Nobuhiro Shiotani

The crystal structure of Mg51Zn20

Abstract The crystal structure of Mg51Zn20, a phase designated conventionally as “Mg7Zn3,” has been determined by the single-crystal X-ray diffraction method. It was solved by the examination of a Patterson synthesis, and refined by the ordinary Fourier and least-squares method; the R value obtained was 4.8% for 1167 observed reflections. The crystal is orthorhombic, space group Immm, with a = 14.083(3), b = 14.486(3), c = 14.025(3) A, and Z = 2. There are 18 independent atomic sites, Zn1Zn6, Mg1Mg10, A, and B, and the last two sites are statistically occupied by Zn and Mg atoms with the occupancies; 0.46(2)Zn7 + 0.52(2)Mg11 and 0.24(2)Zn8 + 0.74(2)Mg12, for A and B, respectively. The structure of the crystal is described as an arrangement of icosahedral coordination polyhedra, to which all the atomic sites but Zn3 site belong. In this arrangement the Zn atoms other than the Zn3 and Zn8(B) center the icosahedral coordination polyhedra with coordination number 12. The Zn3, Zn8 atoms, and all the Mg atoms except Mg11(A) are located at the centers of various coordination polyhedra with the coordination numbers from 11 to 15. The distances between neighboring atoms are 2.71–3.07, 2.82–3.65, and 2.60–3.20 A for ZnZn, MgMg, and ZnMg, respectively.

An x‐ray spectrometer for Compton scattering

An x‐ray spectrometer has been designed and constructed for Compton scattering measurements using 40–70 keV x‐rays from an ellipsoid multipole wiggler (EMPW) installed in the accumulation ring of the National Laboratory for High Energy Physics at Tsukuba. The spectrometer has four sets of a Cauchois‐type energy analyzer and an imaging plate, which are arranged on the surface of a cone and share a scattering angle of 160°. In each energy‐analyzing system, to increase signal to noise ratio a set of vertical and horizontal slits are inserted between the analyzer and the imaging plate. A resolution of 0.13 a.u. in terms of electron momentum was achieved. A Compton profile of a vanadium single crystal was measured with an integrated counting rate of 400 counts/s.

Positron Study of Electron Momentum Density and Fermi Surface in Titanium and Zirconium

The three dimensional electron-positron momentum densities have been obtained on Ti and Zr from measurements of two dimensional angular correlation of positron annihilation radiation followed by an image reconstruction technique based on direct Fourier transformation. Augmented-plane wave band structure calculations have been carried out and the results are compared with the experiments. Agreement between the experiment and the theory leads to a conclusion that both Ti and Zr have electron surface sheets which are centered at H and hole surface sheets which are running along the \(\varGamma\)-A axis.

An X-ray spectrometer for Compton scattering experiments with synchrotron radiation

An X-ray spectrometer has been designed and constructed for Compton-scattering experiments using 29.5 keV X-rays from a vertical wiggler inserted in the 2.5 GeV storage ring of the Photon Factory at Tsukuba. It consists of a bent-crystal monochromator, a Cauchois-type bent-crystal analyzer and a position-sensitive detector. The measured incident flux on a sample is just over 1011 photons/s. An overall resolution in momentum of 0.10 atomic units (FWHM) has been achieved. The Compton profile of an aluminum single crystal was measured with a mean count rate of 28 cps. As a result of the high resolution in the measurements a sharp cutoff at the Fermi momentum was readily observed.

High-resolution Compton scattering study of the electron momentum density in Al

We report high-resolution Compton profiles (CPs) of Al along the three principal symmetry directions at a photon energy of 59.38 keV, together with corresponding highly accurate theoretical profiles obtained within the local-density approximation (LDA) based band-theory framework. A good accord between theory and experiment is found with respect to the overall shapes of the CPs, their first and second derivatives, as well as the anisotropies in the CPs defined as differences between pairs of various CPs. There are however discrepancies in that, in comparison to the LDA predictions, the measured profiles are lower at low momenta, show a Fermi cutoff which is broader, and display a tail which is higher at momenta above the Fermi momentum. A number of simple model calculations are carried out in order to gain insight into the nature of the underlying 3D momentum density in Al, and the role of the Fermi surface in inducing fine structure in the CPs. The present results when compared with those on Li show clearly that the size of discrepancies between theoretical and experimental CPs is markedly smaller in Al than in Li. This indicates that, with increasing electron density, the conventional picture of the electron gas becomes more representative of the momentum density and that shortcomings of the LDA framework in describing the electron correlation effects become less important.

