Note to electron–phonon interaction in ternary mixed crystals

Optical vibrations of the lattice and the electron–phonon interaction in polar ternary mixed crystals are studied in the framework of the continuum model of Born and Huang and the random-element-isodisplacement model. A normal-coordinate system is correctly derived. A new Fröhlich-like Hamiltonian for the electron–phonon interaction including the unit-cell volume variation is derived. The numerical results of the electron–phonon coupling constants and the polaronic energies for several typical materials are given. The non-linearity of the electron–phonon coupling effects varying with the composition is obtained.