Charge Distribution and Electric Field Gradients in Ionic Crystals

A method is presented by means of which one can investigate the validity of the point-charge model often used for the calculation of electric field gradients in ionic crystals. The asymmetry parameter of the electric field gradient at a nucleus and the Eulerian angles describing the orientation of the field gradient's principal axes with respect to the crystallographic axes are linear functions of the point charges assigned to each set of atoms in the lattice. If the unit cell is of low symmetry and if there are more than one set of nuclei for which quadrupole interaction data can be observed, the number of observables and equations may equal or exceed the number of unknown charges, thereby enabling the charge distribution to be determined and its internal consistency checked. Such is the case for spodumene, for which the charge distribution thus calculated is neither internally consistent nor very reasonable. An analysis is made of the sensitivity of the apparent charge distribution to experimental errors in the quadrupole interactions, and the errors are found to be much too small to account for the anomalies. However, further investigations, including a refinement of the crystallographic parameters of spodumene, are necessary before the anomalies could be attributed to deficiencies in the point-charge model. With allowance for the uncertainties in the charge distribution, the analysis lends some support to a value of ≈0.04 b for Q7, the nuclear quadrupole moment of Li7. Further charge distribution anomalies result from a similar, but less detailed treatment of another silicate, beryl, which gives a very approximate value of Q9≈0.1 b for Be9.