Focusing of electrons reflected from layered crystal

The mechanism of the formation of the diffraction patterns upon inelastic reflection of mean-energy electrons from the VSe₂(0001) layered crystal has been investigated. It is found that the strong scattering of electrons by short atomic chains of the Se-V-Se layer triads leads to the weakening of electron focusing and the enhancement of diffraction scattering in deeper layers, which gives rise to the Kikuchi lines. It is demonstrated that, at an energy of 2 keV, the diffraction pattern is adequately described by the cluster model of single scattering. The atomic structure of thin near-the-surface layer of VSe₂ has been investigated by the computer simulation of experimental data.     

Most probable and average energy losses of the beam of monoenergetic charge particles with average and low energies at multiple scattering

The results of statistical modeling of the discrete process of multiple inelastic scattering are presented. This process is modeled to find the most probable and average energy losses of a beam of charged particles (electrons and protons) passing through a material layer with a given thickness. The proposed approach is based on determining the most probable energy loss at single small-angle scattering, on including the effect of the statistical probability on this quantity at multiple scattering, and on determining the average number of inelastic interactions for particles in a film with a known thickness. The dependence of the particle energy lost during interaction with atomic electrons on their relative motion is taken into account for low-energy particles. A new interpretation is offered for the parameter J in the logarithmic term in the formulas for the average and most probable energy losses of charged particles. A computational scheme for this parameter as an average potential energy of atomic electrons is given.     

Simultaneous energy analysis in a large angular range: A novel neutron spectrometer,its resolution and applications

A new type of crystal spectrometer for elastic and inelastic neutron scattering has been set up by modifying an existing flat-cone diffractormeter at the BER II-reactor in Berlin (West). The main difference to conventional triple axis spectrometers is the analyser part. It consists of large crystal plates which reflect the neutrons out of the horizontal plane into a curved multicounter. This allows simultaneous measurements in a large and continuous range of scattering angles for a constant energy transfer. The resolution function has been calculated and compared with experimental results. There is the possibility to focus acoustical phonons. We present applications together with experimental results such as quasielastic diffuse scattering in orientationally disordered crystals and inelastic scattering due to acoustical phonons. In combination with the flat-cone technique all elastic and inelastic scattering events of a single crystal can be collected in a systematic and efficient way.in collaboration with the Hahn-Meitner Institut, Berlin (West)     

Elastische Energieverluste kristallgestreuter Elektronen

Elastic energy losses due to scattering of fast electrons (20–40keV) by crystals into large angles (≧45⁰) are experimentally and theoretically investigated. Energy losses up to a few electron volts appear, which depend on the mass of the atoms composing the crystal, of the scattering angle, and of the primary energy of the electrons. These results agree with the assumption of elastic scattering by single atoms and not by the crystal as a whole. The width of the energy losses increases with the energy loss himself, and with the temperature of the crystal. In a first theoretical approximation this effect can be explained by the thermal motion of free atoms.     

Dynamische Theorie der elastischen Elektronenbeugung unter Verwendung komplexer Atomformfaktoren

The two-beam approximation of dynamic electron diffraction in crystals is deduced from successive scattering by two-dimensional gratings. The scattering-amplitude caused by the single grating (phase-grating) is determined by the atomic scattering factors of the single atoms. The use of real atomic scattering factors leads here to the same solutions as the twobeam theory, using the Schroedinger-equation. Anomalous absorptions effects are described in the usual theory by introducing a complex lattice potential into the Schroedinger-equation, taking into account inelastic scattering. A more exact calculation of only elastic scattering by a single atom results in complex atomic scattering factors. Using the complex atomic scattering factors one can describe the anomalous absorption, if recursion-formulae for successive scattering are applied. On the other hand, the transformation to differential equations leads to results, which are not in agreement with experiments. The influence of inelastic scattering for the anomalous absorption can be neglected compared with the complex atomic scattering factors.     

Elastic and inelastic diffraction of Mössbauer γ-rays from KCN

Mössbauer γ-ray diffraction was used to discriminate between the elastic and inelastic scattering intensities from the (1 1 1) to (5 5 5) Bragg reflections of a single crystal of KCN. The energy resolution of our experiment was 28 neV. We observe pronounced inelastic peaks at each Bragg point, while the elastic scattering dies out rapidly due to a large Debye-Waller factor. Thus in case of (4 4 4) and (5 5 5) the inelastic scattering is larger in magnitude than the elastic one.     

Ranges and profiles of distribution of low-energy ions channeling in metal and semiconductor single crystals

In the present work peculiarities of trajectories and energy losses, ranges and profiles of distribution of low-energy different-mass ions channeling in thin single crystals of metals and semiconductors have been thoroughly studied by computer simulation in binary collision approximation. The character of oscillations of channeled-ion trajectories depending on their energies, aiming points from the axis of a channel, kind of interaction potential, crystal lattice type and temperature has been determined. It has been found that, in the case of light ions even at low energy, the main contribution to energy loss is made by inelastic energy losses, whereas for heavy ions, already at E < 10 keV, elastic energy losses exceed inelastic ones. Profiles of the distribution of channeled ions have been calculated depending on crystal lattice type, kind of ions and their energy.     

