Valence Electron Contribution Research Articles

Calculation of spontaneous radiation during channeling of relativistic positrons in non-chiral nanotubes using a quadratic approximation

The work investigates the conditions for the possibility of using the quadratic approximation U(ρ) = αρ2 for the interaction potentials of channeled positrons with the inner walls of non-chiral carbon nanotubes of types (n, 0) and (n, n). In particular, (8, 0), (10, 0), (12, 0) and (8, 8), (10, 10), (12, 12) nanotubes were selected. In this case, when calculating the single-particle potential of the carbon atom, only the contribution of valence electrons was taken into account. As a result of this approximation, the parameters α were determined for all the nanotubes studied. Using wave functions and the corresponding quantum levels of transverse energy obtained by solving the Schrödinger equation, the probabilities of occupation of these levels were calculated for positron beams with zero angular dispersion moving along the axes of nanotubes. Based on this information, values of the longitudinal energy of positrons for which the quadratic approximation is applicable were determined for all the studied nanotubes. Spectral distributions of spontaneous radiation were calculated in the dipole approximation for non-dispersive relativistic positron beams, both within the framework of quantum-mechanical and classical approaches.

Ab initio based study of the diamagnetism of diamond, silicon and germanium

Diamond, silicon and germanium are widely used technological materials, whose electron structures are tabulated and understood very well. Yet the detailed picture of various diamagnetic contributions and their interplay with the paramagnetic effect, especially at the ab initio level, due to the complexity of this problem remains largely unknown. In our study, based on the ab initio electron band structure approach, all possible magnetic contributions, including the Langevin (Larmor) diamagnetism and the Van Vleck paramagnetism accounted in the second order of the perturbation treatment, are analyzed quantitatively. The Van Vleck contribution has been adapted to the band structure calculations by performing integration over k-points. Also, the partial diamagnetic contributions of core and valence electrons are obtained and discussed in detail. Of all terms there is only one — the Langevin diamagnetism of the valence electrons, which is not well defined quantitatively due to the contribution from the interstitial region. We discuss possible approaches to partitioning this contribution among neighboring crystal sites, based on the Bader charge separation and introducing the area of depleted electron density, excluded from the integration. Under various assumptions for the interstitial region, we have found that the magnetic susceptibilities for diamond, silicon and germanium lie in the range -13.4/-9.3, -4.7/-4.0 and -8.4/-8.8 (volume values, in units of 10−7), correspondingly. In general, this is consistent with the available experimental values, albeit the numerical uncertainty typically reaches tens of percent.

Calculations of electronic excitation by protons and α particles in silicon

This paper presents a method of calculating the valence electron contribution to the stopping and interaction cross sections of swift ions in matter using linear response calculations of the dielectric function in crystals. The ab initio response function is used to calculate excitations at low energy and momentum transfers to account for material-specific effects, while higher energy and momentum transfers use a free electron gas response for increased computational efficiency. The ECPSSR method for computing core cross sections is modified to allow predictions of the core contribution to electronic stopping. The charge distribution by entrained electrons is explicitly modeled to account for the additional screening beyond linear response. We use the methods developed to predict the electronic stopping of protons and $\ensuremath{\alpha}$ particles in silicon and compare to measured values.

A single-phase ScTiZrHf high-entropy alloy with thermally stable hexagonal close-packed structure

High-entropy alloys forming non-cubic crystal structures are intriguing systems for both scientific and functional viewpoints. Hexagonal-structured HEAs are among them. In this work, we have fabricated a single-phase hexagonal close-packed phase in ScTiZrHf system. To verify its structural stability, we anneal the alloy samples at 973 K for a long time from 15 up to 140 h. Structural analysis reveals that the HEA retains its single-phase structure after the thermal treatment. To characterize the material, we examine its electron-transport and magnetic properties over a wide temperature range. The alloy electrical resistivity has purely metallic temperature dependence, while its absolute values are rather high. The thermal conductivity in this material is very low. The analysis of the transport properties reveals a noticeable lattice contribution (≈ 50% ) in total thermal conductivity probably caused by a strongly defected crystal structure. The alloy magnetization demonstrates complicated temperature dependence, which is well described by a superposition of Curie–Weiss and valence-electron contributions. Based on this suggestion, we fit experimental magnetization data and extract the electron density of states (DOS) at the Fermi level as ≈1eV−1. To address the properties of interatomic interaction in the system, we perform ab-initio molecular dynamics simulations of the liquid phase. The data obtained indicate unambiguously the absence of strong chemical interaction between alloy components as well as the nearly additive character of the liquid mixture that supports the results obtained experimentally.

