PKA Energy Research Articles

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 84eV, respectively. The order of these values are consistent with the number of generated defects in displacement cascade simulation with initial PKA energy of 1–5keV, 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.

Frequency of occurrence of LCS per cascade in bcc iron by PKA energy 30 keV

The frequency of occurrence per cascade in bcc iron is studied by PKA energy 30keV using the fitting of potentials on linear collision sequences (LCS). Two embedded atom potentials that essentially differ by their repulsive branches are used in classical molecular dynamic (MD) with the code DYMOKA and its binary collision approximation (BCA) The Molière and Born Mayer potentials are used in the Binary Collision Approximation (BCA). The linear collision sequences (LCS) in iron can be generated with Marlowe code in BCA, using the potentials parameters. The BCA is used to accumulate cascade statistics and to build linear collision sequences distributions.

Modeling of cascade and sub-cascade formation at high PKA energies in irradiated fusion structural materials

A new theoretical model is developed for the investigations of cascade and sub-cascade formation in fusion structural materials under fast neutron irradiation at high primary knock-on atom energies. Light fusion structural materials: such as Be, C and SiC under 14 MeV neutron irradiation in fusion reactor will have the primary knock-on atoms with the energies up to 1 MeV. It is very difficult to use at such high energies the Monte-Carlo or molecular dynamic simulations [H.L. Heinisch, B.N. Singh, Philos. Mag. A67 (1993) 407; H.L. Heinisch, B.N. Singh, J. Nucl. Mater. 251 (1997) 77]. The developed model is based on the analytical consideration of elastic collisions between displaced moving atoms produced by primary knock-on atoms with some kinetic energies obtained from fast neutrons and crystal lattice atoms. The Thomas–Fermi interaction potential is used here for the description of these elastic atomic collisions. The suggested model takes into account also the electronic losses for moving atoms between elastic collisions. The self-consistent criterion for sub-cascade formation is suggested here which is based on the comparison of mean distance of primary knock-on atoms between consequent collisions of them with the target atoms and a size of sub-cascade produced by moving secondary knock-on atoms produced in such collisions. The analytical relations for the most important characteristics of cascades and sub-cascades are determined including the average number of sub-cascades per one primary knock-on atom in the dependence on its energy, the distance between sub-cascades and the average cascade and sub-cascade sizes. The developed model allows determining the total numbers, distribution functions of cascades and sub-cascades in dependence on their sizes and generation rate of cascades and sub-cascades for the different fusion neutron energy spectra. On the basis of this developed model the numerical calculations for main characteristics of cascades and sub-cascades in different fusion structural materials: Fe, V, C, Al, Be and W are performed here using the neutron fluxes and primary knock-on atom energy spectra for fusion reactors: ITER and DEMO.

Molecular dynamics simulation of irradiation damage in tungsten

Molecular dynamics (MD) simulations have been performed for the radiation damage of tungsten using a modified Finnis-Sinclair type many-body interatomic potential. The interstitial defects and vacancies are distinguished by the Wigner–Seitz cell method and the types of the interstitial dumbbells are also identified by the azimuth and polar angles of dumbbell line vectors. It is observed that the number of interstitial defects and vacancies initially sharply increases and passing through the peak position, relaxes to the steady state for all PKA energies and that all residual interstitial dumbbells at the steady state are the <111>-oriented. Based on the variation of the orientation angles of dumbbells during the radiation damage simulation, it is found that the recombination of the <111>-oriented dumbbells with the vacancies is much faster than that of two other types of dumbbells and that the population of the <100> dumbbells is much larger than that of the <110> ones in spite of its higher formation energy, the reason of which is explained with the dynamics of the individual dumbbell.

Erbium implantation in silica studied by molecular dynamics simulations

Defect formation induced by erbium implantation in silica glass and cristobalite was studied using molecular dynamics simulations employing a partial charge model in combination with the ZBL potential. The results show that the number of displaced atoms generated at the same PKA energy is similar in silica and cristobalite but the number of coordination defects created is much lower in the cristobalite than in silica glass. In both cases, the erbium ion is able to create an optimal coordination environment at the end of the collision cascade. Subsequent thermal annealing causes the relaxation of the silicon oxygen network structure along with a reduction of silicon and oxygen defects.

