Binary Collision Approximation Research Articles

A Monte Carlo algorithm for degenerate plasmas

A procedure for performing Monte Carlo calculations of plasmas with an arbitrary level of degeneracy is outlined. It has possible applications in inertial confinement fusion and astrophysics. Degenerate particles are initialised according to the Fermi–Dirac distribution function, and scattering is via a Pauli blocked binary collision approximation. The algorithm is tested against degenerate electron–ion equilibration, and the degenerate resistivity transport coefficient from unmagnetised first order transport theory. The code is applied to the cold fuel shell and alpha particle equilibration problem of inertial confinement fusion.

Erosion of beryllium under high-flux plasma impact

Be sputtering yields, measured by weight loss, in PISCES-B are a factor of 5–10 less than that predicted by binary collision approximations. Measurements show the BeO surface is removed early in the plasma bombardment. Modeling of molecular ions (D2+ and D3+) species and redeposition cannot explain the difference. Surface morphology that evolves during the exposure reduces the sputtering yield by a factor of 2–3. Plasma fuel atoms retained in the surface decrease the sputtering yield compared to calculations of a pure Be surface. These effects may explain the measured erosion rates in the absence of Be impurities within the plasma. By introducing Be impurity ions into the plasma, it is possible to simulate a controllable amount of redeposition. The weight loss from eroding Be targets, with Be seeding, is unchanged until the concentration of Be ions in the plasma greatly exceeds the sputtering yield in the non-beryllium seeded exposure.

Comparison of molecular dynamics and binary collision approximation simulations for atom displacement analysis

Molecular dynamics (MD) and binary collision approximation (BCA) computer simulations are employed to study surface damage by single ion impacts. The predictions of BCA and MD simulations of displacement cascades in amorphous and crystalline silicon and BCC tungsten by 1keV Ar+ ion bombardment are compared. Single ion impacts are studied at angles of 50°, 60° and 80° from normal incidence. Four parameters for BCA simulations have been optimized to obtain the best agreement of the results with MD. For the conditions reported here, BCA agrees with MD simulation results at displacements larger than 5Å for amorphous Si, whereas at small displacements a difference between BCA and MD arises due to a material flow component observed in MD simulations but absent from a regular BCA approach due to the algorithm limitations. MD and BCA simulation results for crystalline W are found to be in a good agreement even at small displacements, while in crystalline Si there is some difference due to displacements in amorphous pockets.

Cooperative effect of electronic and nuclear stopping on ion irradiation damage in silica

Radiation damage by ions is conventionally believed to be produced either by displacement cascades or electronic energy deposition acting separately. There is, however, a range of ion energies where both processes are significant and can contribute to irradiation damage. The combination of two computational methods, namely binary collision approximation and molecular dynamics, the latter with input from the inelastic thermal spike model, makes it possible to examine the simultaneous contribution of both energy deposition mechanisms on the structural damage in the irradiated structure. We study the effect in amorphous SiO2 irradiated by Au ions with energies ranging between 0.6 and 76.5 MeV. We find that in the intermediate energy regime, the local heating due to electronic excitations gives a significant contribution to the displacement cascade damage.

Atomistic simulations of MeV ion irradiation of silica

We used molecular dynamics simulations to study 2.3MeV Au ion irradiation of silica. In this energy regime, the energy loss of the ion is divided almost equally between electronic and nuclear energy loss. The inelastic thermal spike model was used to model the electron–phonon interactions due to the high electronic energy loss. Binary collision approximation calculations provided input for the recoil energies due to MeV ions. We performed simulations of the damage due to the separate damage mechanisms as well as together, and found that the inelastic thermal spike is needed to accurately simulate the irradiation damage from MeV ions.

