“phonons” - stony brook universityfelix.physics.sunysb.edu/~allen/pdffiles/phonons.pdf · p. b....
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“Phonons”Vibrational normal modes
–Evolution from molecule to solid–Heat conduction–What are vibrations like in glasses?
P. B. Allen, visiting Applied Physics at ColumbiaOn leave from SUNY Stony Brook
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EukenEinsteinDebyeBornPeierlsFrenkelBrockhouse
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group velocityphase velocity
PBA and J. KelnerAm. J. Phys. 66, 497 (1998)
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Energy transport, weakly disordered 1d chain0.93 < K < 1.07 uniform random deviations
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Ballistic motion of wavepacket for 0 < t < 100Center of energy stops systematic motion by t=200
Non-Chaotic Evolution
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Diffusive motion, 100 < t < 1000Localization, t > 2000 (no further energy transport)
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“first principles” calculationDensity-functional theory
C. Bungaro, thesis, SISSA, 1995(with Baroni and Gironcoli)
Phonon dispersion in tungsten metal
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Heat Conduction by Phonons
Experiments: EukenTheories: Einstein, DebyeR. Peierls, thesis, Zurich, 1929
“Phonon gas model”
4000 W/mK
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KCl
Thesis supervised by Arne Claesson
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“plateau”
1 W/mK
3000 W/mK
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“Phase diagram of silicon by molecular dynamics” J. Q. Broughton and X. P. Li
Phys. Rev. B 35, 9120-9127 (1987)
interatomic forces
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Neutron Scattering data
atom coordinates
amorphous siliconPBA, J. L. Feldman, J. Fabian
vibrational density of states
crystal vs. amorphous
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Phonon gas model:
does not apply! Group velocity vi is undefined!
Lattice analog of Kubo-Greenwood formula (Allen and Feldman, 1987)
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“Anharmonic Decay of Vibrational Statesin Amorphous Silicon”
Jaroslav Fabian and Philip B. Allen Phys. Rev. Lett. 77, 3839 (1996)
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Observation of Giant Kohn Anomaly in the One-Dimensional Conductor K2Pt(CN)4Br0.3· 3H2O
B. Renker, H. Rietschel, L. Pintschovius, W. Gläser, P. Brüesch, D. Kuse, and M. J. Rice Phys. Rev. Lett. 30, 1144 (1973)
Peierls-Overhauser Insulator, or“band Jahn-Teller system”
2D“Peierlsgap”
partly-filled electron energy band