Valence Electron Charge Density Research Articles

Asphericity in the Valence Electron Charge Density of Vanadium

Analysis of recent X-ray data shows that the valence electrons in bcc vanadium metal, usually designed as a 3d4s4p band, display large aspherical deformations. These electrons have been transferred from the [110] direction to the [111] direction. In the analysis both spherical harmonic expansion in reciprocal space and Fourier inversion were used.

Nonlinear X-ray diffraction. Determination of valence electron charge distributions

A new, nonlinear X-ray diffraction technique is described which permits the direct experimental determination of the valence electron charge density in a wide variety of covalently bonded materials.

Valence charge density in grey tin

The Fourier components of the valence electron charge density in grey tin were calculated using an empirical pseudopotential.

Theoretical X-Ray Scattering Factors Based on Energy-Band Structure

The energy bands for the $3d$ and $4s$ states of copper and the $2p$ states of aluminum are calculated by the augmented-plane-wave method. The crystal charge density is calculated for copper and aluminum and is used to find the scattering factors. For copper these factors are in better agreement with experiment than are those determined from Hartree-Fock atomic calculations. This improvement is shown to be due to the fact that the copper valence-electron charge density is more spread out in the solid than in the atom. The calculated scattering factors are sensitive to the starting crystal potential because of the difficulty of handling exchange in the solid. For aluminum, no improvement over Hartree-Fock scattering factors is realized by performing an energy-band calculation.

T-Matrix Approach to Electron Distribution in Crystals

The wave functions for valence or conduction electrons are given in the form proposed by Phillips and Kleinmran. The wave equation for the smooth part of the electron wave functions is rewritten as an integral eiluation that is solved by using the t-matrix formalism. The smooth part of the wave function is then given by a plane wave plus waves arising from electron scattering by the effective potential of the crystal which might contain point imperfections. Approximate expressions for the wave functions, density andd energy of the valence electroms and the self-consistent crystal potential are given. Numerical results obtained for the Fourier coefficients of the valence electron charge density in diamond exhibit covalent bonding anrd are in good agreement with experimental results. (auth)

Crystal Potential and Energy Bands of Semiconductors. II. Self-Consistent Calculations for Cubic Boron Nitride

A self-consistent crystal potential is constructed for cubic BN. Exchange is included according to the Slater free-electron approximation. The effect of the heteropolar character of the potential is included explicitly in an approximately self-consistent treatment of the valence-electron charge density. The energy gap is found to be about twice that of diamond, consistent with the results of other zincblende crystals and their diamond-type analogs. The maximum of valence band and the minimum in the conduction band are at the center and (100) face of the Brillouin zone, respectively. It is suggested that the heteropolar potential splits the valence band into two sub-bands. The lower sub-band width is about 5 ev, while the higher (which contain three times as many states) has a band width of about 4 ev. The energy gap between the sub-bands is about 10 ev. The effect should be common to all zincblende crystals and may be observable by soft x-ray emission.