Molecular-dynamics simulation of threshold displacement energies in lithium aluminate

Threshold displacement energies in LiAlO₂ were evaluated using molecular dynamics technique. A pairwise potential model was adopted for simplicity, with reliance on high ionicity of LiAlO₂. In all the three elements, the threshold displacement energy varied considerably depending on the displacement direction of the primary knock-on atom. The average displacement energies of Li, O and Al over 342 displacement directions were evaluated to be 22, 37 and 84 eV, respectively. The order of these values are consistent with the number of generated defects in displacement cascade simulation with initial PKA energy of 1-5 keV, where the number of generated defects was the largest in Li and the smallest in Al in proportion to the number of atoms included in the system, regardless of the initial PKA energy.     

First-principles approach to the properties of point defects and small helium-vacancy clusters in palladium

First-principles calculations based on density functional theory (DFT) have been performed to study the properties of interstitial helium atoms, the vacancy, substitutional, and small helium-vacancy clusters He_mV_n (m, n = 0-4) in palladium. The result indicates that the vacancy has the strongest ability of capturing helium atoms and the octahedral interstitial configuration is more stable than the tetrahedral one, while the energy difference between them is very small. In the palladium crystal, helium atom will migrate from one octahedral interstitial site to another one through the O-T-O path. The formation energies and binding energies of an interstitial helium atom and an isolated vacancy to the helium-vacancy clusters are also determined in palladium. It is found that the formation energies increase with the increasing of helium atoms and the binding energies mainly depend on the helium to vacancy ratio of the clusters rather than the cluster size.     

Modelling of deposition processes on the TiO2 rutile (1 1 0) surface

Deposition of Ti_xO_y clusters onto the rutile TiO₂ (1 1 0) surface has been modelled using empirical potential based molecular dynamics. Deposition energies in the range 10-40 eV have been considered so as to model typical deposition energies of magnetron sputtering. Defects formed as a function of both the deposition energy and deposition species have been studied.The results show that in the majority of cases Ti interstitial atoms are formed, irrespective of whether Ti was contained within the deposited cluster. Furthermore that the majority of these interstitials are formed by displacing a surface Ti atom into the interstitial site. O surface atoms are also relatively common, with Ti and TiO₂ surface units often occurring when the deposited cluster contains Ti but becoming less frequent as the deposition energy is increased. Structures that would give rise to the growth of further layers of rutile are not observed and in the majority of the simulations the energy barriers for diffusion of the end-products is high.     

Molecular dynamics simulation of helium-vacancy interaction in plutonium

The formation energies of small He_nV_m clusters (n and m denote the number of He atoms and vacancy, respectively) in Pu have been calculated with molecular dynamics (MD) simulations using the embedded atom method (EAM) potential, the Mores potential and the Lennard-Jones potential for describing the interactions of Pu-Pu, Pu-He and He-He, respectively. The binding energies of an interstitial He atom, an isolated vacancy and a self-interstitial Pu atom to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. All the binding energies mainly depend on the He-vacancy ratio (n/m) of clusters rather than the clusters size. With the increase of the n/m ratio, the binding energies of a He atom and a Pu atom to a He_nV_m cluster decrease with the ratio, and the binding energy of a vacancy to a He_nV_m cluster increases. He atoms act as a catalyst for the formation of He_nV_m clusters.     

Dependence of cluster ranges on target cohesive energy: Molecular-dynamics study of energetic Au402 cluster impacts