Atomistic simulation of helium-defect interaction in alpha-iron

Molecular dynamics (MD) methods are utilized to study the formation of vacancy clusters created by displacement cascades in α-Fe containing different concentrations of substitutional He atoms. Primary knock-on atom energies, Ep, from 500eV to 20keV are considered at a temperature of 100K, and the results are compared with those performed in pure α-Fe. There are distinct differences in the number and size of vacancy clusters within displacement cascades with and without substitutional helium atoms. It is found that many large vacancy clusters can be formed within cascade cores in α-Fe with helium atoms, in contrast to a few small vacancy clusters observed in pure α-Fe. The number and size of helium/vacancy clusters generally increase with increasing helium concentration and PKA energy. One of the striking results is that the number of self-interstitial atoms (SIAs) and the size of interstitial clusters are much smaller than those in pure α-Fe.

Modified embedded-atom method interatomic potential for theFe−Cualloy system and cascade simulations on pure Fe andFe−Cualloys

A modified embedded-atom method (MEAM) interatomic potential for the $\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Cu}$ binary system has been developed using previously developed MEAM potentials of Fe and Cu. The $\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Cu}$ potential was determined by fitting to data on the mixing enthalpy and the composition dependencies of the lattice parameters in terminal solid solutions. The potential gives a value of $0.65\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the dilute heat of solution and reproduces the increase of lattice parameter of Fe with addition of Cu in good agreement with experiments. The potential was used to investigate the primary irradiation defect formation in pure Fe and $\mathrm{Fe}\text{\ensuremath{-}}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%\phantom{\rule{0.3em}{0ex}}\mathrm{Cu}$ alloy by a molecular dynamics cascade simulation study with a PKA energy of $2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ at $573\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A tendency for self-interstitial atom-Cu binding, the formation of mixed $(\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Cu})$ dumbbells and even $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Cu}$ dumbbells was observed. Given a positive binding energy between Cu atoms and self-interstitials, Cu transport by an interstitial diffusion mechanism could be proposed to contribute to the formation of Cu-rich precipitates and irradiation-induced embrittlement in nuclear structural steels.

Structure‐stability correlations for imine formation in aqueous solution

AbstractImine formation between 25 aldehydes and 13 amines in aqueous solution in the pH range 7–11 was studied by 1H NMR spectroscopy. A three‐parameter linear equation correlating logarithms of imine formation constants with pKa and HOMO energies of amines and LUMO energies of aldehydes is proposed. In view of the widespread occurrence of imine‐forming processes in both chemistry and biology, the data presented are of significance for physical organic chemistry and of particular interest for dynamic combinatorial chemistry. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Factors That Influence Cascade-Induced Defect Growth in Pure Metals and Model Alloys

For the development of materials in a fusion reactor environment without a fusion reactor, it is important to understand the generation and accumulation of point defects. This paper discusses five important factors in metals that influence the initial stage of defect clustering under cascade damage conditions. The effect of the PKA energy spectrum on damage evolution was explained from the viewpoint of subcascade formation. Two origins of damage rate dependence of defect cluster formation, direct mutual annihilation of point defects and annihilation of point defects at cascade-induced defect clusters, were mentioned. As the effect of motion of interstitial clusters, an example was given to illustrate the strong correlation between the mobility of interstitial clusters and void growth. Thermal activation processes depend on irradiation temperature. Varying irradiation temperature experiment was evaluated as a technique for investigating the point defect processes during irradiation. Migration of alloying elements during irradiation was reviewed from the standpoint of the interaction of alloying elements with point defects.

