Atomic Strings Research Articles

Computer simulation of the reflection of energetic ions from crystal surfaces at glancing incidence

A two-dimensional classical dynamics model for calculation of the reflection coefficient for scattering of keV beams at glancing incidence using potentials with cylindrical symmetry is presented. The target in the model consists of a single layer or two layers of atomic strings and reflects the (1 1 1) surface in the most open [1 1̄ 0], direction. The critical transverse energy of several primary ions for total reflection (100% reflection) from the surface is determined for Al, Ag, Au, Cu, Ni and Pt crystal (1 1 1) surfaces. The results are obtained using cylindrical potentials constructed from recently updated “individual” ion–surface interaction pair potential. We compare the results of the simulation with the 2-D row-model to experimental data for the energy losses. The model most suitable for describing these data is the Oen–Robinson empirical formula for the inelastic losses. Various expressions for the position-dependent friction force as a function of the local electron density are investigated. For the last simulation, the electron density is averaged over the atomic rows in a manner similar to the construction of cylindrical potentials according to Lindhard's theory. The simulations with the 2-D row-model are available as a compact computer code with good visualization.

Dynamic Chaos Phenomenon at Axial Channeling and Over-Barrier Motion of Relativistic Ions in Crystals

Characteristics of relativistic ion motion through a crystal near one of the crystal axes are discussed. The main features of such motion in a crystal are compared for protons and for highly charged ions. The possibility of bending of relativistic ion beams due to their multiple scattering on atomic strings in a bent crystal is discussed.

X-ray standing wave and ion scattering studies on Au-implanted LiNbO 3(0001) single crystals

X-ray standing wave and combined Rutherford backscattering spectrometry and channeling experiments have been performed on Au-implanted and annealed (0001)-oriented LiNbO 3 single crystals. At an ion dose of ⋍ 1 × 10 15 cm −2 confined in a 117 nm thick (FWHM) layer, resulting in a Au Nb ratio of ≅ 5 × 10 −3, no significant cluster formation has been observed. Most of the Au atoms have been found to lie on the c-axis of the LiNbO 3 structure. However, they do not occupy a single lattice site. Rather they appear to be distributed over several sites on the [0001] atomic strings, which contain Nb, Li and structural vacancy sites. A small fraction (∼ ca. 20%) of the Au atoms appear to be displaced from the threefold symmetry axis - most likely at tetrahedral sites. The possibility of this fraction of Au atoms existing as small clusters like dimers or trimers cannot be ruled out.

Pair production by 5–150 GeV photons in the strong crystalline fields of germanium, tungsten and iridium

Experimental results for pair production by 20–150 GeV photons in a Ge crystal cooled to 100 K are presented. The results include total and differential enhancements for incidence of the photons along the (1 1 0) plane with angles 0–4.5 mrad to the 〈1 1 0〉 axis. For the first time, a comparison can be made with theoretical results which for incidence along the plane predict pronounced structural changes of a resonance type in the pair production yield as a function of angle to the axis. These changes originate from the coherent interaction with the strong field of the atomic strings in the crystal. Furthermore, results for pair production by 5–55 GeV photons in W and Ir crystals at temperatures between 100 and 300 K are presented. These results are for total enhancements with photons incident along the strongest axes in these materials, i.e. the 〈1 1 1〉 axis in W and the 〈1 1 0〉 axis in Ir. A clear disagreement with theoretical curves calls for improved calculations.

Total reflection of energetic ions from crystal surfaces at glancing incidence

A two-dimensional classical dynamics model for calculating the reflection coefficient of keV-ion beams backscattered from a crystal surface at glancing incidence is presented. The target is considered as consisting of one or two layers of atomic strings. A string potential of cylindrical symmetry was constructed by using the well-known iuniversali pair potential or the Molire interatomic potential. The critical transverse energy needed for a 100% reflection of light ions from the surface is assessed for the most open (11 _ 0) direction of Cu(111), Ni(111), and Al(111) crystal surfaces. The distribution of the backscattered ions on the azimuthal scattering angle exhibits the multimode structure related to the zig-zag trajectories in surface semichannels. The energy spectra are compared to the experimental data. The simulations show that the reflection coefficient is substantially dependent on the interatomic potential used but is not much affected by the model adopted for description of the inelastic losses. The inelastic-interaction model affects mostly the energy peak position, so that an estimate based on OennRobinson empirical formulae compares better with the experimental data than the original Firsov model. Resume : Nous prOsentons un modle de dynamique classique en 2-D pour calculer le

