Aperiodic Crystals: From Modulated Phases to Quasicrystals

Aperiodic Crystals: From Modulated Phases to Quasicrystals

Volumn 9780198567776, Issue , 2007, Pages 1-480

  Janssen, Ted ^a   Chapuis, Gervais ^b   de Boissieu, Marc ^c  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b EPFL   (Switzerland)

^c CNRS   (France)

Author keywords

Anorganic compounds; Aperiodic crystals; Crystallography; Metallic alloys; Minerals; Organic compounds; Solid state matter; Superspace; Theory of condensed matter

Indexed keywords

AMORPHOUS MATERIALS; CONDENSED MATTER PHYSICS; CRYSTALLOGRAPHY; CRYSTALS; ELECTRONIC PROPERTIES; MINERALS; ORGANIC COMPOUNDS; ORGANIC MINERALS; QUASICRYSTALS;

ANORGANIC COMPOUNDS; CONDENSED MATTER; LATTICE PERIODICITY; METALLIC ALLOYS; ORDERED STRUCTURES; STRUCTURE AND PHYSICAL PROPERTIES; STRUCTURE DETERMINATION; SUPERSPACE;

CRYSTAL STRUCTURE;

EID: 84921840741     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780198567776.001.0001     Document Type: Book

References (339)

1. Abe, E., Pennycook, S. J., and Tsai, A.P. (2003). Direct observation of a local thermal vibration anomaly in a quasicrystal. Nature, 421, 347-50.
2. Abe, E., Yan, Y., and Pennycook, S.J. (2004). Quasicrystals as cluster aggregates. Nature Materials, 3, 759-767.
3. Amemiya, Y. (1995). Imaging Plates for Use with Synchrotron-Radiation. Journal of Synchrotron Radiation, 2, 13-21.
4. Arakcheeva, A. (2006). Personal communication.
5. Arakcheeva, A. and Chapuis, G. (2005). Atomic clusters and phase transitions in the metastable β-Ta phase between 4.2 and 293 K. Europhysics Letters, 69, 378-84.
6. 4. Acta Cryst. B, 62, 52-9.
7. Ashraff, J.A., Luck, J.-M., and Stinchcombe, R.B. (1990). Dynamical properties of twodimensional quasicrystals. Phys. Rev. B, 41, 4314.
8. Aubry, S. and André, G. (1980). Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Israel Phys. Soc., 3, 133.
9. Aubry, S. and Le Daeron, P.Y. (1983). The discrete Frenkel-Kontorova model and its extensions I. Exact results for the ground-states. Physica D, 8, 381-422.
10. Audier, M., Duneau, M., de Boissieu, M., Boudard, M., and Letoublon, A. (1999). Superlattice ordering of cubic symmetry in an icosahedral AlPdMn phase. Phil. Mag. A., 79, 255-70.
11. 4. Phys. Rev. B, 22, 3408-13.
12. Axel, F. and Aubry, S. (1981). Spatially modulated phases of a one-dimensional lattice model with competing interactions. J. Phys. C, 14, 5433-51.
13. Baake, M. and Moody, R.V. (2000). Directions in mathematical quasicrystals. Providence R.I.: American Mathematical Society.
14. Baake, M., Moody, R.V., Richard, C., and Sing, B. (2003). Which distributions of matter diffract? In Quasicrystals (ed. H.-R. Trebin), pp. 188-207. Weinheim: Wiley-VCH.
15. Bachheimer, J. P. (1980). An anomaly in the beta-phase near the alpha-beta transition of quartz. Journal De Physique Lettres, 41, L559-61.
16. Bak, P. and von Boehm, J. (1980). Ising model with solitons, phasons and 'the devil's staircase'. Phys. Rev. B, 21, 5297-308.
17. Barbier, L., Floc, D. Le, Calvayrac, Y., and Gratias, D. (2002). Identification of the atomic structure of the fivefold surface of an icosahedral Al-Pd-Mn quasicrystal: helium diffraction and scanning tunneling microscopy studies. Phys. Rev.Lett., 88, 0855061-4.
18. Belin-Ferré, E., Fontaine, M.-F., Thirion, J., Kameoka, S., Tsai, A.P., and Dubois, J.M. (2006). Electronic structure of leached AlCuFe quasicrystals used as catalysts. Phil. Mag., 86, 687-92.
19. Bennema, P., Balzuweit, K., Dam, B., Meekes, H., Verheijen, M.A., and Vogels, L.J.P. (1991). Morphology of modulated crystals and quasicrystals. J. Phys. D, 24, 186-98.
20. Bernard, L., Currat, R., Delamoye, P., Zeyen, C.M.E., Hubert, S., and de Kouchkovsky, R. (1983). ThBr4 phasons. J. Phys. C, 16, 433.
21. Beurskens, P.T., Beurskens, G., Bosman, W.P., de Gelder, R., Garcia-Granda, S., Gould, R.O., Israel, R., and Smits, J.M.M. (1996). The DIRDIF-96 program system. Crystallography Laboratory, University of Nijmegen, The Netherlands.
22. Bindi, L., Bonazzi, P., Dušek, M., Petříček, V., and Chapuis, G. (2001). Five-dimensional structure refinement of natural melilite, (Ca1.89Sr0.01Na0.08K0.02)(Mg0.92Al0.08) (Si1.98Al0.02)O7. Acta Cryst. B, 57, 739-46.
23. Blinc R. and Levanyuk A.P. (ed.) (1986). Incommensurate phases in dielectrics-fundamentals, Amsterdam. North-Holland, Modern Problems in Condensed Matter Sciences Vol.14.1.
24. Böhm, H. (1975). Interpretation of X-ray-scattering patterns due to periodic structural fluctuations. Journal of Applied Crystallography, 8, 202.
25. Bohr, H. (1952). Collected Mathematical Works. II Almost periodic functions. Copenhagen: Dansk Matematisk Forening.
26. Bombieri, E. and Taylor, J.E. (1986). Which distributions of matter diffract? An initial investigation. In International workshop on aperiodic crystals (ed. D. Gratias and L. Michel), pp. C3: 19-28. Les Ulis: Les éditions de physique.
27. Boudard, M., Bourgeat-Lami, E., de Boissieu, M., Janot, C., Durand-Charre, M., Klein, H., Audier, M., and Hennion, B. (1995). Czokralski growth of AlPdMn quasicrystal. Phil. Mag. Lett., 71, 11-6.
28. Boudard, M., de Boissieu, M., Janot, C., Heger, G., Beeli, C., Nissen, H-U., Vincent, H., Ibberson, R., Audier, M., and Dubois, J.-M. (1992). Neutron and X-ray single-crystal study of the Al-Pd-Mn icosahedral phase. J.Phys. Cond. Matt., 4, 10149-68.
29. Boudard, M., de Boissieu, M., Letoublon, A., Hennion, B., Bellissent, R., and Janot, C. (1996). Phason softening in the AlPdMn icosahedral phase. Europhys. Lett., 33(3), 199-204.
30. Brill, W. and Ehses, K-H. (1985). The incommensurate phase of betaine calcium chloridedihydrate. Jap. J. Appl. Phys. Suppl., 24, 826.
31. Brouns, E., Visser, J.W., and de Wolff, P.M. (1964). An anomaly in the crystal structure of Na2CO3. Acta Cryst., 17, 614.
32. 6: an X-ray crystallographic study of a novel mercury compound containing metallically bonded infinite cations. Can.J.Chem., 52, 791-3.
33. Brown, K S, Avansov, A A, and Elser, V (2000). Solving the crystallographic phase problem in i(AlPdMn). Phys. Rev. Lett., 85, 4084-7.
34. Brun, T.O., Sinha, S.K., Wakabayashi, N., Lander, G.H., Edwards, L.R., and Spedding, F.H. (1970). Temperature dependence of the periodicity of the magnetic structure of thullium metal. Phys.Rev. B, 1, 1251-3.
35. Burckhardt, J.J. (1947). Die Bewegungsgruppen der Kristallographie. Basel: Birkhäuser.
36. Burckhardt, J.J. (1988). Die Symmetrie der Kristalle. Basel: Birkhäuser.
37. Burkov, S.E. (1991). Structure model of the Al-Cu-Co decagonal quasicrystal. Phys. Rev. Lett., 67, 614-617.
38. Bussien-Gaillard, V., Paciorek, W., Schenk, K., and Chapuis, G. (1996). Hexamethylenetetramine suberate, a strongly anharmonic modulated structure. Acta Cryst. B, 52, 1036-47.
