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A new method is presented for computing the electric lead field of a realistic head shape model which has piecewise homogenous conductivity. The basic formulae are derived using the well-known reciprocity theorem. Previously described methods are also based upon this theorem, but these first calculate the electric potential inside the head by a scalar boundary element method (BEM), and then approximate the ohmic current density by some sort of gradient. In contrast, this paper proposes the direct evaluation of the ohmic current density by discretizing the vector Green's second identity which leads to a rector version of BEM. This approach also allows the derivation of the same equations for the three concentric spheres model as obtained by Rush and Driscoll (1969). The results of simulations on a spherical head model indicate that the use of a vector BEM leads to an improvement of accuracy in the computation of the ohmic current density with respect to those reported previously, in term of different measures of error.

The room temperature structure of BaBi 4 Ti 4 O 15 is determined by means of high resolution synchrotron x-ray powder diffraction. At Stanford Synchrotron Radiation Lab., the sample was mounted on a zero background holder and data was collected in reflection geometry at 10 KeV (1.24 Å) from 2° to 138° in 2θ. Rietveld refinement was performed with programs FULLPROF and GSAS. Starting space group followed Aurivillius' choice 14/mmm. This tetragonal symmetry group does not explain observed peaks splitting, so orthorhombic symmetry was selected. Symmetry F2mm was considered, for it is consistent with observed electric dipole moment in the elementary cell. The selected space group allowed stable and accurate convergence of the refinement. Treatment of the experimental data included diffuse scattering characterization. Structured background fitting gave place to the derivation of the radial distribution function, as a measurement of short range segregation. BaBi 4 Ti 4 O 15 is orthorhombic, polar and with partial short-range ordering of the Ba and Bi ions. Variations of atomic coordinates, relative to those corresponding to the tetragonal paraelectric condition, give place to the appearance of spontaneous electric polarisation.