Molecular dynamics simulation of defect production in collision cascades in zircon

Defect production in collision cascades in zircon has been examined by molecular dynamics simulations using a partial charge model combined with the Ziegler–Biersack–Littmark potential. U, Zr, Si and O recoils with energies ranging from 250eV to 5keV were simulated in the NVE ensemble. To obtain good statistics, 5–10 cascades in randomly chosen directions were simulated for each ion and energy. The damage consists of mainly Si and O Frenkel pairs, a smaller number of Zr Frenkel pairs, and Zr on Si antisite defects. Defect production, interstitial clustering, ion beam mixing and Si–O–Si polymerization increase with PKA mass and energy.

Vacancy-type defect production in iron under ion beam irradiation investigated with positron beam Doppler broadening technique

Accumulation of vacancy-type defects in iron produced by various ion irradiations at room temperature was investigated with positron beam Doppler broadening technique. Various ion species (He, C, O, Fe) were used for investigation of the effect of PKA energy on vacancy-type defect production. Accumulation of vacancy-type defects leads to sharpening of Doppler broadening spectra, i.e., increase of S parameter. S parameter was measured as a function of ion fluence for various ion species at a fixed positron energy of 15 keV. At the early stage of irradiation, S parameter increases with increasing fluence, and then it reaches some saturated S parameter value that varies with ion species. The saturated S parameter values tend to be higher for heavier ion irradiation. When compared with the incremental change of S parameter at the same low dpa level, heavier ions also lead to a greater change.

Analysis of defect structural evolution in fcc metals irradiated with neutrons under well defined boundary conditions

Defect structural evolutions near pre-existing defects such as surfaces, grain boundaries and dislocations in fcc metals are studied to clarify point defect processes during irradiation. By the comparison of Au irradiated as thin foils with fission neutrons and fusion neutrons, the PKA energy to produce a stacking fault tetrahedron is determined to be 80 keV with a production efficiency of 0.05. Grain boundaries are effectively used to detect the existence of one-dimensional motion of interstitial clusters. In Ni and Ni binary alloys (2 at.% Si, Cu, Ge or Sn), there is a good coincidence between the void growth and one-dimensional motion of interstitial clusters. The coincidence is, however, not good for Cu. Screw dislocations with jogs turn into helical dislocations by absorbing one type of point defects. The difference of freely migrating defects between fission and fusion neutron irradiation is measured as a function of irradiation dose and it is concluded that the same number of freely migrating defects is generated from each subcascade in fission and fusion neutron irradiated Ni.

Temperature-dependence of defect creation and clustering by displacement cascades in α-zirconium

Molecular dynamics (MD) modelling has been employed to investigate the effect of lattice temperature on the production of vacancies and interstitials in the primary damage process of displacement cascades with energy up to 20 keV in α-zirconium. The final number of Frenkel pairs decreases with increasing temperature due to the increase in lifetime of the thermal spike at high temperature. The production efficiency behaves in a similar fashion to that simulated at 100 K, but it is reduced further and saturates at about 20% over the energy range considered at 600 K. The number and size of clusters, both vacancy and interstitial, are increased by increasing PKA energy, and the fraction of interstitials in clusters also increases with increasing lattice temperature. The interstitial clusters can glide back and forth by one-dimensional migration along the crowdion direction at 100 K, but small clusters of less than four SIAs can change their glide direction on and off basal-planes at 600 K. It is also observed that single interstitials and some small clusters can migrate along both 〈1 1 2 ̄ 0〉 and 〈 2 ̄ 2 0 3〉 directions at 600 K. Clusters containing up to 25 interstitials and 24 vacancies were formed by 20 keV cascades at 600 K, and almost all of the clusters have the form of a dislocation loop with Burgers vector 1/3〈1 1 2 ̄ 0〉 . It was found that the 25-interstitial cluster is glissile and dissociates on the basal and prism-planes that form its glide cylinder. Collapse of the 24-vacancy cluster to a perfect vacancy dislocation loop was found to occur in the primary damage process due to the longer lifetime of the thermal spike at higher temperature. The results are discussed in terms of experimental data and compared with those simulated at 100 K.

