The dynamical behaviour of impurity atoms in crystals

Abstract

Abstract The dynamical behavior of a substituted impurity atom in an infinite crystal is discussed using partitioning and Green's function techniques in a super-matrix representation. The theory is characterized by dynamic response functions which are expressed in terms of the force constant perturbation matrix and Green's function matrices for the host lattice in the symmetry coordinate representation associated with the impurity atom and its perturbed neighbors. Calculations of the temperature dependence of the mean square displacement ( x 2 ) av , mean square velocity ( v 2 ) av , and the dynamical response function, K , characterizing the γ -ray cross-section of Sn 19 isotopically substituted into germanium have been made. The Green's function for the host lattice is calculated from the frequency spectrum of Phillips obtained from the experimental dispersion curves. More general calculations have been carried out for impurity atoms substituted into the aluminum lattice with arbitrary changes in the first neighbor force constants of the impurity atom using a generalized tensor force model. The symmetry adapted host lattice Green's function matrices are determined from X-ray data. Results for ( x 2 ) av ′ ( v 2 ) av ′ and K are given for various impurities in the Al lattice and extrapolations are made to other face-centered cubic metallic lattices. Comparison of theory with current experiments is discussed.