The mystery of perpendicular fivefold axes and the fourth dimension in intermetallic structures

Chemistry - A European Journal

Volumn 14, Issue 13, 2008, Pages 3908-3930

  Berger, Robert F ^a   Lee, Stephen ^a   Johnson, Jeffreys ^a   Nebgen, Ben ^a   Sha, Fernando ^a   Xu, Jiaqi ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Higher dimension; Intermetallic phases; Polytopes; Solid state structures; X ray diffraction

Indexed keywords

HIGHER DIMENSION; INTERMETALLIC PHASES; POLYTOPES; SOLID-STATE STRUCTURES; X-RAY DIFFRACTION;

LITHIUM;

EID: 53849106835     PISSN: 09476539     EISSN: 15213765     Source Type: Journal    
DOI: 10.1002/chem.200701396     Document Type: Article

References (54)

1. C. Janot, Quasicrystals: A Primer, 2nd ed., Clarendon, Oxford, 1994.
2. G. Friedel, C. R. Hebd, Seances Acad. Sci. 1913, 157, 1533-1536.
3. J. Kasper. Theory of Alloy Phases, American Society of Metals, Cleveland. OH, 1956.
4. F. Frank, J. Kasper, Acta Crystallogr. 1958, 11, 184-190.
5. F. Frank, J. Kasper, Acta Crystallogr. 1959, 12, 483-499.
6. W. Pearson, C. Shoemaker, Acta Crystallogr. Sect. B 1969, 25, 1178-1183.
7. C. Shoemaker, D. Shoemaker, Acta Crystallogr, Sect. B 1972, 28, 2957-2965.
8. Y. Yarmolyuk, P. Kripyakevich, Kristallografiya 1974, 19, 539-545.
9. D. Shoemaker, C. Shoemaker, Acta Crystallogr. Sect. B 1986, 42, 3-11.
10. S. Samson, Nature 1962, 195, 259-262.
11. S. Samson, Acta Crystallogr. 1967, 23, 586-600.
12. S. Samson, D. Hansen. Acta Crystallogr. Sect. B 1972, 28, 930-935.
13. S. Samson, Acta Crystallogr. Sect. B 1972, 28, 936-945.
14. V. Khare, N. Lalla, R. Tiwari, O. Srivaslava, J. Mater. Res. 1995, 10, 1905-1912.
15. C. Dong, Philos. Mag. A 1996, 73, 1519-1528.
16. V. Demange, J. Ghanbaja, F. Machizaud, J. Dubois, Philos. Mag. 2005, 85, 1261-1272.
17. H. Nyman, S. Andersson, Acta Crystallogr. Sect. A 1979, 35, 580-583.
18. H. Nyman, S. Andersson, Acta Crystallogr. Sect. A 1979, 35, 934-937.
19. B. Hyde, S. Andersson, Inorganic Crystal Structures, Wiley, New York. NY, 1989.
20. J.-F. Sadoc, J. Phys. Let. 1983, 44, L707-L715.
21. J.-F. Sadoc, R. Mosseri, Geometrical Frustration, Cambridge University Press, Cambridge, UK, 1999.
22. P. Villars, L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases, 2nd ed., ASM International, Materials Park, OH, 1991.
23. R. Ramirez, R. Nesper, H.-G. von Schnering, Z. Naturforsch. A. 1986, 41, 1267-1282.
24. R. Nesper, H.-G. von Schnering, J. Solid State Chem. 1987, 70, 48-57.
25. A. Johansson, S. Westman, Acta Chem. Scand. 1970, 24, 3471-3479.
26. S. Thimmaiah, K. Richter, S. Lee, B. Harbrecht, Solid State Sci. 2003, 5, 1309-1317.
27. L. Arnberg, A. Jonsson, S. Westman, Acta Chem. Scand. Ser.A 1976, 30, 187-192.
28. M. Booth, J. Brandon, R. Brizard, C. Chieh, W. Pearson, Ada Crystallogr. Sect. B 1977, 33, 30-36.
29. L. Westin, Chem. Ser. 1971, 1, 127-135.
30. A. Koster, J. Schoone, Acta Crystallogr. Sect. B 1981, 37, 1905-1907.
31. L. Westin, L.-E. Erdshammar, Acra Chem. Scand. 1972, 26, 3619-3626.
32. S. Lidin, M. Jacob, A.-K. Larsson, Acta Crystallogr. Sect. C 1994, 50, 340-342.
33. F. Bonhomme, K. Yvon, J. Alloys Compd. 1995, 227, L1-L3.
34. W. Hornfeck, S. Thimmaiah, S. Lee, B. Harbrecht, Chem. Eur. J. 2004, 10, 4616-4626.
35. V. Smetana, V. Babizhetskyy, G. Vajenine, A. Simon, Angew. Chem. 2006, 118, 6197-6200:
36. Angew. Chem. Int. Ed. 2006, 45, 6051-6053.
37. S. Mahne, B. Harbrecht, J. Alloys Compd. 1994, 203, 271-279.
38. A. Bradley, P. Jones, J. Inst. Met. 1933, 51, 131-162.
39. C. Gazzara, R. Middleton, R. Weiss, E. Hall, Acta Crystallogr. 1967, 22, 859-862.
40. R. Berger, S. Lee, R. Hoffmann, Chem. Eur. J. 2007, 7852-7863.
41. T. Nasch, W. Jeitschko, J. Solid State Chem. 1999, 143, 95-103.
42. M. Fomasini, B. Chabot, E. Parthé, Acta Crystallogr. Sect. B 1978, 34, 2093-2099.
43. Cerius2, version 3.8. Molecular Simulations, San Diego, CA, 1998.
44. H. Manning, Geometry of Four Dimensions, Macmillan, New York, NY, 1914.
45. E. Jouffret, Traité Elémentaire de Géomé trie àQuatre Dimensions et Introduction à la Géomé trie ân-Dimensions. Gauthier-Villars, Paris, 1903.
46. I. Stringham, Am. J. Math. 1880, 3, 1-14.
47. H. Coxeter, Regular Polytopes, 3rd ed., Dover, New York, NY, 1973.
48. M. Kléman, J.-F. Sadoc, A Phys. Lett. 1979, 40, L569-L574.
49. D. Nelson, M. Widom, Nucl. Phys. B 1984, 240, 113-139.
50. T. Banchoff, Beyond the Third Dimension; Scientific American Library, New York, NY, 1990.
51. M. Ladd, R. Palmer, Structure Determination by X-ray Crystallography, 2nd ed., Plenum, New York, NY. 1985.
52. S. Samson, Acta Crystallogr. 1965, 19, 401-413.
53. M. Feuerbacher, Z. Kristallogr, 2007, 222, 259-288.
54. V. Elser, N. Sloane, A Phys. A 1987, 20, 6161-6168.