Comparative analysis of characteristic electron energy loss spectra and inelastic scattering cross-section spectra of Fe

The inelastic electron scattering cross section spectra of Fe have been calculated based on experimental spectra of characteristic reflection electron energy loss as dependences of the product of the inelastic mean free path by the differential inelastic electron scattering cross section on the electron energy loss. It has been shown that the inelastic electron scattering cross-section spectra have certain advantages over the electron energy loss spectra in the analysis of the interaction of electrons with substance. The peaks of energy loss in the spectra of characteristic electron energy loss and inelastic electron scattering cross sections have been determined from the integral and differential spectra. It has been shown that the energy of the bulk plasmon is practically independent of the energy of primary electrons in the characteristic electron energy loss spectra and monotonically increases with increasing energy of primary electrons in the inelastic electron scattering cross-section spectra. The variation in the maximum energy of the inelastic electron scattering cross-section spectra is caused by the redistribution of intensities over the peaks of losses due to various excitations. The inelastic electron scattering cross-section spectra have been analyzed using the decomposition of the spectra into peaks of the energy loss. This method has been used for the quantitative estimation of the contributions from different energy loss processes to the inelastic electron scattering cross-section spectra of Fe and for the determination of the nature of the energy loss peaks.     

Neutron scattering studies of crystal structure and crystalline electric field in high-Tc ErBa2Cu3Ox disordered by fast neutron irradiation

The crystal structure and the crystalline-electric-field splitting of the Er³⁺ 4f-shell in the high-T_c superconductor ErBa₂Cu₃O_x (x = 6.95, 6.18) disordered with fast neutron irradiation has been investigated by elastic and inelastic neutron scattering techniques, respectively. The results yield evidence for the absence of a charge transfer between the planes and chains under disorder and point to the atomic displacements being the main radiation-induced defects in the CuO₂ planes.     

The scattering of thermal neutrons by crystals

The present article describes some experiments with thermal neutrons to investigate a variety of properties of crystals. Elastic scattering of the neutrons, like Bragg scattering of X-rays, helps to determine the atomic structure of crystals, and is particularly useful for locating light atoms, such as hydrogen, where X-rays fail. It also gives information on the arrangement of electron spins and the density distribution of unpaired electrons in magnetic atoms. Measurement of the change in energy of the neutrons in inelastic scattering gives the frequencies of the normal modes of vibration of the crystal, which are related to the interatomic forces. For magnetic crystals, inelastic scattering also gives the frequencies of spin waves, which depend on the magnetic interactions between the atoms. The article concludes with an account of the experimental techniques of thermal neutron scattering.     

Distorted wave theory of scattering of nucleons with intermediate energies on nuclei

In the context of nonrelativistic theory in the distorted wave approximation, a three-dimensional form of analytical expression for the differential cross section of scattering of nucleons with intermediate energies on atomic nuclei is derived. In the context of this theory, the main parameters of elastic scattering of protons with incident energy of 1 GeV on the ²⁰⁸Pb nucleus are determined. For inelastic scattering of protons with nuclear surface vibrations, giant multipole resonances in the excited nucleus are investigated for the collective nucleus model. The energy losses of the scattered proton are calculated together with the energies of giant dipole and quadrupole resonances and nuclear surface vibration energy. This allows the deformation parameter of the excited nucleus to be calculated.     

Optical constants of Cu measured with reflection electron energy loss spectroscopy (REELS)

Two energy loss spectra of 1000 and 3000 eV electrons reflected from a Cu surface are analysed to give the normalized distribution of energy losses in a single surface and volume inelastic scattering process. These single scattering loss distributions are subsequently fitted to theoretical expressions for the differential inverse inelastic mean free path (DIIMFP) and differential surface excitation probability (DSEP) providing the real and imaginary part of the dielectric function in terms of a set of Drude-Lorentz oscillators. The optical constants obtained in this way are subjected to several sum rule checks and compared with other experimental data and with density-functional-theory (DFT) calculations. The present optical data agree excellently with the DFT-results, while the earlier optical data deviate significantly from these two data sets for energies below 30 eV. The mean free path for inelastic electron scattering for energies below 2000 eV is derived from the dielectric data and is found to agree satisfactorily with values reported earlier.     

