Question: 5 fold diffraction pattern symmetries were discovered in 1982 by dan shechtman when he discovered this phase which opened new field of study in quasiperiodic crystals

full_context: Document 1: Yitzhak Apeloig: Yitzhak Apeloig (born September 1, 1944 in Uzbekistan) is a pioneer in the computational chemistry field of the Ab initio quantum chemistry methods for predicting and preparing the physical and chemical properties of materials. He was the president of the Technion from 2001 until 2009 where the position was handed off to Peretz Lavie. Distinguished Prof. Apeloig currently holds the Joseph Israel Freund Chair in Chemistry and is the co-director of the Lise Meitner Minerva Center for Computational Quantum Chemistry at the Technion. He served as dean of the Faculty of Chemistry from 1995 to 1999, where he was named Teacher of the Year at three occasions.
Document 2: Yuval Golan: Yuval Golan is an Israeli materials scientist who works at Ben-Gurion University of the Negev (BGU). Golan, a professor of materials engineering, studies materials at the nanoscale level and focuses on their synthesis, characterization and applications. Golan is the Director of the Ilse Katz Institute for Nanoscale Science and Technology, and chairman of the synchrotron committee of the Israeli Academy of Sciences and Humanities.
Document 3: Dan Shechtman: Dan Shechtman (Hebrew: דן שכטמן; born January 24, 1941) is the Philip Tobias Professor of Materials Science at the Technion – Israel Institute of Technology, an Associate of the US Department of Energy's Ames Laboratory, and Professor of Materials Science at Iowa State University. On April 8, 1982, while on sabbatical at the U.S. National Bureau of Standards in Washington, D.C., Shechtman discovered the icosahedral phase, which opened the new field of quasiperiodic crystals. Shechtman was awarded the 2011 Nobel Prize in Chemistry for the discovery of quasicrystals, making him one of six Israelis who have won the Nobel Prize in Chemistry.
Document 4: Debye frequency: The Debye frequency of a crystal is a theoretical maximum frequency of vibration for the atoms that make up the crystal . It was proposed by Peter Debye as part of the Debye model. It is generally not the same as the actual maximum oscillation frequency for the crystal, due to approximations in the model, however it is still a useful quantity . It plays a role in the computation of the specific heat capacity of solids and in theoretical estimates of rates of diffusion. It is related to the speed of sound (formula_1) in the crystal and the number density of the crystal formula_2 as follows :
Document 5: Ada Yonath: Ada E. Yonath (Hebrew: עדה יונת‎ ‎ , ] ) (born 22 June 1939) is an Israeli crystallographer best known for her pioneering work on the structure of the ribosome. She is the current director of the Helen and Milton A. Kimmelman Center for Biomolecular Structure and Assembly of the Weizmann Institute of Science. In 2009, she received the Nobel Prize in Chemistry along with Venkatraman Ramakrishnan and Thomas A. Steitz for her studies on the structure and function of the ribosome, becoming the first Israeli woman to win the Nobel Prize out of ten Israeli Nobel laureates, the first woman from the Middle East to win a Nobel prize in the sciences, and the first woman in 45 years to win the Nobel Prize for Chemistry. However, she said herself that there was nothing special about a woman winning the Prize.
Document 6: Fiber diffraction: Fiber diffraction is a subarea of scattering, an area in which molecular structure is determined from scattering data (usually of X-rays, electrons or neutrons). In fiber diffraction the scattering pattern does not change, as the sample is rotated about a unique axis (the fiber axis). Such uniaxial symmetry is frequent with filaments or fibers consisting of biological or man-made macromolecules. In crystallography fiber symmetry is an aggravation regarding the determination of crystal structure, because reflexions are smeared and may overlap in the fiber diffraction pattern. Materials science considers fiber symmetry a simplification, because almost the complete obtainable structure information is in a single two-dimensional (2D) diffraction pattern exposed on photographic film or on a 2D detector. 2 instead of 3 co-ordinate directions suffice to describe fiber diffraction.
Document 7: Donnayite-(Y): Donnayite-(Y) is a rare-earth carbonate mineral containing the rare-earth metal yttrium. It was first discovered in 1978 at Mont St-Hilaire, Quebec. Donnayite was subsequently identified and named after Joseph D. H. Donnay and his wife, Gabrielle Donnay. Both were prominent mineralogists and crystallographers, and J. D. H. Donnay was awarded the Roebling Award by the Mineralogical Society of America in 1971 for his emphasis on the importance of optical mineralogy and crystal morphology. Donnayite tends to occur in small quantities in the pegmatite dykes and miarolitic cavities of mountainous regions. It crystallizes in this environment with increasing alkalinity values until the alkalinity suddenly drops during the last stage of crystallization. This results in increasing amounts of Na carbonates and REE minerals. First discovered at Mont St-Hilaire, donnayite has since been found in the Southern Ural Mountains of Russia and the Narssarssuk pegmatite of South Greenland. Donnayite crystals tend to be small and the color is commonly pale yellow to yellow with a white streak and a vitreous luster. Donnayite crystals usually display trigonal or hexagonal symmetry and have a hardness of 3. Twinning is extremely common in this mineral. Minerals closely related to donnayite include synchysite, calcite, sphalerite, microcline, and analcime. Donnayite is isomorphous with weloganite and mckelveyite.