39. 6 alloy. Phys. Rev. B, 38, 1643-7.
40. Cahn, J.W., Shechtman, D., and Gratias, D. (1986). Indexing of icosahedral quasiperiodic crystals. J. Mat. Res., 1, 13-26.
41. Cervellino, A., Haibach, T., and Steurer, W. (2002). Structure solution of the basic decagonal Al-Co-Ni phase by the atomic surfaces modelling method. Acta Cryst. B, 58, 8-33.
42. Chaikin, P.M. and Lubensky, T.C. (1995). Principles of condensed matter physics. Cambridge: Cambridge University Press.
43. Chen, Z.Y. and Walker, M.B. (1991). Theory of the phase transition sequence in betaine calcium chloride dihydrate BCCD. Phys. Rev.B, 43, 760-4.
44. 21. Phys. Rev. B, 48, 3058-65.
45. Cipriani, F., Castagna, J.C., Lehmann, M.S., and Wilkinson, C. (1995). A large image-plate detector for neutrons. Physica B, 213, 975-7.
46. Coddens, G., Lyonnard, S., Hennion, B., and Calvayrac, Y. (1999). Correlated simultaneous phason jumps in an icosahedral Al-Pd-Mn quasicrystal. Phys. Rev. Lett., 83, 3226-9.
47. Cornier-Quiqandon, M., Quivy, A., Lefebvre, S., Elkaim, E., Heger, G., Katz, A., and Gratias, D. (1991). Neutron-diffraction study of icosahedral Al-Cu-Fe single quasicrystals. Phys. Rev. B, 44, 2071-84.
48. Curien, H. (1952). Diffusion thermique des rayons-X par des monocristaux de Fer-Alpha et dynamique du reseau cubique centré. Acta. Cryst., 5, 393.
49. Currat, R. and Janssen, T. (1988). Excitations in incommensurate crystal phases. In Solid State Physics (ed. H. Ehrenreich and D. Turnbull), Volume 41, pp. 201-302. San Diego:Academic Press.
50. Currat, R., Kats, E., and Luk'yanchuk, I. (2002). Sound modes in composite incommensurate crystals. Eur. Phys. J. B, 26, 339-47.
51. Cutforth, B.D., Datars, W.R., Gillespie, R.J., and van Schijndel, A. (1976). In Unusual properties of Inorganic Complexes, Volume 150, pp. 56-62. Adv. Chem.Ser,.
52. Dam, B. (1985). In situ observation of a roughening transition of the satellite crystal surface of modulated TMA-ZC. Phys. Rev. Lett., 5, 2806-9.
53. 2+. Acta Cryst. B, 42, 69-77.
54. Daniel, V. and Lipson, H. (1943). An X-ray study of the disociation of an alloy of copper, iron and nickel. Proc. Roy. Soc. A, 181, 368-78.
55. Daniel, V. and Lipson, H. (1944). The dissociation of an alloy of copper, iron and nickel:further X-ray work. Proc. Roy. Soc. A, 182, 378-87.
56. Dattoli, G., Giannessi, L., Mezi, L., and Torre, A. (1990). Theory of generalized Besselfunctions. Nuovo Cimento B, 105(3), 327-48.
57. de Boissieu, M., Boudard, M., Bellissent, R., Quilichini, M., Hennion, B., Currat, R., Goldman, A.I., and Janot, C. (1993). Dynamics of the AlPdMn Icosahedral Phase. J Phys:Condens Matter, 5, 4945-66.
58. de Boissieu, M., Boudard, M., Hennion, B., Bellissent, R., Kycia, S., Goldman, A.I., Janot, C., and Audier, M. (1995). Diffuse scattering and phason elasticity in the AlPdMn icosahedral phase. Phys. Rev. Lett., 75, 89.
59. de Boissieu, M., Boudard, M., Ishimasa, T., Lauriat, J.P., Letoublon, A., Audier, M., Duneau, M., and Davroski, A. (1998). Reversible transformation between an icosahedral AlPdMn phase and a modulated structure of cubic symmetry. Phil. Mag. A, 78, 305-26.
60. de Boissieu, M., Currat, R., and Francoual, S. Phason modes in aperiodic crystals. In Physics of quasicrystals (ed. T. Fujiwara and Y. Ishii), Advances in Metal Physics, (to be published). Amsterdam: Elsevier.
61. de Boissieu, M., Durand-Charre, M., Bastie, P., Carabelli, A., Boudard, M., Bessiere, M., Lefebvre, S., Janot, C., and Audier, M. (1992). Centimetre-size single grain of the perfect Al-Pd-Mn icosahedral phase. Phil Mag Lett, 65, 147-53.
62. de Boissieu, M. and Francoual, S. (2005). Diffuse scattering and phason modes in the i-AlPdMn quasicrystalline phases. Z. Kristallogr., 220, 1043-51.
63. de Boissieu, M., Francoual, S., Kaneko, Y., and Ishimasa, T. (2005). Diffuse Scattering and phason fluctuations in the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic (101 ) 2-ZnCl2-. 4 approximant. Phys. Rev. Lett., 95, 105503.
64. de Boissieu, M., Janot, C., Dubois, J.M., Audier, M., and Dubost, B. (1991). Atomic structure of the icosahedral AL-Li-Cu quasicrystal. J. Phys.: Cond. Matter, 3, 1-25.
65. de Boissieu, M, Stephens, P, Boudard, M, and Janot, C (1994a). Is the AlPd-Mn icosahedral phase centrosymmetric? J. Phys.: Condensed Matter, 6, 363-73.
66. de Boissieu, M., Stephens, P., Boudard, M., Janot, C., Chapman, D., and Audier, M. (1994b). Anonalous X-ray diffraction study of the AlPdMn icosahedral phase. J. Phys.:Cond. Matter, 6, 10725-10745.
67. de Boissieu, M., Stephens, P., Boudard, M., Janot, C., Chapman, D., and Audier, M. (1994c). Disorder and complexity in the atomic structure of the perfect icosahedral alloy Al-Pd-Mn. Phys. Rev. Lett., 72, 3538-41.
68. de Boissieu, M., Takakura, H., Bletry, M., Guo, J.Q., and Tsai, A.P. (2002). Phason fluctuations in i-AlPdRe and i-CdYb phases. Journal of Alloys and Compounds, 342, 265-70.
69. de Lange, C. and Janssen, T. (1981). Incommensurability and recursivity: Lattice dynamics of incommensurate modulated crystals. J.Phys. C, 14, 5269-92.
70. de Lange, C. and Janssen, T. (1984). Modulated Kronig-Penney model in superspace. Physica A, 127, 125-40.
71. De Ridder, R., van Tendeloo, G., and Amelinckx, S. (1976). A cluster model for the transition state and its study by means of electron diffraction. phys. stat. sol. (a), 33, 383.
72. de Wolff, P.M. (1974). The pseudo-symmetry of modulated crystal structures. Acta Cryst. A, 30, 777-85.
73. de Wolff, P.M., Janssen, T., and Janner, A. (1981). The superspace groups for incommensurate crystal structures with a one-dimensional modulation. Acta Cryst. A, 37(5), 625-636.
74. Dehlinger, U. (1929). Zur Theorie der Rekristallisation reiner Metalle. Annalen der Physik, 5. Folge, 2, 749-93.
75. Dmitriev, S.V., Semagin, D.A., Shigenari, T., Abe, K., Nagamine, M., and Aslanyan, T.A. (2003). Molecular and lattice dynamical study on modulated structures in quartz. Phys. Rev. B, 68, 052101.
76. 3(0001) interface in terms of interatomic potentials fitted to ab initio results. Act. Mat., 52, 1959-70.
77. Dolinšek, J., Klanjšek, M., Apih, T., Gavilano, J.L., Gianno, K., Ott, H.R., Dubois, J.M., and Urban, K. (2001). Mn magnetism in icosahedral quasicrystalline Al72.4Pd20.5Mn7.1. Phys. Rev. B, 64, 024203.
78. Dotera, T. and Steinhard, P.J. (1994). Ising-like transition and phason unlocking in icosahedral quasicrystals. Phys. Rev. Lett., 72, 1670.
