Inelastic Intensities Research Articles

Principles and procedures for determining absolute differential electron-molecule (atom) scattering cross sections

Procedures and calibration techniques for measuring the absolute elastic and inelastic differential cross sections (DCS) for electron impact on molecular (atomic) species are described and illustrated by examples. The elastic DCS for the molecule under study is first determined by calibration against helium using the relative flow technique. The second step involves the production of energy-loss spectra for the instrument response function, the unfolding of overlapping inelastic structures and the normalization of inelastic intensities to the elastic cross sections. It is concluded that this method of determining absolute differential electron-molecule (atom) scattering cross sections is generally applicable and provides reliable results.

Electron inelastic plasmon scattering and its resonance propagation at crystal surfaces in RHEED

The modified multislice theory [Wang (1989). Acta Cryst. A45, 193-199] has been employed to calculate the electron reflection intensity with and without considering the plasmon diffuse scattering in the geometry of reflection high-energy electron diffraction (RHEED). It has been shown that the inelastic scattering can greatly enhance the reflectance of a surface, depending critically on the incident conditions of the electrons. At some incidences, the inelastic resonance reflection is enhanced, which is considered as the 'true' surface resonance state. This happens within a very narrow angular range (<1 mrad). For 'true' resonance states, the inelastic intensity is much stronger than for other conditions as shown both theoretically and experimentally. The enhancement of the reflection intensity may not be the proper criterion for identifying the 'true' surface resonance. Besides the surface plasmon peaks, an 'extra' peak, located at 4.5 eV, is observed in the reflection electron energy-loss spectroscopy (REELS) study of the 'true' resonance of GaAs (110) surface. This is considered as a characteristic of the resonance propagations of the electrons along the surface and may result from the generation of resonance radiation.

Atom scattering from surface Einstein modes.

We consider the scattering of thermal-energy atoms by a surface with a dilute coverage of adsorbates having a dispersionless Einstein vibrational mode. We show that the diffuse elastic scattered intensity has a Debye-Waller-type thermal attenuation only at low temperatures, and at large temperatures the attenuation saturates to a much weaker form. Similar thermal attenuation behavior occurs for the diffuse inelastic intensities. For an ordered adsorbate layer there is also a diffuse elastic intensity which increases with temperature at small temperatures.

Structural relaxation in vitreous silica.

The temperature dependence of the inelastic neutron-scattering intensity from vitreous silica has been studied between 50 and 300 K down to frequencies of 150 GHz. Above 500 GHz one finds essentially harmonic behavior. Low-frequency anharmonic behavior can be described by a relaxational model using parameters determined from ultrasonic measurements. The dynamic structure factor shows that relaxation involves coupled rotational jumps of ${\mathrm{SiO}}_{4}$ tetrahedra, with a jump width of the atoms smaller than 0.8 A\r{}. These results support the hypothesis of a common origin of low-temperature glass anomalies.

Interaction potential for one-phonon inelastic He–Cu(111) and He–Ag(111) scattering

The interaction potential for the elastic and inelastic scattering of low-energy He atoms from the Cu(111) and the Ag (111) crystal surface is derived from the sum of semi ab initio pair potentials modified by a damping function which takes into account the smoothing effect of the conduction electrons at large parallel momentum transfer. By adjusting only two free parameters of the potential model a very good fit to published experimental diffraction intensities and bound state levels is obtained. Without any further adjustment of the potential new experimental data of one-phonon inelastic reflection coefficients can be reproduced within the experimental error by calculations based on the distorted wave Born approximation. This new potential model has made it possible to study the dependence of the inelastic intensities on potential parameters and different experimental conditions.

Experimental and theoretical studies of small‐angle electron scattering by the water molecule

AbstractThe total (elastic plus inelastic) intensities of 51 keV electrons scattered by water molecules have been measured over a range of 1 ≦ K = (4π/λ) sin(θ/2) ≦ 12 Å−1. A computer program, ELIC, has been written for calculating the total intensities of electrons scattered by free molecules. The intensities can be calculated with self‐consistent field and configuration interaction wavefunctions. The theoretical intensities based on a CI wavefunction are in good agreement with the observed intensities.

