The spherical crystal potential and physical properties of ions in crystals. A HF-calculation for the 10, 18, and 36 electron closed shell ions of X-ray scattering factors, diamagnetic susceptibilities, and dipole polarizabilities

Abstract

The diamagnetic susceptibilities Χ_d, the dipole polarizabilities α^D, and the atomic form factors f are calculated for 10, 18, and 36 electron closed shell ions (Na^⊕, Mg^2⊕, Al^3⊕, N^3⊖, O^2⊖, F^⊖, K^⊕, Ca^2⊕, P^3⊖, S^2⊖, Cl^⊖, Rb^⊕, Sr^2⊕, Br^⊖). Three effects on the physical properties are studied a. the quantum mechanical method to calculate the wave functions; b. the influence of the spherical crystal potential on the wave functions and c. the inclusion of self consistency in deriving α^D from the wave functions. The investigation of the polarizability shows that the best choice for the crystal potential is to adjust the charged compensating sphere to the Madelung potential; thereby agreement between experimental and theoretical data is good. -Deviations of atomic form factors for crystal ions from free ion values are high; for soft ions such as N^3⊖, O^2⊖, and S^2⊖f is changed up to 18% (N^3⊖) near sin ϑ/λ=0.1 Å⁻¹ compared to the quasi free ion value. From the crystal ion atomic scattering factors f_{free ion} is deduced by extrapolation for the unstable free ions N^3⊖, O^2⊖, and S^2⊖.