79. Dubbeldam, G.C. and de Wolff, P.M. (1969). The average crystal structure of γ-Na2CO3. Acta Cryst., B25, 2665-67.
80. Dubois, J.M. (2004). A model of wetting of quasicrystals in ambient air. J. Non-Cryst. Sol, 334{left triangle beside vertical bar}5, 481-4.
81. Dubois, J.M. (2005). Useful quasicrystals. Singapore: World Scientific.
82. Dubost, B., Lang, J.M., Tanaka, M., Sainfort, P., and Audier, M. (1986). Large AlCuLi single quasicrystals with triacontahedral solidification morphology. Nature, 324, 48-50.
83. Duneau, M. and Katz, A. (1985). Quasiperiodic patterns. Phys. Rev. Lett., 54, 2688-91.
84. Durand, D., Papoular, R., Currat, R., Lambert, M., Legrand, J. F., and Mezei, F. (1990). NaNO2 relaxation rate. Phys. Rev. B, 43, 10690.
85. Dušek, M., Chapuis, G., Meyer, M., and Petříček, V. (2003). Sodium carbonate revisited. Acta Cryst. B, 59(3), 337-52.
86. Dušek, M., Chapuis, G., Schobinger-Papamantellos, P., Wilkinson, C., Petříček, V., Tung, L.D., and Buschow, K.H.J. (2000). Modulated structure of La2Co1.7 from neutron and Xray diffraction data. Acta Cryst. B, 56, 959-71.
87. Eagen, C.F. and Werner, S.A. (1975). Neutron-diffraction investigation of the sinusoidal displacement-wave in pure Cr. Sol. State Comm., 16, 1113-6.
88. Ebert, Ph., Yurechko, M., Kluge, F., Horn, K., and Urban, K. (2003). Cleavage surfaces of quasicrystals. In Quasicrystals (ed. H. Trebin), pp. 572-597. Weinheim; EVCH-Wiley.
89. Edagawa, K., Suzuki, K., and Takeuchi, S. (2000). High resolution transmission electron microscopy observation of thermally fluctuating phasons in decagonal Al-Cu-Co. Phys. Rev. Lett., 85, 1674-7.
90. Eijt, S.W.H., Currat, R., Lorenzo, J.E., Saint-Grégoire, P., Katano, S., Janssen, T., Hennion, B., and Vysochanskii, Yu.M. (1998). Soft modes and phonon interactions in Sn2P2Se6 studied by inelastic neutron scattering. J. Phys. CM, 10, 4811-44.
91. Elcoro, L., Perez-Mato, J.M., Darriet, J., and El Abed, A. (2003). Superspace description of trigonal and orthorhombic A1+. Acta Cryst. B, 59, 217-33.
92. Elcoro, L., Perez-Mato, J.M., and Withers, R. (2000). Intergrowth polytypoids as modulated structures: the example of the cation deficient oxides LaTi1-x O3. Z. f. Krist., 215, 727-39.
93. Elhor, H., Mihailkovic, M., Roujiaa, M., Scheffer, M., and Suck, J.-B. (2003). Dynamical properties of quasicrystalline alloys investigated by neutron in-elastic scattering and computer simulations based on realistic potentials. In Quasicrystals (ed. H. Trebin), pp. 382-413. Weinheim: Wiley-VCH.
94. Elliott, R.J. (1961). Phenomenological discussion of magnetic ordering in the heavy rareearth metals. Phys. Rev., 124, 346-53.
95. Elser, V (1999). X-ray phase determination by the principle of minimum charge. Acta Cryst. A, 55, 489-99.
96. Estermann, M.A. and Steurer, W. (1998). Diffuse scattering data acquisition techniques. Phase Transitions, 67, 165-95.
97. Etrillard, J., Bourgeois, L., Bourges, P., Liang, B., Lin, C.T., and Keimer, B. (2004). Lowfrequency structural dynamics in the incommensurate composite crystal Bi2Sr2CuO6+δ. Eur. Phys. Lett., 66, 246-52.
98. 8+. Eur. Phys. Lett., 55, 201-7.
99. Etrillard, J., Toudic, B., Bertault, M., Even, J., Gourdji, M., Peneau, A., and Guibe, L. (1993). Cl-35 NQR and calorimetric reinvestigation of the incommensurate phase of bis(4-chlorophenyl) sulfone-evidence for no lock-in transition. J.Phys. I, 3, 2437-49.
100. Etxebarria, I., Perez-Mato, J. M., and Madariaga, G. (1992). Lattice dynamics, structural stability, and phase transitions in incommensurate and commensurate A2BX4 materials. Phys. Rev. B, 46, 2764-74.
101. Fan, H.F. (1999). Direct methods in electron crystallography-image processing and solving incommensurate structures. Microscopy research and technique, 46, 104-16.
102. Fan, H.F., van Smaalen, S., Lam, E.J.W., and Beurskens, P.T. (1993, Sep). Direct methods for incommensurate intergrowth compounds. I. Determination of the modulation. Acta Cryst. A, 49(5), 704-8.
103. Fast, G. and Janssen, T. (1971). Determination of n-dimensional space groups by means of an electronic computer. J.Comp.Phys., 7, 1-11.
104. Francoual, S. (2006). Phonons et phasons dans les quasicristaux de symétrie icosaédrique et dans leurs approximants 1{left triangle beside vertical bar}1 périodiques. Ph. D. thesis, Laboratoire de Thermodynamique et Physicochimie Metallurgiques, Grenoble.
105. Francoual, S., Livet, F., de Boissieu, M., Yakhou, F., Bley, F., Letoublon, A., Caudron, R., and Gastaldi, J. (2003). Dynamics of phason fluctuations in the i-AlPdMn quasicrystal. Phys. Rev. Lett., 91, 225501.
106. Francoual, S., Shibata, K., de Boissieu, M., Baron, A.Q.R., Tsutsui, S., Currat, R., Takakura, H., Tsai, A. P., Lograsso, T., and Ross, A. R. (2004). Experimental study of phonon dynamics in the i-CdYb phase and its 1{left triangle beside vertical bar}1 periodic approximant. Ferroelectrics, 305, 235-8.
107. Frank, F.C. and van der Merwe, J.H. (1949). One-dimensional dislocations. i. Static Case. Proc. Roy. Soc. London, A198, 205-16.
108. Frenkel, Y.I. and Kontorova, T. (1938). In Russian. Zh. Eksp. Teor. Fiz., 8, 89-95, 1340-9, 1349-59.
109. Fujiwara, T. (1999). Theory of electronic structure in quasicrystals. In Physical properties of quasicrystals (ed. Z. Stadnik), pp. 169-208. Berlin: Springer.
110. Garcia, A., Perez-Mato, J.M., and Madariaga, G. (1989). Dynamics of incommensurate structures and inelastic neutron scattering. Phys. Rev. B, 39, 2476-83.
111. Gastaldi, J., Agliozzo, S., Letoublon, A., Wang, J., Mancini, L., Klein, H., Hartwig, J., Baruchel, J., Fisher, I.R., Sato, T., Tsai, A.P., and de Boissieu, M. (2003). Degree of structural perfection of icosahedral quasicrystalline grains investigated by synchrotron X-ray diffractometry and imaging techniques. Phil. Mag. B, 83, 1-29.
112. Gastaldi, J., Reiner, E., Jourdan, C., Grange, G., Quivy, A., and Boudard, M. (1995). Loopand band-shaped defects observed in quasicrystals by X-ray topography. Phil. Mag. Lett., 72, 311-21.
113. Gesi, K. (1965). Phenomenological theory of the phase transitions in NaNO2. J.Phys.Soc.Jpn., 20, 1764-1772.
114. Goldschmidt, V., Palache, Ch., and Peacock, M. (1931). Ueber Calaverit. N. Jahrbuch f. Mineralogie, Beil. Abt.A, 63, 1-58.
115. Gomez, C.P. and Lidin, S. (2001). Structure of Ca13Cd76: A novel approximant to the MCd5.7 quasicrystals (M.Ca, Yb). Angew. Chem. Int., 40, 4037-9.
116. Gomez, C.P. and Lidin, S. (2003). Comparative structural study of the disordered MCd6 quasicrystal approximants. Phys. Rev. B, 68, 024203.
