From quartz to quasicrystals: Probing nature's geometric patterns in crystalline substances

Crystallography Reviews

Volumn 12, Issue 2, 2006, Pages 125-180

  Lalena, John N ^a,b,c,d,e  

^a EMBRY RIDDLE AERONAUTICAL UNIVERSITY   (United States)

^b VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

^c Univ of Maryland   (United States)

^d University College Europe   (United States)

^e NONE   (Germany)

Author keywords

Geometric crystallography; Group theory; Polyhedra; Symmetry

Indexed keywords

CRYSTAL STRUCTURE; CRYSTALLINE MATERIALS; FRACTALS; X RAY CRYSTALLOGRAPHY;

CHRONOLOGICAL DOCUMENTATION; GEOMETRIC CRYSTALLOGRAPHY; GROUP THEORY; POLYHEDRA; SYMMETRY;

QUARTZ;

EID: 33750530136     PISSN: 0889311X     EISSN: 14763508     Source Type: Journal    
DOI: 10.1080/08893110600838528     Document Type: Article

References (92)

1. K.H. Veltman. Geometric games: a brief history of the not so regular solids, published electronically at http://www.mmi.unimaas.nl/people/Veltman/ books/1990%20Geometric%20Games.pdf.
2. N. Gier, G. Adele. The regular polyhedra: from the ancient Scots to Johannes Kepler, presented at the Idaho, Coun. Teach. Math., Boise, October (2003).
3. L. Euler. Elemental doctrinae solidorum, Novi commentarii academiae scientarum Petropolitanae, 4 (1752/3) 109,
4. reprinted in Opera Omnia Series I, 26, 71.
5. N.W. Johnson. Canad. J. Math., 18, 169 (1966).
6. V. Zalgaller. Convex Polyhedra with Regular Faces. Consultants Bureau, New York (1969).
7. A. Baki, Al Khwarizmi's Contributions to the Science of Mathematics: Al Kitab Al Jabr Wa'l Muqabalah. J. Islamic Acad. Sci., 5(3) (1992).
8. P.R. Cromwell. Polyhedra. Cambridge, United Kingdom (1997).
9. G.S. Szpiro. Kepler's Conjecture: How Some of the Greatest Minds In History Helped Solve One of the Oldest Math Problems in World, p. 218, Hoboken, New Jersey (2003).
10. A. Schierbeek, Leeuwenhoek and Medicine: the Study of Crystals, Chemistry, Physics and Ecology, in Measuring the Invisible World: the Life and Works of Antoni van Leeuwenhoek FRS, p. 187, Abelard-Schuman, London (1959).
11. L. Touret, Crystal Models: Milestone in the Birth of Crystallography and Mineralogy as Sciences, in Dutch Pioneers of the Earth Sciences, J.L.R. Touret and R.P.W. Visser (Eds), p. 43, Koninklijke Nederlandse Akademie van Wetenschapen, Amsterdam (2004).
12. F.E. Wright. American Miner., 27, 145 (1942).
13. G.F. Kunz. American Miner., 3, 60 (1918).
14. G.F. Black. American Miner., 3, 90 (1918).
15. S. Katzir. Hist. Stud. Phys. Biol. Sci., 35(1), 35 (2004).
16. Friedrich Mohs - More Than 10 Hardness Minerals, in Bulletin of the Mineraiogical Society of Southern California, July (1999), Janet Gordon (Ed.), The Mineralogical Society of Southern California.
17. F. Mohs. Edinburgh Philos. J., 8, 275 (1823).
