Momentum transfer effects in near surface electron energy loss

We examine two formulations for the differential surface excitation parameter (DSEP): one provided by Tung et al. and the other given by the Chen–Kwei position‐dependent differential inverse inelastic mean free path integrated over the electron trajectory. We demonstrate that the latter converges to the former provided that the dielectric function of the solid does not depend on the momentum transfer or it depends on just the momentum transfer component parallel to the surface. Tung's DSEP represents therefore an approximation to the Chen–Kwei DSEP calculated for a dielectric function with no restrictions on the momentum dependence. The approximation is shown to work in the limit of small momentum transfer and to imply an error of 4%–5% for electrons traveling through the solid with energy E = 1 keV. Copyright © 2015 John Wiley & Sons, Ltd.     

Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy

A Monte Carlo simulation including surface excitation, Auger electron‐ and secondary electron production has been performed to calculate the energy spectrum of electrons emitted from silicon in Auger electron spectroscopy (AES), covering the full energy range from the elastic peak down to the true‐secondary‐electron peak. The work aims to provide a more comprehensive understanding of the experimental AES spectrum by integrating the up‐to‐date knowledge of electron scattering and electronic excitation near the solid surface region. The Monte Carlo simulation model of beam–sample interaction includes the atomic ionization and relaxation for Auger electron production with Casnati's ionization cross section, surface plasmon excitation and bulk plasmon excitation as well as other bulk electronic excitation for inelastic scattering of electrons (including primary electrons, Auger electrons and secondary electrons) through a dielectric functional approach, cascade secondary electron production in electron inelastic scattering events, and electron elastic scattering with use of Mott's cross section. The simulated energy spectrum for Si sample describes very well the experimental AES EN(E) spectrum measured with a cylindrical mirror analyzer for primary energies ranging from 500 eV to 3000 eV. Surface excitation is found to affect strongly the loss peak shape and the intensities of the elastic peak and Auger peak, and weakly the low energy backscattering background, but it has less effect to high energy backscattering background and the Auger electron peak shape. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of Main Factors Determining the Prediction of Stabilization Energies of Halide-water Clusters

This work studies the main factors determining the stabilization energy [E _stab(n)] of a series of halide clusters, [X(H₂O) _n ]⁻ (X≡F, Br and I). This property measures the difference between the ionization process of the hydrated and isolated halide. In a previous paper [J. Chem. Phys., 121, 7269 (2004)], the E _stab(n) was studied for a large number of clusters (up to n = 60) by using classical computer simulations based on first-principles polarizable potentials to describe the halide–water interactions. In this work we analyze what features of the MCDHO-type model are necessary for a proper reproduction of the experimental E _stab. The role of the charge redistribution (polarizability) of the water molecule and halide anion, the geometrical relaxation of water molecule (flexibility), as well as the replacement of water clusters by a dielectric continuum of different dielectric permittivities are presented and discussed. The parallel behavior of the E _stab magnitude with the dielectric permittivity of the continuum and with the number of water molecules forming the cluster supports that the electrostatic interactions are the main responsible for the changes induced on the electron structures determining the energetics of the photodetachement process. The photodetachment process does not only occur without nuclear relaxation but also with a small electron redistribution of water molecules.     

Inelastic scattering and energy loss of swift electron beams in biologically relevant materials

The inelastic mean free path and the stopping power of swift electrons in relevant biomaterials, such as liquid water, DNA, protein, lipid, carotene, sugar, and ice are calculated in the framework of the dielectric formalism. The Mermin Energy Loss Function – Generalized Oscillator Strength model is used to determine the energy loss function of these materials for arbitrary energy and momentum transfer using electron energy‐loss spectroscopy data as input. To ensure the consistency of the model, efforts are made so that both the Kramers–Kronig and f‐sum rules are fulfilled to better than 2%. Our findings indicate sizeable differences in the inelastic mean free path and stopping power among these biomaterials for low‐energy electrons. For example, at 100‐eV electron energy, the inelastic mean free path in protein is 25% smaller than for water and around 10% smaller than for the other biomaterials. The stopping power values of protein, DNA, and sugar are rather similar but 20% larger than for water. Taking into account these results, we conclude that electron interactions with living tissues at the nanometric scale cannot be reliably described using only liquid water as the surrogate of the biological target. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved Tougaard background calculation by introduction of fittable parameters for the inelastic electron scattering cross‐section in the peak fit of photoelectron spectra with UNIFIT 2011

