Evolution Of Cascades Research Articles

Parton cascade description of heavy-ion collisions at CERN?

There seems to be a general consensus now that a first glimpse of a QGP-like effect has become visible in the beautiful NA50 data on J/ψ production and the ‘anomalous supression’ phenomenon. On the other hand, it is still widely believed that the dynamics of heavy-ion collisions at CERN SPS energy is predominantly governed by soft, non-perturbative physics. This is ironic: after all, it is unlikely that a QGP could be formed if the underlying dynamics were essentially soft, rather than that it requires intense quark-gluon production with sufficient cascade-like reinteractions which drive the matter to large density and equilibrium. Therefore, I advocate in this contribution that for ultra-relativistic nucleus-nucleus collisions a description based on the pQCD interactions and cascade evolution of involved partons can and should be used, owing to the claim that short-range parton interactions play an important role at sufficiently high beam energies, including CERN energy √s≃ 20 A GeV. Here mini-jet production which liberates of quarks and gluons cannot be considered as an isolated rare phenomenon, but can occur quite copiously and may lead to complex multiple cascade-type processes.

Modeling irradiation growth of zirconium and its alloys

This paper outlines the issues and methodology involved in the modeling of irradiation growth in Zr and its alloys, emphasizing on the effects of production bias and of anisotropic diffusion of the point defects. Due to the anisotropy of the crystal structure, the usual rate theory model for cubic metals, which assumes the isotropic diffusion of point detects, do not accurately reflect the reaction kinetics of point-defects in Zr. A model based on the reaction rate theory of anisotropically diffusing reactants predicts that the duffisional anisotropy difference (DAD) between vacancies and interstitials can produce a large bias. This bias is a zero-order effect and completely dominates the conventional dislocation bias caused by the first-order elastic interaction between the point-defect and the sink. Thus, contrary to the usual rate theory model, the bias for edge dislocations in Zr depends on their line directions, and need not be biased towards interstitials. Grain boundaries and surfaces are biased sinks also, and are biased towards the vacancies or interstitials or vacancies according to their orientations. This large variety of biases for sinks adds a new dimension to the complexity of deformation behaviour to non-cubic metals. In this paper, we show that the diffusional anisotropy can be obtained from loop-growth measurements under HVEM. Under cascade damage conditions, the production and evolution of primary clusters is taken into account within the production bias theory. The possibility of fast diffusing vacancy—impurity atom pairs is also considered. The intergranular compatibility requirement in the growth of polycrystalline samples is satisfied using the self-consistent model. Application of the present model to the growth behaviour of polycrystalline Zircaloy-2 yields results which agrees very well with the observation.

Computer simulation of a 10 keV Si displacement cascade in SiC

The threshold energy for atomic displacement and the evolution of high-energy displacement cascades in β-SiC have been examined using molecular dynamics simulations. A modified form of the Tersoff potential was used in combination with a repulsive potential obtained from density functional theory to describe the interactions between the atoms. The evolution of lattice damage in a 10 keV Si cascade was studied for about 10 ps. The system size varied from 8000 atoms for the displacement energy calculations to 192,000 atoms for the cascade simulations. The results indicate that the minimum displacement energy is about 36 eV for Si and 28 eV for C. The cascade lifetime was found to be of the order of 0.1 ps, and the surviving C vacancies and interstitials outnumbered the corresponding Si defects by a factor of about 3. These results are discussed in light of previous theoretical and experimental studies of radiation damage in SiC.

Mechanisms of ion beam mixing in metals and semiconductors

Ion beam mixing was investigated in crystalline and amorphous semiconductors and metals using molecular dynamics simulations. The magnitude of mixing in an amorphous element compared to its crystalline counterpart was found to be larger by a factor of 2 or more. Mixing in semiconductors was found to be significantly larger than in a face-centered-cubic (fcc) metal of corresponding mass and atomic density. The difference in mixing between amorphous and crystalline materials is attributed to local relaxation mechanisms occurring during the cooling down phase of the cascade. Comparison of mixing in semiconductors and metals shows that short range structural order also has a significant influence on mixing. The mixing results in fcc metals indicate that the role of the electron–phonon coupling in the evolution of collision cascades may be less significant than previously thought.

Parton cascade description of heavy-ion collisions at cern?

