Calculations of electron inelastic mean free paths. IX. Data for 41 elemental solids over the 50 eV to 30 keV range

We have calculated inelastic mean free paths (IMFPs) for 41 elemental solids (Li, Be, graphite, diamond, glassy C, Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au and Bi) for electron energies from 50 eV to 30 keV. The IMFPs were calculated from experimental optical data using the full Penn algorithm for energies up to 300 eV and the simpler single‐pole approximation for higher energies. The calculated IMFPs could be fitted to a modified form of the Bethe equation for inelastic scattering of electrons in matter for energies from 50 eV to 30 keV. The average root‐mean‐square (RMS) deviation in these fits was 0.48%. The new IMFPs were also compared with IMFPs from the predictive TPP‐2M equation; in these comparisons, the average RMS deviation was 12.3% for energies between 50 eV and 30 keV. This RMS deviation is almost the same as that found previously in a similar comparison for the 50 eV–2 keV range. Relatively large RMS deviations were found for diamond, graphite and cesium. If these three elements were excluded in the comparison, the average RMS deviation was 9.2% between 50 eV and 30 keV. We found satisfactory agreement of our calculated IMFPs with IMFPs from recent calculations and from elastic‐peak electron‐spectroscopy experiments. Copyright © 2010 John Wiley & Sons, Ltd.     

Calculations of electron inelastic mean free paths. X. Data for 41 elemental solids over the 50 eV to 200 keV range with the relativistic full Penn algorithm

We have calculated inelastic mean free paths (IMFPs) for 41 elemental solids (Li, Be, graphite, diamond, glassy C, Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au, and Bi) for electron energies from 50 eV to 200 keV. The IMFPs were calculated from measured energy loss functions for each solid with a relativistic version of the full Penn algorithm. The calculated IMFPs could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter for energies from 50 eV to 200 keV. The average root‐mean‐square (RMS) deviation in these fits was 0.68%. The IMFPs were also compared with IMFPs from a relativistic version of our predictive Tanuma, and Powell and Penn (TPP‐2M) equation that was developed from a modified form of the relativistic Bethe equation. In these comparisons, the average RMS deviation was 11.9% for energies between 50 eV and 200 keV. This RMS deviation is almost the same as that found previously in a similar comparison for the 50 eV to 30 keV range (12.3%). Relatively large RMS deviations were found for diamond, graphite, and cesium as in our previous comparisons. If these three elements were excluded in the comparisons, the average RMS deviation was 8.9% between 50 eV and 200 keV. The relativistic TPP‐2M equation can thus be used to estimate IMFPs in solid materials for energies between 50 eV and 200 keV. We found satisfactory agreement between our calculated IMFPs and those from recent calculations and from measurements at energies of 100 and 200 keV. Copyright © 2015 John Wiley & Sons, Ltd.     

Calculations of electron inelastic mean free paths. XIII. Data for 14 organic compounds and water over the 50 eV to 200 keV range with the relativistic full Penn algorithm

We have calculated inelastic mean free paths (IMFPs) for 14 organic compounds (26-n-paraffin, adenine, β-carotene, diphenyl-hexatriene, guanine, Kapton, polyacetylene, poly (butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene, poly(2-vinylpyridine), thymine, and uracil) and liquid water for electron energies from 50 eV to 200 keV with the relativistic full Penn algorithm including the correction of the bandgap effect in insulators. These calculations were made with energy-loss functions (ELFs) obtained from measured optical constants and from calculated atomic scattering factors for X-ray energies. Our calculated IMFPs could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter from 50 eV to 200 keV. The average root-mean-square (RMS) deviation in these fits was 0.17%. The IMFPs were also compared with a relativistic version of our predictive Tanuma–Powell–Penn (TPP-2M) equation. The average RMS deviation in these comparisons was 7.2% for energies between 50 eV and 200 keV. This average RMS deviation is smaller than that found in a similar comparison for our group of 41 elemental solids (11.9%) and for our group of 42 inorganic compounds (10.7%) for the same energy range. We found generally satisfactory agreement between our calculated IMFPs and values from other calculations for energies between 200 eV and 10 keV. We also found reasonable agreement between our IMFPs for organic compounds and measured IMFPs for energies between 50 eV and 200 keV. Substantial progress for IMFP measurements for liquid water has been made in recent years through the invention of liquid water microjet photoelectron spectroscopy and droplet photoelectron imaging. We found that the IMFPs from these experiments and the associated analyses were larger than our IMFPs by factors between two and four for energies between about 30 eV and 1000 eV. The energy dependences of the measured IMFPs are, however, similar to that of our IMFPs in the same energy range. Since IMFPs calculated from the same algorithm for a number of inorganic compounds agree reasonably well with measured IMFPs for energies between 100 eV and 200 keV, the large differences between IMFPs for water from recent experiments and our results are surprising and need to be resolved with additional experiments.     

