Surface Vibration of a Diatomic Simple Cubic Lattice

概要

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An investigation is made of the effect of the surface on the vibrational property of a semi-infinite alternating diatomic simple cubic lattice. By regarding the surface as a special type of defect, equations of motion for the displacement of atoms from their equilibrium positions are solved by means of Green's function method. It is shown that owing to the regularity of the lattice in the plane parallel to the surface, the problem has a one-dimensional character. Two types of vibrational modes are obtained, one type being analogous to the Rayleigh waves of continuum theory whose frequencies are continuousely distributed in the acoustical band and a second type having no analogue in the continuum theory whose frequencies are discrete and split from the bottom of the optical band. It is shown that both types of these "surface waves" are exponentially damped towards the interior of the lattice. The frequencies and the penetration depth of them are obtained as a function of K_2/K_1 and M_2/M_2, where K_1 and K_2 are the central and the noncentral force constants of the lattice, and M_1 and M_2 are the mass of heavier atoms and that of lighter atoms, respectively. For the first type of modes a surface wave dispersion relation is obtained, while for the second type of modes the frequencies and the penetration depth are evaluated numerically.
理論物理学刊行会の論文
1963-07-25