There seems to be a general consensus now that a first glimpse of a QGP-like effect has become visible in the beautiful NA50 data onJ/ϕ production and the ‘anomalous supression’ phenomenon. On the other hand, it is still widely believed that the dynamics of heavy-ion collisions at CERN SPS energy is predominantly governed by soft, nonperturbative physics. This is ironic: after all, it is unlikely that a QGP could be formed if the underlying dynamics were essentially soft, rather than that it requires intense quark-gluon production with sufficient cascade-like reinteractions which drive the matter to large density and equilibrium. Therefore, I advocate in this contribution that for ultrarelativistic nucleus-nucleus collisions a description based on the pQCD interactions and cascade evolution of involved partons can and should be used, owing to the claim that short-range parton interactions play an important role at sufficiently high beam energies, including CERN energy $$\sqrt s \simeq 20$$ A·GeV. Here mini-jet production which liberates of quarks and gluons cannot be considered as an isolated rare phenomenon, but can occur quite copiously and may lead to complex multiple cascade-type processes.

VNI 3.1 MC-simulation program to study high-energy particle collisions in QCD by space-time evolution of parton-cascades and parton-hadron conversion

VNI is a general-purpose Monte Carlo event generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. On the basis of renormalization-group improved parton description and quantum-kinetic theory, it uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme that is governed by the dynamics itself. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons, in position space, momentum space and color space. The parton evolution is described in terms of a space-time generalization of the familiar momentum-space description of multiple (semi) hard interactions in QCD, involving 2 → 2 parton collisions, 2 → 1 parton fusion processes, and 1 → 2 radiation processes. The formation of color-singlet pre-hadronic clusters and their decays into hadrons, on the other hand, is treated by using a spatial criterion motivated by confinement and a non-perturbative model for hadronization. This article gives a brief review of the physics underlying VNI, which is followed by a detailed description of the program itself. The latter program description emphasizes easy-to-use pragmatism and explains how to use the program (including a simple example), annotates input and control parameters, and discusses output data provided by it.

Molecular dynamics simulations of displacement cascades in α-iron

Radiation damage in α-iron has been investigated by molecular dynamics simulations using an embedded atom type many-body potential (EAM). Defect production and clustering were studied in high energy (up to 10 keV) displacement cascades as well as the influence of the lattice temperature on these results. A local approach was developed to measure physical parameters, as the crystalline order or the distribution of the kinetic energy, in selected cells of the initially subdivided crystal during the cascade evolution. The detailed analysis of atomic displacements showed the quasi-channeling of some particles in the crystal. In a preliminary study, atomic mass effects on defect production were pointed out in an α-iron system where the mass for 50% of the atoms was artificially reduced to the mass of aluminum.

Point defect survival and clustering fractions obtained from molecular dynamics simulations of high energy cascades

The evolution of high-energy displacement cascades in iron has been investigated for times up to 200 ps using the method of molecular dynamics simulation. The simulations were carried out using the MOLDY code and a modified version of the many-body interatomic potential developed by Finnis and Sinclair. Previously reported results have been supplemented by a series of 10 keV simulations at 900 K and 20 keV simulations at 100 K. The results indicate that the fraction of the Frenkel pairs escaping in-cascade recombination is somewhat higher and the fraction of the surviving point defects that cluster is lower in iron than in materials such as copper. In particular, vacancy clustering appears to be inhibited in iron. Many of the larger interstitial clusters were observed to exhibit a complex, three-dimensional morphology. The apparent mobility of the 〈111〉 crowdion and clusters of 〈111〉 crowdions was very high.

Binding energy effects in cascade evolution and sputtering

The marlowe model was extended to include a binding energy dependent on the local crystalline order: atoms are bound less strongly to lattice sites near surfaces or damage. Sputtering and cascade evolution were studied in self-ion irradiations of Cu and Au monocrystals. In cascades, the mean binding energy is reduced ∼8% in Cu with little dependence on the initial energy; in Au, it is reduced ∼9% at 1 keV and ∼15% at 100 keV. In sputtering, the mean binding energy is reduced ∼8% in Cu and ∼15% in Au with little energy dependence; the yields are increased less, averaging about half as much. Most sites from which atoms are sputtered are isolated in both metals. Small clusters of sites occur in Cu, but there are some large clusters in Au, especially in {111} targets. There are always more large clusters with damage-dependent binding than with a constant binding energy, but only a few clusters are compact enough to be regarded as pits.