An accurate and simple universal curve for the energy‐dependent electron inelastic mean free path

The values of inelastic mean free paths (IMFPs) calculated from optical data for the three material categories of elements, inorganic compounds and organic compounds are re‐assessed to provide a simple equation giving an estimate of the IMFP, knowing only the identities of the elements in an analysed layer and the atomic density of that layer. This simple equation is required for quantification of the thicknesses for layers of mixed elements in which the required parameters for use of the popular equation, TPP‐2M, are insufficiently known. It describes the published values, calculated from optical data for energies above 100 eV, to a similar root mean square (RMS) deviation as that for TPP‐2M in the three material categories. The RMS deviation for all three categories averages 8.4%, provided the inorganic data are ‘corrected’ for the published sum rule errors. If, in an analysed layer, only elements are identified and the atomic density is unknown, i.e. only the average Z value of the layer is known, a simpler relation is provided for the IMFP in monolayers with only one unknown parameter Z that exhibits an RMS deviation from the IMFPs calculated from optical data of 11.5%. Copyright © 2011 Crown copyright.     

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy‐loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm that has been used for previous IMFP and electron stopping‐power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single‐pole approximation, the relativistic simplified single‐pole approximation, and the relativistic extended Mermin method. These calculations were made by using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP‐2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV, but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the full Penn algorithm. The resulting values were in good agreement with results from first‐principle calculations and with inelastic X‐ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length. There were large variations in the measured IMFPs and effective attenuation lengths (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs. Copyright © 2016 John Wiley & Sons, Ltd.     

Calculations of electron inelastic mean free paths

We report calculations of electron inelastic mean free paths (IMFPs) for 50–2000 eV electrons in 14 elemental solids (Li, Be, diamond, graphite, Na, K, Sc, Ge, In, Sn, Cs, Gd, Tb, and Dy) and for one solid (Al) using better optical data than in our previous work. The new IMFPs have also been used to test our TPP‐2M equation for estimating IMFPs in these materials. We found surprisingly large root‐mean‐square (RMS) deviations (39.3–71.8%) between IMFPs calculated from TPP‐2M and those calculated here from optical data for diamond, graphite and cesium; previously we had found an average RMS deviation of 10.2% for a group of 27 elemental solids. An analysis showed that the large deviations occurred for relatively small computed values of the parameter β in the TPP‐2M equation (β ～ 0.01 for diamond and graphite) and also for relatively large values of β (β ～ 0.25 for Cs). Although such extreme values of β are unlikely to be encountered for many other materials, the present results indicate an additional limitation in the reliability of the TPP‐2M equation. We also show that the parameter N_v in the TPP‐2M equation should be computed for the rare‐earth elements from the number of valence electrons and the six 5p electrons. Copyright © 2004 John Wiley & Sons, Ltd.     

