M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 77
Текст из файла (страница 77)
At that time, however,the new observations were brought into line with classical crystallography. The change in the periodicity paradigm has been discussed[147] in the light of Thomas Kuhn’s The Structure of Scientific Revolutions [148]. Sadly, the giant of 20th century structural chemistry,Linus Pauling never accepted the notion of quasicrystals; instead, hemaintained that the phenomena interpreted as quasicrystals could beexplained in terms of known crystal formations within the realms ofclassical crystallography [149].Figure 9-64 shows some beautiful representatives of quasicrystalsand Figure 9-65 depicts another quasicrystal and a modern sculpturethat could be taken as an artistic expression of a quasicrystal althoughthe artist was not aware of the existence of such materials.
The artisticappearance of quasicrystals, however, predates their scientific entryby centuries [150]. The discovery of such cultural monuments hasgenerated lively discussions even in the general press [151].Concluding, we quote again Mackay [155], who stated thatAmorphous materials may be shapeless, but theyare not without order. Order, like beauty, is in theeyes of the beholder. If you look only with X-raydiffraction eyes, then all you see is translational9.8.
Quasicrystals(a)493(b)(c)Figure 9-64. Quasicrystals: (a–b) Flower-like icosahedral quasicrystal in aquenched Al/Mn sample (from Csanády et al.) [152]; (c) Pentagonal dodecahedronin quasicrystalline Al/Cu/Ru obtained by slow cooling from melt (courtesy of H.-U.Nissen, Zurich) [153].(a)(b)Figure 9-65.
(a) Triacontrahedral quasicrystal Al/Li/Cu (courtesy of F. Dénoyer,Orsay) [154]; (b) Sculpture resembling a quasicrystal, by Peter Hächler, Switzerland. Photograph by the authors.4949 Crystalsorder, to wit crystals. ... there is a wider range ofstructures, between those of crystals and those ofgases, ... Other structures need not be failed crystals but are sui generis.As crystallography is becoming more general, transforming itselfinto the science of structures, so may we anticipate a broadening application of the symmetry concept in the description and understandingof all possible structures [156].9.9.
Returning to ShapesConcluding our discussion of crystal symmetries, let us return nowto those exquisite shapes that we think of when the word crystal ismentioned. The words of the 19th century English writer John Ruskin[157] and drawings of C. Bunn [158] (Figure 9-66) are cited here.And remember, the poor little crystals have to livetheir lives, and mind their own affairs, in the midstof all this, as best they may. They are wonderfullylike humane creatures—forget all that is going onif they don’t see it, however dreadful; and neverthink what is to happen tomorrow. They are spitefulor loving, and indolent or painstaking, with nothought whatever of the lava or the flood whichmay break over them any day; and evaporate theminto air-bubbles, or wash them into a solution ofsalts.
And you may look at them, once understanding the surrounding conditions of their fate,with an endless interest. You will see crowds ofunfortunate little crystals, who have been forcedto constitute themselves in a hurry, their dissolvingelement being fiercely scorched away; you will seethem doing their best, bright and numberless, buttiny. Then you will find indulged crystals, whohave had centuries to form themselves in, and havechanged their mind and ways continually; and havebeen tired, and taken heart again; and have beensick, and got well again; and thought they would9.9. Returning to Shapes495Figure 9-66. Crystal characters from C. Bunn’s book [159].
Reproduced withpermission.try a different diet, and then thought better of it; andmade but a poor use of their advantages, after all.And sometimes you may see hypocritical crystals taking the shape of others, though they arenothing like in their minds; and vampire crystalseating out the hearts of others; and hermitcrab crystals living on the shells of others; and parasite crystals living on the means of others; and courtiercrystals glittering in the attendance upon others;and all these, besides the two great companies ofwar and peace, who ally themselves, resolutely to4969 Crystalsattack, or resolutely to defend. And for the close,you see the broad shadow and deadly force ofinevitable fate, above all this: you see the multitudes of crystals whose time has come; not a settime, as with us, but yet a time, sooner or later,when they all must give up their crystal ghost—when the strength by which they grew, and thebreath given them to breathe, pass away from them;and they fail, and are consumed, and vanish away;and another generation is brought to life, framedout of their ashes.References1.
G. Leclerc (Comte de) Buffon, Historie Naturelle des Minéraux, III. Paris,1783–1788, p. 433; as quoted in A. L. Mackay, A Dictionary of ScientificQuotations. Adam Hilger, Bristol, 1991, p. 43.2. K. Čapek, Anglické Listy, Československý Spisovatel, Praha, 1970. TheEnglish version cited in our text was kindly provided by Alan L. Mackay,London.3. Ibid.4. A. L. Mackay, “Duerer’s technique.” Nature 1983, 301, 652. A careful analysis of the drawing is available: E. Schröder, Dürer. Kunst und Geometrie,Akademie Verlag, Berlin, 1980.5.
S. Alvarez, “Polyhedra in (inorganic) chemistry.” Dalton Trans. 2005,2209-2233.6. Ibid.7. B. Ernst, The Magic Mirror of M. C. Escher, Ballantine Books, New York,1976.8. There is a beautiful book on the history of crystallography, Historical Atlas ofCrystallography, J. Lima-de-Faria, ed., Kluwer, Dordrecht, 1990.9. R. J. Haüy, Traité de Cristallographie, 1822.