Change of electrical properties of alloys and excitation of low-temperature atom mobility by ion bombardment

In situ measurements have been carried out of electrical resistance of submillimetre (100 μm thick) specimens of alloys of the (Pd 1− x Au x ) 3Fe system which have been submitted to ion bombardment by 20 keV Ar + ions at different temperatures (20–450°C). It has been established that ion irradiation brings about a process of atom ordering over the entire depth of initially disordered (quenched from 1000°C) specimens at temperatures substantially lower than thermal disorder-to-order critical temperature. A number of special features has been revealed in the observed action which are difficult to explain in terms of any of the known effects and, in particular, by radiation-enhanced diffusion. The hypothesis is suggested that the observed effect could be connected with atom regrouping at the solitary shock wave front induced by ion bombardment as a result of evolution of atomic collision cascades.

Relocation cross-sections in silicon: Theoretical models

In the calculation of atomic mixing processes induced by energetic ion beams in solids, a key quantity is the relocation cross-section. Very few analysis of these quantities are available for specific targets, and even in the relatively simpler collisional stage of cascade evolution uncertainties still exist as to the correctness of available estimates. The results of a test case study are reported, where a well defined situation is investigated using two theoretical tools, Molecular Dynamics and Analytical Theory. The model case refers to bulk relocations produced in a silicon target by low-energy self recoils. Of special interest is to find ways to improve the theoretical estimates of relocation parameters which may then be used to predict the more complicated fluence dependent evolution of the concentration profile of irradiated targets.

Relocation cross-sections in silicon: Theoretical models

In the calculation of atomic mixing processes induced by energetic ion beams in solids, a key quantity is the relocation cross-section. Very few analysis of these quantities are available for specific targets, and even in the relatively simpler collisional stage of cascade evolution uncertainties still exist as to the correctness of available estimates. The results of a test case study are reported, where a well defined situation is investigated using two theoretical tools, Molecular Dynamics and Analytical Theory. The model case refers to bulk relocations produced in a silicon target by low-energy self recoils. Of special interest is to find ways to improve the theoretical estimates of relocation parameters which may then be used to predict the more complicated fluence dependent evolution of the concentration profile of irradiated targets.

A comparison of displacement cascades in copper and iron by molecular dynamics and its application to microstructural evolution

The use of molecular dynamics simulation and improved many-body potentials make it possible to compare displacement cascade evolution in different materials. However, the extreme variability between individual cascades requires multiple simulations at nominally identical conditions of temperature and energy in order to assure that the comparison is statistically valid. We describe such a comparison of copper and iron in this paper. Over 600 cascades have been investigated, with simulation energies in the range 60 eV to 10 keV and temperatures from 100 to 900 K. The evolution of the cascades is similar in both materials, with the development of a highly disordered core and the emission of focusons and replacement collision sequences during the collisional phase of the cascade. The majority of vacancy-type defects are found in the cascade core when in-cascade recombination is complete, while the interstitial-type defects tend to be distributed around the periphery of this region. The final defect structure has been characterized by the total surviving defect fraction, and the number and size of the point defect clusters produced. Since these parameters have significant implications for the nuclear industry in its assessment of radiation damage, we show how they depend on cascade energy and temperature. To illustrate their importance, we provide an example of how the molecular dynamics results can be used in a rate theory model of ferritic steel embrittlement.

Structural transformations and defect production in ion implanted silicon: a molecular dynamics simulation study.

We have simulated collisions of 5 keV silicon atoms with a silicon substrate. At this energy the simulation provides an atomistic description of the evolution of the displacement cascade. We discuss the structural changes occurring as the cascade regions transform from crystalline to liquid to amorphous phases. We compare the structure of the amorphous material with that of rapidly quenched liquid silicon. We also discuss the time evolution of the stress, kinetic and potential energies, and atomic density. An assessment of defect production mechanisms is made.

Displacement cascades in the ordered compound CuTi studied by molecular-dynamics simulations

The properties of displacement cascades of up to 5 keV in energy in the ordered intermetallic compound CuTi were investigated by molecular-dynamics simulations. Various aspects of the cascade evolution were examined, including the production of Frenkel pairs, “pure” replacements, and antisite defects, as well as the anisotropy of the displacement threshold energy. The minimum displacement threshold energy (15 eV) is found for the 〈100〉 recoil directions. The average threshold energy for displacement initiated by a Ti primary-knock-on atom (78 eV) is ∼ 1.7 times larger than that by a Cu primary-knock-on atom (47 eV). The damage function was analyzed, based on the average number of stable Frenkel pairs generated by both kinds of primary knock-on atoms in 18 directions. Multiple defect production is found for cascade energies ≥ 500 eV. Around this energy, ∼ 25 replacements are created for each stable Frenkel pair. Planar cascades occur in the (100), (010) and (110) planes under certain conditions, producing significantly more Frenkel pairs than in the case of three-dimensional cascades. Melting of the core of a 5 keV cascade during the first 5 ps causes efficient, local atomic mixing. After recrystallization at the end of the event, the impact region shows a high degree of chemical disorder, characterized by a chemical short-range order parameter of 0.49. The efficiency of Frenkel-pair production by a 5 keV recoil is estimated to be 0.14.