117. Gommonai, A.V., Grabar, A.A., Vysochanskii, Yu.M., Belyaev, A.D., Maluchin, V.F., Gurzan, M.I., and Slivka, V.Yu. (1981). In Russian. Fiz. Tverd. Tela, 23, 3602.
118. Gratias, D., Puyraimond, F., and Quiqandon, M. (2001). Atomic clusters in icosahedral ftype quasicrystals. Phys. Rev. B, 63, 024202.
119. Griessen, R., Landolt, M., and Ott, H.R. (1971). New antiferromagnetic phase in EuSe below 1.8 K. Sol. State Comm., 9, 2219-23.
120. Grimm, U. and Schreiber, M. (2003). Energy spectra and eigenstates of quasiperiodic tight-binding hamiltonians. In Quasicrystals (ed. H. Trebin), pp. 210-235. Weinheim: Wiley-VCH.
121. Grünbaum, B. and Shephard, G.C. (1987). Tilings and patterns. San Francisco: W.H. Freeman.
122. Grüner, G. (1994). Density waves in solids. Reading MA: Addison-Wesley.
123. Gummelt, P. (1996). Penrose tilings as coverings of congruent decagons. Geom. dedicata, 62, 1-17.
124. Hafner, J. and Krajčí, M. (1999). Elementary excitations and physical properties. In Physical properties of quasicrystals (ed. Z. Stadnik), pp. 209-56. Berlin: Springer.
125. Hargreaves, M.E. (1951). Modulated structures in some Cu-Ni-Fe alloys. Acta Cryst. A, 4, 301-9.
126. Hartman, P. and Perdok, W.G. (1955). On the relations between structure and morphology of crystals. III. Acta Cryst., 8, 525-9.
127. Haussermann, U., Soderberg, K., and Norrestam, R. (2002). Comparative study of the high-pressure behavior of As, Sb, and Bi. J. Am. Chem. Soc., 124, 15359-67.
128. Henley, C.L. (1986). Sphere packings and local environments in Penrose tilings. Phys. Rev., B34, 797-816.
129. Henley, C.L. (1991a). Cell geometry for cluster-based quasicrystal models. Phys. Rev. B, 43, 993-1020.
130. Henley, C.L. (1991b). Random tiling models. In Quasicrystals: the state of the art (ed. D. DiVicenzo and P. Steinhardt), pp. 429-524. Singapore: World Scientific.
131. 9 quasicrystal. Phil. Mag., 86, 869-74.
132. Hof, A. (1997a). Diffraction by aperiodic structures. In The mathematics of long-range aperiodic order (ed. R. Moody), Mathematical and physical sciences 489, pp. 239-68. Amsterdam: Kluwer.
133. Hof, A. (1997b). On scaling in relation to singular spectra. Comm. Math. Phys., 184, 567-77.
134. Hofstadter, D.R. (1976). Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B, 14, 2239-49.
135. Ingersent, K. (1991). Matching rules for quasicrystalline tilings. In Quasicrystals : the State of the Art (ed. D. Divincenzo and P. Steinhardt), Volume 11 of Directions in Condensed Matter Physics, pp. 185-212. Singapore: World Scientific.
136. Ishibashi, Y. and Dvorak, V. (1978). Incommensurate phase transitions under the existence of the Lifshitz invariants. J. of the Physical Society of Japan, 44, 32-9.
137. Ishibashi, Y. and Shuba, H. (1978). Succesive phase transitions in ferroelectric NaNO2 and SC(NH2)2. J. Phys. Soc. Jp., 45, 409-13.
138. Ishii, Y. (1992). Phason softening and structural transitions in icosahedral quasicrystals. Phys. Rev. B, 45, 5228-39.
139. Ishii, Y (2000). Anisotropic phasonic diffuse scattering from decagonal quasicrystals. Mat. Sc. Eng. A, 294-6, 377-80.
140. Ishii, Y. and Fujiwara, T. (2001). Hybridization mechanism for cohesion of Cd-based quasicrystals. Phys. Rev. Lett., 87, 206408{left triangle beside vertical bar}1-4.
141. Jach, T., Zhang, Y., Colella, R., de Boissieu, M., Boudard, M., Goldman, A.I., Lograsso, T.A., Delaney, D.W., and Kycia, S. (1999). Dynamical diffraction and X-ray standing waves from atomic planes normal to a twofold symmetry axis of the quasicrystal AlPdMn. Phys.. Rev. Letters, 82, 2904-7.
142. Jagličić, Z., Dolinšek, J., and Trontelj, Z. (2004). Magnetic properties of TbMgZn and TbMgCd quasicrystals in comparison with canonical spin glasses. J. Magn. Magn Mat., 272-6, 597-8.
143. Jamieson, P.B., de Fontaine, D., and Abrahams, S.C. (1969). Determination of atomic ordering arrangements from a study of satellite reflections. J.Appl.Cryst., 2, 24-30.
144. Janner, A. and Ascher, E. (1970). Algebraic aspects of crystallography. II. Helv. Phys. Acta, 43, 296.
145. Janner, A. and Dam, B. (1989). The Morphology of calaverite (AuTe2) from data of 1931-Solution of an old problem of rational indexes. Acta Cryst. A, 45, 115-23.
146. Janner, A. and Janssen, T. (1971). Electromagnetic compensating gauge transformations. Physica, 53, 1-27.
147. Janner, A. and Janssen, T. (1972). A charged particle in the field of a transverse electromagnetic plane wave. Physica, 60, 292-321.
148. Janner, A. and Janssen, T. (1977). Symmetry of periodically distorted crystals. Phys. Rev. B, 15, 643-58.
149. Janner, A. and Janssen, T. (1980a). Symmetry of incommensurate crystal phases I. Commensurate basis structure. Acta Cryst. A, 36, 399-408.
150. Janner, A. and Janssen, T. (1980b). Symmetry of incommensurate crystal phases II. Incommensurate basis structure. Acta Cryst. A, 36, 409-15.
151. Janner, A., Rasing, Th., Bennema, P., and van der Linden, W.H. (1980). Identification of satellite faces on single crystals of the incommensurate structures Rb2ZnBr4 and Rb2ZnCl4. Phys. Rev. Lett., 45, 1700-2.
152. Janot, C and de Boissieu, M (1994). Quasicrystals as a hierarchy of clusters. Phys. Rev. Letters, 72, 1674-7.
153. Janssen, T. (1969). Crystallographic groups in space and time. III Four-dimensional Euclidean crystal classes. Physica, 42, 71-99.
154. Janssen, T. (1972). The magnetic structure of an f.c.c. spin lattice system with exchange and dipolar interactions. Phys.kond.Mat., 15, 142-57.
155. Janssen, T. (1986). On the application of a frustration model to the phase diagram of TMAchlorometallates and other A2BX4 compounds. Ferroelectrics, 66, 203-16.
156. Janssen, T. (1988). Aperiodic crystals: a contradictio in terminis? Physics Repts., 168, 55-113.
157. Janssen, T. (2005). Nonlinear dynamics in aperiodic crystals. In Collective dynamics of nonlinear and disordered systems (ed. G. Radons, W. Just, and P. Haussler), Berlin, pp. 237-66. Berlin: Springer.
158. Janssen, T., Birman, J.L., Denoyer, F., Koptsik, V.A., Verger-Gaugry, J.L., Weigel, D., Yamamoto, A., Abrahams, S.C., and Kopsky, V. (2002). Report of a subcommittee on the nomenclature of n-dimensional crystallography: II Symbols for arithmetic crystal classes, Bravais classes and space groups. Acta Cryst. A, 58, 605-21.
159. Janssen, T., Birman, J., Koptsik, V.A., Senechal, M., Yamamoto, A., Abrahams, S.C., and Hahn, Th. (1999). Report of a subcommittee on the nomenclature of n-dimensional crystallography: Symbols for point group transformations, families, systems and geometric crystal classes. Acta Cryst. A, 55, 761-82.
160. Janssen, T., Janner, A., and Ascher, E. (1969). Crystallographic groups in space and time. I General definitions and basic properties. Physica, 41, 541-65.
161. Janssen, T., Janner, A., Looijenga-Vos, A., and de Wolff, P.M. (1992). Incommensurate and commensurate modulated structures. In International Table of Crystallography, Volume C, pp. 899-937. Amsterdam: Kluwer.