Reprinted by Culture et Civilisation, Bruxelles, 1968.10. Ibid.11. Ibid.12. J. Kepler, Strena seu de nive sexangula, Francofurti ad Moenum: GodefridumTampach, 1611. English translation, The Six-Cornered Snowflake, ClarendonPress, Oxford, 1966.13. J. Dalton, Memoirs and Proceedings of the Manchester Literary and Philosophical Society, Manchester, 1805, vol.
6, p. 271; Alembic Club Reprints,Edinburgh, 1961, no. 2, p. 15.References49714. C. J. Schneer, “The Renaissance Background to Crystallography.” Am. Sci.1983, 71, 254–263; C. Schneer, “Kepler’s New Year’s Gift of a Snowflake.”Isis 1960, 51, 531–545.15. Kepler, The Six-Cornered Snowflake.16. Dalton, Memoirs and Proceedings of the Manchester Literary and Philosophical Society, p. 15.17. A. L.
Mackay, “Generalised Crystallography.” Izvj. Jugosl. Cent. Kristallogr.1975, 10, 15−36. See, also, A. L. Mackay, “Generalised Crystallography.”J. Mol. Struct. (Theochem) 1995, 336, 293–303; A. L. Mackay, “GeneralizedCrystallography.” Struct. Chem. 2002, 13, 215–220.18. See, e.g., L. A. Shuvalov, A. A. Urosovskaya, I. S. Zheludev, A. V. Zaleskii,S.
A. Semiletov, B. N. Grechushnikov, I. G. Chistyakov, S. A. Pikin, Sovremennaya Kristallografiya, Vol. 4, Fizicheskie Svoistva Kristallov, Nauka,Moscow, 1981.19. See, e.g., K. N. Trueblood, “Diffraction Studies of Molecular Motion inCrystals” and also, C. M. Gramaccioli, “Lattice-dynamical Interpretation ofCrystallographic Thermal Parameters,” both in Accurate Molecular Structures.
Their Determination and Importance, A. Domenicano, I. Hargittai,eds., Oxford University Press, Oxford, 1992, pp. 199–219 and pp. 220–236,respectively.20. M. J. Buerger, Elementary Crystallography, An Introduction to the Fundamental Geometrical Features of Crystals (Fourth Printing), Wiley, New York,London, Sydney, 1967; E. S. Dana, A Textbook of Mineralogy, Fourth Edition,revised and enlarged by W. E.
Ford, Wiley, New York, London, Sydney, 1932;P. M. Zorky, Arkhitektura Kristallov, Nauka, Moscow, 1968.21. Gy. Lengyel, Kézimunkák, Kossuth, Budapest, 1978.22. See, e.g., L. V. Azaroff, Introduction to Solids, McGraw-Hill, New York,Toronto, London, 1960.23. Ibid.24. Ibid.25. International Tables for Crystallography, Volume A: Space-group symmetry.Ed.
Th. Hahn. Corrected reprint of the fifth edition. Springer, 2005.26. A. V. Shubnikov, V. A. Koptsik, Symmetry in Science and Art, Plenum Press,New York and London, 1974. Russian original: Simmetriya v nauke i iskusstve,Nauka, Moscow, 1972.27. C. P. Brock and E. C. Lingafelter, “Common Misconceptions about CrystalLattices and Crystal Symmetry.” J. Chem. Educ. 1980, 57, 552–554.28. M. Senechal, “Brief History of Geometrical Crystallography.” In HistoricalAtlas of Crystallography, J. Lima-de-Faria, ed.
International Union of Crystallography and Kluwer Academic publishers, Dordrecht, Holland, 1990, pp.43–59, p. 48.29. A. L. Mackay, “The Statistics of the distribution of crystalline substancesamong the space groups.”Acta Crystallogr. 1967, 22, 329–330.30. See, e.g., A. I. Kitaigorodsky, Molecular Crystals and Molecules, AcademicPress, New York, 1973. Russian original: A. I.
Kitaigorodskii, Molekulyarnie49831.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.51.9 CrystalsKristalli, Nauka, Moscow, 1971; A. D. Mighell, V. L. Himes, J. R. Rodgers,“Space-group Frequencies for Organic Compounds.” Acta Crystallogr. A1983, 39, 737–740; J.
Donohue, “Revised Space-group Frequencies forOrganic Compounds.” Acta Crystallogr. A 1985, 41, 203–204; R. Srinivasan,“On the Space-group Frequency in Organic Structures.” Acta Crystallogr.A 1991, 47, 452; C. P. Brock, J. D. Dunitz, “Space-group frequencies.”Acta Crystallogr. A 1991, 47, 854; A. J. C. Wilson, “Kitajgorodskij andSpace-group Popularity.” ACH—Models in Chemistry 1993, 130, 183–196;C. P. Brock and J. D. Dunitz, “Towards a Grammar of Crystal Packing.” Chem.Mater. 1994, 6, 1118–1127.Shubnikov, Koptsik, Symmetry in Science and Art. Russian original:Simmetriya v nauke i isskustve.Ibid.Ibid.J. Dalton, A New System of Chemical Philosophy, p.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
