tema03 - Física del Estado Sólido F. D–Adame JJ J N I...

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Unformatted text preview: Física del Estado Sólido F. D–Adame JJ J N I II 1/20 JJ J N I II 1/20 Tema 3 Teor´ ıa cl´asica de las vibraciones at´omicas Física del Estado Sólido F. D–Adame JJ J N I II 2/20 JJ J N I II 2/20 Cadena monoat´ omica unidimensional U arm tot = 1 2 K X n h u ( na )- u ([ n + 1] a ) i 2 K ≡ U 00 ( a ) > M ¨ u ( na ) =- K h 2 u ( na )- u ([ n + 1] a )- u ([ n- 1] a ) i u ( na, t ) = Ae i ( κna- ωt ) u ([ N + 1] a ) = u ( a ) y u (0) = u ( Na ) | {z } Born-von Karman e iκNa = 1 = ⇒ κ = 2 π a n N κ ∈ h- π a , π a i | {z } 1 a Zona Brillouin Física del Estado Sólido F. D–Adame JJ J N I II 3/20 JJ J N I II 3/20 Relaci´ on de dispersi´ on ω ( κ ) = 2 r K M sen κa 2 ω ( κ ) ' a r K M | κ | | κ | a π dω dκ = 0 si κ = ± π/a Física del Estado Sólido F. D–Adame JJ J N I II 4/20 JJ J N I II 4/20 Zonas de Brillouin (1D) Física del Estado Sólido F. D–Adame JJ J N I II 5/20 JJ J N I II 5/20 Zonas de Brillouin (2D) Física del Estado Sólido F. D–Adame JJ J N I II 6/20 JJ J N I II 6/20 Zonas de Brillouin (3D) Física del Estado Sólido F. D–Adame JJ J N I II 7/20 JJ J N I II 7/20 Cadena unidimensional con base U arm tot = 1 2 K X n h u 1 ( na )- u 2 ( na ) i 2 + 1 2 G X n h u 2 ( na )- u 1 ([ n + 1] a ) i 2 M ¨ u 1 ( na ) =- K h u 1 ( na )- u 2 ( na ) i- G h u 1 ( na )- u 2 ([ n- 1] a ) i M ¨ u 2 ( na ) =- K h u 2 ( na )- u 1 ( na ) i- G h u 2 ( na )- u 1 ([ n + 1] a ) i u 1 ( na, t ) = A 1 e i ( κna- ωt ) u 2 ( na, t ) = A 2 e i ( κna- ωt ) Física del Estado Sólido F. D–Adame JJ J N I II 8/20 JJ J N I II 8/20 Relaci´ on de dispersi´ on...
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This note was uploaded on 09/21/2011 for the course PHYSICS 101 taught by Professor Wormer during the Spring '08 term at Aarhus Universitet.

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tema03 - Física del Estado Sólido F. D–Adame JJ J N I...

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