A (1928). “X-ray Investigation of Long Chain Compounds (n. Hydrocarbons)”Proc. R. Soc. Lond. 120 (785): 437. Bibcode:1928RSPSA.120..437Mdoi:10.1098/rspa.1928.0158.
  85. ^ Piper SH (1929). “Some Examples of Information Obtainable from the long Spacings of Fatty Acids”. Transactions of the Faraday Society25: 348. doi:10.1039/tf9292500348.

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