New insight on the Mössbauer spectra for Fe16N2 thin films with high saturation magnetization

Mössbauer spectroscopy was conducted on partially ordered Fe16N2 thin films. Besides the dominant polarized core-s electron Fermi contact term, valence electron contribution was counted as a necessity for the explanation of a combination of a high magnetic moment and a relatively low magnetic hyperfine splitting, which were obtained on Fe16N2 thin films with both GaAs and MgO substrates. Essentially, the “cluster + atom” model was applied to understand the high degree hybridization of s–p–d electron, which allows the increase of the positive valence electron contribution and the decrease of the total hyperfine field.

Absence of first order magnetic transition, a curious case of Mn3InC

The volume expanding magnetostructural transition in Mn3GaC and Mn3SnC has been identified to be due to distortion of Mn6C octahedra. Despite a similar lattice volume as Mn3SnC and similar valence electron contribution to density of states as in Mn3GaC, Mn3InC does not undergo a first order magnetostructural transformation like the Ga and Sn antiperovskite counterparts. A systematic investigation of its structure and magnetic properties using probes like x-ray diffraction, magnetization measurements, neutron diffraction, and extended x-ray absorption fine structure reveals that though the octahedra are distorted resulting in long and short Mn–Mn bonds and different magnetic moments on Mn atoms, the interaction between them remains ferromagnetic. This has been attributed to the strain on the Mn6C octahedra produced due to a relatively larger size of In atoms compared to Sn and Ga. The size of In atoms constricts the deformation of Mn6C octahedra giving rise to Mn–Mn distances that favor only ferromagnetic interactions in the compound.

Mössbauer Studies of LixFe1/3Mn1/3Ni1/3PO4 Cathode Materials

We report on the crystallographic and magnetic properties of LixFe1/3Mn1/3Ni1/3 PO4 (x = 0, 1) using x-ray diffraction (XRD), a vibrating sample magne- tometer (VSM), and Mossbauer spectroscopy. XRD analysis confirmed that the samples have an orthorhombic structure with space group Pnma. From the VSM measurements the samples exhibited an antiferromagnetic behavior with a Curie–Weiss temperature θ = − 162 K for x = 1, and θ = − 303 K for x = 0. The Neel temperature (TN) and spin reorientation temperature (TS) were determined to be 40 K and 10 K for x = 1, and 66 K and 25 K for x = 0. The hyperfine field (Hhf) of LiFe1/3Mn1/3Ni1/3PO4 had smaller values than that of Fe1/3Mn1/3Ni1/3PO4 due to the magnitude of the nearest-neighbor superexchange interaction. Isomer shift (δ) values indicate that the charge states of LiFe1/3Mn1/3Ni1/3PO4 are ferrous (Fe2+), and that of Fe1/3Mn1/3Ni1/3PO4 are ferric (Fe3+). The larger values of the electric quadrupole splitting (δEQ) for the Fe2+ phase compared to the Fe3+ phased originated from the different lattice and valence electron contributions due to the crystalline field and valence transition. Debye temperatures (θD) of 338 ± 5 K (x = 1), and 370 ± 5 K (x = 0) were obtained for the samples.