It has long been known that the stopping and ranges of atoms and clusters depends on the projectile-target atom mass ratio. Recently, Carroll et al. [S.J. Carroll, P.D. Nellist, R.E. Palmer, S. Hobday, R. Smith, Phys. Rev. Lett. 84 (2000) 2654] proposed that the stopping of clusters also depends on the cohesive energy of the target. We investigate this dependence using a series of molecular-dynamics simulations, in which we systematically change the target cohesive energy, while keeping all other parameters fixed. We focus on the specific case of Au₄₀₂ cluster impact on van-der-Waals bonded targets. As target, we employ Lennard-Jones materials based on the parameters of Ar, but for which we vary the cohesive energy artificially up to a factor of 20. We show that for small impact energies, E₀ ? 100 eV/atom, the range D depends on the target cohesive energy U, D ∝ U^−β. The exponent β increases with decreasing projectile energy and assumes values up to β = 0.25 for E₀ = 10 eV/atom. For higher impact energies, the cluster range becomes independent of the target cohesive energy. These results have their origin in the so-called ‘clearing-the way’ effect of the heavy Au₄₀₂ cluster; this effect is strongly reduced for E₀ ? 100 eV/atom when projectile fragmentation sets in, and the fragments are stopped independently of each other. These results are relevant for studies of cluster stopping and ranges in soft matter.     

Desorption of gold nanoclusters from gold nanodispersed targets by 200 keV Au5 polyatomic ions in the elastic stopping mode: Experiment and molecular-dynamics simulation

Au nanoislet targets (∅ 2-60 nm) were bombarded by 200 keV polyatomic ions (40 keV/atom), which deposit their energy mainly in the nuclear stopping mode: ∑(dE/dx)_n = 30 keV/nm and ∑(dE/dx)_e = 2 keV/nm. The matter desorbed in the form of nanoclusters was registered by TEM. The total transfer of matter was determined by neutron-activation analysis. The total yield of the ejected gold reached high values of up to 2.6 × 10⁴ atoms per Au₅ ion. The major part (2 × 10⁴ atoms per ion Au₅) of the emission is in the form of nanoclusters. The results are compared with the data of similar experiments with 1 MeV Au₅ (200 keV/atom) and other projectiles. The analysis of the experimental data and the comparison to molecular-dynamics simulation results of the desorption process show that the desorption of Au nanoislets is induced by their melting, build-up of pressure and thermal expansion.     

Temporal development of sputtered atom distributions from Au(1 1 1) targets following bombardment with 100 keV/atom Au2 ions

Recently Bouneau et al. measured the angular and energy distributions of negative Au_n (n=2–7) ions emitted from gold targets following bombardment with swift gold cluster projectiles. They found that the energy distributions could be fitted with a spike-like model, and that the angular distributions were independent of the azimuthal emission angle and relatively strongly forward directed. We have used MD simulations to investigate the temporal development of energy and angular distributions of sputtered atoms from Au(1 1 1) targets following bombardment with 100 keV/atom Au₂ ions. Our results show that during the very early stages of the collision cascade the energy distribution of sputtered atoms is described well by the linear cascade model. Essentially all high energy sputtered atoms are emitted during this phase of the collision cascade. However, the energy distributions of atoms sputtered after 0.5 ps were typical of emission from a thermal spike and could be fitted well with a Sigmund–Claussen model. The polar angle distributions of sputtered atoms were strongly forward directed early in the collision cascade, but became less forward directed as the thermal spike developed.     

Synergism in sputtering of copper nanoclusters on graphite substrate at low energy Cu2 bombardment

Molecular dynamics simulation of Cu cluster sputtering by 50-200 eV/atom Cu₂ dimers and Cu single atoms has been performed. The clusters were located on a (0 0 0 1) graphite surface and consisted of 13-195 atoms. Synergy features were identified in the sputtering yield and energy distributions of sputtered particles calculated for the cases of cluster bombardment with Cu dimers and monomers at the same velocity. The reason for the nonlinear effects in surface cluster sputtering is the overlapping of collision cascades generated by each of the dimer atoms.     

Effects of the density of collision cascades: Separating contributions from dynamic annealing and energy spikes

We present a quantitative model for the efficiency of the molecular effect in damage buildup in semiconductors. Our model takes into account only one mechanism of the dependence of damage buildup efficiency on the density of collision cascades: nonlinear energy spikes. In our three-dimensional analysis, the volume of each individual collision cascade is divided into small cubic cells, and the number of cells that have an average density of displacements above some threshold value is calculated. We assume that such cells experience a catastrophic crystalline-to-amorphous phase transition, while defects in the cells with lower displacement densities have perfect annihilation. For the two limiting cases of heavy (500 keV/atom ²⁰⁹Bi) and light (40 keV/atom ¹⁴N) ion bombardment of Si, theory predictions are in good agreement with experimental data for a threshold displacement density of 4.5 at.%. For intermediate density cascades produced by small 2.1 keV/amu PF_n clusters, we show that dynamic annealing processes entirely dominate cascade density effects for PF₂ ions, while energy spikes begin contributing in the case of PF₄ cluster bombardment.     

