Independent Atom Approximation Research Articles

Mean inner potential of elemental crystals from density-functional theory calculations: Efficient computation and trends

The mean inner potential (V0) of crystals plays an important role in electron microscopy. In a few cases, it has been measured experimentally, using mostly electron holography; however, it is not uncommon to find reports that disagree by a few volts regarding the mean inner potential of the same material. Different levels of theory have also been used to estimate its value, often by building the crystal as a superposition of isolated atoms or ions—an independent-atom approximation that does not take bonding into account. In a few cases, density-functional theory (DFT) calculations were done to capture such bonding, frequently using computer-intensive all-electron approaches. In this article, we describe in detail a faster implementation based on postprocessing files produced by a DFT code that relies on the projector-augmented wave method. We deployed this approach to compute values of V0 for 44 elemental solids, and we provide the first quantum-mechanical calculation of the mean inner potential beyond the independent-atom approximation for many of them. We also report instances in which different surface terminations for the same material led to differences in V0 of more than 3 V, highlighting the dependence of the mean inner potential on the boundary conditions of the sample. Finally, by comparing our values of V0 with other material properties, we show that it correlates mostly linearly with the mass density, that it can be used to compute a good approximation to the orbital diamagnetic contribution to the magnetic susceptibility, and that it provides a simple route to compute atomic scattering amplitudes for forward scattering of electrons.

Scattering of e± by C2H6 Molecule over a Wide Range of Energy: A Theoretical Investigation.

The present work reports the theoretical investigation of the scattering of electrons and positrons by the ethane (C2H6) molecule over the energy range 1 eV-1 MeV. The investigation was carried out by taking into account the screening correction arising from a semiclassical analysis of the atomic geometrical overlapping of the scattering observables calculated in the independent atom approximation. The study is presented through the calculations of a broad spectrum of observable quantities, namely differential, integrated elastic, momentum transfer, viscosity, inelastic, grand total, and total ionization cross-sections and the Sherman functions. A comparative study was carried out between scattering observables for electron impact with those for positron impact to exhibit the similarity and dissimilarity arising out of the difference of the collisions of impinging projectiles with the target. Partial-wave decomposition of the scattering states within the Dirac relativistic framework employing a free-atom complex optical model potential was used to calculate the corresponding observable quantities of the constituent atoms. The results, calculated using our recipe, were compared with the experimental and theoretical works available in the literature. The Sherman function for a e±-C2H6 scattering system is presented for the first time in the literature. The addition of the screening correction to the independent atom approximation method was found to substantially reduce the scattering cross-sections, particularly at forward angles for lower incident energies.

Scattering of e± from CF3I Molecule

Theoretical investigation of the scattering of electrons and positrons from the plasma etching gas trifluoroiodomethane (CF3I) is presented in the present work. The investigation is carried out by taking into account the screening correction arising from a semiclassical analysis of atomic geometrical overlapping of the scattering cross-sections calculated in the independent atom approximation. The scattering system e±-CF3I is studied through the calculations of the observable quantities, namely, absolute differential, Sherman function, total elastic and inelastic, momentum transfer, viscosity, ionization and total cross sections over the energy range 1 eV–1 MeV. Energy dependency of the differential cross section and Sherman function are also picturized in this work. A comparative study is carried out between scattering observables for electron impact with those for positron impact to get a better understanding of the interaction and dynamics of the collision process. The corresponding scattering quantities of the constituent atoms are calculated employing a complex optical model potential by solving the Dirac relativistic wave equations in the framework of partial wave analysis. The comparison of our results with the available experimental and theoretical data shows a reasonable agreement.

