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Generalized Crystallography

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Science of Crystal Structures
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Abstract

X-ray crystal structure analysis can now be seen as a special kind of microscopy which is being extended to the recognition and examination of many kinds of ordered structure more general than crystals and which leads to their synthesis or construction by various methods. Electron microscopy and many other techniques now combine to give a coherent science of structure at the scale range of Ångstroms to microns, atoms to assemblies visible to the eye, which should continue to be called “crystallography” although it overlaps with nanotechnology, molecular biology, and solid state physics. Most generally, “a crystal is a structure the description of which is much smaller than the structure itself” and this view leads to the consideration of structures as carriers of information and on to wider concerns with growth, form, morphogenesis, and life itself.

Nulla cogente natura, sed concursu quodam fortuito atomorum

Cicero [2] (106–43 bc) De Natura Deorum 1:24

(Not by teleology, but by the chance association of atoms).

Structural Chemistry 2002, 13(3/4):215–220.

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References

  1. A. L. Mackay, 2001.

    Google Scholar 

  2. Cicero, better known for his literary writings, was the editor of the text of Lucretius’ “De rerum natura,” [“On the Nature of Things,” a title also used by William Bragg for a lecture series on the structure of matter at the Royal Institution]. He also found and restored the tomb of Archimedes in Sicily and perhaps also saw the anti-Kythera machine, a complex analog astronomical computer, or something like it. Our school teaching has underestimated the scientific activities of antiquity.

    Google Scholar 

  3. Plato, in particular, in spite of the reputed legend “let no one ignorant of geometry enter here,” is supposed to have suppressed the works of Democritos and propagated the technology of state myths to which would be attributed the social order.

    Google Scholar 

  4. George Sarton, doyen of historians of science, labels the influence of Plato’s “Timaeus” as an evil one.

    Google Scholar 

  5. Sokal, Alan; Bricmont, Jean, Intellectual Impostures; Profile: London 1998.

    Google Scholar 

  6. However, the social structure of the those dealing with crystallography is so coherent and is formalized by many national crystallographic societies and by the International Union of Crystallography, that a change of name would be quite undesirable, although the subject matter and techniques may change. See Fifty Years of X-ray Diffraction; Ewald, P. P., ed; IUC, in 1992.

    Google Scholar 

  7. van 't Hoff, J. H. Stereo-isomerism, Encyclop. Brit., 11th edn., 1910, 25, 890.

    Google Scholar 

  8. Bernal, J. D. Science and Industry in the Nineteenth Century; London, 1953. Routledge, Kegan Paul, London.

    Google Scholar 

  9. Newton was born, a posthumous child, on Christmas day in the year (1642) that Galileo died.

    Google Scholar 

  10. Tandy, P. Crystallogr. News (BCA), 15–23 (June 1999) and earlier in Geolo. Curator, 1998, 6, 333. Groth, P. Physikalische Krystallographie; Engelmann, Leipzig, 1895 (contains a large section of advertisements for crystallographic models).

    Google Scholar 

  11. See the important essay by Ludwig Boltzmann Models, Encyclop. Brit. 11th edn., 1910.

    Google Scholar 

  12. P. Redondi, in “Galileo, Heretic” suggests that Galileo was induced to plead guilty to the heresy of heliocentricism so that the more serious crime of atomism (which would question the nature of transsubstantiation) should not be ventilated.

    Google Scholar 

  13. There are about four different types of machine. It is used for making prototypes and models in the size range of 1 to 30 cm, but is as yet not economic for serial production.

    Google Scholar 

  14. Microcosmic salt, an ammonium sodium hydrogen orthophosphate, was so named because it is found in decomposing human urine, “the microcosmos.”

    Google Scholar 

  15. Blanchard, P. Alliage (Nice), 1999, p. 47.

    Google Scholar 

  16. At the other end of the scale of sizes, the devices for using Global Positioning System (GPS), now extremely cheap through nanotechnology, apply the nonintuitive equations of general relativity.

    Google Scholar 

  17. Nature (London), 1996, 383, 772, (1996).

    Google Scholar 

  18. Rudyard Kipling, in “The Secret of the Machines,” wrote “But remember please the Law by which we live, / We are not built to comprehend a lie, / We can neither love nor pity nor forgive, / If you make a slip in handling us you die.” (Not really well-designed poetry, but like the first machines themselves!)

    Google Scholar 

  19. See the essay on Hessen by Paul Josephson. Introducer of Quantum Mechanics and Relativity into Russia, Hessen’s fate showed the tight connections between science, technology, ideology, and power.

    Google Scholar 

  20. James Clerk Maxwell’s essay on atoms (from the 9th edn.) is to be found quoted in the 11th edn. of the Encycl. Brit. under “Molecule.” The scale of molecular structure was then (about 1900) estimated at 10−8 cm.