Radiation effect on the photoluminescence properties of Si/SiO2 thin films

Silicon ions were implanted into SiO₂ thin films with various doses and energies. For the films implanted with various ion doses the photoluminescence (PL) intensity of 470 nm firstly increased with the increase of Si ion dose, which is similar to the variation trend of displacement per atom (DPA) number during ion radiation. Further increasing Si ion dose the PL intensity of 470 nm decreased gradually since the neutral oxygen vacancy centers were destroyed. For the samples implanted with different energy the variation trend of PL intensity for 470 nm peak is similar to the result of DPA under different radiation energy according to SRIM2006 simulation. With the increase of radiation energy a new PL peak at 550 nm appeared because of the variation of defect type. Combining with the simulation results and PL spectra the radiation effect on Si/SiO₂ thin films were proposed.     

Monte Carlo simulation study of the positron contribution to displacements per atom production in YBCO superconductors

The contribution from positrons to the displacements per atom (dpa) distribution induced by the gamma irradiation on YBCO superconducting slabs is presented. The procedure implemented previously by the authors was adapted to take into account the contribution from positrons to dpa induced by the gamma radiation. The results show that, when positrons are considered in the atom displacement process, the total dpa almost doubles at 10 MeV of incident gamma radiation. At that energy positrons contribute 7% more to the total dpa than electrons, although electrons maintain having the highest contribution up to about 8 MeV.     

Alkali ion scattering from Ag(0 0 1) and Ag thin films at low and hyperthermal energies

We have investigated the scattering of K⁺ and Cs⁺ ions from a single crystal Ag(0 0 1) surface and from a Ag-Si(1 0 0) Schottky diode structure. For the K⁺ ions, incident energies of 25 eV to 1 keV were used to obtain energy-resolved spectra of scattered ions at θ_i = θ_f = 45°. These results are compared to the classical trajectory simulation safari and show features indicative of light atom-surface scattering where sequential binary collisions can describe the observed energy loss spectra. Energy-resolved spectra obtained for Cs⁺ ions at incident energies of 75 eV and 200 eV also show features consistent with binary collisions. However, for this heavy atom-surface scattering system, the dominant trajectory type involves at least two surface atoms, as large angular deflections are not classically allowed for any single scattering event. In addition, a significant deviation from the classical double-collision prediction is observed for incident energies around 100 eV, and molecular dynamics studies are proposed to investigate the role of collective lattice effects. Data are also presented for the scattering of K⁺ ions from a Schottky diode structure, which is a prototype device for the development of active targets to probe energy loss at a surface.     

Multiple-interactions of displacement cascades with He-vacancy clusters in α-iron: Computer simulations

Multiple-interactions of displacement cascades with He-vacancy (He-V) clusters are investigated using molecular dynamics simulations. The effects of a single displacement cascade on the stability of a He-V cluster depend on the He-to-vacancy (He/V) ratio and the primary knock-on atom (PKA) energy. Initial He-V clusters consist of 10 and 20 vacancies with He/V ratios ranging from 0.2 to 3 and the PKA energy, E_p, varying from 2 keV to 10 keV. The size of He-V clusters was found to generally increase with increasing He/V ratios for the same PKA energy, but the stability of He-V clusters decreases with increasing PKA energy. The results are compared with those for voids impacted by collisional cascades. During multiple 5 keV, cascade events, the final size of He-V clusters depends on only the initial He/V ratios. It is of interest to notice that the number of vacancies in a He-V cluster is determined by the first cascade event, while subsequent cascade overlap has a significant effect on its stability. These results are discussed in terms of the internal pressure of He-V clusters, the mobility of He atoms, the number of vacancies produced by cascades and the He/V ratio.     

