Moliere Potential Research Articles

Computational Study on Characteristic Radiation Originated from Channeled Relativistic Electrons in Single-Wall Carbon Nanotubes

I calculated the number of bound states n for channeled electrons through single wall carbon nanotubes (n,m) at different values of electrons energy by using (Wetzel, Kramer's, Brillouin approximation)(WKB) method. The calculations executed according to the continuum model approximation given by Lindhard for the case of an axial channeling in single crystals. The estimated results of the maximum number of bound states of the channeled electrons in a zigzag (n, 0), armchair (n,n) and chiral(n,m) nanotubes have been performed using the Moliere potential. In this work we determined the emitted photon energy due to n, (n-1) transitions between higher -quantum states as a function of the electron energy up to 500 MeV. Also the energy levels of electrons channeled in different types of single wall carbon nanotubes by using Moliere potential were defined. It has been showed that the emitted photon energy in the forward direction is the energy difference between the successive initial and final states of the channeled electron. The energy of the emitted channeling radiation has been calculated for incident electron at 50 MeV. We calculated the emitted channeling radiation for incident electrons at 10, 50 and500 MeV with frequency in X-ray range.

Analysis of the Results of Silicon Sputtering Simulation as Functions of Different Ar–Si Potentials

The influence of the form of the Ar–Si interatomic potential on the results of simulating the physical sputtering of amorphous Si by low-energy Ar ions is analyzed. The yields of Si sputtering by Ar ions with an energy of 50–300 eV at normal incidence are calculated using the molecular dynamics (LAMMPS software) and the Monte Carlo methods by means of the MOTREV program developed at the Skobeltsyn Institute of Nuclear Physics, the Moscow State University, and used quantum-mechanical elastic-scattering cross sections. The semiempirical Moliere and ZBL pair potentials and a potential developed on the basis of density functional theory calculations are applied to describe Ar–Si interaction. The energy dependences of the sputtering yields obtained using different potentials are analyzed in this paper. Conclusions concerning the applicability of the considered Ar—Si interaction potentials to simulation of the physical sputtering of amorphous Si in the indicated range of projectile energies are drawn.

Round‐robin test of medium‐energy ion scattering for quantitative depth profiling of ultrathin HfO2/SiO2/Si films

Medium‐energy ion scattering (MEIS) has been used for quantitative depth profiling with single atomic layer resolution to determine the composition, thickness, and interface structure of ultrathin films and nanoparticles. To assure the consistency of the MEIS analysis, an international round‐robin test (RRT) with nominally 1‐, 3‐, 5‐, and 7‐nm thick HfO2 films was conducted among 12 institutions. The measurements were performed at each participating laboratory under their own conditions, and the collected data were analyzed. For the data analysis, the Moliere potential, the stopping and range of ions in matter (SRIM) 95 and new fitted electronic stopping power and the Chu straggling were used. For analyzing the MEIS data from the magnetic sector and electrostatic analyzers, the neutralization corrections of Marion and Young for 100‐keV H+ and He+ ions and of Armstrong for 400‐ to 500‐keV He+ ions were used. The standard deviations were 5.3% for the composition, 15.3% for the thickness, and 13.3% for the Hf content, and they were improved to 7.3%, 4.5%, and 7.0% by using refitted electronic stopping powers based on the experimental data. Hence, this study suggests that correct electronic stopping powers are critical for quantitative MEIS analysis.

Energy Spectrum of Relativistic Electrons Channeled Through Single-Wall Carbon Nanotubes

The energy eigenvalues of the channeled electrons through single wall carbon nanotubes (n,m) was calculated. According to the continuum model approximation given by Lindhard for the case of an axial channeling in single crystals, the actual periodic potential of a row of atoms is replaced by a potential averaged over a direction parallel to the row, called continuum potential. The calculations was executed by using the atomic interaction potential as given by Moliere potential. The maximum number of bound states and the energy eigenvalues is calculated for positrons of 100 MeV energy incident in a direction parallel to the nanotube axis, by using WKB method. The calculations showed that the effect of temperature by using Debye approximation of thermal vibration amplitude on the channeling potential is very small and gave the same eigenvalues and the same number of bound states as that for the static nanotubes.