The shape of the background in x‐ray photoemission spectra is strongly affected by scattered electrons from inelastic energy loss processes. A polynomial of low order has very often been applied to model the secondary‐electron background, giving satisfying results in some cases. An improved analysis employing the Tougaard background model has been successfully used to characterize the inelastic loss processes. However, the correct usage of the Tougaard background needs a well defined inelastic electron scattering cross‐section function λ(E) · K(E, T) (λ = inelastic mean free path, E = kinetic energy, T = energy loss). This paper presents a four‐parameter loss function λ(E) · K(E, T) = B · T/(C + C′ · T²)² + D · T² with the fitting parameters B, C, C′ and D implemented in the background function allowing the improved estimation of the λ(E) · K(E, T) function for homogenous materials. The fit of the background parameters is carried out parallel to the peak fit. The results will be compared with the parameters recommended by Tougaard. The calculation of inelastic electron scattering cross‐sections of clean surfaces from different materials using UNIFIT 2011 will be demonstrated. Copyright © 2011 John Wiley & Sons, Ltd.     

Effective depths for surface excitation derived by reflection electron energy‐loss spectroscopy analysis

A method of estimation is proposed for determining the effective depth of surface excitation. For this, the effective differential inverse inelastic mean free path (DIIMFP) is presumed to be represented as a linear combination of theoretical DIIMFPs for surface and bulk excitation, which are derived by the use of optical dielectric constants. The effective DIIMFP in the approach is derived by a reflected electron energy‐loss spectroscopy analysis based on the extended Landau approach. The present analysis for 1 kV electrons has led to a simple estimation of the effective depth for surface excitations (～14.5 Å for Al and ～21 Å for Ag), agreeing well with an estimation given by υ/ω _s, where υ and ω _s are the velocity of the primary electrons and the average surface plasmon frequency, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison between theoretical and experimental values of the volume changes accompanying rubber extension

The molecular theory of rubber elasticity assumes the free energy to consist of two parts: a liquidlike free energy that is governed by intermolecular interactions and is independent of strain at constant volume and an intramolecular interaction free energy equal to the sum of the free energies of the chains making up the network. The volume increases of rubber samples as a function of their length were found to be considerably larger than predicted by the molecular theory. Therefore, contrary to common belief, the values of (?E/?L)_V,T might not be related solely to changes in intramolecular interactions with extension. Also, the usual procedure to obtain values of (?E/?L)_V,T from measurements of (?f/?T)_p,L with the aid of the molecular theory is not correct.     

Intermolecular interactions: Elaboration on an additive procedure including an explicit charge-transfer contribution

An additive procedure is derived for the computation of intermolecular interactions, in which an explicit expression for the charge-transfer energy contribution E_CT is implemented. In the total interaction energy, the electrostatic terms E_MTP and E_pol are calculated as in our previous treatment. The dispersion contribution is calibrated by reference to variation-perturbation computations on model systems and the repulsion contribution is computed as a sum of bond—bond, bond—lone pair, and lone pair—lone pair interactions. Tests of the procedure are given for representative hydrogen-bonded systems.     

Simple universal curve for the energy‐dependent electron attenuation length for all materials

An analysis is presented for a simple, universal equation for the computation of attenuation lengths (L) for any material, necessary for quantifying layer thicknesses in Auger electron spectroscopy (AES) and X‐ray photoelectron spectroscopy (XPS). Attenuation lengths for selected materials may be computed from the inelastic mean free path (λ_Opt) computed, in turn, from optical data. The computation of L involves the transport mean free path and gives good L values where values of λ_Opt are available. However, λ_Opt values are not available for all materials. Instead, λ may be calculated from the TPP‐2M relation, but this requires the accurate estimation of a number of materials parameters that vary over a wide range. Although these procedures are all soundly based, they are impractical in many analytical situations. L is therefore simply reexpressed, here, in terms of the average Z of the layer which may be deduced from the AES or XPS analysis, the average atomic size a (varies in a small range) and the kinetic energy E of the emitted electron. For strongly bonded materials, such as oxides and alkali halides, a small extra term is included for the heat of formation. A new equation, S3, is established with a root mean square (RMS) deviation of 8% compared with the values of attenuation length calculated from λ_Opt available for elements, inorganic compounds, and organic compounds. This excellent result is suitable for practical analysis. In many films, an average value of a of 0.25 nm is appropriate, and then L may be expressed only in terms of the average Z and E. Then, L expressed in monolayers, equation S4, exhibits an RMS deviation of 9% for many elements. These results are valid for the energy range 100 to 30 000 eV and for angles of emission up to 65°. Copyright © 2012 Crown copyright.     