Transient optical properties of dielectrics and semiconductors excited by an ultrashort laser pulse

The transient permittivity of dielectrics and semiconductors excited by a powerful ultrashort laser pulse is introduced here in explicit form, which shows a decreasing contribution of valence electrons and an increasing contribution of free carriers with rising laser fluence. We describe the evolution of permittivity from the initial state up to transformation into plasma before ablation. A two orders of magnitude change in the electrons’ collision rate during this transition is taken into account explicitly. The interplay between ionization nonlinearity and electron collisions dominates the transient optical properties of a swiftly excited material and results in unexpected minima and maxima in the permittivity and reflectivity. Our analysis of the transient permittivity of silica and silicon at 800 and 1300 nm reveals the differences in the femtosecond excitation of narrow- and wide-band-gap material, and also distinguishes a metal-like state of the ionized dielectric from the excited state in metals. The dependence of transient permittivity on electron density obtained can be directly mapped onto the fluence distribution in the time and space domains. We briefly discuss the possibility to measure these transient properties in pump–probe experiments.

Surfaces of colloidal PbSe nanocrystals probed by thin-film positron annihilation spectroscopy

Positron annihilation lifetime spectroscopy and positron-electron momentum density (PEMD) studies on multilayers of PbSenanocrystals (NCs),supported by transmission electron microscopy, show that positrons are strongly trapped at NC surfaces, where they provide insight into the surface composition and electronic structure of PbSeNCs. Our analysis indicates abundant annihilation of positrons with Se electrons at the NC surfaces and with O electrons of the oleic ligands bound to Pb ad-atoms at the NC surfaces, which demonstrates that positrons can be used as a sensitive probe to investigate the surface physics and chemistry of nanocrystals inside multilayers. Ab initio electronic structure calculations provide detailed insight in the valence and semi-core electron contributions to the positron-electron momentum density of PbSe. Both lifetime and PEMD are found to correlate with changes in the particle morphology characteristic of partial ligand removal.

Mössbauer analysis of silicate Li2FeSiO4 and delithiated Li2−xFeSiO4 (x = 0.66) compounds

Lithium iron silicate compounds of Li2FeSiO4 and partially delithiated Li2−xFeSiO4 (x = 0.66) were synthesized by vacuum-sealed solid-state and chemical delithiation reactions, and their magnetic properties were characterized based on Mössbauer analysis. Crystal structures of both Li2FeSiO4 and Li2−xFeSiO4 (x = 0.66) compounds are found to be γs-type (P21/n) monoclinic structures with difference in the lattice parameters due to lithium delithiation. Mössbauer spectrum of Li2FeSiO4 below TN1 = 20 K exhibits eight Lorentzians of Fe2+ with antiferromagnetic ordering. However, the spectrum of intermediate Li2−xFeSiO4 (x = 0.66) compound shows the appearance of magnetically ordered Fe3+ sextet below TN2 = 28 K. The temperature-dependent isomer shift of Li2−xFeSiO4 indicates the coexistence of nonequivalent Fe2+/Fe3+ valence states with the partial oxidation of FeO4, enhanced by the lithium ion deficiency. Also, we have observed a considerable change in electric quadrupole interaction between Fe2+/Fe3+ ions in Li2−xFeSiO4, when compared to that of Li2FeSiO4, due to the different lattice and valence electron contributions, being originated from crystalline and valence transitions caused by the lithiation/delithiation process.

Experimental and theoretical study of the energy loss of C and O in Zn

We present a combined experimental-theoretical study of the energy loss of C and O ions in Zn in the energy range 50--1000 keV/amu. This contribution has a double purpose, experimental and theoretical. On the experimental side, we present stopping power measurements that fill a gap in the literature for these projectile-target combinations and cover an extended energy range, including the stopping maximum. On the theoretical side, we make a quantitative test on the applicability of various theoretical approaches to calculate the energy loss of heavy swift ions in solids. The description is performed using different models for valence and inner-shell electrons: a nonperturbative scattering calculation based on the transport cross section formalism to describe the Zn valence electron contribution, and two different models for the inner-shell contribution: the shellwise local plasma approximation (SLPA) and the convolution approximation for swift particles (CasP). The experimental results indicate that C is the limit for the applicability of the SLPA approach, which previously was successfully applied to projectiles from H to B. We find that this model clearly overestimates the stopping data for O ions. The origin of these discrepancies is related to the perturbative approximation involved in the SLPA. This shortcoming has been solved by using the nonperturbative CasP results to describe the inner-shell contribution, which yields a very good agreement with the experiments for both C and O ions.

