Calculated Asymmetry Parameters Research Articles

Photoelectron angular distribution of benzene: Can the asymmetry parameter be considered a benchmark?

The calculated asymmetry parameter (β) and photoionisation cross sections for eight outermost orbitals (1e1g, 3e2g, 1a2u, 3e1u, 1b2u, 2b1u, 3a1g, and 2e2g) of benzene, in the gas phase, are presented in the range from threshold to 35 eV. The Schwinger Variational Method with Padé approximants was employed to generate the continuum wavefunction of photoelectrons and the dipole matrix transition was computed in the velocity (V) and length (L) approach of the dipole operator. This operator in V or L form does not affect significantly β values in the energy range studied. The cross sections in V form produce lower magnitudes than L and are closer to the measurements. The resonance peaks were observed in the cross sections for some orbitals and their positions were not affected by the dipole approach. Finally, symmetry analysis is done on the partial cross sections to assign the main contributing final state to the resonance feature and also link this to the minimum in the asymmetry parameter. The comparison of our results with other theories has, in general, good qualitative and some quantitative agreement. For some orbitals (1a2u, 2b1u), severe disagreements between theory and experiment are highlighted. Some possible causes for these differences are pointed out. Because of this, we conclude that some asymmetry parameters and PICS for benzene, in ionisation studies, cannot yet be considered as a benchmark and will be necessary further investigation to clarify such discrepancies.

Weak-localization effect in Fano asymmetry of C implanted rutile TiO2 nanostructure

Fano resonance is the degree of asymmetry that describes the interference of continuum states with discrete states and causes asymmetric line shape in the optical response. The hydrothermally synthesized TiO 2 nanostructures in this work are doped with 1.5 MeV carbon (C) ion beams to explore the Fano effect via the asymmetry in the Raman spectra. It is observed that the E g and A 1 g modes are asymmetric toward the lower wavenumber. The Fano effect is responsible for the peak asymmetry, which rises with C ion fluence. The Breit–Wigner–Fano line shape fits well the E g and A 1 g modes. The calculated asymmetry parameter (1/q) for implanted TiO 2 nanostructures represents weakly localized asymmetry with temperature. The electron–phonon coupling strength grows with the C ion fluence. The effects of temperature and defect level on the asymmetry parameter are also discussed.

Development of 166Er Mössbauer spectroscopy in KURNS

We have newly developed 166Er Mossbauer spectroscopy in Institute for Integrated Radiation and Nuclear Science, Kyoto University (KURNS). As 166Ho radioactive source, HoAl2 was used. The compound was irradiated in the nuclear reactor (1 MW) for 5 min. The source has the intensity of 19 MBq and the half-life of 26.8 h. It is our privilege to conduct measurement immediately after the preparation of the radioactive source, since the spectroscopic equipment is situated just next to the reactor. The spectra of three typical Er oxides, Er2O3, ErFeO3, and ErMnO3 were measured at 40 K. On the basis of the calculated asymmetry parameter η and the evaluated sign of the quadrupole coupling constant e2qQ/2 from the structure parameters, we have successfully analyzed the spectra by using the quadrupole Hamiltonian assuming the transmission integral line shapes. The 166Er Mossbauer parameters, isomer shift IS, e2qQ/2, and line width W were obtained for the three specimens.

Local Structure and Li Ion Dynamics in Garnet Li7-2xGaxLa3Zr2O12 Solid Electrolytes