Modelling of target effects in reactive HIPIMS

In reactive High Power Impulse Magnetron Sputtering (HIPIMS) of oxides, target effects such as reduced surface oxidation during pulse off time, increased implantation of reactive gas due to the higher discharge voltage as compared to normal DC sputtering, and enhanced target cleaning during on time are considered to be responsible for the differences compared to reactive DC sputtering. These effects are assumed to cause changes in the target oxide coverage and hence lead to the hysteresis shifts observed in experimental studies. In this contribution, the target processes are simulated using the binary collision approximation code TRIDYN. Using an Al target sputtered in Ar+O2 mixture as a model system, a range of pulse configurations is simulated for different oxygen partial pressures. The results indicate that the target effects alone are not sufficient to explain the observed shift of hysteresis and its frequency dependence.

Simulation of silicon surface-pattern formation under irradiation with 1-keV Ar ions

Simulation has been used to model the formation of the amorphous Si surface pattern under 1-keV Ar ion irradiation. Cascades have been calculated in the binary-collision approximation; density relaxation is due to defect diffusion in the field of their interaction. The morphology of the formed pattern significantly depends on the inclusion of atomic displacement under the solid surface.

Modelling of sputtering yield amplification in serial reactive magnetron co-sputtering

Serial magnetron co-sputtering can be used to increase the deposition rate in reactive deposition of thin films. The increase in deposition rate is achieved by sputtering yield amplification through doping the sputtering target by a heavy element. The dopant is introduced by means of sputtering from an auxiliary target onto a rotating primary magnetron. During sputtering of the primary target, the dopant is implanted into the target surface. Here we present a model describing the serial co-sputtering technique. The model is based on the binary collision approximation and takes into account the dynamical sputtering and mixing at the target surface. As an example, W and Bi doping in reactive sputter deposition of Al2O3 is analyzed. W is shown to be very efficient dopant which can increase the deposition rate for oxide up to 100% with 1.6at.% of W in the resulting coating. Doping by Bi is not very effective due to the low surface binding energy of Bi. The simulations show that sputtering yield amplification can be realized in the serial co-sputtering setup with rotating magnetrons.

Distribution of transverse chain fluctuations in harmonically confined semiflexible polymers

Two different experimental studies of polymer dynamics based on single-molecule fluorescence imaging have recently found evidence of heterogeneities in the widths of the putative tubes that surround filaments of F-actin during their motion in concentrated solution. In one [J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchesner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)], the observations were explained in terms of the statistics of a worm-like chain confined to a potential determined self-consistently by a binary collision approximation, and in the other [B. Wang, J. Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010)], they were explained in terms of the scaling properties of a random fluid of thin rods. In this paper, we show, using an exact path integral calculation, that the distribution of the length-averaged transverse fluctuations of a harmonically confined weakly bendable rod (one possible realization of a semiflexible chain in a tube), is in good qualitative agreement with the experimental data, although it is qualitatively different in analytic structure from the earlier theoretical predictions. We also show that similar path integral techniques can be used to obtain an exact expression for the time correlation function of fluctuations in the tube cross section.

Transport coefficients in strongly coupled plasmas

Transport coefficients for Coulomb collision processes in correlated plasmas are calculated within the binary collision approximation. Considering plasmas with flowing Maxwellian distributions and Debye screened particle potentials as an example, it is shown that the friction and energy exchange densities are similar to those in weakly coupled plasmas, but a generalized Coulomb logarithm, Ξ(Λ), is required. This asymptotes to lnΛ in the weakly coupled limit, but is significantly modified when Λ≲102 due to large angle collisions. The results show excellent agreement with molecular dynamics simulations of temperature relaxation.

Binary collision approximation for solitary wave in periodic dimer granular chains

We study solitary wave propagation in periodic dimer granular chains of beads with the same material but different sizes by binary collision approximation. This kind of chain which is called N:1 dimer consists of pairs of N big beads and one small bead. First we present a method to map the actual chain into an effective chain, then use the binary collision approximation to obtain the transmitted solitary wave speed, the total time taken by the pulse to pass through the chain, and the frequency of oscillation of the small particle. Frequency of oscillation, which increases with the decrease of the radius of the small particle, is analytically obtained. And the results are in excellent agreement with numerical results. For the total time of the pulse passing through the chain, the results of theoretical analysis is in good agreement with numerical results when N 2. The relative error seems no change with the chain length but becomes larger with the increase of the value of N.