DFT Study of the Group Interactions in 1,3,5‐Triamino‐2,4,6‐Trinitrobenzene and 1,3,5‐Triamino‐2,4,6‐Tridifluoroaminobenzene

Density functional calculations on isodesmic disproportionation reactions of 1,3,5‐triamino‐2,4,6‐trinitrobenzene (TATB) and 1,3,5‐triamino‐2,4,6‐tridifluoroaminobenzene (TATDB) indicate that the interaction between nitro groups on meta carbons of TATB, which brings about unstability to the molecule, is surprisingly larger than that between difluroamino groups in TATDB. The electron‐withdrawing and electron‐donating groups generate large positive and very small negative values of E_{disproportion}, respectively. When both electron‐withdrawing and electron‐donating groups are attached to the benzene skeleton at the same time, large negative disproportionation energy is produced, which stabilizes the derivatives. The values of E_{disproportion} for TATB and TATDB are predicted to be ‐48.03 kJ/mol and ‐63.54 kJ/mol, respectively, indicating that the total interaction among groups with stabilization effects in TATDB is larger than that in TATB. The large difference of the E_{disproportion} values between TATB and TATDB is derived from the large difference between the interactions of the meta‐nitro group and those of meta‐difluoroamino groups. The energy barriers for the C‐N internal rotation of NO₂ group and NF₂ groups are 74.7 kJ/mol and 185.8 kJ/mol for TATB and TATDB, respectively. The large energy barrier for the rotation of the NF₂ group is caused by its stabilization interaction with neighbor amino groups, instead of steric effects. When the number of pairs of amino‐nitro or amino‐difluoroamino groups increases, there are more negative charges on the NO₂/NF₂ groups and on the O/F atoms.     

Hydrogen‐Bond Cooperative Effects in Small Cyclic Water Clusters as Revealed by the Interacting Quantum Atoms Approach

The cooperative effects of hydrogen bonding in small water clusters (H₂O)_n (n=3–6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density (ρ( r )) compliant with the quantum theory of atoms‐in‐molecules (QTAIM) and the calculation of electrostatic interactions by using one‐ and two‐electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1) the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2) the interaction energy (E_int) of these contorted molecules in (H₂O)_n. Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of E_int for a pair of water molecules in the cluster (H₂O)_n?1 become more attractive when a new H₂O unit is incorporated to generate the system (H₂O)_n with the last‐mentioned contribution being consistently the most important part of E_int throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, δ(Ω,Ω′), the QTAIM atomic charges, the topology of ρ( r ), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra‐ and intermolecular interactions present in hydrogen‐bonded systems.     

Structure/Property Relationships for Polyamide 6 / Organoclay Nanocomposites in the Melt and in the Solid State

Commercial nanocomposites of polyamide 6 prepared by melt compounding with organoclays were characterized by complex viscosities and relaxation time spectra derived from storage and loss shear moduli measured in the melt state at 230°C, and by wide- and small-angle X-ray scattering, differential scanning calorimetry and stretching calorimetry in the solid state. In the melt state, the decrease of ∼ 25 % (compared to the pristine sample) in Newtonian viscosity at the lowest clay loading (2.5 %) suggested a lower equilibrium elasticity modulus of an entangled melt, as the small amounts of organoclay nanoparticles acted as specific “diluents” for the initial entanglement network. However, by increasing the clay loading this effect disappeared due to the importance of strong interactions at the nanoparticle/melt interface, leading to the formation of a fairly thick boundary interphase (BI) around the nanoparticles and ending up in the build-up of an “infinite cluster” of clay nanoparticles coated with BI at the highest (albeit still unusually low) clay loading (7.5 %). In the solid state, organoclay nanoparticles proved to induce the crystallographic α → γ transformation of PA6 , while the matrix crystallinity in nanocomposites remained essentially unchanged. In the range of elastic (reversible) behavior below the apparent yield strains ϵ* , the highest Young's moduli E and the lowest linear thermal expansion coefficients α_L were observed for dried nanocomposites, while the lowest E and the highest α_L corresponded to the moisturized, pristine PA6. The endothermal process of shape distortion of the lamellar crystals was assumed to precede the onset of the exothermal process of lamellar fragmentation in the range of inelastic (irreversible) behaviour of PA6 above ϵ* . The energy balance of the inelastic behaviour of nanocomposites was dominated by the endothermal process of lamellar shape distortion.     

