Atomic coordination and the distribution of electric field gradients in amorphous solids

Abstract

The observation of nuclear quadrupole interactions in amorphous solids provides a unique possibility of obtaining information about the angular distribution of local ionic coordinations, complementary to the information about radial distributions deduced from x-ray and neutron diffraction and from extended x-ray absorption fine structure measurements. In the present paper the relation between ionic coordinations and the distribution of electric field gradients (EFG) is investigated. It is shown that the distribution function $P({V}_{\mathrm{zz}},\ensuremath{\eta})$ of the splitting parameters ${V}_{\mathrm{zz}}$ (the electric field gradient) and $\ensuremath{\eta}$ (the asymmetry parameter) in general yields zero probability both for ${V}_{\mathrm{zz}}=0$ and for $\ensuremath{\eta}=0$. For solids which are isotropic on the average, the distribution function of the components ${V}_{\mathrm{ik}}$ of the EFG tensor depends only on two variables, the invariant functions of the tensor components [$\mathrm{Det}({V}_{\mathrm{ik}}) \mathrm{and} \ensuremath{\Sigma}{V}_{\mathrm{ik}}^{2}$]. Expressions for these quantities in terms of the radial coordinates of the ions causing the EFG and of the bond angles between pairs of ions are given. For amorphous solids with random ionic coordination an analytic approximation for the distribution function $P({V}_{\mathrm{zz}},\ensuremath{\eta})$ is derived. This function is strongly dominated by the distribution of ions in the first coordination shell. The results are applied to the analysis of M\ossbauer spectra of $^{155}\mathrm{Gd}$ in amorphous Gd-Ni alloys.