18. B. Kahr. Cryst. Growth Des., 4, 3 (2004).
19. F. Arago. Memoires de la Classe des Sciences Mathematiques et Physiques de l'Institut Imperial de France, 1, 93 (1811).
20. L. Pasteur, First lecture from Leçons de chimie professées en 1860 (Delivered to the Société Chimique of Paris, published in 1861 (translation from Researches on the Molecular Asymmetry of Natural Organic Products, Alembic Club Reprints, No. 14).
21. J.B. Biot. Memoires de la Classe des Sciences Mathematiques et Physiques de l'Institut Imperial de France, 1, 1 (1812).
22. D. Brewster, Mem. Wernerian Nat. Hist. Soc., 3, 50 (1819-20);
23. Ann. Phys., 69, 1 (1881).
24. F.E. Neumann. Annales de Chimie et de Physique, 31, 177 (1834).
25. P. Curie, J. Curie. Bull. Soc. Fr. Mineral, 3, 90 (1880).
26. W.G. Hankel. Abh. Sachs., 12, 457 (1881).
27. G. Lippmann. C.R. Hebd. Seances Acad. Sci., 92, 1049 (1881).
28. R.W. Calhn. Nature, 400(6745), 625 (1999).
29. R.G. Kostyanovsky, Mendeleev Communications, Electronic version, Issue 3 (2003).
30. L. Pasteur, Mem. Wernerian Nat. Hist. Soc., 3, 50 (1819-20);
31. Ann. Phys., 69, 1 (1821).
32. Lord Kelvin. Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. London (1904), Appendix H, 602.
33. M.L. Frankenheim. Die Lehre von der Cohäsion, umfussened die Elasticität der Gase, die Elasticitcät und Coharenz der Flüssigen und festen Körper und die Krystallkunde, Breslau (1835).
34. M.A. Bravais. J. École. Polytech., 19, 1 (1850).
35. M.A. Bravais. J. École. Polytech., 20, 101 (1851).
36. J.A.J. Crilly. Arthur Cavley: Mathematician Laureate of the Victorian Age, John Hopkins University Press (2003).
37. Fifty Years of X-Ray Diffraction, P.P. Ewald (Ed.), I.U.Cr. Press, p. 17 (1962).
38. B.N. Delone. Tr. Inst. Istor. Estestvozn. Tekh. Akad. Nauk. SSSR, 10, 5 (1956).
39. M. Senechal, R.V. Galiuilin. Struct. Topol., 10, 5 (1984).
40. R.V. Galiuilin. Crystallogr. Reports, 48, 899 (2003).
41. A.V. Shubnikov. Fifty Years of X-Ray Diffraction, p. 493, I.U.Cr. Press (1962).
42. P. Engel. American Miner., 74, 1394 (1989).
43. W. Barlow. Z. Kryst. Min., 23, 1 (1894).
44. Autobiography by Max von Laue in Fifty Years of X-Ray Diffraction, P.P. Ewald (Ed.), p. 278, I.U.Cr. Press (1962).
45. W. Friedrich, P. Snipping, M. Laue. Sitzber. Math.-Physik. Klasse Bayer. Akad. Wiss. München, 303 (1912).
46. B. Lemmel, The Nobel Medals and the Medal for the Memorial Prize in Economic Sciences, The Nobel Foundation.
47. W.H. Bragg, Nature (London), 90, 219 (1912);
48. W.H. Bragg, idem, Nature, (London) 90, 360 (1912);
49. W.H. Bragg, idem, Nature (London), 90, 572 (1912).
50. W.H. Bragg, W.L. Bragg, Proc. of the Royal Soc. (London), 88, 428;
51. W.H. Bragg, W.L. Bragg, idem, 89, 246 (1913).
52. P. Debye, P. Scherrer. Phys. Z., 17, 277 (1916).