Benchmark Theoretical Study on the Dissociation Energy of Chlorine

The currently accepted D(0)((35)Cl(2)) is 239.221 ± 0.001 kJ/mol, whereas popular theoretical model chemistries provide values in the range of 233-247 kJ/mol, and even the so-called high-accuracy protocols can yield values as low as 237.9 kJ/mol and as high as 240.1 kJ/mol for D(0)((35)Cl(2)). The aim of this study was to uncover the sources of error inherent in the theoretical approaches. Therefore, a coupled-cluster-based composite model chemistry was utilized that included contributions of up to pentuple excitations, as well as corrections beyond the nonrelativistic and Born-Oppenheimer approximations. In our calculations, correlation consistent basis set families were used up to octuple-ζ basis sets. It was found that the following factors, in order of significance, can be identified as the most important error sources: (i) the considerably large relativistic contributions carrying large uncertainties, (ii) the very slow convergence of the Møller-Plesset (MP2) correlation energy (with the octuple-ζ basis set, it still contains an error of a few tenth of a kJ/mol), (iii) the slow convergence of the coupled-cluster singles and doubles (CCSD) contribution (it needs a octuple-ζ basis set to converge within 0.1 kJ/mol), and (iv) the relatively large basis set (quadruple-ζ) needed in the calculation of an accurate perturbative quadruples contribution. It is also notable that, for chlorine, the use of a quintuple-ζ basis set for the Hartree-Fock energy, the MP2 correlation energy, and for the CCSD and perturbative triples contributions, which is the usual treatment in almost every high-accuracy model chemistry, resulted in the overestimation of all of these contributions (altogether about by 1.8 kJ/mol). However, this overestimation is accidentally compensated by (i) using an inappropriate, small basis set for the valence electron contribution due to quadruple excitations (∼1.2 kJ/mol), (ii) neglecting the effects of core electron contributions due to quadruple excitations (∼0.2 kJ/mol), and (iii) neglecting relativistic effects beyond the scalar relativistic treatment (∼0.3 kJ/mol). The most reliable theoretical estimate for D(0)((35)Cl(2)) obtained in this study, 239.27 ± 1.30 kJ/mol, differs by only 0.05 kJ/mol from the most accurate experimental result. This study also underpins the effect of relativistic contributions, which precludes current model chemistries to enter the range of sub-kJ/mol accuracy for second-row systems.

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.

Stopping of ∼0.2–3.4MeV/amu 1H+ and 4He+ ions in polyvinyl formal

Abstract The stopping powers of polyvinyl formal resin for protons and alpha particles have been measured over the energy range ∼(0.2–3.4) MeV/amu with an overall relative uncertainty of less than 2.5% using the ion beam transmission method. The obtained results are discussed in comparison to scarce experimental data from the literature and to values calculated by the SRIM-2008 computer code assuming Bragg-Kleeman’s additivity rule of stopping powers. Departures from additivity attaining ∼5.5% and ∼3.0% for the proton and alpha particle data, respectively, are observed at moderate projectile velocities, increasingly as one evolves towards the stopping power maximum dominated by charge exchange effects. They are presumed to be mainly due to valence structure effects involving the C–H bonds of the studied polymer compound. The less pronounced deviation for alpha particles is probably due to the projectile screening effect that occurs in distant collisions tending to reduce the contribution of valence electrons in the low projectile velocity regime.

Role of valence electrons for formation of glassy alloys

The role of valence electrons for formation of glassy alloys was investigated as a function of their valence electron concentration (VEC). The glass transition temperature T g of 121 kinds of glassy alloys can be expressed as a linear function of VEC: T g = 131VEC + 65 (2.3 < VEC < 5.2) for metal/metal bonding type and T g = −240VEC + 2408 (6.6 < VEC < 9.1) for metal/metalloid bonding one. The thermal stability of the glassy alloys increases by the unsynchronized resonance of electron-pair bonds, and decreases due to increase in covalency by metalloid elements, with an increasing number of valence electrons, respectively. Ab initio molecular orbital calculations of the optimized structures for the Mg monoanion clusters warranted application of the valence electron rule, which is based on a valence electron contribution associated with spd or spf hybridization for glass formation.

