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 The size and spatial aspects of this are analysed in detail in part II [unpublished], where the stability of clusters when another cascade overlaps them is also investigated.     

Positron annihilation study and computational modeling of defect production in neutron-irradiated reactor pressure vessel steels

Positron annihilation spectroscopy (PAS) and a computer simulation were used to investigate a defect production in reactor pressure vessel (RPV) steels irradiated by neutrons. The RPV steels were irradiated at 250 °C in a high-flux advanced neutron application reactor. The PAS results showed that mainly single vacancies were created to a great extent as a result of a neutron irradiation. Formation of vacancies in the irradiated materials was also confirmed by a coincidence Doppler broadening measurement. For estimating the concentration of the point defects in the RPV steels, we applied computer simulation methods, including molecular dynamics (MD) simulation and point defect kinetics model calculation. MD simulations of displacement cascades in pure Fe were performed with a 4.7 keV primary knock-on atom to obtain the parameters related to displacement cascades. Then, we employed the point defect kinetics model to calculate the concentration of the point defects. By combining the positron trapping rate from the PAS measurement and the calculated vacancy concentrations, the trapping coefficient for the vacancies in the RPV steels was determined, which was about 0.97 × 10¹⁵ s⁻¹. The application of two techniques, PAS and computer simulation, provided complementary information on radiation-induced defect production.     

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.     

A molecular dynamics study of radiation induced diffusion in uranium dioxide

The nuclear oxide fuels are submitted ‘in-pile’ to strong structural and chemical modifications due to the fissions and temperature. The diffusion of species is notably the result of a thermal activation and of radiation induced diffusion. This study proposes to estimate to what extent the radiation induced diffusion contributes to the diffusion of lattice atoms in UO₂. Irradiations are simulated using molecular dynamics simulation by displacement cascades induced by uranium primary knock-on atoms between 1 and 80 keV. As atoms are easier to displace when their vibration amplitude increases, the temperature range which have been investigated is 300-1400 K. Cascade overlaps were also simulated. The material is shown to melt at the end of cascades, yielding a reduced threshold energy displacement. The nuclear contribution to the radiation induced diffusion is compared to thermally activated diffusion under in-reactor and long-term storage conditions.     

Molecular simulations of cluster ejection by CO2 cluster impact on carbon-based surfaces

Single (CO₂)_N (N = 1-20) cluster impact on three different carbon-based surfaces of fullerite (1 1 1), graphite and diamond (1 0 0) has been investigated by MD simulations with the cluster collision energy from 5 to 14 keV/cluster as a first step toward the general modeling of the reactive sputtering by cluster impact of a solid surface. A crater permanently remained on the fullerite and graphite surfaces while it was quickly replenished with fluidized carbon material on the diamond surface. In spite of the smaller crater size as well as the crater recovery resulting in the reduction of the surface area, the sputtering yields were the highest on diamond. The effective energy deposition near the surface contributes to the temperature rise and consequent sputtering seemed highly reduced due to the collision cascades especially on the fullerite target.     

Simulating radiation damage in Ga stabilised δ-Pu

Radiation events in Ga stablised δ-Pu are investigated by means of Molecular Dynamics simulations. Pu 5 at.% Ga is considered using the Modified Embedded Atom Method to govern the atomic interactions. Cascades were initiated with Primary Knock-on Atom (PKA) energies in the range of 0.4-10 keV, with trajectories deduced through comprehensive sampling of a representative set of directions, combined with different Ga atomic positions. The displacement threshold energy, E_d, for Pu and Ga atoms was also determined through similar extensive studies to aid the understanding and interpretation of the cascade results.Values of E_d between 5 and 40 eV were determined for Pu, with Ga PKAs requiring generally more energy to create a defect with E_d between 8 and 70 eV. Low energy collision cascades, initiated with energies in the range of 0.4-1 keV, show that the cascades form in a similar manner to other fcc metals with a vacancy rich zone surrounded by isolated interstitial defects. A feature of these cascades is that the displaced Ga atoms return to lattice sites during the ballistic phase, leading to a lack of Ga-type residual defects. Higher energy cascades show similar features but with the development of an amorphous region at the cascade core of around 5 nm diameter at 5 keV. Quantitatively, the residual number of defects found shows no distinct variation to that for previous work on pure Pu, suggesting the inclusion of Ga does not significantly effect the susceptibility or resistance of Pu to initial cascade development.     