Indentation properties of Cu–Zr–Al metallic-glass thin films at elevated temperatures via molecular dynamics simulation

Abstract Metallic glasses, also known as amorphous metals, exhibit unique mechanical properties in terms of their strength and ductility. In this work, molecular dynamics simulation techniques were adopted to construct (Cu50Zr50)100−xAlx thin-film glasses, with x being the atomic percentage of aluminum, through simulated sputter deposition processes. The deposition simulations were conducted with a tight-binding interatomic potential, and argon working gas was modeled by the pair-wise Moliere potential. The calculated radial distribution functions of the films show more amorphous microstructures, consisting distorted icosahedral clusters. The as-deposited films were annealed at various temperature with the NPT ensemble, and aluminum clusters were found at temperature T > 800 K. The formation of the aluminum clusters may be due to the system being trapped into a local energy minimum. For their indentation properties at elevated temperatures, a right-angle conical carbon indenter tip was adopted with the NVT ensemble. No aluminum clusters were found with the NVT ensemble at high temperatures. In addition, the hardness and Young’s modulus show strong temperature dependence above the glass transition temperature. Pileup index, viscosity and elastic anisotropy exhibit anomalies around glass transition temperature.

Mechanical Behavior of Polycrystalline Aluminum under Penetration with Extremely Large Loading Rates via Molecular Dynamics Simulation

In this study, polycrystalline aluminum nanoscale thin sheets are constructed by sputter deposition simulations with the molecular dynamics (MD) simulation. Subsequently, the penetration problem of a conical rigid projectile moving through the aluminum thin sheet is simulated by the MD technique. The MD simulations adopted the interatomic potential of a tight-binding type. During the deposition simulation, in order to include the ion-ion interactions, the pair-wise Moliere potential was adopted to model the interaction between working gas argon and deposited atoms. The as-deposited films did not show clear grain boundaries, but after thermal annealing, grains grow and form nanocrystalline structure with a grain size of 8 nm. The thin sheets consisted of the face-centered cubic phases of crystal unit cells, separated by grain boundaries. For the penetration simulations, four velocities were chosen 102, 103, 104 and 105 m/s. The first two velocities are called high velocity case and the rest two velocities are the hypervelocity case. Our results show that, as the penetration rate increases, more stresses are required to move the projectile through the Al film due to temperature effects from the high velocity to hypervelocity case. In addition, defects, such as dislocations, increase during the projectile penetration. In the high velocity case, the penetrated hole in the film may be recovered, but not in the hypervelocity case. The temperature difference increased in the hypervelocity case is significantly than that in the high velocity case.

Evolution of Mechanical Anisotropy in Nano-scale Metallic-glass thin Films Under Indentation

The mechanical behavior of Cu-Zr-Al metallic-glass thin films under indentation was studied with the molecular dynamics simulation methodology to investigate changes of microstructures through degrees of elastic anisotropy. In this work, the (Cu50Zr50)100-xAlx, where x is measured by atomic percentage, was studied by molecular dynamics (MD) simulation. Our metallic-glass models were first sputter-deposited on crystalline substrate by MD with consideration argon working gas. The interaction between argon working gas and metallic atoms was modeled by the pair-wise Moliere potential. The as-deposited films were amorphous after equilibration, and their mechanical properties were characterized by ultra-nano-indentation simulations by MD with a right-angle diamond conical indenter tip, as well as a strain perturbation method to identify full elastic constants under the tip. Through region-by-region probes of the elastic properties of the film after being indented, it is found that local elastic anisotropy changes in relation to locations and penetration depth.