Observation and theory of strong circular dichroism in angle-revolved photoemission from graphite

Experimental angle-resolved photoemission spectra (ARPES) and its circular dichroism (CD) from a graphite surface are reported together with calculations in the one-step model of photoemission. For photoelectrons emitted with surface parallel momentum k∥ perpendicular to the incoming light, a strong and complex CD signal is observed and analyzed along the Γ-K and Γ-M lines of the Brillouin zone. Calculations using real-space multiple scattering theory agree well with the data both for the total ARPES and the CD intensity maps. In the independent atomic approximation, i.e. when photoelectron scattering is neglected, the total ARPES intensity map is still well described, but not the CD. We find that photoelectron scattering makes a large contribution to the CD signal and may change its sign. Moreover, the CD of the bands depends strongly on photon energy, while this is much less the case for the total ARPES intensity. The present findings show that an accurate description of the photoemission final state, including photoelectron scattering effects, is crucial for understanding the CD in ARPES from surfaces and two-dimensional materials.

Accuracy of the independent atom approximation in digital tomosynthesis Monte Carlo simulations

Monte Carlo (MC) codes serve as the gold standard simulation tool during design and optimisation of x-ray imaging systems. Such simulations often model Rayleigh scattering based on the Independent Atom Approximation Model (IAM). This model neglects the low range molecular interference (MI) effects of non-crystalline materials such as human tissues. Previous work has found discrepancies in the simulated images of planar x-ray images between IAM and MI models. However, insignificant differences were found for computed tomography (CT) reconstructions. In this work we present Geant4 MC simulations of a flat panel source digital tomosynthesis (DT) system for human extremities. Results show that with a 1:9 scatter to primary ratio (SPR) in the x-ray projections, the DT reconstructions are insensitive to the differences of the IAM and MI models. Therefore, MC codes that use the IAM model are sufficient for the study of DT systems. That is because DT algorithms have a larger effect on image quality than the few percent change in the noise due to a physical model and noise suppression methods make this change even less important. Dependency of this conclusion on SPR must be considered in other DT modalities where SPR might be larger.

Scattering of NO(ν = 3) from Au(111): a stochastic dissipative quantum dynamical perspective.

In this work, we present a theoretical study of the scattering dynamics of NO(ν = 3) from an ideal unreconstructed Au(111) surface. The simulations are performed in reduced dimensions at the three high-symmetry sites employing our recent modification to the stochastic wave packet approach for diatomic-metal scattering [J. Chem. Phys., 2019, 150, 184105]. Energy exchange between molecular vibrational degrees of freedom and the electron-hole pairs (EHP) of the metal is accounted for by quantized stochastic jump operators, with associated rates obtained from a microscopic model based on Fermi's golden rule. The simulations are found to reproduce the experimentally observed trend of enhanced vibrational relaxation probabilities with increasing initial translational energy. Molecular dynamics simulations with electronic friction (MDEF) in the independent atom approximation were performed to compare classical and quantum dynamical descriptions of that system. Significant differences between these two descriptions were found indicating that intermode coupling must be described accurately by using a good potential energy surface, and pointing out at the potentially important influence of a quantized description of energy relaxation in describing the scattering of NO from Au(111).

Scatter Corrections in X-Ray Computed Tomography: A Physics-Based Analysis.

Fundamental limits for the calculation of scattering corrections within X-ray computed tomography (CT) are found within the independent atom approximation from an analysis of the cross sections, CT geometry, and the Nyquist sampling theorem, suggesting large reductions in computational time compared to existing methods. By modifying the scatter by less than 1 %, it is possible to treat some of the elastic scattering in the forward direction as inelastic to achieve a smoother elastic scattering distribution. We present an analysis showing that the number of samples required for the smoother distribution can be greatly reduced. We show that fixed forced detection can be used with many fewer points for inelastic scattering, but that for pure elastic scattering, a standard Monte Carlo calculation is preferred. We use smoothing for both elastic and inelastic scattering because the intrinsic angular resolution is much poorer than can be achieved for projective tomography. Representative numerical examples are given.

Y2O3 optical constants between 5 nm and 50 nm.