Grain boundary influence on displacement cascades in UO2: A molecular dynamics study

The influence of grain boundaries on the primary damage state created by a recoil nucleus in UO₂ matrix is studied here by molecular dynamics simulations. This study is divided in two steps: (1) the study of the structural properties of several symmetrical tilt boundaries for different misorientation angles ranging from 12.7° to 61.9°; and (2) the study of displacement cascades near these grain boundaries. For all the grain boundaries studied, the structure around the interface up to about 2 nm presents a perturbed but stable fluorite lattice. The type of defect at the interface depends directly on the value of the misorientation angles. For the small angles (12.7° and 16.3°) the interface defects correspond to edge dislocations. For higher misorientation angles, a gap of about 0.3 nm exists between the two halves of the bicrystal. This gap is composed of Schottky defects involving numerous vacancies along the interface. About 10 keV displacement cascades were initiated with an uranium projectile close to the interface. In all the cases, numerous point defects are created in the grain boundary core, and the mobility of these defects increases. However, cascade morphologies depend strongly on the grain boundary structure. For grain boundaries with edge dislocations, the evolution of the displacement cascades is similar to those carried out in monocrystals. On the other hand, cascades initiated in grain boundaries with vacancy layer defects present an asymmetry on the number of displaced atoms and the number of point defects created.     

Influence of the projectile charge state on the ionization probability of sputtered particles

We present a computational study of the effect of the projectile charge state on secondary ion formation in sputtering. A molecular dynamics simulation of an atomic collision cascade is combined with a kinetic excitation model including electronic friction and electron promotion in close atomic collisions. The model is extended to account for potential excitation following the bombardment with a highly charged ion (HCI). The spatial spreading of the excitation generated in the cascade is treated in an diffusive approach. The excitation energy density profile obtained this way is parametrized via an effective electron temperature, which is then used to calculate the ionization probability of each sputtered atom in terms of a simple charge exchange model. The results obtained for the impact of a 5 keV Ag atom onto a solid silver surface show that the average ionization probability increases from 4.7×10^-4 for a neutral projectile to 5.4×10^-4 for a highly charged projectile ion with a total ionization energy of 576 eV.     

Ion irradiation damage effects in δ-phase Y6W1O12

Polycrystalline Y₆W₁O₁₂ samples were irradiated with 280 keV Kr²⁺ ions to fluences up to 2 × 10²⁰ ions/m² at cryogenic temperature (100 K). Ion irradiation damage effects in these samples were examined using grazing incidence X-ray diffraction (GIXRD) and cross-sectional transmission electron microscopy (TEM). The pristine Y₆W₁O₁₂ possesses rhombohedral symmetry (structure known as the δ-phase), which is closely related to cubic fluorite structure. GIXRD and TEM observations revealed that the irradiated Y₆W₁O₁₂ experiences an ordered rhombohedral to disordered cubic fluorite transformation by a displacement damage dose of ∼12 displacements per atom (dpa). At the highest experimental dose of ∼50 dpa, the uppermost irradiated region was found to be partially amorphous while the buried damage region was found to contain the same fluorite structure as observed at lower dose.     

Dynamical simulations of radiation damage induced by 10 keV energetic recoils in UO2

We have performed classical molecular dynamics simulations to simulate the primary damage state induced by 10 keV energetic recoils in UO₂. The numbers versus time and the distance distributions for the displaced uranium and oxygen atoms were investigated with the energetic recoils accelerated along four different directions. The simulations suggest that the direction of the primary knock-on atom (PKA) has no effect on the final primary damage state. In addition, it was found that atomic displacement events consisted of replacement collision sequences in addition to the production of Frenkel pairs. The spatial distribution of defects introduced by 10 keV collision cascades was also presented and the results were similar to that of energetic recoils with lower energy.     

Simulating radiation damage in δ-plutonium

Radiation events in δ-Pu (fcc) have been simulated in an attempt to understand the fundamental mechanisms that contribute to the Pu ageing process. The Pu interactions are modelled using a potential based on the modified embedded atom method (MEAM). The energetics of point defects have been investigated using static calculations together with molecular dynamics (MD) to simulate radiation events. All MD simulations were carried out with Pu initially in the face-centred-cubic (fcc) structure, although this is not the lowest energy configuration for the pure metal.The point defect study suggests that the mono-vacancy has the lowest formation energy (0.46 eV), with interstitial defects favouring the - split orientation over occupation of the native fcc octahedral site. Displacement threshold energy calculations at room temperature give a minimum value of between 5 and 6 eV, increasing to 8-14 eV along the major crystallographic directions.Low energy collision cascades, initiated with energies in the range of 0.4-1 keV, show that the cascades form in a similar manner to other fcc metals with a vacancy rich zone at the cascade core, surrounded by isolated interstitial defects. Higher energy cascades show similar features but with occasional channelling of energetic atoms and sub-cascade branching which significantly reduces defect production. A common trait observed across all the cascades was the relatively slow annealing period, compared to cascades in other fcc metals, with simulations at energies above 5 keV requiring many 10’s of picoseconds before the ballistic phase was completed.     