Two Kinds of Localized Oscillating Modes in Strongly Nonlinear Hertzian Chains with Defect

We study mechanical energy localization, which has been experimentally observed by Job [Phys. Rev. E 80 (2009) 025602(R)], using computer simulations and the binary-collision approximation. We find interactions of a solitary wave with a light intruder exciting two kinds of localized modes. One is visible in the tail of the incident impulse, and the other is observed when the defect is loaded by the solitary wave. The frequency of localized oscillations is analytically obtained and is in excellent agreement with the numerical results.

Ion-beam mixing in crystalline and amorphous germanium isotope multilayers

Gallium (Ga) implantation induced self-atom mixing in crystalline and amorphous germanium (Ge) is investigated utilizing isotopically controlled Ge multilayer structures grown by molecular beam epitaxy. The distribution of the Ga ions and the ion-beam induced depth-dependent mixing of the isotope structure was determined by means of secondary ion mass spectrometry. Whereas the distribution of Ga in the crystalline and amorphous Ge is very similar and accurately reproduced by computer simulations based on binary collision approximation (BCA), the ion-beam induced self-atom mixing is found to depend strongly on the state of the Ge structure. The experiments reveal stronger self-atom mixing in crystalline than in amorphous Ge. Atomistic simulations based on BCA reproduce the experimental results only when unphysically low Ge displacement energies are assumed. Analysis of the self-atom mixing induced by silicon implantation confirms the low displacement energy deduced within the BCA approach. This demonstrates that thermal spike mixing contributes significantly to the overall mixing of the Ge isotope structures. The disparity observed in the ion-beam mixing efficiency of crystalline and amorphous Ge indicates different dominant mixing mechanisms. We propose that self-atom mixing in crystalline Ge is mainly controlled by radiation enhanced diffusion during the early stage of mixing before the crystalline structure turns amorphous, whereas in an already amorphous state self-atom mixing is mediated by cooperative diffusion events.

Tube-width fluctuations of entangled stiff polymers

The tubelike cages of stiff polymers in entangled solutions have been shown to exhibit characteristic spatial heterogeneities. We explain these observations by a systematic theory generalizing previous work by Morse [Phys. Rev. E 63, 031502 (2001)]. With a local version of the binary collision approximation, the distribution of confinement strengths is calculated, and the magnitude and the distribution function of tube radius fluctuations are predicted. Our main result is a unique scaling function for the tube radius distribution, in good agreement with experimental and simulation data.

How to Combine Binary Collision Approximation and Multi-Body Potential for Molecular Dynamics

Our group has been developing a hybrid simulation of the molecular dynamics (MD) and the binary collision approximation (BCA) simulation. One of the main problems of this hybridization model is that the multi-body potential suddenly appears at the moment when the simulation method switches from the BCA to the MD. This instantaneously emerged multi-body potential causes the acceleration or deceleration of atoms of the system. To solve this problem, the kinetic energy of atoms should be corrected to conserve the total energy in the system. This paper gives the solution. The hybrid simulation for hydrogen atom injection into a graphite material is executed in order to demonstrate the solution.

Epitaxial growth of Ge nanoislands on Si/Ge heterostructure by ion-assisted MBE method

The ion-assisted molecular beam epitaxy (MBE) method allows for construction of self-assembling quantum dot structures in a controllable manner. In the present work we have clearly observed the dependence of the formation behaviour of Ge nanoislands on the ion energy during ion-assisted MBE deposition of Ge on a silicon substrate. In our experiment, we have employed the partial ionization of the Ge atom flow, with the following acceleration of the ions to the desired energy. The best quantum dot structure (the smallest size and the densest population of the nanoislands) has been achieved at the ion energy of 1keV. We suggest a theoretical model, which describes the process of ion-assisted formation of Ge nanoislands on the surface. In order to estimate the effect of radiation damage on the process of nanoisland formation we performed computer simulation of the cascades in the binary collision approximation and by means of molecular dynamics technique.

