Radiation Damage Cascades Research Articles

Disordering in the Ni-Al system under low dose ion-irradiation: a computer simulation study

ABSTRACTStarting from the radiation damage cascades, as obtained using the binary collision approximation, we derive the spatial distribution of the energy deposited into the lattice by the primary knock-on atom (PKA). We follow the time evolution of the cascade core in two ordered intermetallics Ni3Al and NiAl, using the molecular dynamics (MD) method with the embedded potential and with the liquid droplet model (LDM) in which a simplified version of the heat equation is solved. Moreover, the MD was used to determine the evolution of the local structure and to identify the disordered zones. The LDM allows us, after a calibration with MD results, to estimate the dependence of the molten volume on the PKA energy up to 1 MeV. The results show good agreement with other published simulations and the available transmission electron microscopy (TEM) observation experiments.

Atomistic computer simulations of shock waves

I present a brief history, from my own personal perspective, of molecular dynamics (MD) computer simulations of shock waves without chemical reaction. Beginning with radiation-damage cascades in the 1960's, followed by shock waves in perfect crystals in the 1970's, dense fluids in the 1980's, and dilute gases in the 1990's, the field of MD simulations (not to mention the computers supporting them) has evolved to the point where we can begin to study weakshock induced plasticity in the solid state, which is dominated by sparsely distributed initial defects. Finally, I conclude with a brief discussion of new developments in the related area of simulating shock-induced spallation in solids, and comment on atomistic simulations of shockwave phenomena of the future (including chemical reaction), made possible by the advent of massively parallel computers.

Liquid drop model and effects of electronic energy loss on radiation damage cascades

Abstract We present two aspects of the thermal behaviour of cascades, related to the mechanisms of heat transport. The first aspect concerns the PKA energy range where subcascades are produced and discusses the thermal interaction between them. For this description we couple the results of the Binary Collision Approximation (BCA) to a simplified solution of the heat equation. Comparison with Molecular Dynamics (MD) results when available supports this approach. However this analysis only considers lattice conductivity, neglecting the possible effects of electronic transport. In the second part of this presentation we consider the effects of the electronic energy loss on the dynamics of thermal spikes in Cu. This study is based on a simple model of the stopping power and the electron phonon interaction in the framework of the Embedded Atom Model (EAM) for MD. This approach is only valid for weak-coupling systems, like Cu, where we obtain quantitative information on the effect.

Simulation of thin foils and bulk irradiations: recoil emission from surfaces and thermal spike effects

Cooling of radiation damage cascades in the bulk, close to a perfect heat sink or close to a reflecting boundary has been followed using the liquid droplet model. Time evolutions of the molten volume and of ion mixing showed rather small differences in cooling behaviour.

Radiation Damage Cascades: The Liquid Drop Model with the Lattice at Finite Temperature

Radiation Damage Cascades: The Liquid Drop Model with the Lattice at Finite Temperature

Radiation damage cascades: Liquid droplet treatment of subcascade interactions

Starting from the radiation damage cascades, as obtained using the binary collision approximation, we derive the energy density deposited into the lattice by the primary knock-on atom. Assuming cascade core melting we follow the time evolution of the System by solving a simplified version of the beat equation. This procedure gives a thermodynamic description of the cascades that allows us to analyze the influence of the cascade geometry on parameters like ion mixing, life time and volume of the melt. This is done in an energy range which is not covered by more precise descriptions, such as molecular dynamics (MD), representing then a useful technique to qualitatively evaluate the effects of radiation damage.

Thermal behavior of radiation damage cascades via the binary collision approximation: Comparison with molecular dynamics results

Based on the profile of the energy deposition obtained using the binary collision model, we follow the diffusion of energy by solving a simplified version of the heat equation. An estimation of the molten zone compares very well with the molecular dynamics prediction for the same event. We discuss the reasons for this agreement and the relevance of such simplified procedure in terms of present-day computer limitations to simulate high energy cascades using molecular dynamics.

Hyperfine interactions of impurities in defect sites in ion-implanted metals

The lattice location of ion-implanted radioactive isotopes in metals and their interactions with defects in their own radiation damage cascade are of importance for studies of the hyperfine interactions of such probe atoms by nuclear methods. Recent results from Mössbauer and PAC experiments in particular are reviewed. Emphasis is put on lattice site identifications, which can be inferred from measured lattice-dynamical and hyperfine interaction parameters of probe atoms. Some general conclusions on the hyperfine interactions in interstitial- and vacancy-type complexes are drawn.

Impurity-vacancy complexes in ion-implanted iron

The formation and annealing of impurity-defect complexes in ion-implanted iron has been studied by 119Sn Mössbauer spectroscopy. Radioactive 119In ions, decaying to the 24 keV Mössbauer state of 119Sn, have been implanted with an energy of 60 keV at temperatures around stage III (100–500 K). Large fractions of the implanted impurities are located on substitutional lattice sites. In-defect complexes are formed both athermally in the radiation-damage cascades (below 180 K) and by trapping of mobile defects (∼ 200K) at the impurities. For two different complexes, one of which anneals around 300 K, the magnetic field at the Sn nucleus is found to be larger by 10 and 20%, respectively, compared to the field of substitutional Sn. A third complex with a field lower by about a factor of three is formed in the whole temperature range up to 500 K. From the measured Mössbauer parameters the impurity-defect structures are proposed to be of the impurity-vacancy type.

