Analysis of the 3-dimensional electron distribution in silicon using directional Compton profile measurements

A method of reconstructing the electron momentum density (p), and its Fourier transform,B(t), from a series of directional Compton profiles is described. It is based on a double Fourier inversion technique and an expansion in lattice harmonic functions. The effect of random errors has been analysed, and the implications for the data collection discussed. We have used the reconstruction technique to obtain (p) andB(t) for silicon from six directional Compton profiles measured with 412 KeV gamma-radiation. The experimental result is in good agreement with earlier measurements and with available solid state theories. A recent Wannier function calculation for silicon using orthogonalised bond orbitals provides a useful tool for identifying the physical origins of the observed anisotropies. A comparison between the information presented in position and momentum space shows that the ease of interpretation depends upon the degree to which the various interactions give rise to localised features in each representation.     

Derivation of the radial distribution function from experimental Compton profiles

The analysis of experimental Compton profiles in position rather than momentum space provides a useful method of interpreting Compton data. A density matrix approach is employed to establish the relationship between the Compton profile J(p), and the Fourier transform of the momentum density B(r), and, for a homogeneous system, the radial distribution function g(r). An earlier Compton profile measurement on sodium provides the data for a demonstration of the long range charge correlations in a metal, in analogy with the Friedel oscillations in a screening charge.     

Effect of bcc-fcc phase transition on the compton profiles of iron

The effect of the- or bcc-fcc phase transition on the electron momentum distribution and Compton profiles of iron has been theoretically examined by a band structure calculation in the two phases. The calculated band Compton profile for the bcc phase shows a good agreement with the experimental results by Phillips and Weiss. The calculated directional Compton profiles show significant changes while going from the bcc to the fcc phase.     

Anisotropy effects in the A-15 superconductor Nb3Sn

Experimental B_c2(T) characteristics of two Nb₃Sn samples are analyzed using a full strong coupling theory of B_c2(T) which also includes anisotropy effects. The analysis requires a rather pronounced anisotropy of the electron-phonon interaction and of the Fermi velocity and Pauli paramagnetic limiting in order to reproduce the experimental B_c2(T) data over the whole temperature range. The analysis of the second, dirty sample shows that a pronounced change in the electron density of states at the Fermi energy is required together with reduction of the Fermi velocity anisotropy to reproduce the experimental B_c2(T) data. The analysis does not require any contributions from spin-orbit scattering processes to achieve an excellent match between theory and experiment.     

Strong anisotropy in the low temperature Compton profiles of electron momentum distribution in α-Ga metal

Compton profiles of momentum distribution of conduction electrons in the orthorhombic phase of α-Ga metal at low temperature are calculated in the band model for the three crystallographic directions (100), (010), and (001). Unlike the results at room temperature, previously reported by Lengeler, Lasser and Mair, the present results show strong anisotropy in the Compton profiles with the momentum distribution along (001) direction being substantially different from the other two directions. While experimental data on Compton profiles at low temperatures are not available for comparison with theory, the resistivity data in α-Ga at low temperature strongly support this anisotropic behaviour. Besides, the electronic heat capacity constant γ available from both experiment and present calculation suggests that the conduction electron distribution at low temperature in the orthorhombic phase is markedly different from the free-electron-like-distribution at room temperature, thus lending additional support to anisotropic behaviour of Compton profiles. It would be nice to have Compton profiles data from experiment at low temperature for direct comparison with theory. It is hoped that the present work would stimulate enough interest in that direction.     

Electron momentum density in Cu<Subscript>0.9</Subscript>Al<Subscript>0.1</Subscript>

A reconstruction technique based on the solution of the Radon transform in terms of Jacobi polynomials is used to obtain the 3D electron momentum density, ϱ(p), from nine high-resolution Compton profiles (CPs) for a Cu_0.9Al_0.1 disordered alloy single crystal. The method was also applied to theoretical CPs computed within the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA) first-principles scheme for the same nine orientations of the crystal. The experimental ϱ(p) is in satisfactory agreement with the theoretical ϱ(p), shows most details of the Fermi surface (FS) and exhibits electron correlation effects. We comment on the map of the FS obtained by folding the reconstructed ϱ(p) into the first Brillouin zone, which yields the occupation number density, ϱ(k). A test of the validity of data via a consistency condition (within our reconstruction algorithm) as well as the propagation of experimental noise in the reconstruction of both ϱ(p) and ϱ(k) are investigated. Received: 24 October 2001 / Accepted: 20 January 2002 / Published online: 3 June 2002 RID="*" ID="*"Corresponding author. Fax: +48-71/344-10-29, E-mail: samsel@int.pan.wroc.pl     

Momentum distribution and one-body density matrix in liquid3He.