162. Janssen, T., Radulescu, O., and Rubtsov, A.N. (2002). Phasons, sliding modes and friction. Eur.Phys.J. B, 29, 85-95.
163. Janssen, T. and Tjon, J.A. (1981). One-dimensional model for a crystal with displacive modulation. Phys.Rev. B, 24, 2248.
164. Janssen, T. and Tjon, J.A. (1982). Microscopic model for incommensurate crystal phases. Phys.Rev., 25, 3767-85.
165. Janssen, T. and Tjon, J.A. (1983). Incommensurate crystal phases in mean-field approximation. J.Phys.C, 16, 4789-810.
166. Jarič, M.V. and Nelson, D.R. (1988). Diffuse scattering from quasicrystals. Phys. Rev. B, 37, 4458-72.
167. Jarič, M.V. and Qiu, S.Y. (1993). On the solution of the phase problem in quasiperiodic crystals. Acta Cryst. A, 49, 576-85.
168. Jaszczak, J.A. (1994). Quasicrystals: Novel forms of solid matter. The Miner-alogical Record, 25, 85-93.
169. Jehanno, G. and Perio, P. (1962). Structure of AuCu II. J.Phys.Radium, 23, 854.
170. Jeong, H-C. and Steinhardt, P.J. (1997). Constructing Penrose-like tilings from a single prototile and the implications for quasicrystals. Phys. Rev. B, 55, 3520-32.
171. Johnson, C.K. and Watson, C.R. (1976). Superstructure and modulation wave analysis for the unidimensional conductor hepta-(tetrathiafulvalene) pentaiodide. J.Chem.Phys., 64, 2271-86.
172. Kashimoto, S., Motomura, S., Nakano, H., Kaneko, Y., Ishimasa, T., and Matsuo, S. (2002). Magnetic property of a ZnMgSc icosahedral quasicrystal. J. Alloys Comp., 342, 384-8.
173. Katz, A. and Gratias, D. (1994). Tilings and quasicrystals. In Lectures on Quasicrystals (ed. F. Hippert and D. Gratias), pp. 187-264. Les Ulis: Les Editions de Physique.
174. Kobas, M., Weber, T., and Steurer, W. (2005). Structural disorder in decagonal Al-Ni-Co. Part II: Modelling. Phys. Rev. B, 71, 224206.
175. Kocinski, J. (1985). Theory of symmetry changes in phase transitions. Amsterdam:Elsevier.
176. Koehler, W.C., Cable, J.W., Wollan, E.O., and Wilkinson, M.K. (1962). Neutron diffraction study of magnetic ordering in Thulium. J.Appl.Phys., 33, 1124-5.
177. Kohmoto, M., Kadanoff, L.P., and Tang, C. (1983). Localization problem in one dimension:mapping and escape. Phys. Rev. Lett., 50, 1870-2.
178. Korekawa, M. (1967). Theorie der Satellitenreflexe. Habilitationsschrift, München:Ludwig-Maximilians-Universität.
179. Koschella, U., Gähler, F., Roth, J., and Trebin, H.-R. (2002). Phason elastic constants of a binary tiling quasicrystal. J. Alloys and Comp., 342, 287-90.
180. Krajčí, M. and Hafner, J. (2002). Phonons and electrons in quasicrystals. In Quasicrystals (ed. J.-B. Suck, M. Schreiber, and P. Haussler), pp. 393-422. Berlin: Springer.
181. Krajči, M., Hafner, J., and Mihalkovic, M. (2000). Atomic and electronic structure of decagonal Al-Ni-Co alloys and approximant phases. Phys. Rev. B, 62, 243-55.
182. Kremers, M., Meekes, H., Bennema, P., Balzuweit, K., and Verheijen, M.A. (1994). A superspace description for the morphology of modulated crystals: an explanation for the occurrence of faces (hklm). Phil. Mag. B, 69, 69-82.
183. Kycia, S.W., Goldman, A.I., Lograsso, T.A., Delaney, D.W., Black, D., Sutton, M., Dufresne, E., Bruning, R., and Rodricks, B. (1993). Dynamical X-ray diffraction from an icosahedral quasicrystal. Phys Rev B, 48, 3544-7.
184. Lagarias, J.C. (2000). Mathematical quasicrystals and the problem of diffraction. In Directions in mathematical quasicrystals (ed. M. Baake and R. Moody), pp. 61-93. Providence RI: AMS.
185. Landau, L.D. and Lifshitz, E.M. (1959). Statistical Physics. London: Pergamon Press.
186. Laval, J. (1938). Diffusion of X-rays by a crystal. C. R. Acad. Sci., 207, 169.
187. Lei, T. and Henley, C.L. (1991). Equilibrium faceting shape of quasicrystals at low temperature: cluster model. Phil. Mag. B, 63, 677-85.
188. Letoublon, A., de Boissieu, M., Boudard, M., Mancini, L., Gastaldi, J., Hennion, B., Caudron, R., and Bellissent, R. (2001). Phason elastic constants of the icosahedral Al-Pd-Mn phase derived from diffuse scattering measurements. Phil. Mag. Lett., 81, 273-83.
189. Letoublon, A., Fisher, I.R., Sato, T.J., de Boissieu, M., Boudard, M., Agliozzo, S., Mancini, L., Gastaldi, J., Canfield, P.C., Goldman, A.I., and Tsai, A.P. (2000a). Phason strain and structural perfection in the Zn-Mg-rare-earth icosahedral phases. Materials Science & Engineering A, A294-A6, 127-30.
190. Letoublon, A., Ishimasa, T., de Boissieu, M., Boudard, M., Hennion, B., and Mori, M. (2000b). Stability of the F2-(Al-Pd-Mn) phase. Phil. Mag. Lett., 80, 205-13.
191. Letoublon, A., Yakhou, F., Livet, F., Bley, F., de Boissieu, M., Mancini, L., Caudron, R., Vettier, C., and Gastaldi, J. (2001). Coherent X-ray diffraction and phason fluctuations in quasicrystals. Europhysics Letters, 54, 753-9.
192. Levanyuk, A.P. and Sannikov, D.G. (1975). Theory of structural phase transitions in boracites. Sov. Phys. Sol. St., 17, 245-8 and 1122-5.
193. Levine, D. and Steinhardt, P.J. (1984). Quasicrystals: a new class of ordered structures. Phys. Rev. Lett, 53, 2477-80.
194. Lifshitz, R. (1997). Theory of color symmetry for periodic and quasiperiodic crystals. Rev. Mod. Phys., 69, 1181.
195. Livet, F., Bley, F., Mainville, J., Caudron, R., Mochrie, S.G., Geissler, E., Dolino, G., D., Abernathy, Grebel, G., and Sutton, M. (2000). Using direct illumination CCDs as highresolution area detectors for X-ray scattering. Nuc. Inst. Meth., 451, 596.
196. Los, J., Janssen, T., and Gahler, F. (1993a). The phonon spectra of the octagonal tiling. Int. J. Mod. Phys. B, 7, 1505-25.
197. Los, J., Janssen, T., and Gahler, F. (1993b). Scaling properties of vibrational spectra and eigenstates for tiling models of icosahedral quasicrystals. J. Physique France, 3, 107-34.
198. Lubensky, T.C (1988). Symmetry, elasticity, and hydrodynamics in quasiperiodic structures. In Aperiodicity and order: Introduction to quasicrystals (ed. M. Jarič), Volume 1, pp. 199-277. Academic Press.
199. Lubensky, T.C., Socolar, J.E.S., Steinhardt, P.J., Bancel, P.A., and Heiney, P. (1986). Distortion and peak broadening in quasicrystal diffraction patterns. Phys. Rev. Lett., 57, 1440-3.
200. Lyons, K.B., Bhatt, R.N., Negram, T.J., and Guggenheim, H.J. (1982). Incommensurate structural phase transition in BaMnF4. Phys. Rev. B, 25, 1791-804.
201. Mackay, A.L. (1962). A dense non-crystallographic packing of equal spheres. Acta Cryst., 15, 916-8.
202. Maple, J.R., Hwang, M.J., Stockfisch, T.P., Dinur, U., Waldman, M., Ewig, C.S., and Hagler, A.T. (1994). Derivation of class-ii force-fields.1. Methodology and quantum force-field for the alkyl functional-group and alkane molecules. J. of Comp. Chem., 15, 162-82.