Elastic diffuse and inelastic electron scattering from surfaces with disordered overlayers

The elastic diffuse scattering of electrons can be used for structure analysis of disordered species on surfaces. Effective data acquisition is achieved with instruments which do not resolve between elastic diffuse scattering and inelastic scattering due to phonons. With a newly designed high resolution spectrometer it is shown that the inelastic intensity is of the same magnitude or larger than the elastic diffuse scattering. It is also shown however, that the total inelastic intensity changes little when a lattice gas of adsorbates is present on the surface, whereas the elastic diffuse intensity increases linearly with coverage. Thus instruments with low energy resolution may be used for the analysis of local structure of disordered adsorbates provided one measures the difference between the total diffuse scattering of the adsorbate covered and the clean surface.

Differential cross sections for elastic and inelastic scattering of electrons by N2O in the range from 10 to 80 eV

Differential electron impact cross sections (DCS) for the elastic scattering and excitation of the 1 Pi and 21 Sigma + states of N2O have been measured using a crossed electron beam-molecular beam scattering technique. These measurements were performed at electron impact energies of 10 and 12 eV for elastic as well as at 15, 20, 30, 50 and 80 eV for elastic and inelastic scattering. DCS were obtained over a wide range of scattering angles, up to 150 degrees . The elastic DCS were put on an absolute scale by normalisation to the total electron scattering cross sections. The inelastic DCS are in relative units except for the case of 80 eV impact energy where it was possible to determine the elastic to inelastic intensity ratio and to obtain absolute DCS values. By extrapolation of DCS to zero and 180 degrees scattering angles, integral and momentum transfer cross sections were obtained.

Theory of inelastic electron tunneling intensities which includes a nonconstant barrier potential.

A theory is developed for calculating the intensities of vibrational transitions as observed by inelastic electron tunneling spectroscopy. It includes a more realistic barrier shape than the theories from which it is derived, with the potential varying linearly with position across the barrier rather than remaining constant. This not only is a more realistic model for electrodes of identical metals, but also allows inclusion in the theory of the contact potentials due to dissimilar electrodes. The new theory is compared to an older model for the test case of the hydroxyl ion, and the frequency dependence of intensities is found to be reversed, with significant implications for interpretation of fits to experimental data.

Scattering of high‐energy electrons and x‐rays from molecules: The 10‐electon series Ne, HF, H2O, NH3, and Ch4

AbstractThe elastic, inelastic, and total intensities for x‐ray and high‐energy electron scattering from the 10‐electron systems Ne, HF, H2O, NH3, and CH4 have been calculated by using SCF‐MO wave functions obtained with double‐zeta quality bases of Gaussian contractd wave functions. The effect of molecular binding and various other trends and systematics in the intensities have been examined with the help of difference functions computed between the present scattering intensities and those for the indpendent atom model (IAM).

Resonant and kinematical enhancement of He scattering from LiF(001) surface and pseudosurface vibrational normal modes.

One-phonon cross sections calculated from sagittally polarized vibrational normal modes account for most salient inelastic-scattering intensities seen in He-LiF(001) 〈100〉 and 〈110〉 measurements published by Brusdeylins, Doak, and Toennies. We have found that most inelastic intensities which cannot be attributed to potential resonances can be explained as kinematically enhanced scattering from both surface and pseudosurface bulk modes.

Off-specular and out-of-plane vibrational electron energy loss spectra of benzene and pyridine adsorbed on Pt(110)

The VEEL spectra of benzene, deuterobenzene, and pyridine adsorbed on Pt(110) at room temperature have been examined in emission planes both coincident with and orthogonal to the plane of incidence. The inelastic peak intensities are found to be almost independent of angle in both directions. This implies that neither of the established mechanisms, nor others presently examined, is an adequate description of the scattering. It also leads to a reassignment of the benzene spectrum.

Origin and structure of streaks in reflection high-energy electron diffraction experiments

An expression for one-phonon inelastic scattering of a high-energy electron beam has been obtained which is different from those of earlier workers. Numerical results for Ag(111) surface are very compatible with the recent experimental results for total (elastic plus inelastic) intensity. The structure seen in the streaks originates mainly from the penetration of the electron beam in the bulk.