We report optical constants of e-beam evaporated yttrium oxide Y2O3 thin films as determined from angle-dependent reflectance measurements at wavelengths from 5 to 50 nm. Samples were measured using synchrotron radiation at the Advanced Light Source. The experimental reflectance data were fit to obtain values for the index of refraction and thin film roughness. We compare our computed constants with those of previous researchers and those computed using the independent atom approximation from the CXRO website. We found that the index of refraction near 36 nm is much lower than previous data from Tomiki as reported by Palik. The real part of the optical constants is about 10% to 15% below CXRO values for wavelengths between 17 nm and 30 nm. Films were also characterized chemically, structurally, and optically by ellipsometry and atomic force microscopy.

Efficient first principles simulation of electron scattering factors for transmission electron microscopy

Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These typically use the independent atom approximation that neglects bonding effects, which may, however, be measurable and of physical interest. Since all electrons and the nuclear cores contribute to the scattering potential, simulations that go beyond this approximation have relied on computationally highly demanding all-electron calculations. Here, we describe a new method to generate ab initio electrostatic potentials when describing the core electrons by projector functions. Combined with an interface to quantitative image simulations, this implementation enables an easy and fast means to model electron scattering. We compare simulated transmission electron microscopy images and diffraction patterns to experimental data, showing an accuracy equivalent to earlier all-electron calculations at a much lower computational cost.

Quantitative Agreement between Electron-Optical Phase Images of WSe_{2} and Simulations Based on Electrostatic Potentials that Include Bonding Effects.

The quantitative analysis of electron-optical phase images recorded using off-axis electron holography often relies on the use of computer simulations of electron propagation through a sample. However, simulations that make use of the independent atom approximation are known to overestimate experimental phase shifts by approximately 10%, as they neglect bonding effects. Here, we compare experimental and simulated phase images for few-layer WSe_{2}. We show that a combination of pseudopotentials and all-electron density functional theory calculations can be used to obtain accurate mean electron phases, as well as improved atomic-resolution spatial distribution of the electron phase. The comparison demonstrates a perfect contrast match between experimental and simulated atomic-resolution phase images for a sample of precisely known thickness. The low computational cost of this approach makes it suitable for the analysis of large electronic systems, including defects, substitutional atoms, and material interfaces.

Scattering of electrons by a 1,2-butadiene (C4H6) molecule: measurements and calculations

We present the results of experimental and theoretical study on electron collisions with a 1,2-butadiene (H2C=C=CHCH3) molecule. Absolute grand-total cross sections (TCSs) were measured using a linear electron-transmission method for collision energies in the 0.5–300 eV range. Two distinct features in the TCS energy curve were detected: a narrow peak located at 2.3 eV and a broad enhancement centered around 9 eV. We attributed these features to the formation of negative-ion resonant states, based on comparisons with the existing data for other targets of similar structure. Experimental findings indicate a bonding effect on the TCS when confronting TCS curves for allenes with those for respective acetylenes. Clear differences in experimental TCS energy dependences for C4H6 isomers (1,2-butadiene, 1,3-butadiene, 1-butyne and 2-butyne) show on the isomeric effect. The independent atom approximation was employed to calculate the elastic (ECS) cross section from 25 to 3000 eV, while the binary-encounter-Bethe approach was used for computation of the ionization (ICS) cross section, from the threshold up to 3 keV. The sum of computed cross sections (ECS+ICS) quite reasonably reproduces the experimental TCS values above 35 eV. The reported TCS experimental values are not corrected for the forward-angle scattering effect.

Electron scattering from hexafluoroacetone molecules: cross section measurements and calculations

Absolute total cross section (TCS) for electron scattering from hexafluoroacetone (HFA: (CF3)2CO) molecules has been measured from 1 to 400 eV, employing a linear electron-transmission technique. The TCS energy function for the electron–HFA collision has two broad enhancements: the first, visible between 2 and 28 eV, can be partly attributed to resonant processes; the second is much broader, centred around 50 eV, and is characteristic of perfluorinated targets. The low-energy enhancement is superimposed with weak features perceptible near 3.6, 8.5 and 17 eV. Calculations were carried out for HFA and for acetone to obtain the integral elastic and ionization cross sections at intermediate and high incident energies, using the independent atom approximation and binary-encounter-Bethe approach, respectively. The computed total (elastic plus ionization) cross sections are above 70 eV in reasonable agreement with the experimental TCSs. A comparison is made between cross sections for HFA and its per-hydrogenated counterpart, acetone ((CH3)2CO); the effect of perfluorination is indicated.