Angular Distribution of Positron Annihilation Radiation in Vanadium and Niobium–Experiment

Angular distributions of two photons resulted from annihilation of positrons in V and Nb were measured along three principal crystallographic directions and conspicuous structures and anisotropies ...

Fermi surface signatures in the compton profile of Be

We report high-resolution Compton profiles of two single crystals of Be with surface normals oriented along the [0001] and [1120] directions. The results are compared and contrasted with corresponding, highly accurate all-electron computations based on the band theory framework within the local-density approximation (LDA). A reasonable overall level of agreement is seen between theory and experiment with respect to the shapes of the Compton profiles, as well as the Fermi-surface-induced finer structure in the first and second spectral derivatives. However, the measured profiles are lower than theory at low momenta, clearly displaying broadened Fermi surface features compared with the theoretical predictions, and point to the importance of electron correlation effects beyond the LDA for a proper description of the momentum density. The aforementioned similarities and differences between theory and experiment in Be are rather like the situation that has been observed in recent high-resolution Compton studies of other materials.

Angular Correlation of Positron Annihilation Radiation in Chromium and Molybdenum

Angular correlation of positron annihilation radiation in Cr and Mo were measured. Self-consistent band structure calculations for Mo were carried out by the APW method with state-dependent potentials. Theoretical angular correlations for Cr and Mo were also calculated by the APW method. Observed fine structures on the angular correlations and the crystalline anisotropies were well reproduced by the calculations. However, when the theoretical and experimental correlation curves were normalized to an equal area, the theoretical curves were consistently lower in counting rate than the experimental ones in small angle region, and higher in large angle region. This type of discrepancy between the theory and the experiment is the same as we previously found in V and Nb, and is ascribed to the electron-positron correlation effects.

Two-dimensional folding technique for enhancing Fermi surface signatures in the momentum density : Application to Compton scattering data from an Al-3 at. % Li disordered alloy

We present a technique for enhancing Fermi surface ~FS! signatures in the two-dimensional ~2D! distribution obtained after the 3D momentum density in a crystal is projected along a specific direction in momentum space. These results are useful for investigating fermiology via high-resolution Compton scattering and positron annihilation spectroscopies. We focus on the particular case of the ~110! projection in a fcc crystal where the standard approach based on the use of the Lock-Crisp-West ~LCW! folding theorem fails to give a clear FS image due to the strong overlap with FS images obtained through projection from higher Brillouin zones. We show how these superposed FS images can be disentangled by using a selected set of reciprocal lattice vectors in the folding process. The applicability of our partial folding scheme is illustrated by considering Compton spectra from an Al‐3 at. % Li disordered alloy single crystal. For this purpose, high-resolution Compton profiles along nine directions in the ~110! plane were measured. Corresponding highly accurate theoretical profiles in Al‐3 at. % Li were computed within the local density approximation~LDA!‐based Korringa-KohnRostoker coherent potential approximation ~KKR-CPA! first-principles framework. A good level of overall accord between theory and experiment is obtained, some expected discrepancies reflecting electron correlation effects notwithstanding, and the partial folding scheme is shown to yield a clear FS image in the ~110! plane in Al‐3 at. % Li.

Compton Scattering Study of Electron Momentum Density in Vanadium

The [100], [110] and [111] Compton profiles of vanadium are measured with a momentum resolution of 0.12 atomic units. The observed profiles have fine structures and directional anisotropies. Comparison of the results with the APW band theoretical predictions shows that the band theory overestimates the momentum density at low momenta and underestimates it at high momenta. The theory also overemphasizes the fine structures and the scale of the anisotropies.