Abstract
The recent experimental and theoretical interest in quasiperiodic structures has been inspired by Shechtman et al.'s discovery1 of precipitates in rapidly cooled Al–Mn, Al–Fe and Al–Cr alloys which exhibit m35 icosahedral point symmetry. Subsequent work has shown how diffraction patterns with the same symmetries as those observed experimentally can be generated from model frameworks of linked icosahedra2,3 and of three-dimensional Penrose tilings (3DPT)4,5, in which space is filled aperiodically by prolate and oblate rhombohedra with equal sides and angles of ±cos−1 (1/√5) (ref. 6). Here we demonstrate that the computed intensities of the diffracted beams of kinematical electron and X-ray diffraction patterns of quasicrystals are sensitive to the choice of atomic decoration of the underlying 3DPT. Significantly, we have been unable to find a unique atomic decoration of the prolate and oblate rhombohedra which can account fully for the experimental diffraction data. We discuss the implications of this in the light of experimental data on the lack of chemical homogeneity of the icosadredral phases.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Phys. Rev. Lett. 53, 1951–1953 (1984).
Shechtman, D. & Blech, I. Met. Trans. A 16, 1005–1012 (1985).
Stephens, P. W. & Goldman, A. I. Phys. Rev. Lett. 56, 1168–1171 (1986).
Duneau, M. & Katz, A. Phys. Rev. Lett. 54, 2688–2691 (1985).
Elser, V. Acta crystallogr. A 42, 36–43 (1986).
Mackay, A. L., Physica A114, 609–613 (1982).
Elser, V. & Henley, C. L. Phys. Rev. Lett. 55, 2883–2886 (1985).
Henley, C. L. J. Non-Crystal. Sol. 75, 91–96 (1985).
Henley, C. L. & Elser, V. Phil. Mag. B53, L59–L66 (1986).
Audier, M. & Guyot, P. Phil. Mag. B53, L43–L51 (1986).
Knowles, K. M., Greer, A. L., Saxton, W. O. & Stobbs, W. M. Phil. Mag. B52, L31–L38 (1985).
Kimura, K. et al. J. phys. Soc. Japan 55, 534–543 (1986).
Bancel, P. A., Heiney, P. A., Stephens, P. W., Goldman, A. I. & Horn, P. M. Phys. Rev. Lett. 54, 2422–2425 (1985).
Elser, V. Phys. Rev. B32, 4892–4898 (1985).
Nicol, A. D. I. Acta crystallogr. 6, 285–293 (1953).
Cooper, M. & Robinson, K. Acta crystallog. 20, 614–617 (1966).
Kimura, K. et al. J. phys. Soc. Japan 54, 3217–3219 (1985).
Zaidi, M. A., Robinson, J. S. & Sheppard, T. Mat. Sci. Technol. 1, 737–742 (1985).
Conway, J. H. & Knowles, K. M. J. Phys. A (in the press).
Smith, G. H. & Burge, R. E. Acta crystallogr. 15, 182–186 1962).
Levine, D. & Steinhardt, P. J. Phys. Rev. Lett. 53, 2477–2480 (1984).
Hiraga, K., Hirabayashi, M., Inoue, A. & Masumoto, T. J. phys. Soc. Japan 54, 4077–4080 (1985).
Poon, S. J., Drehman, A. J. & Lawless, K. R. Phys. Rev. Lett. 55, 21–24 (1985).
Ramachandrarao, P. & Sastry, G. V. Pramana 25, L225–L330 (1985).
Zhang, Z., Ye, H. Q. & Kuo, K. H. Phil Mag. A52, L49–L52 (1985).
Sastry, G. V. S., Rao, V. V., Ramachandrarao, P. & Anantharaman, T. R. Scr. Met. 20, 191–193 (1986).
Pauling, L. Nature, 317, 512–514 (1985).
Bak, P. Phys. Rev. Lett. 56, 861–864 (1986).
Cahn, J. W., Gratias, D. & Shechtman, D. Nature 319, 102–103 (1986).
Mackay, A. L. Nature 319, 103–104 (1986).
Bancel, P. A., Heiney, P. A., Stephens, P. W. & Goldman, A. I. Nature 319, 104 (1986).
Berezin, A. A. Nature 319, 104 (1986).
Stobbs, W. M. Phil. Mag. 35, 1001 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Knowles, K., Stobbs, W. Diffraction pattern simulations of quasiperiodic structures. Nature 323, 313–317 (1986). https://doi.org/10.1038/323313a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/323313a0
This article is cited by
-
Guinier-preston zone, quasicrystal and long-period stacking ordered structure in Mg-based alloys, a review
Acta Metallurgica Sinica (English Letters) (2013)
-
Synthesis and structural aspects of quasicrystals in Mg-Al-Ag system: Mg4Al6Ag
Metallurgical Transactions A (1989)
-
Quasicrystalline materials
Bulletin of Materials Science (1989)
-
Five-fold symmetry: Disorder among the atoms
Nature (1986)
-
Five-fold symmetry: Millimetre-sized quasicrystals grown from aluminium alloy
Nature (1986)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.