LATTICE STATICS GREENS-FUNCTION FOR A SEMIINFINITE CRYSTAL

The lattice statics Green's function describes the linear response of displacement to the application of a force on a crystal lattice. From a macroscopic point of view, the crystal lattice behaves like an aniso tropic elastic body. Therefore, the lattice statics Green's function m ust approach the elastic Green's function for large distances from the point at which the force is applied. The lattice used in calculating the lattice Green's function should have the elastic constants corresp onding to the crystal and a symmetrical stress tensor in the continuum elastic limit. In order to satisfy these conditions, three-body force s are introduced. The Green's function for the infinite lattice with s hort-range atomic interaction is calculated immediately by translation al symmetry. The Green's function for the defective lattice is derived from the Dyson equation. The definitive Green's function for the semi -infinite lattice is presented.