Summary The momentum distributionn(k) and the one-body density matrix ρ₁(r,r' have been calculated in normal liquid³He atT=0. A variational wave function containing two-, three-body and backflow correlations has been used. The Fermi hypernetted chain technique has been employed and the elementary diagrams have been evaluated by the scaling approximation. The present estimate ofn(k) is in good agreement with the Monte Carlo data obtained with similar wave functions.n(k) and the discontinuityZ ofn(k) at the Fermi surface have been computed at several values of the density. The density dependence of the effective massm ^* has been found to be mainly due to that ofZ.     

Investigation of electronic properties of crystalline arsenic chalcogenides: Theory and experiment

The electronic structure of crystalline As₂S₃ and As₂Se₃ has been calculated in this paper. We present the energy bands, density of states (DOS) and the Compton profiles using the linear combination of atomic orbitals (LCAO) scheme based on the density functional theory (DFT). From the calculated total and partial density of states it is seen that the lone-pair p-states of sulphur/selenium contribute closest to the Fermi energy level. To interpret the theoretical data on the Compton line shape, we have measured the Compton profiles on a 100 mCi ²⁴¹Am spectrometer. It is seen that the density functional theory within generalised gradient approximation gives a slightly better agreement with the experimental momentum densities. The nature of chemical bonding in arsenic chalcogenides is studied using Mulliken's population analysis and the experimentally measured equal-valence-electron-density profiles; As₂S₃ is found to be more ionic compared to As₂Se₃.     

Electron momentum distributions and compton profiles of some molecules with FSGO model

The electron momentum distributions and the Compton profiles (within the impulse approximation) of H₂, LiH, methane, water, acetylene, ethylene, ethane cyclopropane and cyclobutane have been calculated using the floating spherical Gaussian orbital (FSGO) wavefunctions. The agreement of the single-FSGO Compton profiles with the corresponding experimental or the Hartree-Fock (HF-SCF) theoretical ones is fairly good in most of the cases examined. The advantages and drawbacks of using the FSGO model for the calculation of Compton profiles are discussed.     

On the use of Fourier-transformed Compton profile for the determination of band occupancies in certain solids

The Pattison-Williams method of using Fourier-transformed Compton profiles for obtaining Fermi momenta in simple metals, is extended to set up a scheme for inferringd orf band occupancies in transition metals, rare earths etc. CP measurements are reported for Ni,α-Mn andβ-Mn and then the new scheme is applied to obtain 3d occupancies in these systems. Some comments on the use of this method for other systems are also made.     

Compton profile of molybdenum

In this paper we report the experimental Compton profile of polycrystalline molybdenum. The measurements have been made by scattering 59.54 keVγ-rays and are compared with the recent band structure calculation of Janiet al. [4]. These results have also been compared with our calculation based on the renormalized-free-atom model for different 4d-5s configurations. It is found that the present experimental data are relatively in good agreement with the band structure calculation.     

Electron momentum density, band structure, and structural properties of SrS

The electron momentum density, the electronic band structure, and the structural properties of SrS are presented in this paper. The isotropic Compton profile, anisotropies in the directional Compton profiles, the electronic band structure and density of states are calculated using the ab initio periodic linear combination of atomic orbitals method with the CRYSTAL06 code. Structural parameters of SrS—lattice constants and bulk moduli in the B1 and B2 phases—are computed together with the transition pressure. The computed parameters are well in agreement with earlier investigations. To compare the calculated isotropic Compton profile, measurement on polycrystalline SrS is performed using 5Ci-²⁴¹Am Compton spectrometer. Additionally, charge transfer is studied by means of the Compton profiles computed from the ionic model. The nature of bonding in the isovalent SrS and SrO compounds is compared on the basis of equal-valenceelectron-density profiles and the bonding in SrS is found to be more covalent than in SrO.     

Paramagnetic susceptibility of Bi-Mn alloys in the liquid state

The magnetic susceptibility of Bi_{100 − x} Mn _x (x = 5, 7.5, 10, 12.5, 15, 17.5, 20, 25) alloys is experimentally studied by the Faraday method in the temperature range T = 300−1200°C and the magnetic-field range B = 0.6−1.3 T. To calculate the electronic characteristics of the Bi-Mn alloys, the experimental results are approximated by the generalized Curie-Weiss law. The calculated parameters of the electronic structure of the alloys demonstrate that manganese is present in the melt in an ionic state with an effective magnetic moment μ_eff ≈ 5μ_B, all Bi-Mn alloys have negative paramagnetic temperatures (which indicate the antiferromagnetic character of the exchange between transition 3d element atoms), and the density of states near the Fermi level n(E _F) is low. Therefore, the Fermi level is outside the d band of manganese and its position is controlled by the sp band of bismuth.     