Rayleigh scatter in kilovoltage x-ray imaging: is the independent atom approximation good enough?

Monte Carlo simulation is the gold standard method for modelling scattering processes in medical x-ray imaging. General-purpose Monte Carlo codes, however, typically use the independent atom approximation (IAA). This is known to be inaccurate for Rayleigh scattering, for many materials, in the forward direction. This work addresses whether the IAA is sufficient for the typical modelling tasks in medical kilovoltage x-ray imaging. As a means of comparison, we incorporate a more realistic ‘interference function’ model into a custom-written Monte Carlo code. First, we conduct simulations of scatter from isolated voxels of soft tissue, adipose, cortical bone and spongiosa. Then, we simulate scatter profiles from a cylinder of water and from phantoms of a patient's head, thorax and pelvis, constructed from diagnostic-quality CT data sets. Lastly, we reconstruct CT numbers from simulated sets of projection images and investigate the quantitative effects of the approximation. We show that the IAA can produce errors of several per cent of the total scatter, across a projection image, for typical x-ray beams and patients. The errors in reconstructed CT number, however, for the phantoms simulated, were small (typically < 10 HU). The IAA can therefore be considered sufficient for the modelling of scatter correction in CT imaging. Where accurate quantitative estimates of scatter in individual projection images are required, however, the appropriate interference functions should be included.

TU-EE-A4-05: Influence of Photon Scatter Modeling On Image Reconstruction Accuracy in CBCT

Purpose: One method for scatter correction in cone beam computed tomography(CBCT) is to compute the scatter with a Monte Carlo simulation. The accuracy of this approach may be influenced by the accuracy of the underlying photon scattering cross sections. The purpose of this study is to investigate the effect of the level of sophistication of photon interaction models on the computed scatter in CBCT and its influence on the accuracy of image reconstruction.Method and Materials: The investigation is performed using egs_cbct, a new EGSnrc based code for use in CBCT imaging. The EGSnrc treatment of Rayleigh scattering is improved to include measured molecular coherent scatteringform factors (MCSFF) in addition to the commonly used independent atom approximation form factors (IAAFF). A more accurate algorithm for sampling coherent scattering angles is also added. Three photonscatter models are investigated: Compton scattering according to the Klein‐Nishina equation and no Rayleigh scattering (simple); Bound Compton scattering modeled in the relativistic impulse approximation (RIA) and IAAFF; RIA and MCSFF. Scatter calculation and image reconstruction accuracy is tested for a 30 cm diameter water sphere with and without inserts of varying density and materials for a scan with 180 projections. Results: The simple model is not sufficiently accurate for estimating photonscatter in CBCT. The influence of MCSFF on the computed scatter distributions is small and only noticeable at the edges of the phantom. No significant difference in the accuracy of the reconstructed images is observed between the MCSFF and IAAFF coherent scattering models. Conclusion:Rayleigh scattering must be included in the Monte Carlo simulation to estimate the scatter in CBCT imaging. The inclusion of molecular interference effects in coherent scattering has no significant effect in the image reconstruction process.

Cross sections for electron scattering from sulfuryl chloride fluoride (SO2ClF) molecules

Absolute total cross section (TCS) for electron scattering from sulfuryl chloride fluoride (SO2ClF) molecules was measured in a linear transmission experiment at energies ranging from 0.6 to 370 eV. The experimental TCS energy function has a deep minimum (30 × 10−20 m2) at 3 eV which separates two distinct TCS enhancements. Below 3 eV the TCS curve increases steeply towards lower energies with a small resonant maximum visible near 2.2 eV. Above 3 eV the TCS is dominated by second pronounced enhancement with the maximum (45 × 10−20 m2) peaked near 9.5 eV. The experimental TCS findings are—at intermediate energies—satisfactorily reproduced with our total cross section estimation based on calculations of integral elastic (in independent atom approximation) and ionization (binary-encounter-Bethe approach) cross sections. The TCS measured for SO2ClF is also compared with experimental TCSs for molecules containing sulfur as a central atom and it is found that some features observed for SO2ClF are shared by others of the compared molecules.

