This chapter provides a background on the technique of structure determination through X-ray crystallography and discusses its importance in the context of modern chemistry. It explains the basis of X-ray crystallography through an optical analogy that outlines the main relevant properties of crystalline materials and aspects of symmetry. It also examines the properties of the diffraction pattern of a single-crystal in relation to features of interest in the crystal structure. The chapter covers the geometry of diffraction, symmetry observed in the pattern, and the variation of intensity in the discrete diffraction measurements. It cites available sources of X-rays for crystallography.<\/p>","DOI":"10.1093\/hesc\/9780198700975.003.0001","type":"book-chapter","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T11:41:27Z","timestamp":1694778087000},"source":"Crossref","is-referenced-by-count":0,"title":["Fundamentals of X-ray crystallography"],"prefix":"10.1093","author":[{"given":"William","family":"Clegg","sequence":"first","affiliation":[]}],"member":"286","published-online":{"date-parts":[[2023,8,31]]},"container-title":["X-Ray Crystallography"],"original-title":["Fundamentals of X-ray crystallography"],"language":"en","link":[{"URL":"https:\/\/www.oxfordsciencetrove.com\/display\/10.1093\/hesc\/9780198700975.001.0001\/isbn-9780198700975-book-part-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T08:42:09Z","timestamp":1707208929000},"score":14.057762,"resource":{"primary":{"URL":"https:\/\/www.oxfordsciencetrove.com\/view\/10.1093\/hesc\/9780198700975.001.0001\/isbn-9780198700975-book-part-1"}},"issued":{"date-parts":[[2015,5,21]]},"ISBN":["9780198700975","9780191992353"],"references-count":0,"URL":"https:\/\/doi.org\/10.1093\/hesc\/9780198700975.003.0001","published":{"date-parts":[[2015,5,21]]}},{"indexed":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T03:39:28Z","timestamp":1715744368694},"reference-count":0,"publisher":"Oxford University Press","isbn-type":[{"value":"9780198700975","type":"print"},{"value":"9780191992353","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2015,5,21]]},"abstract":"
This chapter highlights the various steps of a typical crystal structure determination, and describes a number of commonpotential problems together with ways of dealing with them. It shows an outline of crystal structure determination in a simplified form known as a schematic flowchart. It also analyzes the intensities of X-rays diffracted by a crystal that depend on the crystal size, unit cell volume, and types and numbers of atoms in the unit cell. The chapter talks about diffracted intensities that are directly proportional to the crystal volume and the absorption of X-rays by crystals, which increases exponentially with crystal dimensions. It explains how the amount of absorption depends on the X-ray wavelength and on the chemical composition.<\/p>","DOI":"10.1093\/hesc\/9780198700975.003.0002","type":"book-chapter","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T12:56:52Z","timestamp":1694782612000},"source":"Crossref","is-referenced-by-count":0,"title":["X-ray crystallography in practice"],"prefix":"10.1093","author":[{"given":"William","family":"Clegg","sequence":"first","affiliation":[]}],"member":"286","published-online":{"date-parts":[[2023,8,31]]},"container-title":["X-Ray Crystallography"],"original-title":["X-ray crystallography in practice"],"language":"en","link":[{"URL":"https:\/\/www.oxfordsciencetrove.com\/display\/10.1093\/hesc\/9780198700975.001.0001\/isbn-9780198700975-book-part-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T08:42:10Z","timestamp":1707208930000},"score":14.047288,"resource":{"primary":{"URL":"https:\/\/www.oxfordsciencetrove.com\/view\/10.1093\/hesc\/9780198700975.001.0001\/isbn-9780198700975-book-part-2"}},"issued":{"date-parts":[[2015,5,21]]},"ISBN":["9780198700975","9780191992353"],"references-count":0,"URL":"https:\/\/doi.org\/10.1093\/hesc\/9780198700975.003.0002","published":{"date-parts":[[2015,5,21]]}},{"indexed":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T03:39:27Z","timestamp":1715744367246},"reference-count":0,"publisher":"Oxford University Press","isbn-type":[{"value":"9780198700975","type":"print"},{"value":"9780191992353","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2015,5,21]]},"abstract":"