Monte Carlo simulation of point-defect behavior in cascade

Fraction of point defects produced after quenching stage of cascade damage will escape from the cascade region as freely migrating defects (FMD). The process was simulated using Monte Carlo method. The FMD production ratio, recombination ratio and clustering efficiency were estimated in α-iron at 290°C as a function of PKA energy. In case of single cascade, vacancies tended to form clusters at the center of the cascade, while about 80% of self interstitial atoms (SIAs) escaped from the cascade region as FMDs. This difference caused the imbalance in the production between freely migrating interstitials and vacancies. As for the annihilation of point defects by recombination, the recombination ratio was not sensitive to the cascade size and defect density in it, and the value was about 20% in all calculations. Pre-existing defect clusters around the cascade are affected by the imbalance between SIAs and vacancies. SIA clusters were observed to grow absorbing freely migrating SIAs while vacancy clusters shrank because of SIA-dominant environment which was due to the imbalance in production of FMDs. Quantitative estimation of this cascade overlap effect was investigated to compare with experimental results.

Subcascade formation in displacement cascade simulations: Implications for fusion reactor materials

Displacement cascade formation in iron has been investigated by the method of molecular dynamics (MD) for cascade energies up to 40 keV, corresponding to PKA energies up to 61 keV. The results of these simulations have been used in the SPECOMP code to obtain effective, energy-dependent cross sections for two measures of primary damage production: (1) the number of surviving point defects expressed as a fraction of the those predicted by the standard secondary displacement model by Norgett, Robinson, and Torrens (NRT), and (2) the fraction of the surviving interstitials contained in clusters that formed during the cascade event. The primary knockon atom spectra for iron obtained from the SPECTER code have been used to weight these MD-based damage production cross sections in order to obtain spectrally averaged values for several locations in commercial fission reactors, materials test reactors, and a DT fusion reactor (ITER) first wall. An evaluation of these results indicates that neutron energy spectrum differences between the various environments do not lead to significant differences between the average primary damage formation parameters. This conclusion implies that the displacement damage component of radiation damage produced in a DT fusion reactor should be well simulated by irradiation in a fission reactor neutron spectrum, and that differences in nuclear transmutation production may be the primary source of uncertainty in the prediction of material performance at high doses in DT fusion reactors.

Atomic processes during damage production and defect retention

Fundamental atomic processes during production and retention of radiation damage in structural materials are reviewed. Firmly established damage mechanisms are outlined, and some of the major uncertainties exposed. Damage production under neutron and ion irradiation proceeds through the elementary step of collision cascade formation, with further modification of the nascent cascade structure by inter-, and intra-cascade interaction events. Under fusion neutron irradiation, single cascade damage production occurs within 10 ps in most metals, with spatial extent of several tens to hundreds of nano-meters. Damage accumulation takes place over much longer time and length scales, during which multiple cascades interact leading to further re-structuring of the incipient cascade. Areas which require further investigation are: (1) the mechanisms of vacancy cluster collapse at the cascade core; (2) the athermal nucleation of interstitial loops at the periphery; (3) the migration of interstitial atoms and clusters emanating from the cascade; (4) the replacement of the dpa with a more physical measure of damage retention; (5) cascade structure for high PKA energies (above 20 keV); and (6) Inter- and Intra-cascade interactions, (7) and finally, cascade dynamics in damaged materials at high dose.

Intermolecular Hydrogen Bonds of 5-Benzylidene-2,4-thiazolidinedione Derivatives and Related Compounds in Crystalline State

Abstract From the viewpoint of noncentrosymmetric molecular arrangement design in crystalline state, which is indispensable to second order nonlinear optical materials, intermolecular hydrogen bond formation of eight 5-benzylidene-2,4-thiazolidinedione derivatives and related compounds were investigated by X-ray crystallography. 5-Benzylidene-2,4-thiazolidinedione (1) itself forms centrosymmetric head-to-head (or tail-to-tail) intermolecular hydrogen bonds and takes a centrosymmetric molecular arrangement in crystalline state. Introduction of 4-methoxy group into the phenyl moiety of 1 was the only useful means for head-to-tail type intermolecular hydrogen bond formation. 5-(4-Methoxybenzylidene)-2,4-thiazolidinedione shows head-to-tail type intermolecular hydrogen bonds and noncentrosymmetric molecular arrangement in crystalline state. Similarities in both hydrogen bond formation and molecular arrangement in crystalline state are obtained by conversion of 2,4-thiazolidinedione to 2-thioxo-4-oxazolidinone, but in the case of conversion to 2,4-oxazolidinedione only hydrogen bond formation is shown in a similar manner. In the case of conversion to rhodanine, no similarity in either hydrogen bond formation or molecular arrangement in crystalline state was shown. Such behaviors were considered from viewpoints of pKa and hydrogen bond energy.