203. Martin, P.C., Parodi, O., and Pershan, P.S. (1972). Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids. Phys. Rev. A, 6, 2401-20.
204. McConnell, J.D.C. (1978). Intermediate plagioclase feldspars-example of a structural resonance. Z. Krist., 147, 45-62.
205. McGrath, R., Ledieu, J., Cox, E.J., and Diehl, R.D. (2002). Quasicrystal surfaces: structure and potential as template. J. Phys. Cond. Mat., 14, R119-44.
206. McMahon, M. and Nelmes, R. (2004). Incommensurate crystal structures in the elements at high pressure. Z. f. Krist., 219, 742-8.
207. McMillan, W.L. (1976). Theory of discommensurations and the commensurateincommensurate charge-density-wave phase transition. Phys. Rev. B, 14, 1496-1502.
208. Mermin, N.D. (1992). Copernican crystallography. Phys. Rev. Lett., 68, 1172-5.
209. Mihalkovic, M., Elhor, H., and Suck, J.B. (2001). Atomic dynamics in Al-rich Al-Co alloys near the composition of the decagonal quasicrystal. Phys. Rev. B, 63, 214301{left triangle beside vertical bar}1-14.
210. Mihalkovic, M. and Henley, C.L. (2004). Temperature dependent phason elasticity in a random tiling quasicrystal. Phys. Rev. B, 70, 09202.
211. Mihalkovič, M., Al-Lehyani, I., Cockayne, E., Henley, C.L., Moghadam, N., Moriarty, J.A., Wang, Y., and Widom, M. (2002). Total-energy-based prediction of a quasicrystal structure. Phys. Rev. B, 65, 104205.
212. Mihalkovič, M. and Widom, M. (2004). First-principles prediction of a decagonal quasicrystal containing boron. Phys. Rev. Lett., 93, 95507.
213. Mischo, P., Decker, F., Häcker, U., Holzer, K.-P., and Petersson, J. (1997). Lowfrequency phason and amplitudon dynamics in the incommensurate phase of Rb2ZnCl4. Phys. Rev. Lett., 78, 2152-5.
214. Moody, R.V. (1997). The mathematics of long-range aperiodic order. Amsterdam:Kluwer.
215. Moudden, A.H., Denoyer, F., Benoit, J.P., and Fitzgerald, W. (1978). Inelastic neutronscattering study of commensurate-incommensurate phase-transition in thiourea. Sol. St. Comm., 28, 575.
216. N.G., de Bruijn (1981). Algebraic theory of Penrose's non-periodic tilings of the plane. Indagationes Mathematicae, 43, 39-66.
217. Niizeki, K. (1989). A classification of special points of icosahedral quasilattices. J. Phys. A, 22, 4295-4302.
218. Niizeki, K. (1990a). Icosahedral black-and-white bravais quasilattices and order-disorder transformations of icosahedral quasicrystals. J.Phys. A: Math. Gen., 23, L1069-72.
219. Niizeki, K. (1990b). Three-dimensional black-and-white bravais quasilattices with (2+1)-reducible point groups. J.Phys. A:Math. Gen., 23, 5011-6.
220. Niizeki, K. and Akamatsu, T. (1990). Special points in the reciprocal space of an icosahedral quasicrystal and the quasidispersion relation of electrons. J. Phys. Cond. Mat., 2, 2759-2771.
221. Ollivier, J., Etrillard, J., Toudic, B., Ecolivet, C., Bourges, P., and Levanyuk, A.P. (1998). Direct observation of a phason gap in an incommensurate molecular compound. Phys. Rev. Lett., 81, 3667-70.
222. Olmer, Ph (1948). Dispersion des ondes acoustiques dans l'aluminium. Acta Cryst., 1, 57.
223. Orlov, I. and Chapuis, G. (2005a). New tool based on the superspace concept to discover structure relations. Acta Cryst. A, 61, C105.
224. Orlov, I. and Chapuis, G. (2005b). Superspace tools;.
225. Oszlányi, G. and Süto, A. (2004). Ab initio structure solution by charge-flipping. Acta Cryst. A, 60, 134-41.
226. Oszlányi, G. and Süto, A. (2005). Ab initio structure solution by charge flipping. ii. use of weak reflections. Acta Cryst. A, 61, 147-52.
227. Paciorek, W. and Chapuis, G. (1992). A new algorithm for incommensurate structure refinement. J. Appl. Cryst., 25, 317-22.
228. Paciorek, W. and Chapuis, G. (1994). Generalized Bessel functions in incommensurate structure analysis. Acta Cryst. A, 50, 194-203.
229. Paciorek, W., Gaillard, V.B., Schenk, K., and Chapuis, G. (1996). Molecular geometry of incommensurate structures. Acta Cryst. A, 52, 349-64.
230. Paciorek, W. and Kucharczyk, D. (1985). Structure factor calculations in refinement of a modulated crystal structure. Acta Cryst. A, 41, 462-6.
231. Palatinus, L. (2004). Ab initio determination of incommensurately modulated structures by charge flipping in superspace. Acta Cryst. A, 60, 604-10.
232. Palatinus, L. and Chapuis, G. (2006). Superflip, a program for the solution of crystal structures in arbitrary dimension using the charge-flipping algorithm;.
233. Pan, Y.S., Brown, D., and Chapuis, G. (2003). Molecular dynamics simulation of hexamine and suberic acid. Molecular Simulation, 29, 509-18.
234. Papadopolos, Z., Kasner, G., Ledieu, J., Cox, E.J., Richardson, N.V., Chen, Q., Diehl, R.D., Lograsso, T.A., Ross, A.R., and McGrath, R. (2002). Bulk termination of the quasicrystalline fivefold surface of Al70Pd21Mn9. Phys. Rev. B, 66, 184207-1{left triangle beside vertical bar}13.
235. Papadopolos, Z., Pleasants, P., Kasner, G., Fournee, V., Jenks, C.J., Ledieu, J., and McGrath, R. (2004). Maximum density rule for bulk terminations of quasicrystals. Phys. Rev. B, 69, 224201-1-7.
236. Park, J.Y., Ogletree, D.F., Salmeron, M., Jenks, C.J., and Thiel, P.A. (2004). Friction and adhesion properties of clean and oxidized AlNiCo quasicrystals. Tribology Lett., 17, 629-36.
237. Park, J.Y., Ogletree, D.F., Salmeron, M., Ribeiro, R.A., Canfield, P.C., Jenks, C.J., and Thiel, P.A. (2005). High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface. Science, 309, 1354-6.
238. Parlinski, K. and Chapuis, G. (1993). Mechanisms of phase transitions in a hexagonal model with 1q and 3q incommensurate phases. Phys. Rev. B, 47(21), 13983-91.
239. Parlinski, K. and Chapuis, G. (1994). Phase-transition mechanisms between hexagonal commensurate and incommensurate structures. Phys. Rev. B, 49, 11643-51.
240. Parlinski, K., Kwiecinski, S., and Urbanski, A. (1992). Phase-diagram of a hexagonal model with incommensurate phases. Phys. Rev. B, 46, 5110-15.
241. Penfield, S.L. and Ford, W.E. (1902). Ueber den Calaverit. Z. Kristallogr. Mineral., 35, 430-51.
242. Penrose, R. (1979). Pentaplexity. A class of non-periodic tilings of the plane. Mathematical Intelligencer, 2, 32-37.
243. 3 related to the 2H hexagonal perovskite: relation between composition and modulation. J. Chem. Materials, 9, 2795-808.
244. 6-n (OH) n , n = 0, 1, 2: Application of the heavy-atom method for modulated structures. Acta Cryst. B, 54, 809-18.
245. Petříček, V., Coppens, P., and Becker, P. (1985). Structure-analysis of displacively modulated molecular-crystals. Acta Cryst. A, 41, 478-83.
246. Petříček, V. and Dušek, M. (2000). Jana2000. Technical report, Institute of Physics, Praha, Czech Republic.
247. Petříček, V., Gao, Y., Lee, P., and Coppens, P. (1990). X-ray-analysis of the incommensurate modulation in the 2-2-1-2 Bi-Sr-Ca-Cu-O superconductor including the oxygen atoms. Phys. Rev. B, 42(1), 387-92.
248. Petříček, V., van der Lee, A., and Evain, M. (1995). On the use of crenel functions for occupationally modulated structures. Acta Cryst. A, 51, 529-35.
