Valence Electron Charge Density Research Articles

The electric field gradient at Gd nuclei in intermetallic compounds with CaCu5 related structures

155Gd Mössbauer spectroscopy was used to measure the electric field gradient (EFG) at the Gd nucleus in GdT5 compounds (T=Co, Ni, Cu and Rh) and GdT3B2 compounds (T=Rh, Ru and Co). The crystal structure of these compounds is of the CaCu5 type. Using the results of self-consistent band structure calculations of the valence electron contributions to the EFG, it is shown that the main contribution, comes from the asphericity of the Gd 6p valence electron charge density.

Adsorption dependence of vacant-electronic-state densities: As adatom on a lanthanum oxide surface.

The electronic structure of the lanthanum oxide surface with an adsorbed As atom has been studied by the X\ensuremath{\alpha} method. Analysis of the occupied electronic density of states and contour maps of the valence-electronic charge density for the bulk and adsorbed surface clusters shows pronounced differences connected with As p-- and La s+La d--state hybridization. The influence of these factors on absorption-spectra features is discussed. The surface reduction effects are considered.

Absence of volume metastability in bcc copper

A previous pseudopotential total-energy calculation on bcc copper revealed a structural metastability in the form of a double-well total-energy curve with two local minima (at 6% compression and 7% dilation relative to the observed equilibrium volume of the fcc structure), separated by a barrier. This was explained in terms of a symmetry breaking in the nonspherical components of the valence-electron charge density upon volume change. Our present all-electron calculation shows no such metastability; analysis of the response of the valence-electron charge density to volume deformations indeed shows no cause for such a metastability.

Structural and electronic properties of WC.

We present the results of a pseudopotential local-orbital calculation on hexagonal WC. The calculated lattice constants and cohesive energy are in good agreement with experiment, and the calculated bulk modulus lies within the wide range of measured values. The band structure and Fermi surface obtained are also generally consistent with experimental data, and the Fermi level is found to lie in a deep minimum of the density of states. The calculated valence electron charge density indicates that the bonding in WC consists of a metallic component similar to that found in solid W, and strong W-C bonds.

Structure Factors of InP Determined by the Pendellösung Method Using White Radiation

The Pendellösung intensity beats in wavelength scale were measured to determine the structure factors of InP crystal by the energy-dispersive diffraction method. The clear beats obtained for eleven low-order reflections from the 111 to 440 reflections were analyzed to evaluate the structure factors with their wavelength dependence on the basis of the dynamical diffraction theory. The values were different from those measured by Sirota and Gololobov (Acta Crystallogr. A25 (1969) 223) using the powder diffraction method, especially for high-order reflections. A discussion is made on the charge density of valence electrons using the obtained structure factors and the tetrahedral charge distortion model. The measured wavelength dependence of the structure factors can be interpreted well by the anomalous dispersion terms of Cromer and Liberman (J. Chem. Phys. 53 (1970) 1891).

Structure factors and Debye temperatures of Al–Li solid-solution alloys

By combining the accurate low-angle X-ray structure factors of A1-Li solid-solution alloys (containing 5.25 and 8.06 at.% Li) determined by the critical voltage technique in high-energy electron diffraction (HEED) with higher-angle values obtained by interpolation between best pure-element form factors, a complete set of accurate X-ray structure factors for these alloys has been produced. From the measured Debye-Wailer factors for the alloys it was found to be difficult to determine a Debye temperature trend with composition for AI-Li solid-solution alloys because of the extent of the experimental errors, although the results suggest that the Debye temperatures of the alloys are higher than that of pure aluminium. This is obviously consistent with an increase in Young's modulus; i.e. the stiffness of the alloys appears to be greater than that of pure aluminium. This increase appears to arise predominantly from an increase in the force constant between nearest-neighbour (n.n.) lithium atoms in the alloy as compared with the value for pure lithium. This occurs because n.n. lithium atoms are closer together in Al-Li solid-solution alloys than they are in pure lithium. Because the lithium atoms are closer together in the alloys, the electron charge density, ρ, associated with the valence electrons in the alloys is likely to be higher than if ρ is considered unchanged by alloying. This suggested increase in the charge density of the alloy valence electrons was confirmed, as the experimental 111 low-angle structure factors of the alloys were found to be significantly higher than the equivalent values obtained by interpolation between the best pure-element form factors. Such electronic changes are to be expected for Al-Li alloys as aluminium and lithium have a valency difference of two.

Many-electron model of equilibrium metal-semiconductor contacts and semiconductor heterojunctions.