This chapter illustrates the process of X-ray crystal structure determination through a series of examples drawn from a wide range of structural chemistry research. It analyzes the complex [Et4<\/sub>N] [Hg(SR)3<\/sub>], which is an empirical formula corresponding to a monomeric structure. It also addresses the key questions that are answered by crystal structure determination regarding the anion that can be a dimer with bridging thiolate ligands, a higher oligomer, or a polymer. The chapter talks about the equivalence of different isotopes of an element in X-ray diffraction and the determination of the absolute structure of a chiral molecule by resonant scattering effects. It outlines the occurrence of disorder that can be modelled by the use of atoms with partial occupancy in alternative positions.<\/p>","DOI":"10.1093\/hesc\/9780198700975.003.0003","type":"book-chapter","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T06:55:52Z","timestamp":1694760952000},"source":"Crossref","is-referenced-by-count":0,"title":["X-ray crystallography case studies"],"prefix":"10.1093","author":[{"given":"William","family":"Clegg","sequence":"first","affiliation":[]}],"member":"286","published-online":{"date-parts":[[2023,8,31]]},"container-title":["X-Ray Crystallography"],"original-title":["X-ray crystallography case studies"],"language":"en","link":[{"URL":"https:\/\/www.oxfordsciencetrove.com\/display\/10.1093\/hesc\/9780198700975.001.0001\/isbn-9780198700975-book-part-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T08:42:11Z","timestamp":1707208931000},"score":14.001267,"resource":{"primary":{"URL":"https:\/\/www.oxfordsciencetrove.com\/view\/10.1093\/hesc\/9780198700975.001.0001\/isbn-9780198700975-book-part-3"}},"issued":{"date-parts":[[2015,5,21]]},"ISBN":["9780198700975","9780191992353"],"references-count":0,"URL":"https:\/\/doi.org\/10.1093\/hesc\/9780198700975.003.0003","published":{"date-parts":[[2015,5,21]]}},{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T05:18:11Z","timestamp":1770527891959,"version":"3.49.0"},"reference-count":0,"publisher":"Oxford University Press","isbn-type":[{"value":"9780199686995","type":"print"},{"value":"9780191918377","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2013,12,12]]},"abstract":" In this chapter we summarize the basic concepts, formulas and tables which constitute the essence of general crystallography. In Sections 1.2 to 1.5 we recall, without examples, definitions for unit cells, lattices, crystals, space groups, diffraction conditions, etc. and their main properties: reading these may constitute a useful reminder and support for daily work. In Section 1.6 we establish and discuss the basic postulate of structural crystallography: this was never formulated, but during any practical phasing process it is simply assumed to be true by default. We will also consider the consequences of such a postulate and the caution necessary in its use. We recall the main concepts and definitions concerning crystals and crystallographic symmetry. Crystal. This is the periodic repetition of a motif (e.g. a collection of molecules, see Fig. 1.1). An equivalent mathematical definition is: the crystal is the convolution between a lattice and the unit cell content (for this definition see (1.4) below in this section). Unit cell. This is the parallelepiped containing the motif periodically repeated in the crystal. It is defined by the unit vectors a, b, c, or, by the six scalar parameters a, b, c, \u03b1, \u03b2, \u03b3 (see Fig. 1.1). The generic point into the unit cell is defined by the vector . . . r = x a + y b + z c, . . . where x, y, z are fractional coordinates (dimensionless and lying between 0 and 1). The volume of the unit cell is given by (see Fig. 1.2) . . . V = a \u2227 b \u00b7 c = b \u2227 c \u00b7 a = c \u2227 a \u00b7 b. (1.1). . .<\/p>","DOI":"10.1093\/oso\/9780199686995.003.0006","type":"book-chapter","created":{"date-parts":[[2020,11,11]],"date-time":"2020-11-11T01:34:05Z","timestamp":1605058445000},"source":"Crossref","is-referenced-by-count":1,"title":["Fundamentals of crystallography"],"prefix":"10.1093","author":[{"given":"Carmelo","family":"Giacovazzo","sequence":"first","affiliation":[]}],"member":"286","published-online":{"date-parts":[[2020,11,12]]},"container-title":["Phasing in Crystallography"],"original-title":["Fundamentals of crystallography"],"language":"en","deposited":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T21:40:10Z","timestamp":1659476410000},"score":13.866228,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/book\/42068\/chapter\/355910544"}},"issued":{"date-parts":[[2013,12,12]]},"ISBN":["9780199686995","9780191918377"],"references-count":0,"URL":"https:\/\/doi.org\/10.1093\/oso\/9780199686995.003.0006","published":{"date-parts":[[2013,12,12]]}},{"indexed":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T19:11:13Z","timestamp":1715368273249},"reference-count":57,"publisher":"IntechOpen","isbn-type":[{"value":"9781838818784","type":"print"},{"value":"9781838818791","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T00:00:00Z","timestamp":1567555200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"DOI":"10.5772\/intechopen.82693","type":"book-chapter","created":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T10:27:16Z","timestamp":1551695236000},"source":"Crossref","is-referenced-by-count":1,"title":["Crystallography of Precipitates in Metals and Alloys: (1) Analysis of Crystallography"],"prefix":"10.5772","author":[{"given":"Yoshitaka","family":"Matsukawa","sequence":"first","affiliation":[]}],"member":"3774","published-online":{"date-parts":[[2019,9,4]]},"reference":[{"key":"ref=1","doi-asserted-by":"crossref","unstructured":"Matsukawa Y, Yang HL, Saito K, Murakami Y, Maruyama T, Iwai T, et al. 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