Directional Compton Profiles Research Articles

Electron Momentum Density of Hexagonal Magnesium Studied by Compton Scattering

Directional Compton profiles of single crystal of hcp magnesium have been measured with scattering vectors along the [10 10], [1120] and [0001] directions in reciprocal space (special directions ΓΜ, ΓΚ, ΓΑ) using high-energy (662 keV) gamma radiation from a 137Cs isotope source. The experimental data were compared with corresponding theoretical Korringa-Kohn-Rostoker (KKR) calculations. The directional difference profiles, both experimental (of medium resolution) and theoretical ones, show very small anisotropy of the electron momentum density in magnesium, 2-3 times lower than in zinc and cadmium single crystals, significantly lower than observed in cubic metals. This small directional effect is in good agreement with Compton 60-keV energy experiments and positron annihilation data presented by other authors.

Electron momentum density and the Fermi surface ofβ−PdH0.84by Compton scattering

The geometry of the Fermi surface of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Pd}{\mathrm{H}}_{0.84}$ has been determined by the synchrotron-based Compton scattering experiment with $115\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ x rays. The Fermi surface is mapped out from the electron momentum density which is three-dimensionally reconstructed from 12 directional Compton profiles. It is found that the Fermi surface is a deformed electron sphere with a neck along the [111] direction like a noble metal. The Fermi momenta are $0.63\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\text{atomic}\phantom{\rule{0.3em}{0ex}}\text{units}$ in the [100] direction and $0.65\ifmmode\pm\else\textpm\fi{}0.16\phantom{\rule{0.3em}{0ex}}\text{atomic}\phantom{\rule{0.3em}{0ex}}\text{units}$ in the [110] direction, and the neck radius is $0.18\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.3em}{0ex}}\text{atomic}\phantom{\rule{0.3em}{0ex}}\text{units}$ around the [111] direction. This result agrees satisfactorily with that of first-principles band structure calculations within the effective experimental momentum resolution.

Anisotropy in the momentum density of tantalum

The [1 0 0], [1 1 0] and [1 1 1] directional Compton profiles of tantalum have been measured, at an intermediate resolution, with 661.65 keV γ-radiation and a well-defined scattering vector. We have also computed the Compton profiles within the framework of pseudopotential using CRYSTAL03 code of Torino group. The measured anisotropy is found to be smaller to that predicted by our pseudopotential computations and also the available augmented plane wave (APW) calculations. A comparison of the absolute theoretical and the experimental profiles shows clearly for the first time the importance of anisotropic electron–electron correction effect in the third series transition metals. A quantitative comparison between the experimental and theoretical directional difference profiles reveals some accurate information about the Fermi surface topology of tantalum.

Fermi surface nesting inBa1−xKxBiO3observed by Compton profile measurement

Compton profiles of ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}\mathrm{Bi}{\mathrm{O}}_{3}$ have been measured, where $x=0.13$ and 0.39, to elucidate the relation between the Fermi surface and the metal-insulator transition. The two-dimensional momentum densities, reconstructed from several directional Compton profiles, are compared with those calculated by band theory. The momentum density of the $x=0.39$ metallic sample is explained by the predicted Fermi surface, except for one minor difference. Whereas, that of the $x=0.13$ insulating sample is simply reproduced by the geometry of the fcc-type Brillouin zone, suggesting the disappearance of the Fermi surface at the zone boundaries due to nesting. This result validates the interpretation that the insulating behavior of this system originates from the charge density wave instability.

Compton profile of polycrystalline sodium chloride and sodium fluoride

We present here the Compton profile (CP) of polycrystalline sodium chloride and sodium fluoride. Our results consists of spherical average Compton profile based on measurements and calculation of spherical average Compton profile, directional Compton profile and their anisotropic effect using self-consistent Hartree–Fock wave functions employed on the linear combination of atomic orbital (HF–LCAO) approximation. The experimental results are compared with the HF–LCAO spherical average Compton profile and with tabulated Hartree–Fock free atom results. For both compounds the experimental results are found to be in good agreement with the HF–LCAO results and in qualitative agreement with Hartree–Fock free atom values.