One of the key component in solid-state Li ion rechargeable Li ion batteries is the solid electrolyte. Garnet Li7-xGaxLa3Zr2O12 is one of the solid electrolyte systems that has been reported to demonstrate conductivity values that almost reaches the level of conventional organic-based electrolytes (~10-3 S/cm).1 Interestingly, the dopant cation in this system, Ga3+, occupies Li sites and can directly impede Li ion movement. Meanwhile, experimental results were inconclusive and not unanimous in ascertaining the actual site preference and distribution of Ga3+ in the 24d tetrahedral (Td) and 48g/96hoctahedral (Oh) crystallographic sites. In this work, we attempted to clarify the aforementioned issues by performing computational modelling, emphasizing on the Ga dopant coordination environment and the effects of Ga towards the Li ion transport process. To study the local environment for Ga3+, we calculated the NMR parameters (chemical shift ∂iso, asymmetry factor ηQ, quadrupolar coupling CQ) at the two distinct Li sites using the augmented plane-wave method implemented in WIEN2k. Prior to NMR parameter fitting, model cells for the doped garnet (with Ga at the tetrahedral and octahedral cage, respectively) and several relevant Ga-containing compounds were relaxed by DFT using VASP. Meanwhile, we also analyzed the energy distribution with respect to Ga3+occupancy by uniformly sampling the Li-Ga-vacancy configurations within a 3 x 3 x 3 garnet supercell using fitted Buckingham interatomic potentials and GULP. For Li ion transport study, we employed molecular dynamics by using DL_POLY. Structural information of DFT-relaxed models showed good agreement with experimental results; ~1% difference for lattice constants and < 5% difference for volume. The calculated NMR parameters are as follows: ∂iso,Ga@Td = 231.7 ± 9.30 ppm, ηQ,Ga@Td = 0.4860 ± 0.0053, CQ,Ga@Td = 11.82 ± 0.34 MHz; ∂iso,Ga@Oh = 53.8 ± 9.30 ppm, ηQ,Ga@Oh = 0.4496 ± 0.0053, CQ,Ga@Oh = 5.84 ± 0.34 MHz. For the chemical shift ∂iso for the Td environment (four-fold coordination), our result is consistent with MAS NMR results for Ga-doped garnets (207 ± 10 and 244 ppm).1,2 On the other hand, the calculated asymmetry parameter ηQ is larger than the experimental value for the 24d tetrahedral cage (0.05 ± 0.05)1. However, when compared with the experimental value for LiGaO2 (0.37) in which Ga3+ also sits in a tetrahedral cage,3 our calculated value for ηQ is comparable, indicating that Ga may coordinate assymetrically as well in the 24d tetrahedral cage in the garnet Li sublattice. Based from configuration sampling for Li-Ga-vacancy arrangements (16,000 random configurations of 3 x 3 x 3 supercells, sampling for all-Td, all-Oh, and intermediate distribution for Ga), we found that the energy variation is small (< 15 meV/atom) which means that Ga has no site occupancy preference. Furthermore, Ga can exist in a four-fold coordination inside the octahedral cage (eg., when at the 96hsite). Hence, the inconsistency in experiments may be resolved by viewing the dopant Ga as sitting in a four-fold coordination environment either at the tetrahedral or the octahedral Li cage of the garnet structure. Our molecular dynamics results4 have shown that the first-nearest-neighbor site of Ga is energetically inaccessible for a migrating Li due to strong repulsion, possibly forming defect clusters according to the following association reactions: i) Ga·· Li + V'Li → {Ga·· LiV' Li }·, {Ga·· LiV' Li }· + V'Li → {Ga·· Li2V' Li }X, 2Ga·· Li + 4V'Li → {2Ga·· Li4V'Li}X. We also confirmed the stabilization effect of Ga for the high-conductivity cubic phase (from the low-conductivity tetragonal phase) as evidenced in the calculated thermal expansion profiles. Two distinct regions for conductivity were observed for 0 ≤ x ≤ 0.30 in Li7-xGaxLa3Zr2O12: an abrupt rise followed linear decrease for 0 ≤ x ≤ 0.10 (owing to competing effects of tetragonal → cubic transition and decreasing Li concentration) and a flattrend for 0.10 ≤ x ≤ 0.30 (due to increasing accessible Li vacancies which are crucial for initiating concerted Li motion). REFERENCES 1 Bernuy-Lopez et al., Chem. Mater. 2014, 26, 3610−3617. 2Rettenwander et al., Inorg. Chem. 2014, 53, 6264−6269. 3Ash et al., Magn. Reson. Chem. 2006, 44, 823−831. 4 Jalem et al., Chem. Mater. 2015, 27, 2821–2831.

Near-threshold photoelectron angular distributions from two-photon resonant ionisation of He and Ne atoms

We present an overview of two recent experiments in which photoelectron angular distributions from light-polarised He and Ne atoms are studied, with the emphasis on theoretical description of photoionisation. Polarised He (Ne) atoms are prepared in the 1s4p, 1s5p, or 1s6p (2p53d) states with linearly polarised synchrotron light and ionised with a tunable infrared laser. The asymmetry parameters extracted from the measured velocity map imaging spectra agree well with the calculated asymmetry parameters.