Electronic Structure Calculations under Periodic Boundary Conditions Based on the Gaussian and Fourier Transform (GFT) Method.

We developed the Gaussian and Fourier transform method for crystalline systems. In this method, the Hartree (Coulomb) term of valence electron contribution is taken into account by solving the Poisson equation based on Fourier transform technique. We compared the band structures obtained by the Hartee-Fock (HF) approximation and the density functional theory (DFT). We used three different types of density functional approximations such as the local density approximation (LDA), generalized gradient approximation (GGA), and hybrid density functional. In this paper, we confirm that our calculation technique yields similar results to previous studies.

Charge transfer in silicon clathrates studied by Compton scattering

High-resolution Compton profiles of the clathrates ${\mathrm{Na}}_{8}{\mathrm{Si}}_{46}$, ${\mathrm{K}}_{7.6}{\mathrm{Si}}_{46}$, and ${\mathrm{Si}}_{136}$ were measured to study the charge transfer of the alkali-metal guest atoms to the clathrates silicon host lattice. The experiment was accomplished utilizing the Compton spectrometer at beamline ID15B of the European Synchrotron Radiation Facility with an incident energy of $56.7\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ and a momentum space resolution of $0.16\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ The valence electron contribution to the total Compton profile of the sodium and potassium guest atoms was extracted and is compared with calculations employing density-functional theory using Becke exchange and Perdew-Wang correlation. Good overall agreement between experiment and theory is found and proves the quality of the underlying wave functions used for the theoretical predictions. On this basis, the charge transfer in these systems is estimated by a Mulliken population analysis and discussed for the different guest atoms.

3d-shell contribution to the energy loss of protons during grazing scattering from Cu(111) surfaces

Motivated by a recent experimental work [S. Lederer and H. Winter, Phys. Rev. A 73, 054901 (2006)] we study the contribution of the $3d$ shell electrons to the energy loss of $100\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ protons scattered off from the Cu(111) surface. To describe this process we use a multiple collision formalism, where the interaction of the projectile with $3d$ electrons is described by means of a sequence of single encounters with atoms belonging to the first atomic layer. In order to compare the theoretical energy loss with the experimental data, we add the contribution of valence electrons, which is evaluated in linear response theory using a response function that incorporates information on the surface band structure. For completeness, the energy lost by protons is also calculated within a jellium model that includes $3d$ and valence electrons with equal footing. Fair agreement between theory and experiment exists when the $3d$ shell is taken into account in the calculation.

Electronic rule for formation of glassy alloys

The glass transition temperature Tg of 100 kinds of glassy alloys can be expressed as a function of their valence electron concentration (VEC): Tg=131VEC+57 for metal/metal bonding type and Tg=−236VEC+2375 for metal/metalloid bonding one. The electron valences of the constituent elements of the glassy alloys are somewhat larger than those predicted by crystalline metallic valence bond theory, suggesting a valence electron contribution associated with spd or spf hybridization for glass formation. Ab initio molecular orbital calculations of the optimized structures for Mg monoanion clusters warranted application of the valence electron rule.

Mean excitation energy for the stopping power of light elements

We have evaluated the mean excitation energy or I value for Coulomb excitations by swift charged particles passing through carbon, aluminum and silicon. A self-consistent Kramers–Kronig analysis was used to treat X-ray optical spectra now available from synchrotron light sources allowing us to carry out Bethe’s original program of evaluating I from the observed dielectric response. We find that the K and L shell are the dominant contributors to I in these light elements and that the contribution of valence electrons is relatively small, primarily because of their low binding energy. The optical data indicate that Si and Al have nearly equal I values, in contrast to Bloch’s Thomas–Fermi result, I∝Z. The optically based I values for C and Al are in excellent agreement with experiment. However, the dielectric-response I value for Si is 164±2eV, at variance with the commonly quoted value of 173±3eV derived from stopping-power measurements.