Metric, Myth & Quasicrystals
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The metric is the necessary rule that relates atomic spacings in real space with angles of diffraction in reciprocal space. Quasicrystals display diffraction orders in geometric series. They do not therefore follow Bragg’s law of diffraction, where the series are in linear order on a reciprocal lattice. The geometric series is a restricted form of Fibonacci series and has special properties since the sequence ratio between members is a constant , the golden section. The diffraction patterns are indexed in three dimensions with notational economy, with demonstrated completeness, and without redundancy. Simulations on a hierarchic model show that the ‘quasi lattice parameter’ that is measured in the diffraction, differs from the Bragg equivalent in crystals. This is due partly to a compromise in the multiple interplanar spacings that contribute to the diffraction. The spacings provide approximately half integral coherence at short range, with near integral coherence at long range. A special metric relates the diffraction pattern to the corresponding interplanar structures. The simulations match data in several ways: diffracted beam intensities are correctly calculated; a high resolution electron micrograph is modeled in detail; and the edge sharing unit cell fits known atomic sizes.
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About the Book
Metric, Myth & Quasicrystallography describes the first measurement of the metric in quasicrystals and the first measurement at atomic scale. Quasicrystals are ordinary as window glass, but they have been mistified owing to their sharp diffraction patterns with 5-fold symmetries, impossible in crystals. Out of the fog, the patterns are not in Bragg order; the series is not properly Fibonacci: simplified indexation of the pattern is used to simulate a structure due to a single, aligned, edge-sharing unit-cell that is consistent with all data. Since it is unlikely that the sharp diffraction pattern is due to unmeasured poly polyhedra, does the International Union of Crystallography have to redefine crystals yet again? In modern physics, the metric relates the covariant components of invariant vectors with corresponding contravariant components. In crystallography it relates dimensions in momentum space to atomic locations in real space. In quasicrystals, the pattern in momentum space is logarithmic. Theory and simulation show why this has to be. Consequences follow. In particular, we show not only ‘where the atoms are’ but also ‘why they are there’. A debate is reported so that the reader will be encouraged to make his own mind. When logarithmic periodicity is discovered and explained in one branch of physics, it should be expected in others.
About the Author
Antony Bourdillon M.A., D.Phil. (Oxon) Ph.D. (Cantab) took his degrees at the Clarendon Laboratory, University of Oxford. He did post doctoral work at the Cavendish Laboratory, Cambridge University before joining its Department of Materials Science & Metallurgy as permanent faculty. Subsequently, he was Director of the Electron Microscope Unit at the University of New South Wales and then Professor at the State University of New York. In Singapore he became Professor of Physics; Professor of Materials Science; Principal Fellow at the Institute of Materials Research and Engineering; and proposer, builder and Director of the Singapore Synchrotron Light Source. More recently, he has conducted independent research, consulting for various university institutes and companies, including an X-ray Lithography Consortium that he championed. He has published 6 monographs and 200 journal articles.