A stochastic theory of particle transport. II

For pt.I see Proc. R. Soc., A358, p.105 (1977). The authors are concerned with the development of radiation damage cascades initiated by fast incident particles. They derive a general probability balance equation for the number of vacancies and interstitials in given regions of space, subject to an initial atom of specified velocity. The scattering model is quite general but they do employ the radiation damage model due to Kinchin and Pease (1955). Introduction of a generating function enables the various moments of the vacancy and interstitial distributions to be obtained. Explicit equations for the vacancy and interstitial densities and their two particle correlation functions are derived. They introduce the straight-ahead approximation and solve the resulting density equations by Laplace transform. Explicit expressions are obtained for the two densities over the complete space and energy range. Calculations show the existence of a vacancy rich region near the point of origin of the cascade. The proportionality of the size of the vacancy rich zone to the logarithm of the incident energy is noted and a useful semi-empirical formula is obtained.

On the validity of energy partitioning in the theory of radiation damage cascades

A detailed investigation has been made of the number of defects produced by a primary knock on atom in a medium of similar atoms. Electronic stopping and channelling have been included and it is clearly seen that, for m>1/4, Lindhard's energy partitioning theory is valid to a high degree of accuracy. For m<or=1/4 where the normal energy deposition function diverges, new expressions have been obtained for the number of defects produced in terms of a correction factor to be applied to the Kichin-Pease result (1955). The main assumption underlying the above work is that the angular distribution in the centre of mass system is isotropic but can be partially corrected for by the use of a transport mean free path. The combined effect of channelling, using Oen p-factor (1963), and electronic stopping are studied, and exact solutions enable their relative importance to the cascade to be assessed.

A stochastic theory of particle transport

A probability balance equation is formulated for the number of particles present in a cascade resulting from multiple births at each collision. Janossy’s regeneration point method is used and it leads to an integro differential equation for the generating function from which statistical information can readily be extracted. The technique is applied to the interpretation of radiation damage cascades in a homogeneous, amorphous medium in which two particles are ‘born’ per collision. The history of a single chain is followed and equations for the mean and variance are obtained as well as for individual probabilities. It is further shown how the backward and forward forms of the Boltzmann equation are related via the Green function of the system. Additional study shows that the variance also obeys a forward type of equation although its solution is not obtained as conveniently as that of the corresponding backward equation. Several analogies are made with other branches of particle physics; in particular, cosmic rays and neutron transport.

A fluctuation problem in particle transport theory I

The fluctuation in the number of collision suffered by particles as they slow down in a moderating medium is studied via a probability balance equation. The equation describes the collision history of foreign particles slowing down in a host medium and also accounts for the recoil particles produced in the collision. The equations are solved by the introduction of a generating function from which the space and time dependent probability distributions are obtained. That is, the probability that a particle will suffer just N collisions to reach energy E at a time t after injection. In the space dependent case it is the probability that a particle suffers just N collisions to travel a given path length before coming to rest. Explicit expressions for the means and variances are obtained by solving a difference equation. From this solution it has been possible to obtain exact expressions for hard spheres and for a variety of models based on the inverse power law approximation. A number of new results are presented and some old ones rederived in a more efficient and general manner. The results are of value in the understanding of radiation damage cascades and in neutron slowing down in moderating materials.

The time-energy distribution of atoms in a radiation damage cascade

The time-energy distribution of atoms in a cascade induced by a primary knock-on is obtained by solving the Boltzmann equation. A more general scattering law is used than has hitherto been possible which is based upon a rational approximation to the Thomas-Fermi model of atomic scattering. The virtue of this scheme is that it remains possible to obtain an exact, closed form solution but allows a more realistic description of the scattering process. Time moments of the distribution are obtained from which the slowing down time and associated variance can be calculated. It is shown that the complete time-energy distribution may be reconstructed from the moments.

The time-energy distribution of radiation damage cascades with electronic stopping

Abstract Using a flexible model of scattering for atomic collisions and the continuous energy loss approximation for electronic stopping, we have obtained exact solutions of the time-energy distribution of atoms slowing down in cascade from a primary knock on. The time moments are constructed from which the slowing down time and relative variance may be calculated. Some results of Sanders and Winterbon are generalized and the connection between the backward equation of conventional damage theory and the partial adjoint of the forward equation are pointed out. We also discuss two complementary methods for calculating energy deposition by atoms as they slow down.

Time dependence of radiation damage cascades

Abstract Equations describing the time-dependent evolution of heavy-ion radiation damage cascades are derived, and some numerical calculations are presented. The derivation is more rigorous than the usual time-independent one.