Can thermal spike calculations reproduce displacement cascades?

Molecular dynamics simulations are used to compare the defects created by full displacement cascades and thermal spikes. The spikes are designed from cascade simulations to be of the same energies and of comparable sizes. Quantitatively, one finds that spikes create much less Frenkel pairs than cascades. However qualitatively, the distinction that appears in cascade simulations, between direct impact amorphization and sole creation of point defects is reproduced by thermal spikes calculations.     

Method to measure composition modifications in polyethylene terephthalate during ion beam irradiation

Matter losses of polyethylene terephthalate (PET, Mylar) films induced by 1600 keV deuteron beams have been investigated in situ simultaneously by nuclear reaction analysis (NRA), deuteron forward elastic scattering (DFES) and hydrogen elastic recoil detection (HERD) in the fluence range from 1 × 10¹⁴ to 9 × 10¹⁶ cm⁻². Volatile degradation products escape from the polymeric film, mostly as hydrogen-, oxygen- and carbon-containing molecules. Appropriate experimental conditions for observing the composition and thickness changes during irradiation are determined. ¹⁶O(d,p₀)¹⁷O, ¹⁶O(d,p₁)¹⁷O and ¹²C(d,p₀)¹³C nuclear reactions were used to monitor the oxygen and carbon content as a function of deuteron fluence. Hydrogen release was determined simultaneously by H(d,d)H DFES and H(d,H)d HERD. Comparisons between NRA, DFES and HERD measurements show that the polymer carbonizes at high fluences because most of the oxygen and hydrogen depletion has already occured below a fluence of 3 × 10¹⁶ cm⁻². Release curves for each element are determined. Experimental results are consistent with the bulk molecular recombination (BMR) model.     

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.     

Influence of Cr-ions on the magnetic behaviour of FeCo film

Implantation of Cr-ions in Fe₇₀Co₃₀ thin film have been performed to modify its structural and magnetic properties. From the XRD results, the lattice constant as well as the grain size of the film is increasing with the ion fluence. Cr-ions (1 × 10¹⁷ ions/cm²) reduces the coercivity of the film from 140(3) Oe to 44(3) Oe. Coercivity of the film follows the exponential decay as a function of Cr-ions fluence. 35 keV (projectile range 13.5 nm) and 100 keV Cr-ions (projectile range 34.3 nm) have been used to understand the effects of magnetic Cr-ions and the effects of ballistic collision cascade on the MOKE signal. Similar changes on the coercivity behaviour of the film implanted with these two energies have been observed. It appears that the implantation process creates a solid solution of Cr in FeCo without any other additional treatment in the film. After 5 × 10¹⁶ Cr-ions, film exhibit four fold magnetic anisotropy.     

Properties of Na implanted targets

Ten types of ²³Na implanted targets have been fabricated for the purposes of investigating the effects of proton beam bombardment on the implanted sodium distribution. Targets were implanted at energies of E_Na = 10-30 keV using copper, tantalum, and nickel as host materials. Thin layers (100-200 Å) of chromium and gold were also evaporated over some of the targets to provide a protective layer for the implanted sodium. The ²³Na(p, γ) resonance at a lab proton energy of E_p = 309 keV was used to determine the implanted distribution. Successive resonance profile measurements are presented for each implanted target, and the concurrent loss of ²³Na resulting from beam bombardment is reported. The calculated temperature rise of the targets indicates that beam heating has a negligible effect on the implanted sodium distribution, and that the principal mechanism for ²³Na loss during beam bombardment is sputtering.     