Heavy ion channeling

We discuss recent experiments on heavy ion channeling at high energies. Resonant-capture and loss of electrons has been studied by measurement of the charge state of ions transmitted through a thin Si crystal. The energy loss has been used to define the transverse energy of axially channeled ions and to measure the strength of the resonant processes as a function of transverse energy. We therefore first discuss briefly the average energy loss and the straggling in energy loss for channeled and random penetration. Dielectronic KLL capture (inverse KLL Auger emission) has been measured in the energy range 12–18 A MeV for Br 33+ (He like) ions and the observed dependence of the resonance strength on transverse energy is consistent with the calculated variation of the density of valence electrons seen by the ions. Coherent excitation leading to electron loss has been measured for Si 13+ (H like) ions channeled along a 〈111〉 axis at about 21.7 A MeV, where the energy in the ion rest frame of virtual photons in the 7th harmonic of the axial potential matches the energy of the transition of the bound electron from the ground state to the first excited state. A detailed theoretical discussion of this process is given. The dependence on transverse energy is very strong because the field decreases rapidly with distance from an atomic string. There is good agreement between calculations and experiment, both concerning the dependence of the strength of the resonance on transverse energy and concerning the Stark splitting, which is caused mainly by the zero'th harmonic of the transverse force from 〈111〉 atomic strings.

Channeling, bremsstrahlung and pair creation in single crystals

On the following pages, I shall describe various directional effects associated with the penetration of energetic charged particles through single crystals in directions close to low-index crystallographic directions, that is, close to low-index axes and planes. In particular, I shall focus on the special case of channeling: In channeling, the charged particles are so closely aligned with, say, an axis that their motion is completely governed by many correlated collisions with lattice atoms and their flux is prevented from being uniform in the space transverse to the considered crystal direction. In the interaction with a given atomic row or string, a projectile deflects as off a continuum string obtained by smearing the atomic charges uniformly along the string direction (\(\overset{\wedge }{\mathop{z}}\,\)). The interaction with the crystal is, in lowest approximation, through a z-independent continuum potential.

Influence of electromagnetic radiation on the angular distributions of electrons in oriented crystals

The influence of high energy photon emission on angular distributions of electrons moving close to the atomic strings in single crystals has been studied. It has been shown that radiation makes the angular distribution broarder as compared with the case when no photon emission occurs. This is due to the increase in the critical angle for channeling and due to the enhancement of the role played by multiple scattering as the beam energy decreases. New experimental results have been analysed. The self-focusing effect due to the radiation cooling is discussed in detail.

Coherent radiation under regular and chaotic motion of relativistic electrons and positrons in crystals

Coherent radiation of relativistic electrons and positrons under regular and chaotic patterns of particle motion in a periodic field of atomic strings of a crystal is considered. The motion pattern has been shown to affect substantially the coherent radiation of particles in the crystal.

The Structure of a Metastable Au–Sn Phase Determined by Convergent Beam Electron Diffraction

The structure of a new metastable Au–Sn phase was determined by convergent beam electron diffraction. Micrometer-sized crystals were grown by heating a metal/oxide/metal trilayer and allowing the metals to react. The new phase was tetragonal with space groupP4/nbm, lattice parametersa= 6.63(3) Å andc= 5.92(3) Å, and composition AuSn4. The phase was found to be isostructural with PtPb4with Au atoms located at 2(a) sites and Sn atoms at 8(m) sites. Conditional Patterson transforms parallel to thec-axis were calculated from the quasi-kinematic intensities of first-order Laue zone (FOLZ) reflections diffracted from Bloch states localized on the Sn atom strings. The contour maps showed clear peaks from Au–Sn and Sn–Sn interatomic vectors. A least-squares refinement using the FOLZ reflections gave the Sn atomic parameters asx= 0.167(1),z= 0.25(4).

Nonlinear motion of crack tip atoms during cleavage processes

Nonlinear features of cleavage processes under mode I loading are explored from an atomic scale. Crack tip atom string models coupling with the continuum mechanics analysis are devised. As the stress intensity factor increases, dynamic analysis shows that the atom motion at a crack tip changes from quasi-periodic to chaotic and back to quasi-periodic. The chaotic atom motion characterizes a cleavage precursor in which the inter-atomic bond disintegrates under certain adhesion.

Nonlinear motion of crack tip atoms during dislocation emission processes

Nonlinear features of dislocation emission processes under mode II loads are explored from an atomic scale. Crack tip atom string models coupling with the continuum mechanics analysis are devised. Dynamic analysis shows that the atom motion at the crack tip changes from periodic to chaotic, as the mode II stress intensity factor increases. The chaotic atom motion dictates the dislocation nucleation process at the crack tip. Study on the dislocation emission band reveals the phenomenon of cloudlike drifting of the dislocation core ahead of the crack tip.

