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AbstractModern nuclear physics software is well validated, providing advanced capabilities to support the engineering of the future generations of fission and fusion reactors. Transport simulators can model the transport of neutrons through reactor geometries, and inventory codes can accurately predict transmutation and activation. Meanwhile, material modeling applies a variety of techniques to understand how structural damage and composition changes will alter the properties of materials, ultimately limiting their usable lifetime in a reactor. Bridging the gap between nuclear simulation tools and materials modeling is a necessary step if these lifetimes are to be accurately predicted, which, for fusion, is critical to provide the necessary assurance of commercial viability. SPECTRA-PKA is a tool developed to compute the rates of structural damage source events, i.e. the primary knock-on atoms (PKAs), using the same nuclear data as used by transport and inventory simulations. Now, it has been interfaced with the binary collision approximation code SDTrimSP, allowing those PKA events, distributed spatially and temporally in an atomic system, to be converted into damage cascades. This computational infrastructure provides insight into the variation in damage distributions between different materials under the same nuclear environment. Example simulations for materials under fusion reactor conditions demonstrate how the rich detail of the nuclear environment can be applied directly to modeling, without the need for integral-average measures that omit those details. [ABSTRACT FROM AUTHOR]

In a joint experimental and modeling effort, we have studied 15 keV Ar 2 + , Kr 2 + , and Xe 2 + projectiles scattering off a polycrystalline Ru surface to assess the possible role of surface roughness in the apparent near-absence of the single-collision (SC) peak for Xe, the heaviest of the ions. The surface roughness of the Ru sample was determined by atomic force microscopy (AFM). The AFM image is used as input to simulations by means of the ray tracing code SPRAY. The observed spectra display a significant SC peak in the energy distributions of reflected Ar and Kr ions, which is not the case for Xe. The energy spectrum produced by the reflection of Xe and recoiled Ru ions closely corresponds to the results obtained from our SPRAY simulations. It is evident that surface roughness plays a crucial role in the visibility of the SC peak. From simulations for different target roughnesses, it is clear that a concentrated distribution of inclination angles centered around 2° effectively reduces the intensity of the single-collision peak for Xe ion scattering. The presence of a distinct SC peak for Ar and Kr ions, unlike Xe ions, supports the notion that the absence of a prominent SC peak in Xe ion scattering is not primarily due to geometric blocking of trajectories by surface roughness. This suggests that for slow, heavy ions like Xe, scattering effects arising from the nearest neighbors to the binary collision partner are significant and should be carefully examined. [ABSTRACT FROM AUTHOR]

The evolution of triangular surface structures with different sizes, the roughening of initially smooth surfaces, and the smoothing of initially rough surfaces were studied by computer simulations for sputtering by 5 keV argon on copper at normal incidence as a function of incident fluence. The program SDTrimSP-2D was used in binary collision approximation, diffusion was neglected. As already predicted by Sigmund [J. Mater. Sci.1973, 8, 1545], a triangular ridge is relatively stable under bombardment at low fluences. However, at fluences above a critical fluence, it eventually flattens out and finally disappears. Initially smooth surfaces get rougher during bombardment, the roughness increases as the square root of incident fluence. This effect is more pronounced for larger metaparticle sizes. Initially rough surfaces get smoother by sputtering, the final smoothness depends on the initial degree of roughness. The smoothing process follows a characteristic pattern with smaller-scale roughness disappearing first and larger-scale roughness remaining stable until higher fluences. This effect gets visible in the Fourier-spectrum of the rough surface as damping of higher frequencies. [ABSTRACT FROM AUTHOR]

The sputtering yield of atoms removed from a solid upon ion irradiation can be calculated using Monte Carlo simulations based on the binary collision approximation. These simulations rely on the assumption of a planar surface potential barrier similar to the work-function for electron emission. Although this model yields good agreement with experimental data, the surface binding energy often has to be arbitrarily adjusted. We propose the bulk binding energy model to calculate sputter yields using sublimation enthalpies and a spherically symmetric potential barrier at the position where the sputtered atoms are generated in the bulk. A planar potential barrier at the surface no longer exists. We also consider the energy density deposited in nuclear collisions, which may lead to a lower sublimation enthalpy compared to standard room temperature conditions. The new bulk binding energy model is able to quantitatively explain many experimental sputtering data. [ABSTRACT FROM AUTHOR]

Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Ultra-low energy ion implantation has become an attractive method for doping of two-dimensional materials and ultra-thin films. The new dynamic Monte Carlo program IMINTDYN based on the binary collision approximation allows a reliable prediction of low energy implantation profiles and target compositional changes, as well as efficient simulation of high energy light ion scattering. To demonstrate the quality of these predictions and simulations, we present a model case experiment where we implanted W ions into tetrahedral amorphous carbon with low (10 keV) and ultra-low (20 eV) ion energies and analyzed the W implantation profiles with high resolution Rutherford backscattering spectrometry (HR-RBS). This experiment is compared with a complete simulation of all aspects of ion-solid-interactions of the experiment using the new IMINTDYN program. A unique novel simulation option, also relevant for implantation into 2D materials, is the inclusion of the vacancy as target species with dynamic vacancy generation and annihilation. Whereas simulations neglecting vacancy formation cannot reproduce the measured implantation profiles, we find excellent agreement between simulated and measured HR-RBS spectra. We also demonstrate the important role of simultaneous weak collisions in the binary collision approximation at low projectile energies.

The vacancy production behavior for a broad range of incident ion-target combinations were examined by using both the full cascade (F-C) and quick calculation of damage (Q-C) options of Stopping and Range of Ions in Matter (SRIM-2013) code. Vacancy production for each option was evaluated using both the convenient vacancy text file in SRIM, and by manual manipulation of the energy transfer, ionization, and phonon text file data to calculate the depth-dependent damage energy for the Norgett-Robinson-Torrens (NRT) defect production model. The F-C vacancy text file method was observed to overpredict vacancy production by a factor of ~1.1 to 4 times when compared to values calculated using the F-C damage energy method or either of the SRIM Q-C methods. Based on our extensive data set obtained for 142 unique bombarding ion-target combinations, we show that the SRIM F-C vacancy text file method should not be used for vacancy production calculations. This error appears to be due to mischaracterization within the SRIM F-C option of some near-threshold replacement events as vacancies instead of replacements. Use of the latest SRIM stopping powers in the SRIM F-C approach provides a better calculation of electronic and nuclear stopping compared to the Lindhard stopping power analytical approximation used to calculate the damage energy of recoil atoms in the SRIM Q-C option, and therefore SRIM F-C approach is deemed to provide the best accuracy for vacancy production (within the binary collision approximation) as long as the damage energy method is used. Alternately, the SRIM Q-C option using either the vacancy.txt or damage energy method provides relatively fast calculation speeds with moderate quantitative differences from the F-C damage energy results (~0 to ~ 30% for the investigated ion-target cases). [ABSTRACT FROM AUTHOR]

The dependence of the reflection coefficient on the form of the atom—surface interaction potential for the D—W system was found. Potentials with different potential well depths were considered. Calculations were carried out by simulating projectile trajectories and in the binary collision approximation. [ABSTRACT FROM AUTHOR]

We develop a new method using binary collision approximation simulating the Rutherford backscattering spectrometry in channeling conditions (RBS/C) from molecular dynamics atom coordinates of irradiated cells. The approach allows comparing experimental and simulated RBS/C signals as a function of depth without fitting parameters. The simulated RBS/C spectra of irradiated Ni and concentrated solid solution alloys (CSAs, NiFe and NiCoCr) show a good agreement with the experimental results. The good agreement indicates the damage evolution under damage overlap conditions in Ni and CSAs at room temperature is dominated by defect recombination and migration induced by irradiation rather than activated thermally.