A computational investigation of 11B electric field gradient and chemical shielding tensors as well as NBO analysis in the B80 fullerene

Using first-principles calculations within the frame of the density functional theory, we analyze electronic properties of the boron fullerene B80, based on NMR, NQR parameters and NBO analysis. Our results show three typical ranges for boron chemical shielding parameters corresponding to each of the nonequivalent magnetic sites of the B atoms. These three sites are related to frame atoms and two sets of atoms capping hexagons, endohadral and exohedral caps. Calculating quadrupole coupling components confirm this conclusion with more sensitivity than chemical shielding parameters. In addition calculated asymmetry parameter shows that EFG tensor for boron atoms capping hexagons is axially symmetric, η ≈ 0, while this tensor becomes considerably asymmetric for frame atoms, η = 0.95, as a result of charge transfer from 20 boron atoms capping hexagons to the 60 frame atoms.

MESON EXCHANGE MODEL WITH THE AXIAL VECTOR A1-MESON EXCHANGE AND HYPERNUCLEAR NONMESONIC DECAY ASYMMETRIES

The axial vector a1-meson exchange is introduced in the nonmesonic weak decay model. The a1-exchange is found to give remarkable modifications of the parity-conserving decay potentials in 1,3S → 1,3S and 3S1 → 3D1 channels at short range. Calculated asymmetry parameters αΛ for s- and p-shell hypernuclei in the 'π + 2π/ρ + 2π/σ + ω + K + ρπ/a1 + σπ/a1'-exchange model are obtained to be positive and small, which are consistent with the available data.

Random-phase approximation with exchange for the photoionization of an atom with an inner open shell

A random-phase approximation with exchange method has been developed for the photoionization of atoms (ions) with an inner open shell. The method allows for the inclusion of both intrashell and intershell correlations in the calculation and has been used to study the photoelectron asymmetry parameter and the cross sections of the Sc $4s$ photoionization in which the Sc $3p\text{\ensuremath{-}}3d$ transitions have been successfully included. The results demonstrate that the inclusion of the $3p\text{\ensuremath{-}}3d$ transitions is extremely important in the intershell coupling, which significantly influences the calculated asymmetry parameter and the cross sections of the Sc $4s$ photoionization. Comparison of our calculated asymmetry parameter and the cross sections with the measured data and available calculation is made and discussed. Possible improvements to the present calculated data are offered as well.

Crystal field theory and electric field gradients at 49Ti nuclei sites in LaTiO3

The energy level diagram and the wave functions for the Ti3+ ions (3d1) in LaTiO3 are calculated using modern crystal-field theory. The relative orbital ordering of these ions in the ground state is obtained. It turns out that the states of the ground triplet are considerably split and therefore the effect of the electronic-vibrational interaction is suppressed despite the fact that the distortions of the TiO6 building block seem to be small. The components of the electric field gradient tensor at the Ti3+ nuclei sites are calculated using the wave functions of the ground states obtained. The calculated asymmetry parameter agrees well with the experimental values, which demonstrates the adequacy of the proposed orbital-ordering pattern of the Ti3+ ions in the ground state.

The Asymmetry Parameter of Cirrus Clouds Composed of Hollow Bullet Rosette–Shaped Ice Crystals from Ray-Tracing Calculations

AbstractCirrus clouds in the midlatitude and Arctic regions are often composed of bullet rosette–shaped ice crystals. Bullet rosette–shaped ice crystals are composed of a number of bullets radiating from a central point. The bullets that make up the rosette will grow to be hollow in some conditions. To understand better the radiative impact of cirrus clouds, the authors have used a ray-tracing code to calculate the scattering properties of solid and hollow bullet rosettes at visible wavelengths. Results show that hollow bullet rosettes exhibit a broader forward-scattering peak than do solid bullet rosettes. This difference results in an asymmetry parameter that is as much as 0.08 lower for hollow bullet rosettes than for solid rosettes. The effective asymmetry parameter of spheres with the same particle volume and total surface area of the bullet rosettes has also been calculated. Asymmetry parameter estimates for equivalent spheres were similar to those calculated using the ray tracing. Asymmetry parameter calculations were used in combination with direct aircraft measurements from the Atmospheric Radiation Measurement Program intensive operational period in March of 2000. Asymmetry parameter estimates were used with particle size distributions for three cirrus cloud flights for which the observed large particles were predominantly bullet rosettes. Calculated asymmetry parameter values (0.80–0.84) agreed poorly with published cirrus parameterizations (0.75–0.84) when applied to the same aircraft data. Differences lead to 4.5–9 W m−2 differences in reflected and transmitted visible light energy for a cloud of 0.5 optical depth.

