《固体物理学》课程教学课件（PPT讲稿）Chapter 4 lattice dynamics and lattice capacity 4.1 Normal Modes of Vibration 4.2 Density of States 4.3 Harmonic approximation and normal mode coordinates 4.4 phonon

Two dispersion relation.The lattice constant is 2a,and the reciprocal lattice constant is 9=0 欧-2识“ 4 m+M 心=A-刂-0 木(9q) 9= 23 2a 04 23 m+M[,M-m] 2B 0=B 1+ Gap mM m+M 23 m M 0- 02=B +M M-m]_ mM m+M M M= mM m+M Reduced mass -9 0 π π 2a 2a

mM m M  = + Gap Reduced mass Two dispersion relation. The lattice constant is 2a, and the reciprocal lattice constant is a  2a  + 2a  − q = 0   2 2 2 1 1 m M mM mM m M      + + = + = = + 2 q a  =   2 1 1 0 m M mM   − + = − = 2 2 2 1 2 1 m M M m mM m M m m M M m mM m M M       + − + −   = + =     + + −   = − =     +

③-② B mo2-2B 2B2B A 2Bcosqa @ M m B m02-2 3>0 cosga >0 、A 2B cosqa Neighboring atoms vibrate positively B Long wavelength limit 9=0,02=0 =1 Long wavelength limit,the amplitude for two atoms are the same B Mo2-2B ③-① 2 2B A 28 cosga 0> M cosga>0 B Mo-2 ∠0 Neighboring atoms vibrate oppositely A 2B cosqa Long length limit =0 02(0)= 26 u Mo2-2B =- M Long wavelength limit,the mass centre A 2B m is at rest,called optical branch

2 2 2 cos B m A qa    − = − 2 q = = 0, 0 − 1 B A −     =   2 2 2 M m   −  cos 0 qa  2 2 0 2 cos B m A qa     −   − −  = −      Long wavelength limit 2 2 M  +  2 2 2 cos B M A qa    − = − 2 2 0 2 cos B M A qa     +   + −  = −      cos 0 qa  2 2 2 B M M A m     +   + −   = − = −   Long length limit q＝0 2 2 (0)    + = ③－② ③－① Neighboring atoms vibrate oppositely Neighboring atoms vibrate positively Long wavelength limit, the mass centre is at rest, called optical branch Long wavelength limit, the amplitude for two atoms are the same