Kinetic Monte Carlo Study on the Suppression of Boron Transient Enhanced Diffusion with Carbon Pre-Implant

We report our kinetic Monte Carlo (kMC) study of the effect of carbon co-implantation on the pre-amorphization implant (PAI) process. We employed the BCA (binary collision approximation) approach for the acquisition of the initial as-implanted dopant profile and the kMC method for the simulation of the diffusion process during the annealing. The simulation results implied that carbon co-implantation suppress boron diffusion due to recombination with interstitials. Also, we could compare boron diffusion with carbon diffusion by calculating the reaction of carbon atoms with interstitials, and we found that boron diffusion was affected by the carbon co-implantation energy by enhancing the trapping of interstitials between boron atoms and interstitials. Our KMC simulation implies that the probability of boron's encounterance with interstitial is reduced due to the carbon trapping between boron and an interstitial and that the effectiveness of co-implanted carbon as a interstitial trap is maximized at an implantation energy of 3 keV.

Characterization of ion-irradiation-induced defects in multi-walled carbon nanotubes

We study the effects of Ar+, He+ and C+ ion irradiation on multi-walled carbon nanotubes at room and elevated temperatures with transmission electron microscopy (TEM) and Raman spectroscopy. Based on the TEM data, we introduce a universal damage scale for the visual analysis and characterization of irradiated nanotubes. We show for the first time that the amount of irradiation-induced damage in nanotubes is larger than the value predicted for bulk materials using the simple binary collision approximation, which may be associated with higher defect production due to electronic stopping in these nanoscale systems. The Raman spectra of the irradiated samples are in qualitative agreement with the TEM data and indicate the presence of irradiation-induced defects. However, it is difficult to obtain quantitative information on defect concentration due to non-uniform distribution of defects in the nanotube films and in part due to the presence of other carbon nanosystems in the samples, such as graphitic crystallites and carbon onions.

Study of the fragmentation of a displacement cascade into subcascades within the Binary Collision Approximation framework

When a material is subjected to irradiation, many primary defects are created at the atomic level by sequences of ballistic collision events to form highly disordered regions defined as displacement cascades. The long term evolution of materials under irradiation is dictated by the number and the spatial distribution of the surviving defects in the displacement cascade. The peculiar power law shape of collision cross sections is responsible for the fractal feature of atomic trajectories set and then the fragmentation of a displacement cascade into smaller subcascades. We present a criterion to describe the fragmentation of a displacement cascade into subcascades and to calculate the volume fraction of subcascades in the overall cascade due to this fragmentation. Such a volume fraction then provides a natural framework to estimate the efficiency of different projectiles to induce phase transformation or amorphisation in solids under irradiation. From this definition of the fragmentation of a displacement cascade, this work gives some new insights to compare different irradiations performed with different particles.

An MD simulation to form an NV-N center using N 2 implantation into diamond

We have examined the dissociation process of a low-energy molecular beam making use of an empirical molecular dynamic simulation. The main concern was to explain why two (nitrogen molecule N 2) beams with different energy (sub-keV and keV) give a similar intrapair distance R N-N in diamond. It was due to the peculiar dependence of the lateral range straggling on the incident energy across a few keV. When a sub-keV (N 2) beam was implanted into a diamond, the dissociation elapsed a long time until it was settled in several hundreds fs because of multiple collisions. The range distribution caused by multiple collisions is almost isotropic whereas it becomes anisotropic when used a (N 2) beam with the higher energy than that. From the viewpoint of computation, a few keV is a critical energy to choose an algorithm MD or MC with binary collision approximation. For the case of sub-keV N 2 beam, MD is indispensable. This proved the reason of the apparent contradiction. Much later than the collision stage, a definite change further occurred in the long-range-order of the crystal at around 2 ps in diamond. It seems a phonon-assisted phenomenon would start then and might affect on the further events to be occurred later than 20 ps.