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Vibrational modes induced by a pair of impurities
Affiliation:1. School of Innovation and Entrepreneurship, Pingdingshan University, Pingdingshan, 467000, PR China;2. School of Chemical & Environmental Engineering (Key Lab of Ecological Restoration in Hilly Areas), Pingdingshan University, Pingdingshan, 467000, PR China;3. School of Software, Pingdingshan University, Pingdingshan, 467000, PR China;4. Henan International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan, 467000, PR China;5. College of Materials and Chemical Engineering, Henan University of Urban Construction, Pingdingshan, 467000, PR China;1. Faculty of Materials Metallurgy and Chemistry, Jiangxi University of Science and Technology, Ganzhou, Jiangxi, 341000, PR China;2. Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou, 341000, PR China;3. State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, PR China;1. Faculty of Science and Technology, Jan Długosz University, Armii Krajowej 13/15, PL-42200, Czestochowa, Poland;2. School of Optoelectronics & CQUPT-BUL Innovation Institute, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China;3. Kagami Memorial Research Institute for Materials Science and Technology, Waseda University, Tokyo, 169-0051, Japan;4. Center of Innovative Development of Science and New Technologies, National Academy of Sciences of Tajikistan, Dushanbe, 734025, Tajikistan;5. Frantsevych Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, 3 Krzhyzhanivsky Str., UA-03142, Kyiv, Ukraine;6. Faculty of Science and Engineering, Waseda University, Tokyo, 169-8555, Japan;7. Institute of Condensed-Matter Science, Waseda University, Tokyo, 169-8555, Japan;8. Center of Excellence for Photoconversion, Vinča Institute of Nuclear Sciences – National Institute of the Republic of Serbia, University of Belgrade, Belgrade, Serbia;9. Institute of Physics, University of Tartu, W. Ostwald Str. 1, 50411, Tartu, Estonia;10. Academy of Romanian Scientists, Ilfov Str. No. 3, 050044, Bucharest, Romania
Abstract:
Presence of a polarizable impurity atom in an ionic crystal induces a localized vibrational mode of the lattice. The frequency of the mode is distinct from the propagating modes of the pure crystal. It is shown in this paper that the frequency of the mode depends on the polarizability of the impurity atom and on the distance of separation between two adjacent impurities.
Keywords:
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