The dispersion relation for one dimensional lattice vibrations of chain of identical mass m, in whOach mass is connected to first and second nearest neighbors by coupling constants C; and C;s me =ÉC,(1-cos(nka)). For ka «1, the speed of sound in this limit has fom 4C, +Cka m C+2C, ka m 2C, +C, ka m C+4C, ka m
The dispersion relation for one dimensional lattice vibrations of chain of identical mass m, in whOach mass is connected to first and second nearest neighbors by coupling constants C; and C;s me =ÉC,(1-cos(nka)). For ka «1, the speed of sound in this limit has fom 4C, +Cka m C+2C, ka m 2C, +C, ka m C+4C, ka m
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Transcribed Image Text:The dispersion relation for one dimensional lattice vibrations of chain of identical mass m, in
whach mass is connected to first and second nearest neighbors by coupling constants C:
and Cis me =C,(a-cos(nka). For ka c«1, the speed of sound in this limit has fom
4C,+C ka
C+2C,
ka
m
2C, +C, ka
C+4C, ka
m
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