We present experimental and simulation data on the oblique angle scattering of heavy Sn ions at 14 keV energy from a Mo surface. The simulations are performed with the binary collision approximation codes TRIM, TRIDYN, TRI3DYN, SDTrimSP, and IMSIL. Additional simulations were performed in the molecular dynamics framework with LAMMPS. Our key finding is the absence of an expected peak in the experimental energy spectrum of backscattered Sn ions associated with the pure single collision regime. In sharp contrast to this, however, all simulation codes we applied do show a prominent single collision signature both in the energy spectrum and in the angular scatter pattern. We discuss the possible origin of this important discrepancy and show in the process, that widely used binary collision approximation codes may contain hidden parameters important to know and to understand. [ABSTRACT FROM AUTHOR]

Simulations based on the binary collision approximation (BCA) are in principle less accurate than molecular dynamics (MD) simulations. In this work, we present a comprehensive comparison between BCA and MD for Si ions impinging on a (0 0 1)-Si surface by comparing "channeling maps", i.e., projected ranges of the ions as a function of incidence direction in a representative part of the angular space. We find quantitative differences to develop as the energy decreases below ∼ 100 eV, but find qualitative agreement down to ∼ 10 eV. Moreover, the quality of the BCA channeling maps depends on the implementation of the BCA, which is explained in terms of double-hits and missed collisions. [ABSTRACT FROM AUTHOR]

Atom redistribution is an important mechanism of ion bombardment induced spontaneous pattern formation in amorphous or amorphized targets. It may be characterized by either molecular dynamics (MD) simulations or by Monte Carlo (MC) simulations based on the binary collision approximation (BCA). In this work we analyze problems of the BCA approach in predicting atom redistribution by comparing MC and MD simulations of recoil events in amorphized Si. We find that the MC results critically depend on the displacement energy used, on the choice of the free flight paths and maximum impact parameters, and on the construction of the trajectories. Moreover, the net atom redistribution as determined by MD is significantly larger for recoils starting near the surface than for bulk recoils. The effect is not reproduced by the MC simulations. [ABSTRACT FROM AUTHOR]

In this paper, both the fifth-order Runge–Kutta numerical scheme and binary collision approximation are used to study the phase shift. Both numerical and theoretical results are shown that the solitary wave after head-on collision propagates along the chain behind the reference wave in both even and odd numbers of grain chains. It is the well-known feature of the appearance of the phase shift. Those results are in agreement with the experimental results. Furthermore, it is found that the phase shift is not only related to the collision position of the waves, but also to the position where the time is measured. The value of phase shift increases nonmonotonously with increasing the velocity of the opposite propagation of the wave. Binary collision approximation is applied to analyze the phase shift, and it is found that theoretical results agree well with numerical results, especially in the case of phase shift in odd chain. [ABSTRACT FROM AUTHOR]

Highlights • A Frame work for quantification of defects in Lithium Ceramics for DT reactor neutron spectrum. • PKA energy spectra for Li, Ti and O in Li 2 TiO 3 and corresponding defect distribution in ITER TBM have been obtained. • The average of Li, Ti, O PKAs are 680, 120 and 320 keV respectively in ITER TBM. • The collision cascade simulation shows the expected Bragg peak for the number of defects created. Abstract Lithium based ceramics (Li 2 TiO 3 , Li 4 SiO 4 etc.) in the packed pebble form, used in breeder blankets to breed tritium, are promising candidates for future fusion reactors. Neutron induced trap sites in the ceramic breeder affect the diffusion and inventory of tritium and thereby influence the quantity of tritium recovered. In the present work, a multi model framework has been employed to quantify the number of defects, which can be used to evaluate trap-sites, due to neutron irradiation in porous Li 2 TiO 3 pebbles. This framework is based on a three stage calculation viz. (i) radiation transport, (ii) obtaining the primary knock-on atom (PKA) energy spectrum and (iii) quantifying the ensuing damage by collision cascade simulations. The output of one stage is coupled to the next stage and finally the defect distribution is obtained. We use radiation transport calculations to obtain the neutron spectrum in ceramic pebbles. This is used as an input to SPECTER, a code that uses evaluated cross-sections, to obtain the Primary Knock-on Atom (PKA) energy spectrum. The PKA energy spectrum is then used to find the number and distribution of vacancies and displacements in porous Li 2 TiO 3 pebbles using binary collision approximation (BCA) based Monte Carlo simulations. The vacancy distribution and the number of vacancies in Li 2 TiO 3 have been evaluated for the ITER neutron source using the above frame work. The PKA energy spectrum of Li, Ti and O PKAs, have been obtained using SPECTER, and their average energies are 680, 120 and 320 keV respectively. The collision cascade simulations shows the expected Bragg peak for the number of defects created and has a range of 6–8 microns for O and Li PKA respectively and a fraction of a micron for Ti PKA. The total number of displaced atoms which is equal to the number of vacancies, at the end of the collision cascades, obtained using the above framework has also been used to estimate the displacements per atom (dpa) in Li 2 TiO 3 and this shows a good agreement with the dpa calculated using the NRT model. [ABSTRACT FROM AUTHOR]