Magnetische Untersuchungen der Carbide TiC,ZrC, HfC,VC, NbC und TaC

Zusammenfassung Die magnetische Suszeptibilität an sehr reinen Mono-Carbidproben wird in Abhängigkeit vom Kohlenstoffdefekt gemessen. Mit zunehmendem Kohlenstoffdefekt werden TiC_1–x , ZrC_1–x , HfC_1–x und VC_1–x paramagnetischer. Extrapolation auf stöchiometrisches TiC führt auf Diamagnetismus. NbC_1-x und TaC_1–x zeigen einen davon abweichenden Verlauf; deren Suszeptibilitäten nehmen im wesentlichen mit steigendem C-Defekt ab und erreichen diamagnetische Werte. Eine Vorstellung zur Deutung des Suszeptibilitätsverlaufes bei TiC_1–x , ZrC_1–x , HfC_1–x und VC_1–x unter Berücksichtigung der Bindungsenergie, bei Übergangsmetallen wird entwickelt und eine Erklärung für das magnetische Verhalten von Mischcarbiden gegeben.Mit 2 Abbildungen     

Effect of Different Electron Elastic-Scattering Cross Sections on Inelastic Mean Free Paths Obtained from Elastic-Backscattering Experiments

Inelastic mean free paths (IMFPs) of electrons with energies between 100eV and 5,000eV have been frequently obtained from measurements of elastic-backscattering probabilities for different specimen materials. A calculation of these probabilities is also required to determine IMFPs. We report calculations of elastic-backscattering probabilities for gold at energies of 100eV and 500eV with differential elastic-scattering cross sections obtained from the Thomas-Fermi-Dirac potential and the more reliable Dirac-Hartree-Fock potential. For two representative experimental configurations, the average deviation between IMFPs obtained with cross sections from the two potentials was 11.4%.     

Kβ/Kα X-ray intensity ratios for elements in the range 16⩽Z⩽92 excited by 5.9, 59.5 and 123.6 keV photons

The K shell intensity ratios K_β/K_α for 59 elements in the atomic region 16⩽Z⩽92 have been measured at excitation energies of 5.9, 59.5 and 123.6 keV. K X-rays emitted by samples have been counted by a Si(Li) detector with resolution 160 eV at 5.9 keV. The measured values were compared with the theoretical values calculated using Scofield's tables based on the Hartree–Slater and Hartree–Fock theories and available experimental values. Reasonable agreement is typically obtained between present and theoretical values.     

Variation of the L X-ray fluorescence cross-sections, intensity ratios and fluorescence yields of Sm and Eu in halogen compounds

The chemical effect on the L_i (i=ι, α, β, β₁, β₂, γ) X-ray fluorescence cross-sections, the L X-ray intensity ratios and the average L shell fluorescence yields of Sm and Eu binary compounds with halogen (F, Cl and Br) were investigated. The samples were excited by 59.543 keV photons emitted from an Am-241 radioisotope source. X-rays emitted from the samples were counted by means of a Si(Li) detector, which has a resolution 155 eV at 5.9 keV. The experimental values were compared with the calculated theoretical values     

Magnetic Susceptibility as a Method of Investigation of Short-Range Ordering in Highly Nonstoichiometric Carbides

This paper reviews the results of magnetic susceptibility studies on ordered and disordered Group IV and V transition metal carbides. It is shown that the variations of susceptibility resulting from deviations from stoichiometry are associated with the electronic spectrum features of these compounds. Using magnetic susceptibility as a tool for structural order–disorder transition analysis is discussed. The lower susceptibility of the nonstoichiometric carbides is due to short-range ordering, changing the contribution of orbital paramagnetism. The long- and short-range order parameters have been estimated for NbC _y , TaC _y , TiC _y , and HfC _y based on the experimental susceptibility data.     

Variation of the electron inelastic mean free path during depth profiling of the Fe/Si interface as determined by quantitative REELS

The aim of this work is to determine the dependence of the electron inelastic mean free path (IMFP) at the Fe/Si interface during depth profiling by sputtering with 3 keV Ar⁺ ions. In order to estimate the variation of the IMFP at the interface, reflection electron energy‐loss spectroscopy (REELS) measurements were performed after different sputtering times at the Fe/Si interface with three different primary electron energies (i.e. 0.5, 1 and 1.5 keV). Even though it is highly likely that a compound (i.e. Fe_xSi) is formed at the interface, all the experimental REELS spectra could be analysed as a linear combination of those corresponding to pure Si and Fe. Using the model developed by Yubero and Tougaard for quantitative analysis of these REELS spectra we could estimate the IMFP values along the depth profile at the interface. The resulting IMFPs are observed to vary linearly with the average composition (as determined by REELS) at the Fe/Si interface as it is sputter depth profiled. The energy dependence of the IMFP for different compositions is presented and discussed. For completeness, we have determined the energy‐loss functions as well as the IMFPs of the pure elements (i.e. Fe and Si). Copyright © 2004 John Wiley & Sons, Ltd.     