The Role of Homolytic Bond Dissociation Energy in the Deprotonation of Cation Radicals. Examples in the NADH Analogues Series

The deprotonation of the cation radical of 9-cyanomethylacridane by a series of normal bases is investigated and its pKa and homolytic bond dissociation energy determined experimentally. The latter...

Computer simulation of vacancy and interstitial clusters in bcc and fcc metals

Interstitial clusters in bcc-Fe and fcc-Cu and vacancy clusters in fcc-Cu have been studied by computer simulation using different types of interatomic potentials such as a short-ranged empirical pair potential of Johnson type, short-ranged many-body potentials of Finnis-Sinclair type and long-ranged pair potentials obtained within the generalized pseudopotential theory. The stability of a self interstitial in bcc-Fe was found to be dependent on the range of potential but not on the type. Thus, both short-ranged potentials simulated 〈110〉 dumb-bell as a stable configuration while in the case of the long-ranged potential the stable configuration is the 〈111〉 crowdion. Nevertheless the structure and properties of interstitial clusters were found to be qualitatively the same with all the potentials. Up to 50 interstitials, the most stable clusters were found as perfect dislocation loops with Burgers vector b = 1 2 〈11 1〉 . The stability of interstitial clusters in Cu also does not depend on the potential and for the same sizes the most stable configurations are faulted Frank loops 1 2 〈111〉{111} and edge loops in the {110} plane. The structure and stability of vacancy clusters in fcc-Cu were found to be dependent mainly on both the range of potential and equilibrium conditions. Thus for long-ranged non-equilibrium pair potentials vacancy clusters in the {111} plane collapsed and formed vacancy loops or stacking fault tetrahedra depending on the shape of the initial vacancy platelet. For the short-ranged equilibrium many-body potential vacancy clusters do not collapse into loops or tetrahedra. The process of vacancy clustering in the cascade region has been studied by molecular dynamics. This study has been done for the case of a PKA energy of about 20–25 keV. We found that the processes simulated with the short-ranged many-body potential and the long-ranged pair potential are qualitatively different. Thus for the many-body potential we have observed melting and crystallization of the central part of the cascade region, sweeping of vacancies inside due to the moving of the liquid-solid interface and increasing of vacancy concentration in the centre of the cascade region; however no significant clustering was observed. Contrarily for the long-ranged pair potential we have observed a very fast diffusion in the solid crystallite and the formation of stacking fault tetrahedra. The results obtained have been discussed and compared with the experimental data.

Implications of fundamental radiation damage studies in the research and development of materials for a fusion reactor

Development of materials for first wall and blanket structures which are resistant to high fluence irradiation of fusion spectrum neutrons is a key issue of realizing fusion energy systems. Since fusion reactor environment has not been realized as yet, prediction of materials behavior must be based on fundamental radiation damage studies combined with the data from existing irradiation facilities. High fluence irradiation, high PKA energies and high nuclear transmutation rates are the important factors in considering the fusion radiation effects. Experimentally, various surrogate means have to be used, for which establishing irradiation correlation is important. The correlation should not merely be a phenomenological one but it should be based on physics-based mechanisms. The methodology of irradiation correlation will be discussed. This includes discussion of PKA dependent damage parameters, computer simulation, modeling and model integration. The methodology, once established, will also be applicable to lifetime prediction of materials of neutron interactive components in the fusion reactor as well as those in the existing nuclear energy systems.