Summary
Understanding the growth of quasicrystals poses a challenging problem, not the least because the quasiperiodic order present in idealized mathematical models of quasicrystals prohibits simple local growth algorithms. This can only be circumvented by allowing for some degree of disorder, which of course is always present in real quasicrystalline samples. In this review, we give an overview of the present state of theoretical research, addressing the problems, the different approaches and the results obtained so far.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aragón J.L., Romeu D., Gómez A. (1991): Phys. Rev. B 44, 584
Baake M. (2002): See Chapter 2 of this book
de Boissieu M., Boudard M., Hennion B., Bellissent R., Kycia S., Goldman A., Janot C., Audier M. (1995): Phys. Rev. Lett. 75, 89
Boudard M., de Boissieu M., Letoublon A., Hennion B., Bellissent R., Janot C. (1996): Europhys. Lett. 33, 199
Cockayne E. (1995): Phys. Rev. B 51, 14958
DiVincenzo D.P. (1997): In The Mathematics of Long-Range Aperiodic Order (NATO ASI C 489), ed. R.V. Moody, Kluwer, Dordrecht, p. 127
Dmitrienko V.E., Astaf’ev S.B. (1995): Phys. Rev. Lett. 75, 1538
Dmitrienko V.E., Astaf’ev S.B., Kléman M. (1999): Phys. Rev. B 59, 286
Dubois J.-M., Janot C. (2002): See Chapter 8 of this book
Duneau M. (1995): In Quasicrystals, ed. C. Janot, R. Mosseri, World Scientific, Singapore, p. 116
Elser V. (1985): Phys. Rev. Lett. 54, 1730
Elser V. (1987): In Proc. XVth Int. Coll. on Group Theoretical Methods in Physics (Vol. 1), ed. R. Gilmore, D.H. Feng, World Scientific, Singapore, p. 162.
Elser V. (1988): In Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics, ed. A. Amman, L. Cederbaum, W. Gans, Kluwer, Dordrecht, p. 121
Elser V. (1989): In Extended Icosahedral Structures (Aperiodicity and Order, vol. 3), ed. M.V. Jarić, D. Gratias, Academic Press, San Diego, p. 105
Gähler F., Jeong H.-C. (1995): J. Phys. A 28, 1807
Gardner M. (1977): Sci. Am. 236, 110
de Gier J., Nienhuis B. (1998): J. Phys. A 31, 2141
Grimm U., Schreiber M. (2002): See Chapter 3 of this book
Gummelt P. (1995): In Quasicrystals, ed. C. Janot, R. Mosseri, World Scientific, Singapore, p. 84
Gummelt P. (1996): Geom. Ded. 62, 1
Henley C.L. (1991): In Quasicrystals: The State of the Art, ed. D.P. DiVincenzo, P.J. Steinhardt, World Scientific, Singapore, p. 429
Henley C.L. (1991): Phys. Rev. B 43, 993
Henley C.L. (1998): In Proc. 6th Int. Conf. Quasicrystals, ed. S. Takeuchi, T. Fujiwara, World Scientific, Singapore, p. 27
Ho T.L. (1991): In Quasicrystals: The State of the Art, ed. D.P. DiVincenzo, P.J. Steinhardt, World Scientific, Singapore, p. 401
Ho T.L., Jaszczak J.A., Li Y.H., Saam W.F. (1987): Phys. Rev. Lett. 59, 1116
Ho T.L., Li Y.H., Saam W.F., Jaszczak J.A. (1989): Phys. Rev. B 39, 10614
Holland-Moritz D. (2002): See Chapter 11 of this book
Janot C., de Boissieu M. (1994): Phys. Rev. Lett. 72, 1674
Janot C., Patera J. (1997): Phys. Lett. A 233, 110
Jarić M.V., Ronchetti M. (1989): Phys. Rev. Lett. 62, 1209
Jeong H.-C., Steinhardt P.J. (1994): Phys. Rev. Lett. 73, 1943
Jeong H.-C., Steinhardt P.J. (1997): Phys. Rev. B 55, 3520
Joseph D. (1998): Phys. Rev. B 58, 8347
Joseph D., Baake M. (1996): J. Phys. A 29, 6709
Joseph D., Elser V. (1997): Phys. Rev. Lett. 79, 1066
Joseph D., Ritsch S., Beeli C. (1997): Phys. Rev. B 55, 8175