Time dependent density functional study of the symmetry resolved N 1s photoionization in N 2

The time dependent-density functional theory (TD-DFT) has been applied to study the photoionization from the two symmetry resolved initial states (1σ g and 1σ u) of the core N 1s in N 2. The results are compared with very recent experimental data and with previous ab initio calculations. The calculated intensity ratio is in excellent agreement with the experiment and performs better than previous calculations. Good quantitative results are also obtained for the absolute partial cross-section. The calculated asymmetry parameters are also predicted to be very different in the two contributions, so a new experiment to investigate the angular distribution of the photoelectron is suggested.

Perturbed-angular-correlation study of the electric-field gradient indoped181and implanted indium sesquioxide

We studied the hyperfine interactions of $^{181}\mathrm{Ta}$ in ${\mathrm{In}}_{2}$${\mathrm{O}}_{3}$ by means of perturbed-angular-correlation (PAC) measurements. We prepared thin films of indium sesquioxide with different degrees of initial amorphism and implanted them with $^{181}\mathrm{Hf}$. Chemically prepared indium-sesquioxide powder samples were also made starting from neutron-irradiated ${\mathrm{HfCl}}_{4}$, which provides the $^{181}\mathrm{Hf}$ PAC probes. PAC experiments were performed on each sample at room temperature, after each step of annealing programs at increasing temperatures up to the full crystallization of the samples. The results indicate that the PAC probe occupies preferentially the axially symmetric cation site. Point-charge-model calculations were performed. The calculated asymmetry parameters \ensuremath{\eta} were compared with those obtained in $^{181}\mathrm{Hf}$ PAC experiments performed also on other binary oxides, showing that the symmetry of the electric-field-gradient (EFG) tensor at $^{181}\mathrm{Ta}$ cation sites in binary oxides is mainly determined by the nearest-neighbor oxygen-ion distribution around the probe. Comparisons of the experimental results in bixbyites obtained for both PAC probes, $^{111}\mathrm{Cd}$ and $^{181}\mathrm{Ta}$, show that the local EFG in bixbyites, are strongly dependent on the geometry of the sites and the electronic configuration of the probes.

A comparative study on the spin asymmetry and integrated cross sections for the electron-impact ionization of atomic hydrogen

The spin asymmetry and integrated spin-unresolved cross sections for the electron-impact ionization of atomic hydrogen are studied. The influence of individual final-state interactions on these quantities is elucidated by investigating the collision process within the plane-wave impulse approximation, the first Born approximation and within an independent Coulomb particle model. The predictions of the latter approximation for the shape and magnitude of the spin asymmetry are in good agreement with experimental data over the entire measured energy range. The effects of final-state electronic correlations are investigated by the inclusion of the electronic Coulomb density-of-states factor as well as by employing a three-body Coulomb wave-function for the description of the final state. For ionization of hydrogenlike ions the calculated asymmetry parameter has a positive slope near threshold indicating that such an energy dependence is due to the electron-nucleus interactions. At threshold the results are analyzed in light of the Wannier theory of threshold ionization.

Asymmetry parameters of the phase function for densely packed scattering grains

Spatial correlation among densely packed particles can substantially change their single-scattering properties, thus making questionable the applicability of the independent scattering approximation in calculations of light scattering by planetary regoliths. The same problem arises in geophysics in light scattering computations for snow, frosts, and bare soil. In this paper, we use a dense-medium light-scattering theory based on the introduction of the static structure factor to calculate asymmetry parameters of the phase function for densely packed particles with real refractive indices 1.31 and 1.66, approximating water ice and soil particles, respectively, and imaginary refractive indices 0, 0.01, and 0.3. For sparsely distributed, independently scattering grains, the calculated asymmetry parameters are always positive and always larger than those for densely packed particles. For densely packed grains, the asymmetry parameters may be negative but only for radius-to-wavelength ratios from about 0.1 to about 0.4. With decreasing particle size, the calculated asymmetry parameters tend to zero independently of the compaction state. In the geometrical optics regime, the asymmetry parameters for densely packed scatterers are positive and very close to those for independently scattering grains. These results may have important implications for remote sensing of the Earth and solid planetary surfaces. In particular, it is demonstrated that negative asymmetry parameters derived with some approximate multiple-scattering theories may be physically irrelevant and can be the result of using an inaccurate bidirectional reflection function combined with the ill-conditionality of the inverse scattering problem.

Photoelectron angular distributions for atomic chlorine.