A procedure for simulating the scattering of atomic particles at amorphous and crystalline targets is described in the binary collision approximation. The influence of thermal vibrations, choice of the potential, and the inclusion of inelastic energy losses are analyzed using the simulation of hydrogen-atom scattering at a tungsten surface as an example. The coefficients of reflection from crystalline, polycrystalline, and amorphous surfaces are compared. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A BCA-MD method with adaptive volume to simulate cascades in solids is proposed. • The MD cell is adapted and optimized for each cascade using BCA results. • The BCA-MD reproduces very well the different phases of cascades. • The speedup of MD calculations achieved by the BCA-MD increases with the PKA energy. • A speedup of ×312 was estimated for a PKA energy of 0.5 MeV in Fe. Abstract We present a method combining the Binary Collision Approximation (BCA) and Molecular Dynamics (MD) with adaptive volume to simulate high-energy collision cascades in solids under irradiation. The results obtained with the BCA-MD method with adaptive volume are in very good agreement with those obtained with full MD calculations. The BCA-MD predicts very well in a broad range of Primary Knock-on Atom (PKA) energies the different phases of evolution of the cascade, the number of Frenkel pairs, the fraction of point defects in clusters and their size distribution. The BCA-MD method proposed here achieves a considerable acceleration of MD simulations with a speedup factor that increases with the PKA energy. For a PKA energy of 80 keV in Fe, the speedup measured is higher than 30. For a PKA energy of 0.5 MeV in Fe, by comparison with MD simulations performed by other authors, we estimate that the BCA-MD accelerates MD simulations by a factor 312. [ABSTRACT FROM AUTHOR]

We used the binary collision approximation code Marlowe to simulate displacement cascades in tantalum monocarbide. We investigated the damage production, the spatial configurations of the resulting defects, and the vacancy clustering. Statistics over 5000 cascades were accumulated, and primaries with kinetic energies up to 20 keV were launched from lattice sites. Elastic collisions between atoms were modeled by the universal Ziegler-Biersack-Littmark, Molière, and Born-Mayer potentials. The Lindhard-Scharff-Schiott theory was used to account for the inelastic energy losses. Principal components analysis was utilized to evaluate the volume of the damaged zone. Analysis of the simulation results shows that no more than 40% of the displaced Ta and C atoms constitute permanent damage. The number of surviving tantalum Frenkel pairs is about twice the carbon one. The cascade volume distributions deviate from a Gaussian distribution showing high degree of dispersion. Only small vacancy clusters are observed within the investigated range of the primary energies, and 33% of the produced vacancies are considered as isolated point defects in 20 keV cascade. [ABSTRACT FROM AUTHOR]