Inelastic background intensities in XPS spectra

The inelastic background intensity associated with experimental XPS peaks from polycrystalline Cu, Ag and Au samples is evaluated. This signal is compared to the result of the frequently used technique in which the background at any energy is assumed proportional to the integrated intensity at higher energy with the condition that the background matches the spectrum outside the region of the peak. In all cases studied this latter signal was found to be markedly different from the inelastic background signal determined in the present work. The inelastic signal is found to increase slowly within the region of an XPS peak. For narrow peaks it accounts for only a small fraction of the measured intensity on the low energy side of the peak. At larger energy distance to the peak inelastic processes contribute an increasingly larger fraction to the signal and may, 20–30 eV from the peak, account for more than half of the intensity. The inelastic background intensity in the Ag 3d spectrum is found to account for all measured intensity beyond ∼ 70 eV from the peak energy. It is argued that qualitatively these results are expected to be of general validity.

Elastic and Inelastic Scattering of Gamma Rays from V3Si

The elastic and inelastic components of y-ray scattering from a non-transforming VaSi single crystal have been measured using a 57CO Mossbauer source and resonant absorber. The system places an upper limit of � 4 x 10 - 8 e V on the possible energy transfer which distinguishes inelastic from elastic scattering. The scattering at the (440) Bragg reflection with q = 0 and q - 0�1 A -1 has been measured as a function of temperature for two orthogonal orientations of the crystal. Anomalous changes in the elastic and inelastic intensities have been observed. It is suggested that these changes are associated respectively with central mode and soft mode aspects of the dynamics of the vanadium atoms.

Quasiclassical trajectory studies of rigid rotor–rigid surface scattering. I. Flat surface

Rotationally inelastic transition intensities are calculated for a model N2 rigid rotor–rigid flat surface at initial collision energies of 104 and 3800 meV and for many initial beam orientations. The interaction potential is a Morse function modulated by a term which depends on the rotor orientation angle. The calculations are based on the quasiclassical trajectory method and a distorted trajectory perturbation theory. At the low collision energy the rotational excitation is mediated by the attractive part of the potential and by the repulsive part at high energies. The collision dynamics is direct in both energy regimes, however, quite complicated in the former one. Rotational rainbows are clearly observed for the high energy collisions.

Comparison of experimental and theoretical intensities of inelastic electron tunneling spectra for thiourea

A comparison of experimental and calculated inelastic electron tunneling intensities for several modes of thiourea are reported. The measurements were made on aluminum-aluminum oxide-lead tunnel junctions doped with thiourea. The partial charge model of Kirtley, Scalapino and Hansma was used to calculate the relative intensities of each mode. The best agreement between the two sets of intensities occurred when the CS bond was oriented perpendicular to the oxide, the structure was non-planar, and the separation between the molecule and the image plane formed by the lead electrode was about 1.6 Å. The orientation was such that the sulfur was bonded to the aluminum oxide and the plane formed by the SCNN atoms was perpendicular to the surface.

Comparison of experimental and theoretical intensities of inelastic electron tunneling spectra for thiourea

Abstract A comparison of experimental and calculated inelastic electron tunneling intensities for several modes of thiourea are reported. The measurements were made on aluminum-aluminum oxide-lead tunnel junctions doped with thiourea. The partial charge model of Kirtley, Scalapino and Hansma was used to calculate the relative intensities of each mode. The best agreement between the two sets of intensities occurred when the CS bond was oriented perpendicular to the oxide, the structure was non-planar, and the separation between the molecule and the image plane formed by the lead electrode was about 1.6 A. The orientation was such that the sulfur was bonded to the aluminum oxide and the plane formed by the SCNN atoms was perpendicular to the surface.

Kikuchi patterns in transmission electron diffraction

Abstract It was stated by Thomas and Humphreys (1970) that the inelastic electron intensity in a direction K in transmission electron diffraction may be calculated by summing, with appropriate weight factors, the elastic intensities in directions K + g taking K as the incident electron wave-vector. Starting from first principles we derived an exact single-scattering inelastic intensity expression. From this intensity expression it is easily seen that, neglecting some interference terms, the inelastic intensity may be described approximately in the form given by Thomas and Humphreys. Analytical expressions are derived for the weight, factors introduced by these authors.

A Study of Gamma-Ray Diffraction Caused by Thermal Diffuse Scattering in KCl Single Crystal Using the Mössbauer Effect

Dips of the inelastic intensity profiles in 200, 400 and 600 Bragg reflections from a KCl crystal were observed by means of Mossbauer diffraction using 14.4 keV γ-rays and a position sensitive detector. It is concluded that the dips are caused by the thermal diffuse scattering of γ-rays which is reflected secondarily by the net planes in the same crystal.