Kalugin P. (1998): Private communication
Kramer P., Neri R. (1984): Acta Crystallogr. A 40, 580
Kuo K.H., Feng Y.C., Chen H. (1988): Phys. Rev. Lett. 61, 1740
Lançon F., Billard L., Chaudhari P. (1986): Europhys. Lett. 2, 625
Lei T., Henley C.L. (1991): Phil. Mag. B 63, 677
Markov I. V. (1995): Crystal Growth for Beginners: Fundarnentals of Nucleation, Crystal Growth and Epitaxy, World Scientific, Singapore
Minchau B., Szeto K.Y., Villain J. (1987): Phys. Rev. Lett. 58, 1960
Newman M.E.J., Henley C.L. (1995): Phys. Rev. B 52, 6386
Newman M.E.J., Henley C.L., Oxborrow M. (1995): Phil. Mag. B 71, 991
Nissen H.-U., Beeli C. (2002): See Chapter 6 of this book
Nori F., Ronchetti M., Elser V. (1988): Phys. Rev. Lett. 61, 2774
Olami Z. (1991): Europhys. Lett. 16, 361 and
Olami Z. (1991): J. Phys. (France) I 1, 42
Onoda G.Y., Steinhardt P.J., DiVincenzo D.P., Socolar J.E.S. (1988): Phys. Rev. Lett. 60, 2653
Onoda G.Y., Steinhardt P.J., DiVincenzo D.P., Socolar J.E.S. (1989): Phys. Rev. Lett. 62, 1210
Ophuysen G. van, Weber M., Danzer L. (1995): J. Phys. A 28, 281
Oxborrow M., Henley C.L. (1993): Phys. Rev. B 48, 6966
Oxborrow M., Mihalkovic, M. (in press): To appear in Aperiodic’97 (Proc. Int. Conf. Aperiodic Crystals), ed. M. de Boissieu, R. Currat, J.-L. Verger-Gaugry, World Scientific, Singapore
Penrose R. (1989): In Introduction to the Mathematics of Quasicrystals (Aperiodicity and Order, vol. 2), ed. M.V. Jarić, Academic Press, San Diego, p. 53
Robertson J.L., Moss S.C. (1991): Z. Phys. B 83, 391
Romeu D. (1988): Int. J. Mod. Phys. B 2, 77; 265
Romeu D., Aragón J.L. (1993): In Crystal-Quasicrystal Transitions, ed. M.J. Yacamán, M. Torres, North-Holland (Elsevier), Amsterdam, p. 193
Ronchetti M., Jarić M.V. (1990): In Quasicrystals, ed. M.V. Jarić, S. Lundqvist, World Scientific, Singapore, p. 227
Sekimoto K. (1990): Physica A 170, 150 and
Sekimoto K. (1990): in Quasicrystals (Springer Solid-State Sciences 93), ed. T. Fujiwara, T. Ogawa, Springer, Berlin, p. 120
Shechtman D., Blech I.A. (1985): Metall. Trans. A 16A, 1005
Socolar J.E.S. (1991): In Quasicrystals: The State of the Art, ed. D.P. DiVincenzo, P.J. Steinhardt, World Scientific, Singapore, p. 213
Steinhardt P.J. (1990): In Quasicrystals (Springer Solid-State Sciences 93), ed. T. Fujiwara, T. Ogawa, Springer, Berlin, p. 91
Steinhardt P.J., Jeong H.-C. (1996): Nature 382, 431
Stephens P.W. (1989): In Extended Icosahedral Structures (Aperiodicity and Order, vol. 3), ed. M.V. Jarić, D. Gratias, Academic Press, San Diego, p. 37
Stephens P.W., Goldman A.I. (1986): Phys. Rev. Lett. 56, 1168;
Stephens P.W., Goldman A.I. (1986): Phys. Rev. Lett. 57, 2331 (Erratum)
Szeto K.Y., Wang Z.M. (1990): Phys. Rev. B 41, 1347
Trebin H.-R. (2002): See Chapter 12 of this book
Widom M., Strandburg K.J., Swendsen R.H. (1987): Phys. Rev. Lett. 58, 706
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Grimm, U., Joseph, D. (2002). Modeling Quasicrystal Growth. In: Suck, JB., Schreiber, M., Häussler, P. (eds) Quasicrystals. Springer Series in Materials Science, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05028-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-05028-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08390-7
Online ISBN: 978-3-662-05028-6
eBook Packages: Springer Book Archive