Abstract
The theory proposed by Takeno and Goda to explain phonon excitations in topologically disordered systems is used to calculate dispersion relations for two amorphous clusters of copper in a harmonic approximation. The structures are generated by the method of continuous static relaxation [11]. Atomic interaction in model clusters is specified by means of Morse and Ballog empirical potentials. The position of the “roton minimum” of the longitudinal mode coincides with the principal maximum of the static structural factor in both cases, which agrees with well-known results obtained in theories of elementary excitations in amorphous systems. It is found that the highest-frequency waves are those for which wavelength equals the radius of the second coordination sphere, while the nearest neighbors vibrate with the frequency corresponding to the “roton minimum.” A numerical estimate of the ratio of sonic velocity in the longitudinal and transverse directions shows complete agreement with theoretical predictions. Calculations show that due to weak dispersion and thus low transverse sonic velocities, longitudinal vibrations make the main contribution to the density of states.
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Tomsk State Architectural-Building Academy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 31–36, April, 1994.
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Kashirin, V.B. Dispersion of phonon excitations in model amorphous structures. Russ Phys J 37, 332–336 (1994). https://doi.org/10.1007/BF00560215
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DOI: https://doi.org/10.1007/BF00560215