Screening corrections for calculation of electron scattering differential cross sections from polyatomic molecules

An ab initio approximate procedure is obtained for the screening correction of molecular differential cross sections calculated in the independent atom approximation. Proposed corrections arise from a semiclassical analysis of atomic geometrical overlapping as seen by the incident electrons. The resulting treatment is very simple and its application to CO 2, CF 4 and C 3F 8 sample molecules reveals significant improvements in the 10–200 eV incident energy region.

The atomic and electronic structure of liquid N-methylformamide as determined from diffraction experiments

The structure of liquid N-methylformamide (NMF) has been investigated using synchrotron radiation at 77 and 95 keV. The use of high energy photons has several advantages, in this case especially the large accessible momentum transfer range, the low absorption and the direct comparability with neutron diffraction. The range of momentum transfer covered is 0.6 \AA$^{-1} <$ Q $<$24.0 \AA$^{-1}$. Neutron diffraction data on the same sample in the same momentum transfer range have been published previously. In that study two differently isotope - substituted species were investigated. In order to compare neutron and photon diffraction data properly Reverse Monte Carlo (RMC-) simulations have been performed. Some modifications had to be added to the standard RMC- code introducing different constraints for inter- and intramolecular distances as these distances partly overlap in liquid NMF. RMC- simulations having only the neutron data as input were carried out in order to test the quality of the X-ray data. The photon structure factor calculated from the RMC- configurations is found to agree well with the present experimental data, while it deviates considerably from earlier X-ray work using low energy photons (17 keV). Finally we discuss whether the different interaction mechanisms of neutrons and photons can be used to directly access the electronic structure in the liquid. Evidence is presented that the elastic self scattering part of liquid NMF is changed with respect to the independent atom approximation. This modification can be accounted for by a simple charged atoms model.

An X-ray diffraction study of liquid chlorine

The static structure of liquid chlorine at room temperature is investigated by means of X-ray diffraction. From comparisons with previous neutron and X-ray data, it appears that most of the discrepancies present in the liquid structure factor between neutron and X-ray studies have been removed. Some experimental difference in the two structure factors still remains and one possible explanation is that the electron density distribution of liquid chlorine differs from that derived within the independent atom approximation.

X-Ray Diffraction Study on Hydration and Ion-Pairing in Aqueous ZnSO4 Solution

An X-ray diffraction experiment on a 2.98 molar ZnSO4 aqueous solution has been interpreted in terms of coordination models. The best agreement between model and experimental structure functions was reached when the Zn2+ ion is hydrated in octahedral form, with twelve water molecules in a second hydration shell, bonded by shortened H-bonds to the first hydration shell. The sulfate group is loosely coordinated by 8.2 water molecules. Besides the dominating Zn(H2O)2+ 6 complexes, about 40% [Zn(H2O)5SO4] inner complexes were found to be consistent with the X-ray data. Alternative models of cationic hydration are critically examined and for the sulfate group the independent atom approximation is compared with a spherical molecular description.

The molecular correlation function in liquid nitrogen and oxygen: evaluation of effective pair potential

An analysis of the orientation correlation between the neighbouring molecules of nitrogen and oxygen is given. The correlated form factor f2(Q) is formed giving proper weighting to the parallel and perpendicular orientations and taking into account that fact that the centre structure factor in the region of the first peak should be well produced by a hard-sphere potential. These orientation correlations give about 62% and 64% parallel orientations in nitrogen and oxygen respectively using the proper choice of hard-sphere diameters and bond lengths from the measurements of Furumoto and Shaw. The very good agreement between experimental values of Sm(Q) and those calculated on the basis of this simple model shows that the independent-atom approximation is valid even for linear molecules like nitrogen and oxygen.