Fractal-TRIDYN (F-TRIDYN) is an upgraded version of the Monte Carlo, Binary Collision Approximation code TRIDYN for simulating ion-surface interactions. F-TRIDYN adds an explicit model of surface roughness and additional output modes for coupling to both plasma and material codes. Code-coupling represents a compelling path toward whole-device modeling, especially for future fusion reactors. Whole device models need to span length and time scales of many orders of magnitude. Atomic processes in materials that occur on the order of picoseconds, such as changes to surface morphology, will have an effect on fusion plasma performance over many hours of operational time. Conversely, interactions with the plasma will drive chemical, thermal, and morphological processes in the material. Simulating this complex interaction between the plasma and the plasma-facing material demands fast interfaces between material and plasma codes. F-TRIDYN is a flexible code for simulating atomic-scale ion-surface interactions, which are responsible for interactions between plasma and surface such as sputtering and implantation. F-TRIDYNs surface roughness model allows the effect of surface roughness on ion-surface interactions to be simulated. Surface roughness can significantly alter sputtering yields and other ion-surface interaction quantities. Understanding the role surface roughness plays in Plasma-Material Interactions will be crucial to modeling the performance of future fusion reactors such as ITER. F-TRIDYN is also suited for the simulation of a wider range of plasma-surface interactions where surface morphology may play a role, including those utilized for sputter-coating and plasma treating applications. [ABSTRACT FROM AUTHOR]

We develop a new method using binary collision approximation simulating the Rutherford backscattering spectrometry in channeling conditions (RBS/C) from molecular dynamics atom coordinates of irradiated cells. The approach allows comparing experimental and simulated RBS/C signals as a function of depth without fitting parameters. The simulated RBS/C spectra of irradiated Ni and concentrated solid solution alloys (CSAs, NiFe and NiCoCr) show a good agreement with the experimental results. The good agreement indicates the damage evolution under damage overlap conditions in Ni and CSAs at room temperature is dominated by defect recombination and migration induced by irradiation rather than activated thermally. IMPACT STATEMENT A new method simulating the Rutherford backscattering Spectrometry in channeling conditions (RBS/C) was proposed.The RBS/C simulations reveal that the radiation damage buildup in Ni, NiFe and NiCoCr was dominated by athermal defect reactions. [ABSTRACT FROM AUTHOR]

Fractal TRIDYN (F-TRIDYN) is a modified version of the widely used Monte Carlo, Binary Collision Approximation code TRIDYN that includes an explicit model of surface roughness and additional output modes for coupling to plasma edge and material codes. Surface roughness plays an important role in ion irradiation processes such as sputtering; roughness can significantly increase the angle of maximum sputtering and change the maximum observed sputtering yield by a factor of 2 or more. The complete effect of surface roughness on sputtering and other ion irradiation phenomena is not completely understood. Many rough surfaces can be consistently and realistically modeled by fractals, using the fractal dimension and fractal length scale as the sole input parameters. F-TRIDYN includes a robust fractal surface algorithm that is more computationally efficient than those in previous fractal codes and which reproduces available experimental sputtering data from rough surfaces. Fractals provide a compelling path toward a complete and concise understanding of the effect that surface geometry plays on the behavior of plasma-facing materials. F-TRIDYN is a flexible code for simulating ion-solid interactions and coupling to plasma and material codes for multiscale modeling. [ABSTRACT FROM AUTHOR]

Displacement damage caused by ions or neutrons in microelectronic devices can have significant effect on the performance of these devices. Therefore, it is important to predict not only the displacement damage profile, but also its magnitude precisely. Analytical methods and binary collision approximation codes working with amorphous targets use the concept of displacement energy, the energy that a lattice atom has to receive to create a permanent replacement. It was found that this “displacement energy” is direction dependent; it can range from 12 to 32 eV in silicon. Obviously, this model fails in BCA codes that work with crystalline targets, such as Marlowe. Marlowe does not use displacement energy; instead, it uses lattice binding energy only and then pairs the interstitial atoms with vacancies. Then based on the configuration of the Frenkel pairs it classifies them as close, near, or distant pairs, and considers the distant pairs the permanent replacements. Unfortunately, this separation is an ad hoc assumption, and the results do not agree with molecular dynamics calculations. After irradiation, there is a prompt recombination of interstitials and vacancies if they are nearby, within a recombination radius. In order to implement this recombination radius in Marlowe, we used the comparison of MD and Marlowe calculation in a range of ion energies in single crystal silicon target. The calculations showed that a single recombination radius of ∼7.4 Å in Marlowe for a range of ion energies gives an excellent agreement with MD. [ABSTRACT FROM AUTHOR]