[The far-infrared spectrum of the ternary mixed crystal]

Born-Huang equations of lattice dynamics for the ternary mixed crystal AB(1-x)Cx. by using the random-element-isodisplacement model (REI model) were set up, and the dielectric function and the far-infrared reflectivity of lattice vibration in several ternary mixed crystals were discussed. It is shown that this model applies to all circumstances: (1) Single mode--there are one transverse optical phonon and one longitudinal optical phonon in all scope of the composition x(0 < or = x < or =1). (2) Double mode--there are two TO-LO-mode pairs in 0 < or = x < or = 1. (3) The third mode--it shows single mode behavior in a part and shows double mode behavior in another part. It was found that single mode crystal has one reflectance band and double mode has two reflectance bands. For the third mode crystal, there are one band in a part and two bands in another part. The model provides a possible way to understand the optical character of other problem of electron-phonon interaction. mixed crystal. Based on it the authors can discuss other problem of electron-phonon interaction.