Atom scattering as a probe of the surface electron-phonon interaction at conducting surfaces

An atomic projectile colliding with a surface at kinetic energies in the thermal or hyperthermal range interacts with and is reflected by the electronic density well in front of the first layer of target atoms, and it is generally accepted that the repulsive interaction potential is proportional to the density of electrons extending outside the surface. This review develops a complete treatment of the elastic and inelastic scattering of atoms from a conducting surface in which the interaction with the electron density and its vibrations is treated using electron-phonon coupling theory. Starting from the basic principles of formal scattering theory, the elastic and inelastic scattering intensities are developed in a manner that identifies the small overlap region in the surface electron density where the projectile atom is repelled. The effective vibrational displacements of the electron gas, which lead to energy transfer through excitation of phonons, are directly related to the vibrational displacements of the atomic cores in the target crystal via electron-phonon coupling. The effective Debye-Waller factor for atom-surface scattering is developed and related to the mean square displacements of the atomic cores. The complex dependence of the Debye-Waller factor on momentum and energy of the projectile, including the effects of the attractive adsorption well in the interaction potential, are clearly defined. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known electron-phonon coupling constant λ. This treatment reproduces the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the mode specific mass correction components λ_Q,ν defined by the relationship λ = 〈λ_Q,ν〉. The intensities of elastic diffraction peaks are shown to be a weighted sum over the λ_Q,ν, and the Debye-Waller factor can also be expressed in terms of a similar weighted summation. In the simplest case the Debye-Waller exponent is shown to be proportional to λ and for simple metals, metal overlayers, and other kinds of conducting surfaces values of λ are extracted from available experimental data. This dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the electron-phonon coupling constant λ shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density.     

Inelastic collisions of medium energy atomic elements in solids

The stopping of medium atomic elements in solids has been calculated in the framework of classical approximation, taking into account elastic and inelastic collisions. The calculations are based on the 1) revised equations for the law of energy and impulse conservation, which were earlier used to describe inelastic collisions of atomic particles, 2) theory of quasi-small angle scattering, 3) power potential of LNS, and 4) limitation of the maximum distance of atoms approach determined by the interatomic distance in solids. Analytical equations have been obtained to calculate 1) a differential cross-section of elastic scattering in the presence of inelastic collisions, 2) energy transferred, 3) cross-sections of elastic and inelastic stopping, and penetration depth. Implantation into solids was found to be of threshold character.     

Combined nuclear-molecular resonance inelastic scattering of x rays

We report on theoretical and experimental studies of nuclear inelastic scattering in a molecular crystal, whose atoms experience both molecular and lattice vibrations. In this case scattering proceeds as combined nuclear-molecular resonance inelastic scattering. The lattice vibrations give rise to inelastic scattering around the molecular resonances with an energy dependence identical to that around the nuclear resonance. The incoherent nature of the scattering in the molecular resonances results in a proper balance of elastic and inelastic components, which has important implications for studies of heterogeneous systems.     

Lattice dynamics and inelastic neutron scattering experiments on andalusite,Al2SiO5

We report coherent inelastic neutron scattering measurements of the phonon dispersion relations and lattice dynamics shell model calculations of several microscopic and macroscopic properties of andalusite, Al₂SiO₅. Andalusite has an orthorhombic structure with 32 atoms/unit cell. The inelastic neutron scattering measurements (up to energy transfers of 45 meV) were carried out using the triple axis spectrometer at Dhruva reactor, India using a single crystal of andalusite and the phonon dispersion relations along the [100] direction have been measured. The shell model calculations have been used to compute the crystal structure, elastic constants, phonon frequencies, dispersion relations, density of states and the specific heat. The calculated results are in good agreement with available experimental data. The computed one-phonon neutron scattering structure factors based on the shell model have been very useful in the planning and analysis of the inelastic neutron scattering experiments.     

Equivalence of the boson peak in glasses to the transverse acoustic van Hove singularity in crystals

We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.     

Simulation of multiple scattering in argon ion collisions with an aluminum target at grazing angles of 5°–10°

A model for calculating the atom scattering from a polycrystalline surface consisting of randomly oriented single crystals is proposed. In the calculation it is possible to distinguish the contribution of scattering from any surface layer, and it also takes into account inelastic energy losses in primary ion collisions with target atoms. A comparison with the measurements shows that the proposed model well describes the peak positions in the energy spectra of the scattered atoms. A comparison of the calculated and experimental peak-to-background ratios for scattering from polycrystalline and amorphous targets allows a conclusion to be made about the degree of order of surface layers in the material under investigation.     

Gas moderation of positrons

A variety of low-energy positron experiments need an improved brilliance of the beam by means of a remoderator. Conventionally, a tungsten foil or single crystal is used as a remoderator in transmission or reflection geometry. We have developed a new remoderation unit which is based on inelastic positron scattering and the drift of positrons in nitrogen gas. In first measurements we succeeded in detecting fully thermalized positrons. High positron losses occurred at the entrance of the gas cell, and therefore the injection of positrons will be improved for next measurements.