Gamma ray attenuation coefficient measurement for neutron-absorbent materials

The compounds Na₂B₄O₇, H₃BO₃, CdCl₂ and NaCl and their solutions attenuate gamma rays in addition to neutron absorption. These compounds are widely used in the shielding of neutron sources, reactor control and neutron converters. Mass attenuation coefficients of gamma related to the four compounds aforementioned, in energies 662, 778.9, 867.38, 964.1, 1085.9, 1173, 1212.9, 1299.1,1332 and 1408 keV, have been determined by the γ rays transmission method in a good geometry setup; also, these coefficients were calculated by MCNP code. A comparison between experiments, simulations and Xcom code has shown that the study has potential application for determining the attenuation coefficient of various compound materials. Experiment and computation show that H₃BO₃ with the lowest average Z has the highest gamma ray attenuation coefficient among the aforementioned compounds.     

Why are the Elemental Nonmetals (F2, Cl2, Br2, I2, S8, P4) of so Many Hues or of Any Hues and Where is the Chromophore? Insight into Intera-X–X Bonds

A unique approach is used to relate the HOMO-LUMO energy difference to the difference between the ionization potential (IP) and electron affinity (EA) to assist in deducing not only the colors, but also chromophores in elemental nonmetals. Our analysis focuses on compounds with lone pair electrons and σ electrons, namely X₂ (X = F, Cl, Br, I), S₈ and P₄. For the dihalogens, the [IP – EA] energies are found to be: F₂ (12.58 eV), Cl₂ (8.98 eV), Br₂ (7.90 eV), I₂ (6.78 eV). We suggest that the interahalogen X–X bond itself is the chromophore for these dihalogens, in which the light absorbed by the F₂, Cl₂, Br₂, I₂ leads to longer wavelengths in the visible by a π → σ* transition. Trace impurities are a likely case of cyclic S₈ which contains amounts of selenium leading to a yellow color, where the [IP – EA] energy of S₈ is found to be 7.02 eV. Elemental P₄ with an [IP – EA] energy of 9.09 eV contains a tetrahedral and σ aromatic structure. In future work, refinement of the analysis will be required for compounds with π electrons and σ electrons, such as polycyclic aromatic hydrocarbons (PAHs).     

Variation of K X-ray fluorescence cross-sections of Fe in F compounds at an energy interval of 7.6–14.4 keV

The photon-induced K X-ray fluorescence cross-sections (σ_Kα, σ_Kβ) for Fe in F compounds were investigated. Measurements were carried out at 10 different energies in the interval of 7.6–14.4 keV by using a secondary excitation method. K X-rays emitted by samples were counted by a Si(Li) detector with a resolution of 160 eV at 5.9 keV. Obtained values were compared with the theoretical values of pure elements.     

Development of soft X-ray multilayer laminar-type plane gratings and varied-line-spacing spherical grating for flat-field spectrograph in the 1–8 keV region

W/C and Co/SiO₂ multilayer laminar-type holographic plane gratings (groove density 1/σ = 1200 lines/mm) in the 1–8 keV region are developed. For the Co/SiO₂ grating the diffraction efficiencies of 0.41 and 0.47 at 4 and 6 keV, respectively, and for the W/C grating 0.38 at 8 keV are observed. Taking advantage of the outstanding high diffraction efficiencies into practical soft X-ray spectrographs a Mo/SiO₂ multilayer varied-line-spacing (VLS) laminar-type spherical grating (1/σ = 2400 lines/mm) is also developed for use with a flat field spectrograph in the region of 1.7 keV. For the Mo/SiO₂ multilayer grating the diffraction efficiencies of 0.05–0.20 at 0.9–1.8 keV are observed. The FWHMs of the measured line profiles of Hf-Mα₁(1644.6 eV), Si-Kα₁(1740.0 eV), and W-Mα₁ (1775.4 eV) are 13.7 eV, 8.0 eV, and 8.7 eV, respectively.     

