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Extended icosahedral structures
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Journal of Non-Crystalline Solids 122 (1990) 212-213 North-Holland
BOOK REVIEW EXTENDED ICOSAHEDRAL STRUCTURES
(M. V. Jaric and D. Gratias, editors, published by Academic Press © 1989, US$59.50) K.F. K E L T O N Physics Department, Washington University, Box 1105, St. Louis, MO 63130, USA
In 1984 D. Shechtman and co-workers at the National Bureau of Standards discovered a rapidly cooled alloy of aluminum and manganese that showed sharp diffraction patterns with an icosahedral rotational point group symmetry. Their announcement was met with considerable excitement and some skepticism. While there are many examples of biological structures with that symmetry, it is conspicuously absent among crystals, due to a fundamental incompatibility between five-fold rotational symmetry and translational periodicity. Subsequently this novel phase (called the icosahedral phase) has been discovered in a host of other alloys. The icosahedral phase is now known to be only one of many possible noncrystallographic condensed phases that give sharp diffraction patterns; collectively these phases are called quasicrystals. The book, 'Extended Icosahedral Structures', edited by Marko V. Jaric and Denis Gratias, is the third volume in a series of review articles on quasicrystals. This book's greatest strength lies in its emphasis on real materials that possess extended icosahedral order. While the discussion of the icosahedral phase is central, articles on liquid crystals, complex crystals, and embedded structures in a higher dimensional space are also included. Like the first two volumes of this series, all articles are well written and describe the subject in a way that benefits both the novice and the expert. I highly recommend this book for persons working in the field and for those who are interested in this fascinating subject that overlaps crystallography, materials science and physics. Three articles deal specifically with the structure of the icosahedral phase. The article by P.
Stephens, " T h e Icosahedral Glass Model", is particularly valuable. It presents a clear description of the icosahedral glass model, which predicts the diffraction patterns in terms of orientationally ordered, randomly packed icosahedra. A detailed comparison is made between predictions from this model, those from the competing quasicrystal model, and a wide range of experimental data. Another useful article by M. Audier and P. Guyot, "Quasi-Crystal Structure Models Related to Crystalline Structures", discusses the method of predicting atom locations in quasicrystals on the basis of the known chemical decorations of closely related crystalline phases. The article by Linus Pauling, "Icosaliedral and Decagonal Quasicrystals as Multiple Twins of Cubic Crystals", details his thesis that quasicrystals are actually twins of very large ( > 820 atom) primitive cubic crystals. Although the arguments are not compelling in light of current experimental data, the article contains a wealth of information and illustrations of several classes of complex crystal structures that possess local icosahedral order. The remaining three articles are less unified topically. The article by V. Elser, " T h e Growth of Icosahedral Phase", presents a detailed discussion of a computer algorithm for growing structures from icosahedral clusters of atoms. The article by J.F. Sadoc and R. Mosseri, "Icosahedral Order, Curved Space and Quasicrystals", gives a lucid discussion of local icosahedral order produced from projections of ordered structures embedded in a non-Euclidean space. Finally, the article by R.M. Hornreich, " T h e o r y of Icosahedral Liquid Crystal Structures", discusses the extended icosahedral order present in some liquid crystals.
0022-3093/90/$03.50 © 1990 - ElsevierSciencePublishers B.V. (North-Holland)
Book Review
This book completes a series that has concentrated on the structure and mathematical analysis of quasicrystals. Collections of reviews on other important topics such as the criteria for quasicrystal formation, phase stability, phase
213
transformations, physical properties, defects, chemical ordering, diffuse scattering, and high resolution TEM studies do not exist. Future volumes discussing these topics, with the high quality of this series, would be most welcome.
Journal of Non-Crystalline Solids 122 (1990) 212-213 North-Holland
BOOK REVIEW EXTENDED ICOSAHEDRAL STRUCTURES
(M. V. Jaric and D. Gratias, editors, published by Academic Press © 1989, US$59.50) K.F. K E L T O N Physics Department, Washington University, Box 1105, St. Louis, MO 63130, USA
In 1984 D. Shechtman and co-workers at the National Bureau of Standards discovered a rapidly cooled alloy of aluminum and manganese that showed sharp diffraction patterns with an icosahedral rotational point group symmetry. Their announcement was met with considerable excitement and some skepticism. While there are many examples of biological structures with that symmetry, it is conspicuously absent among crystals, due to a fundamental incompatibility between five-fold rotational symmetry and translational periodicity. Subsequently this novel phase (called the icosahedral phase) has been discovered in a host of other alloys. The icosahedral phase is now known to be only one of many possible noncrystallographic condensed phases that give sharp diffraction patterns; collectively these phases are called quasicrystals. The book, 'Extended Icosahedral Structures', edited by Marko V. Jaric and Denis Gratias, is the third volume in a series of review articles on quasicrystals. This book's greatest strength lies in its emphasis on real materials that possess extended icosahedral order. While the discussion of the icosahedral phase is central, articles on liquid crystals, complex crystals, and embedded structures in a higher dimensional space are also included. Like the first two volumes of this series, all articles are well written and describe the subject in a way that benefits both the novice and the expert. I highly recommend this book for persons working in the field and for those who are interested in this fascinating subject that overlaps crystallography, materials science and physics. Three articles deal specifically with the structure of the icosahedral phase. The article by P.
Stephens, " T h e Icosahedral Glass Model", is particularly valuable. It presents a clear description of the icosahedral glass model, which predicts the diffraction patterns in terms of orientationally ordered, randomly packed icosahedra. A detailed comparison is made between predictions from this model, those from the competing quasicrystal model, and a wide range of experimental data. Another useful article by M. Audier and P. Guyot, "Quasi-Crystal Structure Models Related to Crystalline Structures", discusses the method of predicting atom locations in quasicrystals on the basis of the known chemical decorations of closely related crystalline phases. The article by Linus Pauling, "Icosaliedral and Decagonal Quasicrystals as Multiple Twins of Cubic Crystals", details his thesis that quasicrystals are actually twins of very large ( > 820 atom) primitive cubic crystals. Although the arguments are not compelling in light of current experimental data, the article contains a wealth of information and illustrations of several classes of complex crystal structures that possess local icosahedral order. The remaining three articles are less unified topically. The article by V. Elser, " T h e Growth of Icosahedral Phase", presents a detailed discussion of a computer algorithm for growing structures from icosahedral clusters of atoms. The article by J.F. Sadoc and R. Mosseri, "Icosahedral Order, Curved Space and Quasicrystals", gives a lucid discussion of local icosahedral order produced from projections of ordered structures embedded in a non-Euclidean space. Finally, the article by R.M. Hornreich, " T h e o r y of Icosahedral Liquid Crystal Structures", discusses the extended icosahedral order present in some liquid crystals.
0022-3093/90/$03.50 © 1990 - ElsevierSciencePublishers B.V. (North-Holland)
Book Review
This book completes a series that has concentrated on the structure and mathematical analysis of quasicrystals. Collections of reviews on other important topics such as the criteria for quasicrystal formation, phase stability, phase
213
transformations, physical properties, defects, chemical ordering, diffuse scattering, and high resolution TEM studies do not exist. Future volumes discussing these topics, with the high quality of this series, would be most welcome.