Neutron irradiation-induced dimensional changes in MEMS glass substrates

A study is made of radiation-induced expansion/compaction in Pyrex^® (Corning 7740) and Hoya SD-2^® glasses, which are used as substrates for MEMS devices. Glass samples were irradiated with a neutron fluence composed primarily of thermal neutrons, and a flotation technique was employed to measure the resulting density changes in the glass. Transport of Ions in Matter (TRIM) calculations were performed to relate fast (∼1 MeV) neutron atomic displacement damage to that of boron thermal neutron capture events, and measured density changes in the glass samples were thus proportionally attributed to thermal and fast neutron fluences. Pyrex was shown to compact at a rate of (in Δρ/ρ per n/cm²) 8.14 × 10⁻²⁰ (thermal) and 1.79 × 10⁻²⁰ (fast). The corresponding results for Hoya SD-2 were 2.21 × 10⁻²¹ and 1.71 × 10⁻²¹, respectively. On a displacement per atom (dpa) basis, the compaction of the Pyrex was an order of magnitude greater than that of the Hoya SD-2. Our results are the first reported measurement of irridiation-induced densification in Hoya SD-2. The compaction of Pyrex agreed with a previous study. Hoya SD-2 is of considerable importance to MEMS, owing to its close thermal expansivity match to silicon from 25 to 500°C.     

Defects creation in sapphire by swift heavy ions: A fluence depending process

Single crystals of sapphire (α-Al₂O₃) were irradiated at GANIL with 0.7 MeV/amu xenon ions corresponding to an electronic stopping power of 21 keV/nm. Several fluences were applied between 5 × 10¹¹ and 2 × 10¹⁴ ions/cm². Irradiated samples were characterized using optical absorption spectroscopy. This technique exhibited the characteristic bands associated with F and F⁺ centers defects. The F centers density was found to increase with the fluence following two different kinetics: a rapid increase for fluences less than 10¹³ ions/cm² and then, a slow increase for higher fluences. For fluences less than 10¹³ ions/cm², results are in good agreement with those obtained by Canut et al. [B. Canut, A. Benyagoub, G. Marest, A. Meftah, N. Moncoffre, S.M.M. Ramos, F. Studer, P. Thévenard, M. Toulemonde, Phys. Rev. B 51 (1995) 12194]. In the fluences range: 10¹³-10¹⁴ ions/cm², the F centers defects creation process is found to be different from the one evidenced for fluences less than 10¹³ ions/cm².     

Effects of ion irradiation on the structural transformation of sol-gel derived TEOS/MTES thin films

Ion beam processing of organic/inorganic thin films has been shown to be an effective means in converting polymeric films into their final ceramic-like state. In this study, hybrid sol-gel derived thin films based on TEOS (tetraethylorthosilicate) Si(OC₂H₅)₄ and MTES (methyltriethoxysilane) CH₃Si(OC₂H₅)₃ were prepared and deposited on Si substrates by spin coating. After the films were allowed to air dry, they were heat treated at 300 °C for 10 min. Ion irradiation was performed at room temperature using 125 keV H⁺ and 250 keV N²⁺ ions with fluences ranging from 1 × 10¹⁴ to 5 × 10¹⁶ ions/cm². FT-IR and Raman spectroscopies were used to quantify the chemical structural transformations which occurred including the evolution of the organic components, the cross-linking of silica clusters, and the clustering of carbon.     

Radiation damage in ZnO ion implanted at 15 K

Commercial O-face (0 0 0 1) ZnO single crystals were implanted with 200 keV Ar ions. The ion fluences applied cover a wide range from 5 × 10¹¹ to 7 × 10¹⁶ cm⁻². The implantation and the subsequent damage analysis by Rutherford backscattering spectrometry (RBS) in channelling geometry were performed in a special target chamber at 15 K without changing the target temperature of the sample. To analyse the measured channelling spectra the computer code DICADA was used to calculate the relative concentration of displaced lattice atoms.Four stages of the damage evolution can be identified. At low ion fluences up to about 2 × 10¹³ cm⁻² the defect concentration increases nearly linearly with rising fluence (stage I). There are strong indications that only point defects are produced, the absolute concentration of which is reasonably given by SRIM calculations using displacement energies of E_d(Zn) = 65 eV and E_d(O) = 50 eV. In a second stage the defect concentration remains almost constant at a value of about 0.02, which can be interpreted by a balance between production and recombination of point defects. For ion fluences around 5 × 10¹⁵ cm⁻² a second significant increase of the defect concentration is observed (stage III). Within stage IV at fluences above 10¹⁶ cm⁻² the defect concentration tends again to saturate at a level of about 0.5 which is well below amorphisation. Within stages III and IV the damage formation is strongly governed by the implanted ions and it is appropriate to conclude that the damage consists of a mixture of point defects and dislocation loops.