A many-electron model is proposed to describe the electronic structure of metal-semiconductor interfaces and semiconductor heterojunctions. The model is utilized to calculate the self-consistent one-electron potential in the vicinity of the interface. This potential arises from two sources: a short-range dipole contribution due to valence-electron rearrangements at the interface relative to the corresponding vacuum surfaces, and a long-range space-charge contribution caused by band-bending effects extending thousands of angstroms from the interface.The short-range, valence-electron dipole contribution is evaluated by minimizing the interface energy calculated within a local-density description of the valence-electron charge density. The long-range space-charge contribution is determined both by the valence-electron rearrangements, being included in the interface energy through an electrostatic energy term, and by the thermodynamic equilibrium boundary conditions. The boundary conditions ensuring thermal, mechanical, and electron-transfer equilibrium are imposed explicitly. The chemical potentials required to satisfy the electron-transfer boundary condition are obtained from the local-density model at the constant temperature and pressure characteristic of the equilibrium interface.For numerical calculations the ion-core charges are approximated by a uniform positive charge density. The interfaces between the metal and semiconductor as well as the metal-vacuum and semiconductor-vacuum surfaces are defined by abrupt discontinuities in this uniform positive charge density. A version of local-density theory suitable for both metals and semiconductors is utilized to describe the valence-electron charge densities and is extended to incor- porate the dopants in the semiconductor as well. Consequently, a unified model of both the microscopic interface dipole and macroscopic space-charge region is achieved. Numerical calculations reveal that the microscopic interface dipole is independent of the doping in the space-charge region for dopant densities N\ensuremath{\lesssim}${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.These calculations further predict the validity of Schottky's phenomenological boundary condition for metal-semiconductor contacts, the applicability of the electron-affinity rule for semiconductor heterojunctions, and systematic correlations between Schottky-barrier heights and heterojunction band offsets. The latter three results emerge as consequences of the rigorous and complete imposition of thermodynamic equilibrium boundary conditions and of the use of a model of the ion-core charge density in which atomic reconstructions at the interface relative to the vacuum surfaces are not considered explicitly.

Electron charge densities at conduction-band edges of semiconductors.

We demonstrate that both the empirical pseudopotential method (EPM) and the linear combination of atomiclike orbitals (LCAO) approach are capable of producing consistent electronic charge distributions in a compound semiconductor. Since the EPM approach is known to produce total valence electron charge densities which compare well with experimental x-ray data (e.g., Si), this work serves as a further test for the LCAO method. In particular, the EPM scheme, which uses an extended plane-wave basis, and the LCAO scheme, which employs a localized Gaussian basis, are used, with the same empirical potential as input, to analyze both the total valence electron charge density and the charge density of the first conduction band at the \ensuremath{\Gamma}, L, and X k points of the Brillouin zone. These charge densities are decomposed into their s-, p-, and d-orbital contributions, and this information is used to interpret the differences in the topologies of the conduction bands at \ensuremath{\Gamma}, L, and X. Such differences are crucial for a comprehensive understanding of interstitial impurities and the response of specific band states to perturbations in compound semiconductors.

Physical content of electron-charge-density distributions inA15compounds

The starting point of the present article is a careful analysis of the physical meaning of the three deformation electron-charge-density maps for V/sub 3/Si, V/sub 3/Ge, and Cr/sub 3/Si (previously presented by J.-L. Staudenmann et al., Phys. Rev. B 24, 6446 (1981)). Based on the significant differences exhibited in these maps, it was shown that one can organize all the Debye temperatures at 0 K from specific-heat measurements into five collections which were called Debye classes. The findings here presented are not limited to A15 alloys alone, but rather can be applied to any other family of compounds that satisfies the free-atom superposition principle and the small-amplitude vibration hypothesis. It is shown that deformation electron charge densities depend only weakly upon structure and that they are mainly related to physical properties. Furthermore, the use of deformation electron-charge density as a criterion in setting the starting point for the three main Debye classes is justified a posteriori. We point out that when one takes into account the consequences of the dielectric function, the static or bonding electron charge density can only be extracted with great difficulty from any experimental data. This certainly complicates any comparison between experimental and computed electron chargemore » densities. It is shown that the deformation and total electron charge densities are the only well-defined inverse fourier transforms. If the vibration amplitude of the valence-electron orbitals are non-negligible, the valence-electron charge density, in contrast to the deformation and total electron charge densities, has no simple interpretation.« less

A localized orbital description of Si

AbstractIn order to describe the change in electronic structure arising from the presence of impurities in a metal or semiconductor it is convenient to have a localized basis representation of the host. To optimize such impurity calculations it is also necessary that this set of localized basis functions be as small as possible. The best representation of the electronic structure of the diamond and zinc‐blende semiconductors in terms of a small set of localized basis functions has been obtained by Chadi. In this method Bloch sums for describing the pseudo‐wave‐functions and energy bands are constructed from Slater orbitals of different symmetry centred on each atomic site. Using a variational approach to determine the decay constants parametrizing these various orbitals Chadi obtains an accurate description of the bandstructures with a simple four state per atom s–p basis set and reliable pseudo‐charge densities with only ten states per atom. These original calculations of Chadi are not, however, carried through to full convergence. Therefore this analysis is repeated for the case of Si and it is found that, while Chadi's results are indeed fortuitous, it is possible to accurately describe both the bandstructure and valence electron charge density of these semiconductors in terms of a minimum set of well localized basis functions.