Document 8: Eshel Ben-Jacob: Eshel Ben-Jacob (full name Eshel Refael Ben-Jacob Breslav; Hebrew: אשל רפאל בן-יעקב‎ ‎ 13 April 1952 – 5 June 2015), was a theoretical and experimental physicist at Tel Aviv University, holder of the Maguy-Glass Chair in Physics of Complex Systems, and Fellow of the Center for Theoretical Biological Physics (CTBP) at Rice University. During the 1980s he became an international leader in the theory of self-organization and pattern formation in open systems, and later extended this work to adaptive complex systems and biocomplexity. His specialization in self-organization of complex systems yielded the breakthrough of solving the long-standing (since Kepler) snowflake problem. In the late 1980s, he turned to study of bacterial self-organization, believing that bacteria hold the key to understanding the larger biological systems. He developed new pattern forming bacteria species, became a pioneer in the study of bacterial intelligence and social behaviors of bacteria, and was an influential figure in establishing the now rapidly evolving physics of living systems (biological physics and physical biology) disciplines. He was an adviser to the Microbes Mind Forum.
Document 9: Quasicrystal: A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.
Document 10: Alan Lindsay Mackay: Alan Lindsay Mackay FRS (born 6 September 1926) is a British crystallographer, born in Wolverhampton. He spent his scientific career at Birkbeck College, founded by George Birkbeck, one of the Colleges of the University of London, where he was immersed in a liberal scientific atmosphere under the leadership of John Desmond Bernal. He became a Fellow of the Royal Society (FRS) on 17 March 1988 and a Fellow of Birkbeck College on 2 March 2002. He is also a Fellow of the Mexican Academy of Sciences. Mackay has made important scientific contributions related to the structure of materials: In 1962 he published a manuscript that showed how to pack atoms in an icosahedral fashion; a first step towards five-fold symmetry in materials science. These arrangements are now called Mackay icosahedra. He is a pioneer in the introduction of five-fold symmetry in materials and in 1981 predicted quasicrystals in a paper (in Russian) entitled "De Nive Quinquangula" in which he used a Penrose tiling in two and three dimensions to predict a new kind of ordered structures not allowed by traditional crystallography. In a later manuscript, in 1982, he took the optical Fourier transform of a 2-D Penrose tiling decorated with atoms, obtaining a pattern with sharp spots and five-fold symmetry. This brought the possibility of identifying quasiperiodic order in a material through diffraction. Quasicrystals with icosahedral symmetry were found by Dan Shechtman and co-workers in 1984. For his contributions to quasicrystals in 2010 Mackay was awarded the Buckley Prize,
Document 11: Crystallographic restriction theorem: The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.
Document 12: Sharon Glotzer: Sharon C. Glotzer is an American physicist, the John Werner Cahn Distinguished University Professor of Engineering and the Stuart W. Churchill Collegiate Professor of Chemical Engineering at the University of Michigan, where she is also Professor of Materials Science & Engineering, Professor of Physics, Professor of Macromolecular Science & Engineering, and Professor of Applied Physics. She is recognized for her contributions to the fields of soft matter and computational science, most notably on problems in assembly science and engineering, nanoscience, and the glass transition, for which the elucidation of the nature of dynamical heterogeneity in glassy liquids is of particular significance. She is a member of the National Academy of Sciences and the American Academy of Arts and Sciences.
Document 13: Born–von Karman boundary condition: Born–von Karman boundary conditions are periodic boundary conditions which impose the restriction that a wave function must be periodic on a certain Bravais lattice. (Named after Max Born and Theodore von Kármán). This condition is often applied in solid state physics to model an ideal crystal. Born and von Karman
Document 14: Didier Astruc: Didier Astruc (born 9 June 1946 in Versailles) carried out his studies in chemistry in Rennes. After a Ph. D. with professor R. Dabard in organometallic chemistry, he did post-doctoral studies with professor R. R. Schrock (2005 Nobel Laureate) at the Massachusetts Institute of Technology Cambridge, Mass., in the U.S. and later a sabbatical year with professor K. P. C. Vollhardt at the University of California at Berkeley. He became a CNRS Director of research in Rennes, then in 1983 full Professor of Chemistry at the University Bordeaux 1. He is known for his work on “Electron-Reservoir” complexes and dendritic molecular batteries, catalytic processes (olefin metathesis, C-C coupling, catalysis in water) using nanoreactors and molecular recognition using gold nanoparticles and metallodendrimers. He is the author of three books, scientific publications and the editor of five books or special issues. He has been a member of the National CNRS committee from 2000 to 2008 and the President of the Coordination Chemistry Division of the Société Française de Chimie from 2000 to 2004. Didier Astruc is on the Thompson-Reuters list of the top 100 chemists who have achieved the highest citation impact scores for their chemistry papers published between 2000 and 2010. and on the Thomson-Reuters list of the Highest Cited Researchers 2015 and 2016.
Document 15: Jean Fréchet: Professor Jean M.J. Fréchet (born August 19, 1944, Burgundy, France), American chemist, is a Professor Emeritus at the University of California, Berkeley. In addition, he is the head of Materials Synthesis, Materials Science Division,of the Lawrence Berkeley National Laboratory, Director of the Organic and Macromolecular Facility for the Molecular Foundry, Lawrence Berkeley National Laboratory, and Vice-President for research at King Abdullah University of Science and Technology. He has authored nearly 900 scientific papers and holds over 70 United States Patents. His research areas include organic synthesis and polymer chemistry applied to nanoscience and nanotechnology with emphasis on the design, fundamental understanding, synthesis, and applications of functional macromolecules. He was a good friend of influential American chemist Linus Pauling and consistently mentions him in his organic chemistry lectures. As of March 2011, he is 16th on the Hirsch index rating of all living chemists with an H-index of 105. He is an elected fellow of the American Association for the Advancement of Science, the American Chemical Society, and the American Academy of Arts and Sciences, and an elected member of the US National Academy of Sciences, the US National Academy of Engineering, and the Academy of Europe (Academia Europaea).
ground_truth: icosahedral phase