Abstract
The diffraction patterns from Fibonacci quasilattices have been calculated. Finite-size effects are evaluated for weak and strong peaks. For a smaller number of scatterers (<100) there are fluctuations in the intensities of weak and strong peaks. The fluctuations in weak peaks are greater than that in strong peaks. The fluctuations in intensities of weak and strong peaks near the origin are larger than in the corresponding cases of weak and strong peaks far away from the origin. Small shifts in peak-positions are unexpectedly found, the shifts being proportional toN −3/2 for a large number of scatterers. The diffraction pattern of a one-dimensional crystal and random structure is compared with that of the Fibonacci quasilattice. The strong peaks observed in the diffraction pattern of 1-d crystal show negligible peak-shifts, they being comparable with computational errors even when the number of scatterers is as small as 5. The implications for analysing the experiments are briefly indicated.
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References
Bruijn N G de 1981Kon. Nederl. Akad. Wetensch. Proc. Ser. A84 39, 53
Bancel P A and Heiney P A 1986J. Phys. Colloq. 47 C3–341
Budai J D, Tischler J Z, Habenschuss A, Ice G E and Elser V 1987Phys. Rev. Lett. 58 2304
Chattopadhyay K, Lele S, Thangaraj N and Raganatha S 1987Acta. Metall. 35 727
Duneau M and Katz A 1985Phys. Rev. Lett. 54 2688
Elser V 1985Phys. Rev. B32 4892
Elser V 1986Acta Crystallogr. A42 36
Gay J G and Clemens B M 1987Phys. Rev. Lett. 59 2236
Gratias D and Michel L (Eds.) 1986Proc. Int. Conf. on Aperiodic Crystals, Les Houches, (France).J. Phys. Colloq. 47 C3
Gratias D and Cahn J W 1986Scr. Metall. 20 1193
He L X, Li X Z, Zhang Z and Kuo K H 1988Phys. Rev. Lett. 61 1116
Hu A, Tien C, Li X, Wang Y and Feng D 1986Phys. Lett. A119 313
Janssen T 1986J. Phys. Colloq. 47 C3–85
Kramer P and Neri R 1984Acta. Crystallogr. A40 580
Levine D and Steinhardt P J 1984Phys. Rev. Lett. 53 2477
Levine D and Steinhardt P J 1986Phys. Rev. B34 596
Ma Y, Stern E A, Li X and Janot C 1989 Presented at the Int. Conf. Quasicrystals, Mexico City, May 29-2 June
Mackay A L 1982Physica A114 609
Penrose R 1974Bull. Inst. Math. Appl. 10 216
Prince E 1987Acta. Crystallogr. A43 393
Sasisekharan V 1986Pramana — J. Phys. 26 L283
Shechtman D, Blech I, Gratias D and Cahn J W 1984Phys. Rev. Lett. 53 1951
Socolar J E S, Steinhardt P J and Levine D 1985Phys. Rev. B32 5547
Sommerfeld A 1954Optics, (New York: Academic Press)
Terauchi H, Noda Y, Kamigaki K, Matsunaka S, Nakayama M, Kato H, Sano N and Yamada Y 1988J. Phys. Soc. Jpn. 57 2416
Todd J, Merlin R, Clarke R, Mohanty K M and Axe J D 1986Phys. Rev. Lett. 57 1157
Valsakumar M C and Vijaykumar 1986Pramana — J. Phys. 26 215
Zia R K P and Dallas W J 1985J. Phys. A18 L341
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Balagurusamy, V.S.K., Baranidharan, S., Gopal, E.S.R. et al. Diffraction properties of one-dimensional finite size fibonacci quasilattice. Pramana - J Phys 34, 525–536 (1990). https://doi.org/10.1007/BF02846429
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DOI: https://doi.org/10.1007/BF02846429