Directional Compton profiles and reciprocal form factors for the isoelectronic hydridesPH3,H2S and HCl

Isotropic and directional Compton profiles(J(q)) and reciprocalform factors (B(s)),as well as momentum densities and various momentum expectation values, were evaluated for the 18-electronhydrides PH3,H2S andHCl in their ground states, as well as for the argon atom. Density functional theory, Møller–Plessetand configuration interaction wavefunctions were employed for this purpose. Components of theJ(q) andB(s) were obtained for several directions relevant to the molecular structure of these molecules.Results were obtained using a configuration interaction wavefunction with singles anddoubles, and analysed by means of difference curves with the corresponding isotropic andself-consistent field results.

A high-resolution Compton scattering study of hexagonal zinc

The directional Compton profiles (CP) of hcp single crystal of zinc have been measured along the [00·1], [11·0] and [11·1] directions using high energy synchrotron radiation and high-resolution Compton scanning spectrometer at ESRF (Beamline ID15B). The experimental data were compared with corresponding theoretical Korringa–Kohn–Rostoker (KKR) semi-relativistic calculations and previous low-resolution Compton measurements with the use of high-energy γ radiation from Cs isotope. Both the experimental and theoretical directional anisotropies of Compton profiles, shows very small anisotropy of the electron momentum density in hexagonal zinc, at most half of that presented in the literature for cubic systems. No sharp fermiology-related features of momentum density in Zn predicted by theory, especially in the momenta region below 1 a.u., are observed.

Magnetic Compton Profiles of Fcc-Ni, Fcc-Fe50Ni50and Hcp-Co

Experimental and theoretical directional magnetic Compton profiles (MCP's) of hcp-Co, fcc-Fe 50 Ni 50 and fcc-Ni are compared with each other to elucidate the difference of the electronic structure...

Electron momentum density in yttrium

A simultaneous analysis of high-resolution directional Compton profiles and two-dimensional angular correlation of positron annihilation experimental data has been performed by studying both a directional anisotropy of measured spectra and reconstructed densities. The results were compared with theoretical fully relativistic augmented plane-wave calculations with and without including correlation effects. Estimated symmetry selection rules have allowed us to establish some values of Fermi momenta. Both experiments show exactly the same shape of the anisotropy of the momentum densities, in agreement with the band structure results. In the positron annihilation data electron-positron correlations are not seen while in both experiments electron-electron correlations are observed.

Magnetic Compton-Profiles of Fe3Pt

Directional magnetic Compton-profiles of simple cubic Fe 3 Pt alloy are calculated by the full potential linearized augmented-plane-wave (FLAPW) method coded in WIEN97 and a linear tetrahedron method for the two dimensional integration. They are compared with experimental ones. Similarly to the situation for the element metals, the theoretical Compton profiles which are based upon independent-particle model (IPM) are a little greater than the experimental ones around the origin of the momentum space.

A Linear Tetrahedron Method of Compton Profiles for Cubic Crystals

A linear tetrahedron method is introduced to calculate directional Compton profiles of valence electrons for cubic crystals. For the two dimensional integration a linear interpolation of both the energy and momentum density is used within each tetrahedron. They cover one 48th of the BZ (Brillouin zone) of each reciprocal vector. The program is linked to the output of FLAPW (full potential linearized augmented-plane-wave) method coded in WIEN97. As an example results for Al are described.

Investigation of Some Ground State Properties of Lithium with the All Electron MAPW Method

The electronic structure of lithium is evaluated by use of the LDA-MAPW self-consistent scheme and sophisticated exchange correlation functionals. From the volume dependence of the total energy the equilibrium lattice parameter, the bulk modulus, and the cohesion energy are derived. Various magnitudes characterising the shape of the Fermi surface are evaluated and compared with rather controversial experimental facts. The present investigations favour a Fermi surface relatively largely distorted. This conclusion is supported by calculations of the Compton profiles which are found in close accord with recent measurements of the directional Compton profiles by Schulke et al.

High resolution Compton scattering study of molybdenum

In this paper directional Compton profiles of Mo are presented and the results compared with LCGO and APW model calculations. Both electronic structure models describe qualitatively the anisotropy of the electron momentum distribution, which is influenced by the Fermi surface topology. However, the absolute profiles indicate that electron–electron correlation effects are inadequately described within the local density approximation.