249. Prince, E. (1994). Mathematical Techniques in Crystallography and Material Science. Berlin: Springer Verlag.
250. Pynn, R., Press, W., and Shapiro, S.M. (1976). Second and third harmonics of the spin density wave in chromium metal. Phys. Rev.B, 13, 295-8.
251. Queffélec, M. (1987). Substitution dynamical systems, Volume 1294 of Lecture Notes in Mathematics. Berlin: Springer.
252. Quilichini, M. and Janssen, T. (1997). Phonon excitations in quasicrystals. Rev. Mod. Phys., 69, 277-314.
253. Quiquandon, M. and Gratias, D. (2006). An unique ideal structure model for AlPdMn and AlCuFe icosahedral phases. Phys. Rev. B, 74, 214205.
254. Radulescu, O., Janssen, T., and Etrillard, J. (2002). Dynamics of modulated and composite aperiodic crystals: the signature of the inner polarization in the neutron inelastic scattering. Eur.Phys.J. B, 29, 385-98.
255. Rasing, Th., Wyder, P., Janner, A., and Janssen, T. (1982). Far-infrared and Raman studies of the incommensurate structure Rb2ZnBr45. Phys. Rev. B, 25, 7504-19.
256. 18.1. Physica B, 329-33, 1103-4.
257. Rau, D., Gavilano, J.L., Mushkolaj, Sh., Beeli, C., and Ott, H.R. (2004). Inhomogeneous mnmagnetism in AlPdMn quasicrystals. J. Magn. Magn. Mat., 272-276, 1330-1.
258. Robertson, J.L., Misenheimer, M.E., Moss, S.C., and Bendersky, L.A. (1986). X-ray and electron metallographic study of quasi-crystalline Al-Mn-Si alloys. Acta Metallurgica, 34, 2177-89.
259. Rubtsov, A.N. and Janssen, T. (2001). Numerical study of the paraelectricincommensurate-ferroelectric transition in the DIFFOUR model. Europhysics Lett., 53, 216-20.
260. Sato, H. and Toth, R.S. (1961). Effect of additional elements on the period of CuAu II and the origin of the long-period superlattice. Phys.Rev., 124, 1833.
261. Sato, T.J., Takakura, H., Tsai, A.P., Shibata, K., Ohoyama, K., and Andersen, K.H. (2000). Antiferromagnetic spin correlations in the Zn-Mg-Ho icosahedral quasicrystal. Phys.Rev. B, 61, 476-86.
262. Savkin, V.V., Rubtsov, A.N., and Janssen, T. (2003). Monte Carlo simulations of the classical two-dimensional DIFFOUR model. Eur.Phys.J. B, 31, 525-531.
263. Schellnhuber, H.J. and Urbschat, H. (1987). Analyticity breaking of wave functions and fractal phase diagram for simple incommensurate systems. phys. stat. sol. (b), 140, 509-19.
264. Schobinger-Papamantellos, P., Buschow, K.H.J., and Janssen, T. (1994). Neutron powder diffraction study of 2d and 3d incommensurately modulated magnetic structures. Mat. Science Forum, 166-'39, 479-86.
265. 3. J. Alloys Compnds., 183, 181.
266. Schobinger-Papamantellos, P., Rodriguez-Carvajal, J., Janssen, T., and Buschow, K.H.J. (1995). Structure and magnetic phase transitions of the novel compound TbGe3. In Aperiodic '94, pp. 302-6.
267. Schönleber, A. (2002). The Superspace Approach Applied to Modulated Crystals. Ph. D. thesis, Lausanne.
268. Schönleber, A. and Chapuis, G. (2004a). Quininium (R)-mandelate, a structure with large Z′described as an incommensurately modulated structure in (3+1)-dimensional superspace. Acta Cryst. B, 60, 108-20.
269. Schönleber, A. and Chapuis, G. (2004b). The structure of diaqua (15-crown-5) copper (II) dinitrate described in (3+1)-dimensional superspace. Ferroelectrics, 305, 99102.
270. Schönleber, A., Meyer, M., and Chapuis, G. (2001). NADA-a computer program for the simultaneous refinement of orientation matrix and modulation vector(s). J. Appl. Cryst., 34, 777-9.
271. Schönleber, A., Pattison, P., and Chapuis, G. (2003). The (3+1)-dimensional superspace description of the commensurately modulated structure of p-chlorobenzamide (α-form) and its relation to the-form. Z. f. Krist., 218, 507-13.
272. 6. Inorg.Chem., 17, 646-9.
273. 2. Acta Cryst. B, 44, 486-94.
274. Selke, W. (1984). Modulated structures in a simple Ising model. In Proc. ASI Modulated structure materials (ed. Tsakalokos).
275. Shechtman, D., Blech, I., Gratias, D., and Cahn, J.W. (1984). Metallic phase with longerange orientational order and no translational symmetry. Phys.Rev.Lett., 53, 1951-3.
276. Shimoda, M., Sharma, H.R., and Tsai, A.P. (2005). Scanning tunneling microscopy study of the five-fold surface of icosahedral Al-Cu-Ru quasicrystal. Surface Science, 598, 88-95.
277. Slot, J.J.M. and Janssen, T. (1988). Dynamics of kinks in modulated crystals. Physica D, 32, 27-71.
278. Smith, H. (1903). Ueber das bemerkenswerthe Problem der Entwickelung der Krystallformen des Calaverit. Z. Kristallogr. Mineral., 37, 209-34.
279. 4 and quartz. Journal De Physique, 47, 2041-53.
280. Solbrig, H. and Landauro, C.V. (2003). Electronic transport parameters and spectral fine structure: from approximants to quasicrystals. In Quasicrystals (ed. H. Trebin), pp. 254-71. Weinheim: Wiley-VCH.
281. Steinhardt, P.J., Jeong, H.-C., Saitoh, K., Tanaka, M., Abe, E., and Tsai, A.P. (1998). Experimental verification of the quasi-unit-cell model of quasicrystal structure. Nature, 365, 55-7.
282. Steurer, W (2004). Quasicrystal structure analysis: a never-ending story? Journal of Non-Crystalline Solids, 334-5, 137-42.
283. Steurer, W. (2005). Structural phase transitions from and to the quasicrystalline state. Acta Cryst. A, 61, 28-38.
284. Steurer, W. and Cervellino, A. (2001). Quasiperiodicity in decagonal phases forced by inclined net planes? Acta Cryst. A, 57, 333-40.
285. Steurer, W. and Haibach, T. (1999). The periodic average structure of particular quasicrystals. Acta Cryst. A, 55, 48-57.
286. Steurer, W., Haibach, T., Zhang, B., Kek, S., and Luck, R. (1993). The structure of decagonal Al70Ni15Co15. Acta Cryst. B, 49, 661-75.
287. Suck, J.-B. (2002). Vibrational density of states of stable and metastable quasicrystalline solids. In Quasicrystals (ed. J.-B. Suck, M. Schreiber, and P. Haussler), pp. 454-71. Berlin:Springer.
288. Sueno, S., Kimata, M., and Ohmasa, M. (1979). In Modulated Structures-1979, AIP Conference Proceedings No. 53, pp. 333. New York: American Institute of Physics.
289. Sutton, M. (2001). Coherent X-ray diffraction. In Third-Generation Hard X-ray Synchrotron Radiation Sources: Source Properties, Optics, and Experimental Techniques (ed. M. Mills, D.), pp. 101-23. New York: John Wileys & Son.
290. Swainson, I.P., Dove, M.T., and Harris, M.J. (1995). Neutron powder diffraction study of the ferroelastic phase-transition and lattice melting in sodium-carbonate, Na2CO3. J. of Physics-Condensed Matter, 7, 4395-417.
291. Takakura, H., Shiono, M., Sato, T.J., Yamamoto, A., and Tsai, A.P. (2001a). Ab initio structure determination of icosahedral Zn-Mg-Ho quasicrystals by density modification method. Phys. Rev. Lett., 86, 236-9.
292. Takakura, H., Yamamoto, A., de Boissieu, M., Sato, T.J., and Tsai, A.P. (2004b). Ab initio structure determination of quasicrystals via single crystal X-ray diffraction. Mat. Res. Soc. Symp. Proc., 805, LL2.2.1-10.