Ground-state properties of diamond

The ground-state properties of diamond are investigated using an ab initio density-functional pseudopotential scheme. The calculated equilibrium lattice constant, cohesive energy, and bulk modulus are in excellent agreement with experiment. Unlike Si and Ge, a double hump is found in the valence-electron charge density along the tetrahedral bonds.

Self-consistent electronic spectrum of trigonal Te. Charge and momentum density, and Compton profile

The electronic ground state of crystalline trigonal tellurium has been determined according to a self-consistent local-density-dependent approach with the Slater $X\ensuremath{\alpha}$ exchange correlation, and with orthogonalized-plane-wave and linear-combination-of-atomic-orbitals representations for valence and core states. Results are given for the valence electron charge and momentum density, the Compton profile, and the autocorrelation function of the one-electron density matrix. These quantities are discussed with respect to trigonal selenium, since no experimental data are available for these quantities for Te. A discussion of the chemical bonding in trigonal Te is given.

Validity of local density kinetic energy expressions for electronic structure calculations

Local density expressions provide a simple and flexible means of calculating kinetic energies. Recently it has been ascertained that such expressions can be quite accurate (to within 1%) in obtaining the total kinetic energy of an atomic system. However, we shall demonstrate that local density kinetic energy expressions, as presently formulated, are not appropriate for molecular or solid state calculations. In particular, these expressions do not properly describe trends appropriate for valence electron charge density configurations.

Charge distribution in C 6Li

The valence electron charge density of C 6Li has been evaluated from a knowledge of the band structure and is presented along various directions in the crystal. The results illustrate the large anisotropy of this material. It is difficult to quantify a degree of ionization. However, the following qualitative picture emerges. The highest occupied states originate from the π-bands of graphite. These are spatially concentrated near the graphite layers with peak densities approximately 1 Å from the centers of the layers. Occupied low-lying bonding bands hybridize with the metal band so that the valence density of C 6Li has an s-wave-like cusp at each Li nucleus.

Electronic properties of the defect-zincblende semiconductor CdIn 4Se 4

The electronic properties of the defect-zincblende semiconductor α-CdIn 2Se 4 are studied. Electronic band structure, valence-electron charge density and valence density of states are calculated with the pseudopotential method and compared with those of binary zincblende semiconductors.

The quadratic response of a Fermi gas: Electronic charge density of valence electrons in zincblende semiconductors

AbstractThe electronic charge density of a free electron gas is exactly calculated up to second order in the perturbing potential, using a direct density matrix approach. The effect of the second order correction is analysed for both f.c.c.‐lattice metals and zincblende semiconductors and it is found, that the singularity of the quadratic filter function, introduced in this work, leads to the appearance of a covalent bonding charge in semiconductors. For illustration of the method, the charge distribution of Ge is calculated and compared with results of explicit summation of the wave functions.

X-ray determination of valence-electron charge density and its temperature dependence in indium antimonide

X-ray determination of valence-electron charge density and its temperature dependence in indium antimonide

Unified theory of static, dynamic, and electronic properties of aluminium

The problem of including the many-electron interactions into a pseudopotential theory of aluminium is re-considered. It is shown that due to the valence-core exchange and correlation, the pseudopotential is necessarily non-linear in the valence-electron charge density. We propose a simple way to account for this non-linear effect. This improved valence-core exchange potential allows to give a unified theory of static, dynamic, and electronic properties of aluminium.

Electronic charge density of aluminum

The valence electronic charge density is calculated for aluminum from wave-functions obtained via Ashcroft's pseudopotential. A contour plot of the charge density is presented in the (100) plane. The Fourier transform of the charge density is used to calculate the atomic form factors which are compared with experimental X-ray form factors. The accuracy of the wavefunctions are further tested by comparing calculations of the imaginary part of the frequency dependent dielectric function with and without the effect of core states.

Calculation of the Cohesive Energies and Bulk Properties of the Alkali Metals

The cohesive energy and zero-pressure density of the alkali metals have been calculated using the self-consistent augmented-plane-wave method and the statistical ($X\ensuremath{\alpha}$) exchange-correlation approximation. For the value of $\ensuremath{\alpha}$ which makes a single determinant of atomic spin orbitals satisfy the virial theorem, the lighter alkali metals are computed to have cohesive energies and zero-pressure densities which are too large (errors of 22 and 16% for Li) with respect to experiment. To test the sensitivity of these results to the choice of $\ensuremath{\alpha}$, the same calculations have been performed with $\ensuremath{\alpha}$ set equal to $\frac{2}{3}$. This choice of $\ensuremath{\alpha}$ produced more uniformly good results for all the alkali metals with the largest errors occurring for cesium (errors of 7 and 9%, respectively). It is suggested that these results may be a consequence of the large change in the valence electronic charge density that occurs when the lighter alkali-metal atoms come together to form the solid. It is not suggested, however, that $\ensuremath{\alpha}=\frac{2}{3}$ be used in all energy-band calculations.