    Google Scholar 

  21. Zou, X. Electron Crystallography of Inorganic Structures; Stockholm University: Stockholm, 1995.

    Google Scholar 

  22. Delone, B. N.; Padurov, N.; Aleksandrov, A. Matematicheskie Osnovy Strukturnogo Analiza Kristallov; ONTI: Leningrad-Moscow, 1934.

    Google Scholar 

  23. William Kingdon Clifford (1845–1879) (whose tomb is in Highgate Cemetery) was also concerned with the application of mathematics to chemical structure as “chemico-algebraic theory.”

    Google Scholar 

  24. A Mathematica package “Clifford Algebra Calculations” has been prepared by Jose Luis Aragon, who has also demonstrated crystallographic calculations in several papers; email: joseluis@iec.csic.es. “Modern geometric calculations in crystallography” Aragón, G.; Aragon, J. L.; Davila, F.; Gómez, A.; Roderíguez, M. A., Geometric Algebra: A Geometric Approach to Computer Vision, Neural and Quantum Computing, Robotics and Engineering. (eds.) E. BayroCornochano and G. Sobczyk, Bu˙khäusen, Boston, 2001 [ISBN-081-76-4199-8].

    Google Scholar 

  25. Lord, E. A.; Wilson, C. B. The Mathematical Description of Shape and Form; Wiley: New York, 1984; Thompson, D’Arcy Wentworth On Growth and Form, Cambridge, 1917.

    Google Scholar 

  26. Friedrichs, Olaf Delgado; Dress, Andreas W. M.; Huson, Daniel H.; Klinowski, Jacek; Mackay, Alan L. Nature 1999, 400, 644.

    Google Scholar 

  27. Needham, J. Order and Life; Yale University Press: New Haven, CT, 1936.

    Google Scholar 

  28. “Essays on structural crystallography,” XIII Mineral. Sb. L’VOV Geol. Obschch., 1962, 16, 41.

    Google Scholar 

  29. Hardy, H. K.; Silcock, J. M. J. Inst. Met., 19551956, 24, 423.

    Google Scholar 

  30. Shubnikov, A. V. Kristallografiya, 1960, 5, 489.

    Google Scholar 

  31. Klinowski, J.; Mackay, A. L. Phil. Trans. Roy. Soc. London, 1996, A 354, 1069.

    Google Scholar 

  32. Zocher, H.; Török, C. Acta Crystallogr., 1967, 22, 751.

    Article  CAS  Google Scholar 

  33. Klug, A.; Franklin, R. E.; Humphreys-Owen, S. P. F. Biochim. Biophys. Acta 1959, 32, 203.

    Article  CAS  Google Scholar 

  34. Ball, P. “The Self-Made Tapestry. Pattern Formation in Nature”; Oxford Univ. Press: Oxford, 1999; Ozin, G. A. Acc. Chem. Res. 1997, 30, 17; Hyde, S.; Andersson, S.; Larsson, K.; Blum, Z.; Landh, T.; Lidin, S.; Ninham, B. W. The Language of Shape; Elsevier: Amsterdam, 1997.

    Google Scholar 

  35. Mackay, A. L. Izv. Jugosl. Centr. Kristallogr. (Zagreb), 1975, 10, 15; Comp. Math. Appl. 1986, 12B, 21; Proc. R. Soc. London A 1993, 442, 47.

    Google Scholar 

  36. R. E. Latham’s translation in Penguin Classics: “Lucretius: On the Nature of the Universe” (rev. edn, 1994) provides understanding, but I happen to have the 2nd edition of Thomas Creech (1659–1700), London, 1717, which is a marvel of scholarship, and of the technology of printing, and which provides direct access to the actual words of the author formulated more than two thousand years ago. Lucretius final words on chemical bonding: “When the textures of two substances are mutually contrary, so that the hollows in the ones correspond to full sections in the other and vice versa, then connection between them is most perfect. It is even possible for some things to be coupled together, as though linked by rings and hooks” is immediately followed by a horrific description of the medical and social effects of the plague in Athens. Both topics are still worth our attention.

    Google Scholar 

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Acknowledgments

On this special occasion it is appropriate to acknowledge, as well as my immediate colleagues, especially those who have given me a congenial home at Birkbeck, the long-range influences of three of the great polymaths and encyclopedists who continue to affect us with their perceptions of science and civilisation. These are, Titus Lucretius Carus [36] (ca. 99–55 BC), Denis Diderot (1713–1784), and John Desmond Bernal (1901–1971). Modern crystallography has taken place within the Republic of Science, the community of those who seek to acquire “reliable knowledge” about the natural world by verifiable experimentation rather than by revelation and it has been a great privilege to have taken a small part in it.

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Correspondence to Alan L. Mackay .

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Mackay, A.L. (2015). Generalized Crystallography. In: Hargittai, I., Hargittai, B. (eds) Science of Crystal Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-19827-9_4

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