293. Takakura, H., Yamamoto, A., de Boissieu, M., and Tsai, A.P. (2004a). Ab initio structure solution of icosahedral Cd-Yb quasicrystals by a density modification method. Ferroelectrics, 305, 209-12.
294. Takakura, H., Yamamoto, A., Gomez, C.P., de Boissieu, M., and Tsai, A.P. (2007). Atomic structure of the binary icosahedral Yb-Cd quasicrystal. Nature Materials, 6, 58.
295. Takakura, H., Yamamoto, A., and Tsai, A.P. (2001b). The structure of a decagonal Al72Ni20Co8. Acta Cryst. A, 57, 576-85.
296. Takeuchi, T. and Mizutani, U. (1995). Electronic structure, electronic transport properties, and relative stability of quasicrystals and their 1{left triangle beside vertical bar}1 and 2{left triangle beside vertical bar}1 approximants in the Al-Zn-Mg alloy system. Phys. Rev. B, 52, 9300-9.
297. Tang, L.H. (1990). Random tiling quasicrystals in three dimensions. Phys. Rev. Lett., 64, 2390-3.
298. Taniguchi, T., Nakata, K., Takaki, Y., and Sakurai, K. (1978). The crystal structures of the αform of p-chlorobenzamide at room temperature and at 120oC. Acta Cryst. B, 34, 2574-78.
299. Tanisaki, S. (1961). Microdomain structure in paraelectric phase of NaNO2. J.Phys.Soc.Jpn., 16, 579.
300. Tate, M.W., Eikenberry, E. F., and Gruner, S.M. (2001). CCD detectors. In International Tables of Crystallography, Volume F, pp. 148-53. mssterdam: Kluwer.
301. Theis, W., Rotenberg, E., Franke, K.J., Gille, P., and Horn, K. (2003a). Electronic valence bands in decagonal Al-Ni-Co. Phys. Rev. B, 68, 104205.
302. Theis, W., Sharma, H.R., Franke, K.J., and Rieder, K.H. (2003b). Surface phonons and quasicrystalline monolayers. In Quasicrystals (ed. H.-R. Trebin), pp. 622-8. Berlin: VCHWiley.
303. Thiel, P. (2004). Structure and oxidation at quasicrystal surfaces. Progress in Surface Science, 75, 191-204.
304. Toledano, J.C. and Toledano, P. (1987). The Landau theory of phase transitions. Singapore: World Scientific.
305. Trambly de Laissardiére, G. and Mayou, D. (2000). Magnetism in Al(Si)-Mn quasicrystals and related phases. Phys. Rev. Lett., 85, 3273-6.
306. Trambly de Laissardière, G. and Mayou, D. (2002). Magnetic properties of quasicrystals and approximants. In Quasicrystals (ed. J.-B. Suck, M. Schreiber, and P. Haussler), pp. 487-506. Berlin: Springer.
307. Tsai, A.P., Guo, J.Q., Abe, E., Takakura, H., and Sato, T.J. (2000). A stable binary quasicrtystal. Nature, 408, 537-8.
308. Tsai, A.P., Inoue, A., Yokoyama, Y., and Masumoto, T. (1990). Stable icosahedral AlPdMn and AlPdRe alloys. Mat. Trans., JIM, 31, 98-103.
309. Tsai, A.P. and Yoshimura, M. (2001). Highly active quasicrystalline Al-Cu-Fe catalyst for steam reforming of methanol. Appllied Catalysis A, 214, 237-41.
310. Tsunoda, Y., Mori, M., Kunitomi, N., Teraoka, Y., and Kanamori, J. (1974). Strain wave in pure chromium. Sol. State Comm., 14, 287-9.
311. 3 in a harmonic approximation. Acta Cryst. B, 32, 47-58.
312. van Erp, T., Fasolino, A., Radulescu, O., and Janssen, T. (1999). Pinning and phonon localization in Frenkel-Kontorova models on quasiperiodic substrates. Phys. Rev. B, 60, 6522-8.
313. van Landuyt, J., van Tendeloo, G., and Amelinckx, S. (1974). Electron diffraction patterns of distortion modulated structures. Phys.stat.sol.(a), 26, K9-11.
314. van Smaalen, S. (1991). Symmetry of composite crystals. Phys. Rev. B, 43(13), 11330-41.
315. van Smaalen, S. (1993). Theory of incommensurate crystal facets. Phys. Rev. Lett., 70, 2419-22.
316. van Smaalen, S. (1999). The morphology of quasicrystals, incommensurate composite crystals and modulated crystals derived from the broken-bond model. Acta Cryst. A, 55, 401-12.
317. van Smaalen, S. and George, T. F. (1987). Determination of the incommensurately modulated structure of α-uranium below 37 K. Phys. Rev. B, 35, 7939-51.
318. van Smaalen, S., Palatinus, L., and Schneider, M. (2003). The maximum-entropy method in superspace. Acta Cryst. A, 59, 459-69.
319. 3 n (n ≥ 4δ). Journal of Solid State Chemistry, 108(2), 314-35.
320. van Tendeloo, G., Gregoriades, P., and Amelinckx, S. (1983). Electron-microscopy studies of modulated structures in (Au, Ag)Te2. 1. Calaverite AuTe2. Journal of Solid State Chemistry, 50, 321-34.
321. Vanossi, A., Röder, J., Bishop, A.R., and Bortolani, V. (2000). Driven, under-damped Frenkel-Kontorova model on a quasiperiodic substrate. Phys. Rev. E, 63, 017203.
322. Walker, C.B. (1956). X-ray study of lattice vibrations in aluminium. Phys. Rev., B, 547-57.
323. Widom, M. (1991). Elastic stability and diffuse scattering in icosahedral quasicrystals. Phil. Mag. Lett., 64, 297-305.
324. Yamamoto, A. (1982a). Modulated structure of CuAu II (one-dimensional modulation). Acta Cryst. B, 38, 1446-51.
325. Yamamoto, A. (1982b). Structure factor of modulated crystal structures. Acta Cryst. A, 38, 87-92.
326. Yamamoto, A. (1985). Displacive modulation in the sinusoidal antiferroelectric phase of NaNO2. Phys. Rev. B, 31, 5941.
327. Yamamoto, A. (1992). Unified setting and symbols of superspace groups for composite crystals. Acta Cryst. A, 48, 476-83.
328. Yamamoto, A. (1993). Determination of composite crystal-structures and superspace groups. Acta Cryst. A, 49, 831-46.
329. Yamamoto, A. (1999). Superspace groups for one-, two and three-dimensionally modulated structures:.
330. Yamamoto, A. (2004). Section method for projected structures of icosahedral quasicrystals and its application to electron-microscopy-image and surface analysis. Phys. Rev. Lett., 93, 195505.
331. Yamamoto, A., Takakura, H., and Tsai, A.P. (2003). Six-dimensional model of icosahedral Al-Pd-Mn quasicrystals. Phys. Rev. B, 68, 94201-1-13.
332. Yan, Y., Pennycook, S.J., and Tsai, A.P. (1998). Direct imaging of local chemical disorder and columnar vacancies in ideal decagonal Al-Ni-Co quasicrystals. Phys. Rev. Lett., 81, 5145-8.
333. Yokoyama, Y., Tsai, A., Inoue, A., and Masumoto, T. (1991). Production of quasicristalline AlPdMn alloys with large single domain size. Mater. Trans., JIM, 32, 1089-97.
334. Yoshimori, A. (1959). A new type of antiferromagnetic structure in the rutile type crystal. J. Phys. Soc. Jpn., 14, 807-21.
335. Zassenhaus, H. (1947). Über einen Algorithmus zur Bestimmung der Raumgruppen. Comm. Math. Helv., 21, 117-141.
336. Zeyher, R. and Finger, W. (1982). Phason dynamics of incommensurate crystals. Phys. Rev. Lett., 49, 1833-7.
337. Zijlstra, E.S., Fasolino, A., and Janssen, T. (1999). Existence and localization of surface states on Fibonacci quasicrystals: A tight-binding study. Phys. Rev. B, 59, 302-7.
338. Zijlstra, E.S. and Janssen, T. (2000a). Density of states and localization of electrons in the Penrose tiling. Phys. Rev. B, 61, 3377-83.
339. Zijlstra, E.S. and Janssen, T. (2000b). Non-spiky density of states of an icosahedral quasicrystal. Europhys. Lett., 52, 578-83.