Theory of He trapping, diffusion, and clustering in UO2

We have performed ab initio total energy calculations to investigate the behavior of helium and its diffusion properties in uranium dioxide (UO₂). Our investigations are based on the density functional theory within the generalized gradient approximation (GGA). The trapping behavior of He in UO₂ has been modeled with a supercell containing 96-atoms as well as uranium and oxygen vacancy trapping sites. The calculated incorporation energies show that for He a uranium vacancy is more stable than an oxygen vacancy or an octahedral interstitial site (OIS). Interstitial site hopping is found to be the rate-determining mechanism of the He diffusion process and the corresponding migration energy is computed as 2.79 eV at 0 K (with the spin-orbit coupling (SOC) included), and as 2.09 eV by using the thermally expanded lattice parameter of UO₂ at 1200 K, which is relatively close to the experimental value of 2.0 eV. The lattice expansion coefficient of He-induced swelling of UO₂ is calculated as 9 × 10⁻². For two He atoms, we have found that they form a dumbbell configuration if they are close enough to each other, and that the lattice expansion induced by a dumbbell is larger than by two distant interstitial He atoms. The clustering tendency of He has been studied for small clusters of up to six He atoms. We find that He strongly tends to cluster in the vicinity of an OIS, and that the collective action of the He atoms is sufficient to spontaneously create additional point defects around the He cluster in the UO₂ lattice.     

Atomistic behavior of helium-vacancy clusters in aluminum

We have performed a molecular dynamics (MD) technique to calculate the formation energies of small He_nV_m clusters in Al using the embedded atom method (EAM), the Baskes-Melius potential and the Lennard-Jones potential for describing the interactions of Al-Al, Al-He and He-He, respectively. The binding energies of an interstitial He atom, an isolated vacancy and a self-interstitial Al atom to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. All the binding energies mainly depend on the He-vacancy ratio (n/m) of clusters rather than the clusters size. The binding energies of a He atom and an Al atom to a He_nV_m cluster decrease with the ratio, but the binding energy of a vacancy to a He_nV_m cluster increases with the ratio. The results indeed show that He atoms can increase the binding energy of a vacancy to a He_nV_m cluster, and decrease the binding energies of a He atom and an Al atom to the cluster, namely, He atom acts as a catalyst for the formation of He_nV_m clusters.     

Single- and multiple-electron loss cross-sections for fast heavy ions colliding with neutrals: Semi-classical calculations

Extensive calculations of single, multiple and total electron-loss cross-sections of fast heavy ions in collisions with neutral atoms are performed in the semi-classical approximation using the DEPOSIT code based on the energy deposition model and statistical distributions for ionization probabilities. The results are presented for Ar¹⁺, Ar²⁺, Kr⁷⁺, Xe³⁺, Xe¹⁸⁺, Pb²⁵⁺ and U^q+ (q = 10, 28, 39, 62) ions colliding with H, N, Ne, Ar, Kr, Xe and U atoms at energies E > 1 MeV/u and compared with available experimental data and the n-particle classical-trajectory Monte Carlo (nCTMC) calculations. The results show that the present semi-classical model can be applied for estimation of multiple and total electron-loss cross-sections within accuracies of a factor of 2.From calculated data for the total electron-loss cross-sections σ_tot, their dependencies on relative velocity v, the first ionization potential I₁ of the projectile and the target atomic number Z_A are found and a semi-empirical formula for σ_tot is suggested. The velocity range, where the semi-classical approximation can be used, is discussed.     

