THE SCREENED-CHARGE MODEL OF CRYSTAL-FIELD INTERACTION

An analytical approach is developed to calculate crystal-field parameters in rare-earth intermetallics. Unlike the point-charge approach, the model includes all electrostatic crystal-field contributions and accounts for charge penetration of 4f and non-4f electrons. The conduction electrons of the intermetallic alloy are considered as a weakly disturbed homogeneous electron gas with inverse Thomas-Fermi screening length q. Asymptotically, the screened-charge model yields A2(0) is-proportional-to r(-m) exp(-qr) with m = 1, as opposed to the screened point-charge model, where m = 3. The properties of the atoms which create the crystal-field enter the theory as crystal-field charges Q(cf). Methods to calculate Q(cf) are presented, and it is shown that Q(cf) contains a negative contribution due to the finite size of the electronic cores of the surrounding atoms. For instance, helium atoms, which are strongly neutral, are predicted to bear a crystal-field charge Q(cf) = -0.64 e in a q = 3 angstrom-1 electron gas. It is shown how the properties of the rare-earth ion affect the crystal-field parameters and an analytical expression for the dependence of A2(0) on the ratio [r4]4f/[r2]4f is obtained. Interstitially modified iron-rich rare-earth intermetallics are used to discuss the A2(0) dependence on distance and chemical nature of the surrounding atoms.