Ground states of molecules. 53.MNDO calculations for molecules containing chlorine

MNDO calculations of heats of formation, dipole moments, ionization potentials, and structures are reported for a wide range of compounds containing chlorine in its characteristic valence state (Cl^I) and one or more of the elements H, B, Be, C, N, O, and F. The calculated errors in the heats of formation and the dipole moments are not significantly greater than those previously reported for compounds containing no chlorine. First vertical ionization potentials were on average 0.95 eV too high. The ordering of higher cationic states was found to be correct, even for species such as Cl₂O, Cl₂, and HOCl, where ab initio–Koopmans' theorem calculations predict the incorrect ordering. The calculated energies and geometries of compounds such as CIF₃ are qualitatively incorrect, probably because of the lack of 3d atomic orbitals in the orbital basis set.     

螺桨烷型分子BX[(CH_2)_n]_3和BX(CH_2)[CH(CH_2)_nCH](X=N,P)的结构和性质

采用密度泛函理论(DFT)研究了螺桨烷型分子BX[(CH2)n]3和BX(CH2)[CH(CH2)n CH](X=N,P;n=1-6)的结构、稳定性、化学键和电子光谱性质.计算结果表明这些分子都是稳定的.BX[(CH2)n]3(X=N,P;n=1-6)的最高占据分子轨道(HOMO)和最低空分子轨道(LUMO)之间的能隙均大于5.20 eV,其中BN[CH2]3和BP[CH2]3的能隙超过7.0 eV,与C5H6的能隙(7.27 eV)很接近,BX(CH2)[CH(CH2)n CH](X=N,P;n=1-6)的能隙在6.80 eV左右.所研究分子能量的二阶差分表明BN[(CH2)3]3、BP[(CH2)4]3及BX(CH2)[CH(CH2)2CH](X=N,P)是最稳定的.BX[(CH2)n]3的Wiberg键级表明除了BN[(CH2)n]3(n=2和6)中不存在B―N键,其它化合物中B和N均形成了化学键,BP[(CH2)n]3中除了BP[(CH2)2]3不存在B―P键,其它的均存在.电子密度的拓扑分析表明N―B键属于离子键,而P―B键具有共价键特征.BX[(CH2)n]3(X=N,P)的第一垂直激发能分别在191.1-284.8 nm和191.8-270.1 nm之间,BX(CH2)[CH(CH2)n CH](X=N,P)的第一垂直激发能分别在190.5-199.7 nm和209.0-221.3 nm之间.     

Optimization and application of lithium parameters for PM3

Lithium parameters have been optimized for Stewart's standard PM3 method. The average deviation of the heats of formation calculated for 18 reference compounds is 6.2 kcal/mol from the experimental or high-level ab initio data; the average deviation with Li/MNDO is 18.9 kcal/mol. The average error in bond lengths is also reduced by a factor of two to three. Ionization potentials and dipole moments are reproduced with comparable accuracy than Li/MNDO. However, the mean deviation for the heats of formation of both methods increases when being applied to other systems, especially to small inorgnic molecules. The applicability of the new parameter set is demonstrated further for various compounds not included in the reference set, for the calculation of the activation barriers of several lithiation reactions, as well as for the estimation of oligomerization energies of methyl lithium (including the tetramer). Li/PM3 gives reliable results even for large dimeric complexes, like [{4-(CH₃CR)C₅H₄N}Li]₂, containing TMEDA or THF as coligands and reproduces the haptotropic interaction between Li⁺ and π-systems (e.g., in benzyl lithium) as well as the relative energies and structural features of compounds with “hypervalent” atoms (e.g., in lithiated sulfones). © John Wiley & Sons, Inc.