Relativistic double differential cross sections for Compton scattering by bound electrons: Test at low photon energies and predictions at intermediate photon energies

Cross section profiles d²σ/dΩdω′ for Compton scattering of photons by bound electrons are calculated for all subshells of the atom. Results obtained from the form factor approximation and from a relativistic version of the impulse approximation are compared with experimental data for Cu and Pb at a scattering angle ofθ=145° and a photon energy of 662 keV. The impulse approximation proves to be superior to the form factor approximation and is used to predict cross section profiles for a primary energy of 50 MeV and different scattering angles and charge numbers. It is shown that only for the heaviest atoms and scattering angles belowθ=5° there is a non-negligible contribution of Compton scattering to the elastic peak.     

Experimental and theoretical Compton profiles of Be, C and Al

The results of Compton profile measurements, Fermi momentum determinations, and theoretical values obtained from a linear combination of Slater-type orbital (STO) for core electrons in beryllium; carbon and aluminium are presented. In addition, a Thomas-Fermi model is used to estimate the contribution of valence electrons to the Compton profile. Measurements were performed using monoenergetic photons of 59.54 keV provided by a low-intensity Am-241 γ-ray source. Scattered photons were detected at 90° from the beam direction using a p-type coaxial high-purity germanium detector (HPGe). The experimental results are in good agreement with theoretical calculations.     

GW approximation study of the Compton profile of ZnSe

We have obtained the Compton profile of ZnSe from the first principles GW approximation (GWA) method and ground-state density functional theory (DFT) method. We observe that between 0 and 1.5?a.u., there is better agreement to previous studies via the GWA difference profile compared to the ground-state difference profile. Above 1.5?a.u., both cases do not agree with the trend of the previous study; however, the application of the GWA is seen to improve the agreement compared to localized density approximation. Previous studies have reported that discrepancies from experiment are related to pseudopotential calculations which have been observed to overestimate momentum density between 0 and 1.5?a.u., while the reverse trend is seen above 1.5?a.u. We thus conclude that improvement to the pseudopotential technique to obtain the Compton profile is possible if the sharp Fermi break of the momentum distribution between high and low momenta becomes more smeared. Using the broadened spectral functions via the contour deformation method to obtain the momentum distributions, the GWA is a natural tool to achieve this via the contribution from the dielectric screening to the quasiparticle energies.     

Electron correlation effects on Compton profiles of copper in the GW approximation

The Compton profiles (CPs) of copper are calculated by the GW approximation with FLAPW basis sets on the LDA. In the quasiparticle band structure in the GW approximation, the width of fully occupied 3d valence band which is overestimated in the LDA, is in good agreement with experimental observation. The dynamical screening effects are important for band width narrowing. The occupation number densities are evaluated from the spectral function calculation within the GW calculations. The CPs obtained using these GW calculations successfully reproduce experimental results.     

Structure study of simple fluids

The structure function of simple monatomic liquids like neon and argon is studied in an approximation scheme where intermediate functionQ(r) is extended beyond hardcore diameter rather than the direct correlation functionC(r). The calculated values show good agreement with experimental values.     

Optical constants of copper in s-d model

A non-interacting s-d band model is used to evaluate ?₂(ω) in copper. The free electron approximation is used for electrons in s-band, while a simplified tight-binding scheme is used for the d-electrons. It is found that only d-bands with m = 0 contribute to optical transitions. The transition matrix elements are explicitly calculated. The calculated ?₂(ω) gives reasonable agreement with measured optical conductivity.     

Different ways of dealing with Compton scattering and positron annihilation experimental data

Different ways of dealing with one-dimensional (1D) spectra, measured e.g., in the Compton scattering or angular correlation of positron annihilation radiation (ACAR) experiments, are presented. Using the example of divalent hexagonal close packed metals, we show what kind of information on the electronic structure one can get from 1D profiles interpreted in terms of either 2D or 3D momentum densities.2D and 3D densities are reconstructed from merely two and seven 1D profiles, respectively. Applied reconstruction techniques are particular solutions of the Radon transform in terms of orthogonal Gegenabauer polynomials. We propose their modification connected with so-called two-step reconstruction.The analysis is performed both in the extended p and reduced k zone schemes. It is demonstrated that if the positron wave function or many-body effects are strongly momentum dependent, analysis of 2D densities folded into k space may lead to wrong conclusions concerning the Fermi surface. In the case of 2D ACAR data in Mg, we found very strong many-body effects. PACS 71.18.+y; 13.60.Fz; 87.59.Fm