Photoelectron angular distribution asymmetry parameters for photoionization to each of the three term levels of the ${\mathrm{Cl}}^{+}$ ion are calculated above the $^{1}\mathrm{S}$ ionic threshold with use of the open-shell transition-matrix method. Comparison is made with frozen-core Hartree-Fock asymmetry parameters and with the multiconfiguration Hartree-Fock results of Fielder and Armstrong. The calculated asymmetry parameters are used to estimate partial-cross-section branching ratios at 584 A\r{} from the relative experimental photoelec- tron intensity measurements of Kimura, Yamazaki, and Achiba.

Non-empirical calculations of chlorine quadrupole coupling parameters in chloromethanes and chlorosilanes

Non-empirical calculations of the field gradient tensor at the chlorine nucleus are resorted for chloromethane, trichloromethane, chlorosilane and trichlorosilane. The calculations agree quite well with the experimental quadrupole coupling constants. The calculated asymmetry parameters in trichloromethane and trichlorosilane are low and the principal z axis of the field gradient tensor is found nearly to coincide with the CCl and SiCl bond directions.

Electric field gradients in the ionic crystals NaNO 2, NaBF 4, NaNO 3, and Ba(NO 3) 2

The electric field gradients (EFG) at the sites of the cations and the “central” atoms of the anions in the ionic crystals NaNO 2, NaBF 4, NaNO 3 and Ba(NO 3) 2 are calculated by a method based on a combination of the semi-empirical INDO method for the charge distribution and the intramolecular EFG with a lattice summation in the framework of the extended multipole model. At some lattice sites the contribution of the induced dipole and quadrupole moments to the EFG is comparable with the contribution of the point charges. The charge distribution within the molecular ions is found by adjusting either the calculated asymmetry parameter η or the z-component of the EFG to the experimental value deduced from nuclear quadrupole coupling constants. These charge distributions are in good agreement with those gained from INDO calculations. The calculated and experimental quadrupole coupling constants of nuclei in anions and cations are compared.

Quadrupole Interactions in Chrysoberyl

The electric field-gradient tensor has been computed using the point multipole model at the two inequivalent Al sites and at the Be site in chrysoberyl crystal. The calculated asymmetry parameters, the orientation of the principal field-gradient axes, and the quadrupole coupling constants are compared with values obtained from NMR measurements on the single crystal. The oxygen-dipole contributions to the field gradients are found to be very sensitive to the assumed oxygen polarizability. As the exact value is not known, calculations are carried out for three values: 2.19, 1.34, and 1.0 ${\mathrm{\AA{}}}^{3}$, the former two have been used in earlier investigations on ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ and BeO. The results for the three polarizabilities are discussed in the light of experimental observations. The deviations between calculated and observed values of the quadrupole-interaction parameters appear to decrease as the oxygen polarizability is varied from 2.19 to 1.0 ${\mathrm{\AA{}}}^{3}$, and best over-all agreement is obtained for $\ensuremath{\alpha}=1.0$ ${\mathrm{\AA{}}}^{3}$.

Calculations of Electric Field Gradients andgFactors for a Single Crystal of Paramagnetic CuCl2·2H2O

The electric field gradient tensor at the chlorine site in a single crystal of Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O has been evaluated using the point-charge model and also considering the effects of induced dipoles. The quadrupole coupling constant, asymmetry parameter, and orientation of the principal axes of the field gradient tensor with respect to the crystalline $a$, $b$, $c$ axes are also calculated. The theoretical quadrupole resonance frequency, assuming the antishielding factor of the ${\mathrm{Cl}}^{\ensuremath{-}}$ ion to be -56.6, comes out as 6.8 Mc/sec which is to be compared with the observed value of 9.05 Mc/sec. The calculated asymmetry parameter and orientation of the principal axes could not be checked for want of an experimental investigation on the Zeeman effect. Using the same model, $g$ factors of the paramagnetic ${\mathrm{Cu}}^{++}$ ion are evaluated considering spin-orbit interaction by calculating the electrostatic potential at the ${\mathrm{Cu}}^{++}$ site and the consequent crystal-field splittings. The agreement between the theoretical and experimental $g$ factors is better than in the case of the chlorine nuclear quadrupole resonance (NQR) frequency, perhaps due to the fact that the final $g$ values calculated are less sensitive to the percentage covalent character. The contribution of induced dipoles is noted to be significant in both cases. The effect of the paramagnetic ${\mathrm{Cu}}^{++}$ ions on the chlorine NQR, particularly in the antiferromagnetic region (below 4\ifmmode^\circ\else\textdegree\fi{}K), is discussed and the importance of careful experimental investigations to detect the Zeeman splittings even in the absence of an external magnetic field analogous to the zero-field nuclear resonance is indicated.