Abstract
Quasicrystals represent aperiodically ordered form of solids with symmetries long thought forbidden in nature. Since their discovery, the fundamental key question has been “Where are the atoms?” For the last decade major strides have been made in determining atomic structure of quasicrystals, largely by direct imaging using scanning transmission electron microscopy (STEM). In this chapter, we describe effective use of annular dark-field STEM imaging for structural analysis of quasicrystals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Abe, Y. Matsuo, H. Saitoh, T. Kusawake, K. Ohshima, H. Nakao, Jpn. J. Appl. Phys. 39, L1111 (2000)
E. Abe, S.J. Pennycook, A.P. Tsai, Nature 421, 347 (2003)
E. Abe, K. Saitoh, H. Takakura, A.P. Tsai, P.J. Steinhardt, H.-C. Jeong, Phys. Rev. Lett. 84, 4609 (2000)
H. Abe, H. Saitoh, T. Ueno, H. Nakao, Y. Matsuo, K. Ohshima, H. Matsumoto, J. Phys. Soc. Jpn. 72, 1828 (2003)
E. Abe, H. Takakura, A.P. Tsai, J. Electron. Microsc. 50, 187 (2001)
E. Abe, Y. Yan, S.J. Pennycook, Nat. Mater. 3, 759 (2004)
P. Bak, Phys. Rev. Lett. 54, 1517 (1985)
P. Bak, Phys. Rev. Lett. 56, 861 (1986)
P.A. Bancel, Phys. Rev. Lett. 63, 2741 (1989)
P.E. Batson, N. Dellby, O.L. Krivanek, Nature 418, 617 (2002)
C. Beeli, S. Horiuchi, Phil. Mag. B 70, 215 (1994)
L. Bendersky, Phys. Rev. Lett. 55, 1461 (1985)
D.M. Bird, Q.A. King, Acta Cryst. A 46, 202 (1990)
S. Burkov, Phys. Rev. Lett. 67, 614 (1991); J. Phys. 2, 695 (1992)
G. Coddens, S. Lyonnard, B. Hennion, and Y. Calvayrac, Phys. Rev. Lett. 83, 3226 (1999)
G. Coddens, W. Steurer, Phys. Rev. B 60, 270 (1999)
R. Colella, Y. Zhang, J.P. Sutter, S.N. Ehrlich, S.W. Kycia, Phys. Rev. B 63, 014202-1 (2000)
R.A. Cowley, A.D. Bruce, J. Phys. C 11, 3577, 3591, 3609 (1978)
M. de Boissieu, M. Boudard, B. Hennion, R. Bellissent, S. Kycia, A. Goldman, C. Janot, M. Audier, Phys. Rev. Lett. 75, 89 (1995)
N. Dellby, O.L. Krivanek, P.D. Nellist, P.E. Batson, A.R. Lupini, J. Electron. Microsc. 50, 177 (2001)
J. Dolinsek, T. Apih, M. Simsic, J.M. Dubois, Phys. Rev. Lett. 82, 572 (1999)
B. Dubost, J.-M. Lang, M. Tanaka, P. Sainfort, M. Audier, Nature 324, 48 (1986)
K. Edagawa, K. Suzuki, S. Takeuchi, Phys. Rev. Lett. 85, 1674 (2000)
I.R. Fisher, Z. Islam, A.F. Panchula, K.O. Cheon, M.J. Kramer, P.C. Canfield, A.I. Goldman, Phil. Mag. B 77, 1601 (1998)
I.R. Fisher, M.J. Kramer, Z. Islam, A.R. Ross, A. Kracher, T. Wiener, M.J. Sailer, A.I. Goldman, P.C. Canfield, Phil. Mag. B 79, 425 (1999)
S. Francoual, F. Livet, M. de Boissieu, F. Yakhou, F. Bley, A. Létoublon, R. Caudron, J. Gastaldi, Phys. Rev. Lett. 91, 225501 (2003)