Electronmomentum density of hexagonal zinc studied by Compton scattering

We have measured the directional Compton profiles of a single crystalof hexagonal zinc along the [00·1], [10·0], [11·0] and [11·1] directions using high-energy (662 keV)gamma radiation from a 137Cs isotope source. The experimentaldata have been compared with the corresponding theoreticalKorringa-Kohn-Rostoker semi-relativistic calculations. The theoryslightly overestimates the electron momentum densities at low momentaregions for all measured profiles. The directional differenceprofiles, both experimental and theoretical, show very smallanisotropy of the electron momentum density in hexagonal zinc, atmost half of that presented in the literature for cubic systems.

Joint refinement of a local wave-function model from Compton and Bragg scattering data

The first joint refinement of a local wave-function model from diffraction and Compton scattering data is reported. The proposed method suits particularly well the case of insulators. Crystalline magnesium oxide, for which both accurate directional Compton profiles and low-order structure factors are available, is chosen as a test case. In particular, it is shown that Compton scattering provides a wealth of additional information to the structure factors in the case of a chemical bond investigation.

DirectionalCompton profiles, valence orbital momentum distributions and B(r)functions for the silane molecule

Isotropic and directional Compton profiles, momentum densities andvarious momentum expectation values of the SiH4 molecule have beenevaluated for several wavefunctions at different levels of correlation.Directional components for several directions relevant to the molecularstructure of SiH4 using configuration-interaction wavefunctions arealso obtained. Spherically averaged momentum distributions and B(r)functions for the valence orbitals of SiH4 are also calculated andcompared with the measured values obtained from electron momentumspectroscopy.

Ab initio Compton maps of small molecules

A closed form expression for the evaluation of directional Compton profiles (DCP) from the position space one-electron reduced density matrix expanded in Cartesian Gaussian basis functions is presented. The Compton map, i.e. a two-dimensional contour plot of the DCP function J(q) in a selected plane, is introduce as a convenient method for describing the DCP Examples of theoretical Compton maps are given for the hydrogen molecule ion (both ground and excited states), water, ammonia, ethylene and 1A1 methylene molecules in their ground states. Compton maps generated with Hartree-Fock, configuration interaction and density functional theory methods are compared.

Ultra-high Resolution Compton Scattering of Li Metal: Evaluation with Respect to the Correlation Corrected Occupation Number Density

Directional Compton profiles of Li metal measured with ultra-high momentum space resolution (0.02 a.u.) were analysed in terms of their reciprocal form factors

Compton profiles of aluminium corrected by the electroncorrelation effect

Directional Compton profiles of face-centred cubic Al are calculatedby the augmented-plane-wave method and compared with experimentalones. In general, a theoretical Compton profile which is based uponthe IPM (independent-particle model) is a little greater than theexperimental one around the origin of the momentum space. In thiswork, correlation effects are introduced into the results of IPMband calculations and the agreement of theory and experiment isimproved very much.

Effect of shape on molecular directional Compton profiles

It is a pleasure for us to write in honor of Vedene Smith on the occasion of his 65th birthday. Since his first paper was published in 1960 (H.A. Gersch, V.H. Smith, Jr., Phys. Rev. 119 (1960) 886), Vedene has written on subjects ranging from drug design (K.E. Edgecombe, D.F. Weaver, V.H. Smith, Jr., Can. J. Chem. 72 (1994) 1388) to fusion (A.M. Frolov, V.H. Smith, Jr., Phys. Lett. A 196 (1994) 217), and most of the intervening chemical physics. One thread that has recurred throughout his scientific career, so far spanning more than 4% of the millennium, concerns electronic momentum densities in atoms and molecules, and properties that can be derived from these densities. Such properties usually involve scattering in one guise or another, and the particular form of scattering we consider in this contribution is one with which Vedene has concerned himself (R. Benesch, V.H. Smith, Jr., Int. J. Quantum Chem. 3S (1970) 413) for the past 30 years, namely Compton scattering. Vedene has expended much effort on the careful construction of accurate Compton profiles. Here we consider an orthogonal complement to his work, namely a simple, qualitative approach to the prediction of anisotropy in the Compton profiles of molecules. It is a pleasure for us to offer this contribution in honor of Vedene on his 65th birthday, on a subject that he has had much success in exploring.