Cooperativity and cluster growth patterns in acetonitrile: A DFT study

Cooperativity in intermolecular interactions and cluster growth patterns of acetonitrile has been studied using M06L density functional theory. Cyclic, ladder‐type, stacked, cross‐stacked, and mixed patterns are studied. Total interaction energy (E_int) and interaction energy per monomer (E_m) show maximum stability and cooperativity in stacked clusters followed by cross‐stacked ones. As cluster size increased, magnitude of E_m showed significant increase. Compared to E_m of dimer (?2.97 kcal/mol), the increase is 2.6‐fold for 27mer . Higher stabilization in larger clusters is attributed to strong cooperativity in intermolecular C? H···N and dipolar interactions. Enhanced cooperativity in stacked structures is supported by atoms‐in‐molecule electron density (ρ) data. Sum of ρ at intermolecular bond critical points is the highest for stacked clusters. Further, area of negative‐valued molecular electrostatic potential is linearly related with E_int and showed the lowest value in stacked followed by cross‐stacked clusters, indicating maximum utilization of lone pair density and maximum cooperativity in such growth patterns. A red shift in the average C? N stretching frequencies with increase in the number of monomers and its direct correlation with E_int in stacked clusters also supported their stability. Further, two known crystal patterns of acetonitrile (α and β) with 16 monomers are optimized and compared with the most stable hexadecamer pattern and are found to show lower values for E_int and E_m compared to the latter. Based on this result, we predict the existence of a third crystal pattern for acetonitrile which will be more ordered and more stable than α and β forms. © 2014 Wiley Periodicals, Inc.     

Monte Carlo simulation study of reflection electron energy loss spectroscopy of an Fe/Si overlayer sample

Reflection electron energy loss spectroscopy (REELS) has been used to study the optical and electronic properties of semi-infinite solid samples, aided by a theoretical model of the interaction between electrons and a solid. However, REELS has not been used to its full capacity in studying nanomaterial samples because of the difficulty in modeling the electron interaction with a layered nanostructure. In this study, we present a numerical calculation result on the spatially varying inelastic mean free path for a sample comprising an Fe layer of varying thickness on an Si substrate. Furthermore, a Monte Carlo model for electron interaction with this Fe-Si layered structure sample is built based on this inelastic scattering cross section and used to reproduce the REELS spectra of Fe-Si layered structures. The simulated spectra of the sample with varying Fe layer thickness on top of a Si substrate were compared with the experimental spectra. This comparison clearly identifies that the Fe layer remaining on top of the experimental Si substrate after Ar⁺ beam sputtering is in the form of a homogeneous mixed layer, where the Fe/Si interface excitation is absent in the experimental spectra owing to pulverization of the Fe/Si interface during the Ar⁺ sputtering process.     

Application of ESCA to polymer chemistry. XVI. Electron mean free paths as a function of kinetic energy in polymeric films determined by means of ESCA

Electron mean free paths as a function of kinetic energy have been measured by the substrate overlayer technique for in situ-polymerized films of poly(p-xylylene) and the monochloro- and monobromo-substituted derivatives. The results are compared with previous estimates of mean free paths available in the literature for organic materials. Comparison is also drawn with corresponding experimental data for typical metals and semiconductors, and it is shown that organic polymers fit into a consistent picture which may be rationalized on the basis of existing theory. For electrons of kinetic energy ～969 eV, ～1170 eV, 1202 eV, and 1403 eV, mean free paths of ～14 Å, ～22 Å, ～23 Å, and ～29 Å, respectively, are obtained for the poly(p-xylylene) polymer films studied in this work.     

Acid–base complexes of polymers

The physical interactions of polymers with neighboring molecules are determined by only two kinds of interactions: London dispersion forces and Lewis acid–base interactions. These two kinds of attractive energies (together with certain steric restrictions) determine solubility, solvent retention, plasticizer action, wettability, adsorption, adhesion, reinforcement, crystallinity, and mechanical properties. The London dispersion force interaction energies of polymers have been quantified by the dispersion force contribution to cohesive energy density (δ²_d) and the dispersion force contribution to surface energy (δ^d). The Lewis acid–base interactions, often referred to as “polar” interactions, can be best quantified by Drago's C_A and E_A constants for acid sites and C_B and E_B constants for basic sites. In this article infrared spectral shifts are featured as a method of determining enthalpies of acid–base interaction, and the C and E constants for polymers, plasticizers, and solvents. Examples are given where acid–base complexation of polymers with solvents dominate solubility and swelling phenomena. Enthalpies of acid–base complexation in polymer blends are determined from spectral shifts.     

Cation–ligand interactions: Reproduction of extended basis set Ab initio SCF computations by the SIBFA 2 additive procedure

In the framework of the additive SIBFA 2 procedure, the intermolecular interaction energy is computed as a sum of five terms: ΔE = E_MTP + E_rep + E_pol + E_CT + E_disp. In order to assess the accuracy of the procedure to compute cation–ligand interactions, the interaction of alkali (Na⁺, K⁺) and alkaline-earth (Mg²⁺, Ca²⁺) cations with two representative ligands H₂O and HCOO^? has been studied and the results compared with those of ab initio SCF extended basis set computations. The additive procedure reproduces very satisfactorily the results of ab initio computations as concerns the numerical values of the interaction energies and the equilibrium cation–ligand distances, as well as the evolution of the energy components. A detailed study of these components at different distances helps, in particular, to delineate the relative weights of the charge-transfer and polarization contributions within the second-order energy.     

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.