T. Goedecke, M, Scheffer, R. Luck, S. Ritsch, C. Beeli, Z. Metallkd. 89, 687 (1998)
P. Gummelt, Geometriae Dedicata 62, 1 (1996)
M. Haider, S. Uhlemann, E. Schwan, H. Rose, B. Kabius, K. Urban, Nature 392, 768 (1998)
H. Hashimoto, A. Howie, M.J. Whelan, Proc. R. Soc. London Ser. A, 269, 80 (1962).
C.L. Henley, in Quasicrystals: The State of the Art, ed. by D. DiVincenzo, P.J. Steinhardt (World Scientific, Singapore, 1991) pp. 429–524
C.L. Henley, M. Mihalkovic, M. Widom, J. Alloys Compd. 342, 221 (2002)
K. Hiraga, in Advances in Imaging and Electron Physics, ed. by P.W. Hawkes (Academic, London, 1998), pp. 37–98
K. Hiraga, T. Ohsuna, W. Sun, K. Sugiyama, Mater. Trans. 42, 2354 (2001)
W. Hume-Rothery, J. Inst. Met. 36, 295 (1926)
Y. Ishii, Phys. Rev. B 45, 5228 (1992)
K.N. Ishihara, A. Yamamoto, Acta Crystallogr. A 44, 508 (1988)
K. Ishizuka, Ultramicroscopy 90, 71 (2002)
T. Janssen, Acta Crystallogr. A 42, 261 (1986)
M.V. Jaric, D.R. Nelson, Phys. Rev. B 37, 4458 (1988)
H.-C. Jeong, P.J. Steinhardt, Phys. Rev. B 48, 9394 (1993)
D. Joseph, S. Ritsch, C. Beeli, Phys. Rev. B 55, 8175 (1997)
D. Levine, T.C. Lubensky, S. Ostlund, S. Rawaswamy, P.J. Steinhardt, Phys. Rev. Lett. 54, 1520 (1985)
D. Levine, P.J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984)
R.F. Loane, P. Xu, J. Silcox, Acta Cryst. A 47, 267 (1991)
W. Ohashi, F. Spaepen, Nature 330, 555 (1987)
M. Mihalkovic, I. Al-Lehyani, E. Cockayne, C.L. Henley, N. Moghadam, J.A. Moriarty, Y. Wang, M. Widom, Phys. Rev. B 65, 104205 (2002)
D.A. Muller, B. Edward, E.J. Kirkland, J. Silcox, Ultramicroscopy 86, 371 (2001)
P.D. Nellist, M.F. Chisholm, N. Dellby, O.L. Krivanek, M.F. Murfitt, Z.S. Szilagyi, A.R. Lupini, A. Borisevich, W.H. Sides Jr., S.J. Pennycook, Science 305, 1741 (2004)
L. Pauling, Nature 317, 512 (1986)
S.J. Pennycook, L.A. Boatner, Nature 336, 565 (1988)
S.J. Pennycook, D.E. Jesson, Ultramicroscopy 37, 14 (1991); Phys. Rev. Lett. 64, 938 (1990)
R. Penrose, Bull. Inst. Math. App. 10, 266 (1974)
L. Randall, Phys. Today 60, 80 (2007)
S. Ritsch, C. Beeli, H.-U. Nissen, T. Godecke, M, Scheffer, R. Luck, Phil. Mag. Lett. 74, 99 (1996)
S. Ritsch, C. Beeli, H.-U. Nissen, T. Godecke, M, Scheffer, R. Luck, Phil. Mag. Lett. 78, 67 (1998)
K. Saitoh, K. Tsuda, M. Tanaka, K. Kaneko, A.P. Tsai, Jpn. J. Appl. Phys. 36, L1400 (1997)
D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)
P.J. Steinhardt, H.-C. Jeong, Nature 382, 431 (1996)
P.J. Steinhardt, H.-C. Jeong, K. Saitoh, M. Tanaka, E. Abe, A.P. Tsai, Nature 396, 55 (1998)
P.W. Stephens, A.I. Goldman, Phys. Rev. Lett. 56, 1168 (1986), ibid. 57 2331 (1986)
H. Takakura, A. Yamamoto, A.P. Tsai, Acta Crystallogr. A 57, 576 (2001)
S. Taniguchi, E. Abe, Philos. Mag. 88, 1949 (2008)
A.P. Tsai, in Physical Properties of Quasicrystals, ed. by Z M. Stadnik (Springer, Heidelberg, 1999), pp. 5–50
A.P. Tsai, A. Inoue, T. Masumoto, Jpn. J. Appl. Phys. 26, L1505 (1987)
K. Tsuda, Y. Nishida, K. Saitoh, M. Tanaka, A.P. Tsai, A. Inoue, T. Masumoto, Phil. Mag. A 74, 697 (1996)
M. Varela, A.R. Lupini, K. van Benthem, A. Borisevich, M.F. Chisholm, N. Shibata, E. Abe, S.J. Pennycook, Annu. Rev. Mater. Res. 35, 539 (2005)
A. Weickenmeier, H. Kohl, Acta Crystallogr. A 47, 590 (1991)
A. Yamamoto, Acta Crystallogr. A 52, 509 (1996)
A. Yamamoto, H. Takakura, E. Abe, Phys. Rev. B 72, 144202-1 (2005)
Y. Yan, S.J. Pennycook, A.P. Tsai, Phys. Rev. Lett. 81, 5145 (1998)
Y. Yan, S.J. Pennycook, Phys. Rev. Lett. 86, 1542 (2001)
G. Zeger, D. Plachke, H.D. Carstanjen, H.-R. Trebin, Phys. Rev. Lett. 82, 5273 (1999)
Acknowledgments
I would be grateful to A. P. Tsai, S. J. Pennycook, K. Saitoh, H. Takakura, P. J. Steinhardt, H.-C. Jeong, and Y. Yan for collaborations, on which the present chapter is based. I would also thank T. J. Sato, M. Widom, C. L. Henley, M. Miharcovic, W. Steurer, M. de Boissieu, A. Yamamoto, N. Tanaka, and K. Ishizuka for valuable comments and discussions. I acknowledge support from the CREST-JST and SORST-JST (1996–2001, 2002–2007 Project leader: A. P. Tsai), a Grant-in-Aid for Scientific Research of Priority Areas “Atomic Scale Modification” from the Ministry of Education, Science, Sports and Culture of Japan, and by Kazato Research Foundation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Abe, E. (2011). Structure of Quasicrystals. In: Pennycook, S., Nellist, P. (eds) Scanning Transmission Electron Microscopy. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7200-2_14
Download citation
DOI: https://doi.org/10.1007/978-1-4419-7200-2_14
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7199-9
Online ISBN: 978-1-4419-7200-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)