High-angle electron scattering from amorphous silicon

Channeling occurs when fast electrons follow atomic strings in a crystal where there is a minimum in the potential energy (1). Channeling has a strong effect on high-angle scattering. Deviations in atomic position along a channel due to structural defects or thermal vibrations increase the probability of scattering (2-5). Since there are no extended channels in an amorphous material the question arises: for a given material with constant thickness, will the high-angle scattering be higher from a crystal or a glass?Figure la shows a HAADF STEM image collected using a Philips CM20 FEG TEM/STEM with inner and outer collection angles of 35mrad and lOOmrad. The specimen (6) was a cross section of singlecrystal Si containing: amorphous Si (region A), defective Si containing many stacking faults (B), two coherent Ge layers (CI; C2), and a contamination layer (D). CBED patterns (fig. lb), PEELS spectra, and HAADF signals (fig. lc) were collected at 106K and 300K along the indicated line.

Multiple scattering of ultrahigh-energy charged particles on atomic strings of a bent crystal

A theory of multiple scattering of fast charged particles on atomic strings of a bent crystal located parallel to one of the crystal axes is proposed. These conditions are obtained when overbarrier particles can deflect, guided by the crystal axis bending. This phenomenon is shown to provide for the bending of positively as well as negatively charged particles at angles that exceed considerably the critical angle of axial channeling.

Atomic String Potentials and the Form of [0001] Zone Axis Patterns of GaS, GaSe and InSe

The relationship between the form of hexagonal zone axis patterns and the projected atomic potential is explored as a method for polytype identification of GaS, GaSe and InSe. As the various known polytypes of these materials project to give unit cells with very different simple-string potentials this relationship may be exploited by making use of previous related work. It is found that this method is simple to apply and consistent with the results of more conventional analyses based on the symmetry of convergent beam electron diffraction patterns. Growth faults could, however, cause ambiguities in the method of analysis. Microsc. Microana 1. Microstruct.

Electron-diffraction channeling effect on defect formation in Si with 〈110〉 zone-axis incidence

We describe the electron-diffraction channeling effect on displacement damage for zone-axis incidence, in which the 1s-type “bound” Bloch wave localized at the atomic strings plays an essential role. Based on this consideration of the defects introduced in a high-resolution high-voltage electron microscope, we have examined the nature, the depth distribution and the structure of the small defects on {111} in Si, which are introduced by electron (1MeV) irradiation with 〈110〉 zone-axis incidence and appear inhomogeneously in a wedge-shaped single crystal. According to simulation of images and electron current density, it is suggested that the defects are created near the electron exit surface. The planar void model for the defect accounts for the features of the observed images.

Crystal rainbows in the cases of square very thin crystals with one atomic string per primitive cell

The transmission of H + ions through the 〈100〉 very thin crystals of 28 elements with the body-centered, face-centered or diamond-type cubic structures starting with C and finishing with Th is studied; the ion energy is 10 MeV, and the crystal thicknesses are 100 nm. These are the cases of square very thin crystals with one atomic string per primitive cell. In this study we use the Lindhard's continuum potential in the crystal as the “exact” one, and model the crystal rainbow effect by the 4X 9 catastrophe. The analysis is focused on the dependences of the parameters of the model continuum potential in the crystal on the position of the element in the periodic table of elements.

Deflection of high energy particles during multiple scattering by atomic strings of a bent crystal

Simulation results of high energy particle passage through thick bent crystals near the crystal axis are reported. The bending of positively and negatively charged particles by a bent crystal is shown to occur due to multiple scattering by the atomic strings. It is established that bending is possible for regular as well as chaotic motion of particles in the periodic field of atomic strings of a crystal. The beam is shown to split into several beams separated in angle.

A new method for producing high energy gamma-quanta with circular polarization

Spectral-angular and polarization properties of the gamma-radiation produced by ultrarelativistic electrons in an aligned monocrystal are investigated. An efficient source of circularly polarized gamma-quanta of high energy may be created on the ground of collimating in certain directions the coherent radiation of electrons scattered by atomic strings of a crystal.

Structure of a metastable Al-Ge phase determined from large angle CBED patterns

Abstract The structure of a new metastable Al-Ge phase recrystallized at 300°C from amorphous films with equiatomic composition deposited on to NaCl substrates cooled with liquid nitrogen was determined by convergent beam electron diffraction (CBED). The micron-sized crystals were tetragonal with space group 14/mcm, lattice parameters a = 6.13 Å and c = 4.92 Å, and composition Al0·9 Ge0·9. The structure was the C16 type with nominal AB 2 composition, although there was no evidence for preferential location of Ge on either A or B sites. The A atoms occupied 4(a) sites, and the B atoms were located on 8(h) sites with x = 0·158. Conditional Patterson transforms parallel to the c axis were calculated from kinematic intensities measured in focused large-angle CBED patterns. The contour maps showed clear peaks from A-B and B-B interatomic vectors. Dynamical perturbations reduced peak visibility but did not affect peak positions. The x parameter for B atoms was refined from the quasi-kinematic intensities of first-order Laue zone reflections diffracted from Bloch states localized on B atom strings in conventional CBED patterns.