53. Autobiography by Albert W. Hull in Fifty Years of X-Ray Diffraction, P.P. Ewald (Ed.), p. 582, I.U.Cr. Press (1962).
54. A.W. Hull. Phys. Rev., 10, 661 (1917).
55. H.M. Rietveld. Acta Cryst., 20, 508 (1966).
56. C.G. Darwin. Phil. Mag., 27, 315 (1914).
57. P.P. Ewald. Ann. Phys., 54, 519 (1917).
58. P. Niggli. Geometrishe Kristillographie des Diskontinuums, p. 482, Gebrüder Burntraeger, Leipzig (1919).
59. The Development of X-Ray Diffraction in U.S.A. in Fifty Years of X-Ray Diffraction, R.W.G. Wyekoff, P.P. Ewald (Eds), p. 430," I.U.Cr. Press (1962).
60. C. Hermann. Z. Kristallogr., 76, 559 (1931).
61. C. Mauguin. Z. Kristallogr., 76, 542 (1931).
62. N.D. Mermin. Phys. Rev. Lett., 68(8), 72 (1992);
63. A. Bienenstock, P.P. Ewald. Acta Cryst., 15, 1253 (1962).
64. F. Hargreaves, R.T. Hill. J. Inst. Metals, 41, 237 (1929).
65. G. Friedel. Lecons de Cristallographie, Berger-Levrault, Paris (1926).
66. N.F. Mott. Proc. Phys. Soc. London, 60, 391 (1948).
67. M.L. Kronberg, F.H. Wilson. Trans. Met Soc. AIME, 185, 501 (1949).
68. H. Bethe. Ann. Phys., 3, 133 (1929).
69. J.H. van Vleck, A. Sherman, Revs. Modern Phys., 7, 167 (1935).
70. F. Seitz. Ann. Math., 37, 17 (1936).
71. L.P. Bouckaert, R. Smoluchoeski, E. Wigner. Phys. Rev., 50, 58 (1936).
72. L. Brillouin. Compt. Rend., 191, 198, 292 (1930).
73. K. Lonsdale. Nature, 122, 810 (London) (1928).
74. J.M. Robertson. J. Chem. Soc., 615 (1935).
75. J.M. Bijvoet. Proc. K. Ned. Akad. Wet. Ser. B, 52, 313 (1949).
76. A.F. Peerdeman, A.J. van Bommel, J.M. Bijvoet. Proc. K. Ned. Akad. Wet. Ser. B, 54, 16 (1951).
77. J.D. Bernal, D. Crowfoot. Nature, 133, 794 (1934).
78. J.D. Watson, F.H.C. Crick. Nature, 171, 964 (1953).
79. L. Muldawer. J. Appl. Cryst., 29, 309 (1996).
80. A.L. Patternson. Z. Kryst., A90, 517 (1935).
81. W.H. Zachariasen. Acta Cryst., 5, 68 (1952).
82. D. Marker, J.S. Kasper. Acta Cryst., 1, 70 (1948).
83. Fifty Years of X-Ray Diffraction, P.P. Ewald (Ed.), p. 701, I.U.Cr., Press (1962).
84. D. Shechtman, I. Blech, D. Gratias, J.W. Calm. Phys. Rev. Lett., 53, 1951 (1984).
85. A.L. Mackay, P. Kramer. Nature, 316, 17 (1985).
86. R. Munro, NIST Virtual Library at http://nvl.nist.gov/pub/nistpubs/sp958- lide/300-302.pdr
87. D. Turnbull, M.J. Aziz, The Science of Alloys for the 21st Century: a Hume-Rothery Symposium Celebration, in The Minerals, P.E.A. Turchi and R.D. Shull (Eds), Metals & Materials Society, Warrendale. PA (2000).
88. R. Towle, Personal communication, (2006).
89. J.W. Cahn. J. Res. Nat. Inst. Stand. Tech., 106, 975 (2001).
90. D.A. Rabson, N.D. Mermin, D.S. Rokhsar, D.C. Wright. Rev. Mod. Phys., 63, 699 (1991).
91. R. Lifshitz, N.D. Menmin. Acta Cryst., A48, 928 (1992).
92. R. Lifshitz, Introduction to Fourier-Space Crystallography, in Lecture Notes for the International School on Quasicrystals, May 13-20, Balatonfiüred, Hungary (1995).