Energy distributions of neutral atoms sputtered by very low energy heavy ions

Polycrystalline Cu was sputtered by normally incident, very low energy Ar⁺ ions (E₀ = 40–1000 eV). The kinetic energy (E) distributions of the neutral Cu atoms sputtered normally from the Cu surface were measured, using secondary neutral mass spectrometry. For values of E₀ above approximately 600 eV, the observed energy distributions agreed closely with the Thompson-Sigmund theory. For values of E₀ less than about 600 eV the distributions fell off faster than predicted by the Thompson-Sigmund theory, and the peak value of the distribution shifted to somewhat lower energies. Both these effects were exaggerated as E₀ was further lowered. The average kinetic energy of the sputtered neutral Cu atoms increased with increasing E₀. The rate of this increase was less at higher values of E₀.     

Displacement cascade simulation of LiAlO2 using molecular dynamics

To elucidate the radiation damage process on an atomic scale, displacement cascade simulations of LiAlO₂ were performed using molecular dynamics. Results of simulations obtained when an oxygen atom as the primary knock-on atom was displaced with the energy of 1-5 keV showed that the correlation between migration barriers of point defects and the declining rate of the maximum kinetic energy of atom in the system determined the thermal spike duration. The thermal spike of each element might finish when the maximum kinetic energy among all atoms of each element diminishes at around the point defects’ migration barrier. Defect-cluster analysis revealed that vacancies produce larger clusters than interstitials do, perhaps because the strong Coulomb interaction in ionic materials renders interstitials resistant to aggregation.     

Computer simulation of primary damage creation in displacement cascades in copper. I. Defect creation and cluster statistics

Atomic-scale computer simulation has been used to investigate the primary damage created by displacement cascades in copper over a wide range of temperature (100 K ? T ? 900 K) and primary knock-on atom energy (5 keV ? E_PKA ? 25 keV). A technique was introduced to improve computational efficiency and at least 20 cascades for each (E_PKA, T) pair were simulated in order to provide statistical reliability of the results. The total of almost 450 simulated cascades is the largest yet reported for this metal. The mean number of surviving point defects per cascade is only 15-20% of the NRT model value. It decreases with increasing T at fixed E_PKA and is proportional to (E_PKA)^1.1 at fixed T. A high proportion (60-80%) of self-interstitial atoms (SIAs) form clusters during the cascade process. The proportion of clustered vacancies is smaller and sensitive to T, falling from 30% to 60% for T ? 600 K to less than 20% when T = 900 K. The structure of clusters has been examined in detail. Vacancies cluster predominantly in stacking-fault-tetrahedron-type configurations. SIAs tend to form either glissile dislocation loops with Burgers vector b = 1/2<1 1 0> or sessile faulted Frank loops with b = 1/3<1 1 1>. Despite the fact that cascades at a given E_PKA and T exhibit a wide range of defect numbers and clustered fractions, there appears to be a correlation in the formation of vacancy clusters and SIA clusters in the same cascade. The size and spatial aspects of this are analysed in detail in part II [unpublished], where the stability of clusters when another cascade overlaps them is also investigated.     

Total and net displacement functions for polyatomic materials

Using a continuous-slowing-down, random amorphous material model in which displacement and recombination processes are determined by sharp displacement thresholds and capture energies, we have studied displacement cascades in a number of diatomic materials and a few triatomic materials. The results obtained are presented here in terms of a set of displacement efficiencies for each material which correlate the calculated number of net displacements with the damage energies, displacement thresholds, and stoichiometry of the material. Materials for which the ratio of heavy to light mass is less than about four (Type 1) show somewhat different displacement cascade characteristics than those for which the mass ratio is greater than four (Type 2). In addition, for each material the dependence of the cascades on the energy of the primary has different properties in two different energy ranges. In Region I, extending from the lowest displacement threshold to about I keV for Type-1 materials and to about 100 keV for Type-2 materials, the displacement efficiencies show strong dependence on energy and on the atom type of the primary. In Region 2 (energies higher than Region 1) the displacement efficiencies are nearly independent of energy and of the type of the primary. Cascades in Type-1 materials can show strong dependence on the capture probability for atoms on sites of unlike type; this dependence is discussed, as is the dependence of cascade structure on displacement threshold. Rather strong nonstoichiometric behavior is demonstrated for certain Type-2 materials. Comparisons are made with a few previous calculations for diatomic materials.