Evaluation of screening length corrections for interaction potentials in impact-collision ion scattering spectroscopy

Since in impact-collision ion scattering spectroscopy (ICISS) data analysis the interaction potential represented by the screening length as the screening effect is not satisfactorily established up to the present, we introduce commonly the correction factor in the screening length. Previously, Yamamura, Takeuchi and Kawamura (YTK) have suggested the theory taking the shell effect of electron distributions into account for the correction factor to Firsov screening length in the Moliere potential. The application of YTK theory to the evaluation of screening length corrections for the interaction potentials in ICISS manifested that the screening length corrections calculated by the YTK theory agree almost with those determined by simulations or numerical calculations in ICISS and its variants data analyses, being superior to the evaluation of screening length corrections with the O’Connor and Biersack (OB) formula.

A new screening length for small angle multiple scattering

A new screening length formulation that incorporates the charge state of the projectile is applied to multiple scattering. The present screening length is derived from an interatomic potential that accounts for electron–electron, electron–nuclear, and nuclear–nuclear interactions using the Thomas–Fermi–Moliere potential. We examined the charge state effect on multiple scattering angular distributions. We successfully estimate the charge state effects and predict angular distributions. The present screening length is compared with many low energy ion scattering experiments and with O’Connor–Biersack prediction values.

Molecular dynamics simulation of Cu-Zr-Al metallic-glass films under indentation

In this paper, the (Cu50Zr50)100-xAlx (X=0, 2, 4, 5, 6, 8, 10, 12, atomic percent) metallic-glass thin films on the titanium crystalline substrate were constructed by using molecular dynamics (MD) to simulate sputter deposition. The deposition simulations adopted a tight-binding potential with consideration of argon working gas from the pair-wise Moliere potential. The as-deposited films were amorphous and used as initial structures for nano-indentation simulations with a right-angle conical indenter tip to obtain their mechanical properties. All simulations were carried out at temperature 300 K to compare with experimental data. The radial distribution function of the film is calculated and compared with synchrotron experimental data. From the nanoindentation simulations, the hardness and Young's modulus of the films were calculated, as well as the pileup index under two different depth-to-thickness ratios. Our MD simulation results are consistent with experimental data. Furthermore, atomic strains were calculated to reveal deformation localization. In addition, elastic constants of the film and associated degrees of elastic anisotropy were studied to correlate structural anisotropy and to reveal structural relaxation. It is found that the deposited and MD-equilibrated films have notable anisotropic elastic constants, and their relaxation can be observed at the MD time scales.

Optimization of the Profiles in MeV Implanted Silicon Through the Modification of Electronic Stopping Power

The elements B, P and As can each be implanted in silicon; for the fabrication of integrated semiconductor devices and the wells in CMOS (complementary metal oxide semiconductor). The implanted range due to different implanted species calculated using TRIM (Transport of Ions in Matter) simulation results was considered. The profiles of implanted samples could be measured using SIMS (secondary ion mass spectrometry). In the comparison between the measured and simulated data, some deviations were shown in the profiles of MeV implanted silicon. The Moliere, C-Kr, and ZBL potentials were used for the range calculations, and the results showed almost no change in the MeV energy region. However, the calculations showed remarkably improved results through the modification of the electronic stopping power. The results also matched very well with SIMS data. The calculated tolerances of <TEX>$R_p$</TEX> and <TEX>${\Delta}R_p$</TEX> between the modified <TEX>$S_e$</TEX> of TRIM and SIMS data were remarkably better than the tolerances between the TRIM and SIMS data.

Indentation Behavior of Zr-Based Metallic-Glass Films via Molecular-Dynamics Simulations

Molecular dynamics (MD) models of the Zr-based metallic-glass film (Zr47Cu31Al13Ni9, in atomic percent) were constructed by simulating sputter depositions on the titanium substrate. The as-deposited films were used as initial structures for subsequent nanoindentation simulations. For the deposition simulations, a many-body, tight-binding (TB) potential was adopted for interatomic interactions among the multiple species of atoms. The interactions between the metallic atoms and working gas (Ar+) were modeled with the pairwise Moliere potential. The TB potential parameters for unlike atoms were chosen to be the algebraic average of those for like ones, and hence, the MD simulations provide qualitative information. The deposition simulations revealed an amorphous morphology in the as-deposited films. Indentation simulations with a right-angle conical indenter tip showed a homogeneous flow to form pileups on the surface of the metallic glass around the indent. The pileup index calculated from MD is consistent with that obtained from the experiment. Moreover, our MD results show that the pileup index exhibits anomalies, which are defined as unusual changes in the values of the pileup index, around the experimentally found glass-transformation temperature through in situ indentation simulations at elevated temperatures. From indentation load-displacement curves at various temperatures, indentation modulus and hardness obtained from MD simulations were in qualitative agreement with experimental findings in terms of their decreasing rates with respect to the temperature. Three-dimensional atomic-strain calculations revealed strain localization and propagation of shear bands under the indenter tip at their initial evolution stages after the formation of shear transformation zones. In addition, higher loading rates decrease hardness, cause larger disturbed regions under the indent, and enlarge shear-banding patterns.

Azimuthal scans in LEIS: Influence of the scattering potential

Angular scans were performed for a Cu(100) single crystal and 3keV He+ ions. The results were compared to simulations using the Monte-Carlo code TRIC [R. Andrzejewski, Ph.D. thesis, Universidad Autonóma de Madrid, 2008; V.A. Khodyrev, R. Andrzejewski, A. Rivera, D.O. Boerma, J.E. Prieto, in press] to obtain information on the ion–atom interaction. Different potentials were used in the simulations, e.g. the Thomas–Fermi–Moliere potential with a modified screening length and a Hartree–Fock potential. It was found that the experimental results can be very well reproduced by use of two potentials that exhibit a significantly different distance dependence, when properly scaled. This leads to the conclusion that care must be taken when deducing a scattering potential from comparison of experimental and simulated azimuthal scans.

New method of evaluation for interatomic interaction potential in LEIS with large-angle scattering using the two-atom scattering model

The interaction potential between an incident ion and a target atom in impact-collision ion scattering spectroscopy (ICISS), which is a specialization of low energy ion scattering (LEIS) and its variants, i.e. ICISS with detection of neutrals (NICISS), coaxial ICISS (CAICISS) and impact-collision atom scattering spectroscopy with detection of neutrals (NICASS), has been evaluated by the new method using the dependence of the total scattering angle on the impact parameter for the first collision in the numerical calculations based on the two-atom scattering model (TWASM). From the comparison of determined values of scaling factor for the Firsov screening length by three-dimensional computer simulations with calculated ones by TWASM, it became obviously that the interatomic potentials for the various combinations of an incident ion and a target atom in LEIS are suitably given by the Moliere potential with the reduced Firsov screening length employing the scaling factor obtained in TWASM calculations.

Interatomic potentials between noble gas and Ag atoms from axial surface channeling

He, Ne, and Ar atoms with energies from 3keV to 60keV are scattered from a Ag(111) surface under axial surface channeling conditions. From peaked structures in the angular distributions owing to “rainbow-scattering” we derive effective scattering potentials. We compare the observed rainbow angles with results from computer simulations using different types of established interatomic potentials and focus on a detailed discussion for potential energies larger than 10eV. It turns out that an approximation proposed by O’Connor and Biersack using a Moliere potential with an adjustment of the screening length [D.J. O’Connor, J.P. Biersack, Nucl. Instr. and Meth. B 15 (1986) 14) is in good agreement with the experimental data. In our simulations we investigate the sensitivity of the rainbow angles on a variation of the interatomic potential.

The sine-squared potential and the band structure for channelling effects

The interaction between the charged particle and the crystal is described by quantum mechanics. The schrdinger equation describing a paticle moving in the channel is reduced to Mathieu equation by using a sine-squared potential. The band structure of this system is discussed based on Bloch theorem. The instability zone and the stop-band width are found by the perturbation techniques. It is shown that the width of the 1-st order and 2-nd order instability zones are ΔE1=Kβ/2 and ΔE2=md2p(Kβ)2/16π22, respectively, and this system presents automatical the band structure, which is not present in Lindhard potential and Moliere potentials.

Determination of a correction factor for the interaction potential of He+ ions backscattered from a Cu(1 0 0) surface

We have used coaxial impact collision ion scattering spectroscopy (CAICISS) data collected from 3keV He+ ions backscattered from a Cu(100) surface in different azimuthal orientations to investigate the influence of the screening length on CAICISS polar angle scans. We have compared the experimental data to computer simulations generated with the FAN code and found that for our experimental conditions an exceptionally low value of 0.53 was required for the correction factor to the Firsov screening length used with the Thomas–Fermi–Moliere potential. In addition we found that the Ziegler–Biersack–Littmark potential is not applicable, resulting in incorrect peak positions in the CAICISS polar angle plots.

Interatomic potentials from rainbow scattering of keV noble gas atoms under axial surface channeling

For grazing scattering of keV Ne and Ar atoms from a Ag(111) and a Cu(111) surface under axial surface channeling conditions we observe well defined peaks in the angular distributions for scattered projectiles. These peaks can be attributed to “rainbow-scattering” and are closely related to the geometry of potential energy surfaces which can be approximated by the superposition of continuum potentials along strings of atoms in the surface plane. The dependence of rainbow angles on the scattering geometry provides stringent tests on the scattering potentials. From classical trajectory calculations based on universal (ZBL), adjusted Moliere (O’Connor and Biersack), and individual interatomic potentials we obtain corresponding rainbow angles for comparison with the experimental data. We find good overall agreement with the experiments for a description of trajectories based on adjusted Moliere and individual potentials, whereas the agreement is poorer for potentials with ZBL screening.

Angular dispersion of protons passing through thin metallic films

The angular distributions of protons after traversing thin polycrystalline Al targets (∼15nm) with an incident energy of 10keV have been measured and an analysis of the targets by means of transmission electron microscopy (TEM) techniques has been made. The separate influence of the different crystal characteristics and defects has been evaluated by numerical simulation considering the interaction of the ion with all the nearest neighboring atoms simultaneously. In the analysis we included the evaluation of the effects of lattice vibrations, oxide layers and foil roughness on the angular distributions. Previous experimental data in monocrystalline and polycrystalline Au targets has also been analyzed. For a consistency check a comparison with the results of the MARLOWE code for the simpler case of proton channeling in 〈100〉 Al has been performed. As in the case of Au, the present results indicate that the experiments can be explained in terms of a modified Moliere potential, and confirm the critical influence of crystal characteristics, in this case the amorphous oxide layer on the surface and the thermal vibration of the lattice atoms.

Study of argon characteristics in ion physical vapor deposition using molecular dynamics simulation

This article uses molecular dynamics simulation to investigate the role of Ar ions in the ion physical vapor deposition (IPVD) process for different Ar+-to-Cu+ ratios, and to analyze the influence of different Ar+-to-Cu+ ratios on the trench filling morphology. Also compared are the trench filling morphology observed for the IPVD process with that found in the conventional collimated magnetron deposition process. The molecular dynamics simulation includes a trench model and a deposition model, and uses the many-body, tight-binding potential method to represent the interatomic force acting among neutral atoms. The interatomic force acting between the ions and the neutral atoms is modeled by the pairwise Moliere potential method. The simulation indicates that the incident Ar ions influence the trench filling mechanisms in two significant ways; peeling of the cluster atoms, which promotes migration of the cluster atoms along the sidewall, and breaking of the bridge which forms when two clusters of atoms join. Both phenomena are beneficial since they promote a more complete filling of the trench.