Multifractality and multiscaling in collision cascades.

It is shown that self-ion collisional cascades exhibit multifractality. The structure of the cascades was studied by analyzing the length distribution n(l,L) of the free flight path l traveled by particles during the cascade evolution. It was found that the collisional cascade can be partitioned into an infinity of subsets, each one characterized by a fixed value of x=lnl/lnL (where L is the system size) and a distinct value of the fractal dimension \ensuremath{\varphi}(x). The mechanism for multifractality based on an underlying multiplicative process is illustrated on a simple geometrical model. The multiscaling structure of the function n(l,L) is discussed.

Molecular dynamics study of sputtering of Cu (111) under Ar ion bombardment

Abstract We have used the molecular dynamics (MD) technique using many-body interaction potentials to analyse in detail the processes leading to sputter emission, in order to gain a microscopic understanding of low energy bombardment phenomena. Calculations were performed for a Cu (111) single crystal surface bombarded with Ar atoms in the energy range from 10–1000 eV. The results presented for low bombarding energies are mainly concerned with the near sputtering threshold behaviour, yields and depth of origin of sputtered atoms. Furthermore, it is found, that in addition to sputtered atoms, a large number of ad-atoms at the surface are generated during the evolution of the collision cascade. At higher energies the question of cluster emission and especially their energy distribution and angular distribution are addressed. It was found that the energy distributions for the dimers and monomer atoms exhibit a similar dependence on emission energy as has been observed recently also experimentally. For atoms ...

Molecular dynamics simulation of irradiation damage cascades in copper using a many-body potential

Abstract The evolution of irradiation damage cascades in copper has been simulated by molecular dynamics, using a many-body potential. Nearly 200 cascades have been produced with random knock-on directions and primary knock-on atom (PKA) energies in the range from 60 eV to 10 keV. The starting temperature for these simulations was 100 K and 600 K, this report will confine itself to the data obtained at 100 K. The cascade evolution has been followed for times typically up to ∼10 psec and in some cases up to ∼30 psec. The cascades are characterised by the sudden emission of replacement collision sequences and with shape variations due to local channelling events. At the higher energies the core has been shown to be liquid-like structure with cavitation. The annealing phase leaves loosely clustered vacancies at the cascade centre but collapse to a vacancy loop is not generally observed. A feature of the more energetic cascades is the production by a ballistic mechanism of interstitial atom clusters at the pe...

A molecular dynamics study on the collisional and cooling phases of cascade damage

Abstract Presented at the IEA Workshop on the Use of Molecular Dynamics in Modelling Radiation Effects and Other Non-equilibrium Phenomena, May 6–8, 1991 at La Jolla, USA Molecular dynamics calculations were performed to study the cascade damage evolution initiated from a primary knock-on atom of 250 eV. The thermodynamic characterization of the cascade was investigated by the Morse potential and it is found that during the cooling phase of the cascade local equilibrium was realized. Cascade evolution by the simple embedded atom method (EAM) potential was also calculated and the effects of initial target temperatures on the cascade processes were discussed.

Time and temperature dependence of cascade induced defect production in in situ experiments and computer simulation

Understanding of the defect production and annihilation processes in a cascade is important in modelling of radiation damage for establishing irradiation correlation. In situ observation of heavy ion radiation damage has a great prospect in this respect. Time and temperature dependence of formation and annihilation of vacancy clusters in a cascade with a time resolution of 30 ms has been studied with a facility which comprises a heavy ion accelerator and an electron microscope. Formation and annihilation rates of defect clusters have been separately measured by this technique. The observed processes have been analysed by simple kinetic equations, taking into account the sink effect of surface and the defect clusters themselves together with the annihilation process due to thermal emission of vacancies from the defect clusters. Another tool to study time and temperature dependence of defect production in a cascade is computer simulation. Recent results of molecular dynamics calculations on the temperature dependence of cascade evolution are presented, including directional and temperature dependence of the lengths of replacement collision sequences, temperature dependence of the process to reach thermal equilibrium and so on. These results are discussed under general time frame of radiation damage evolution covering from 10 −15 to 10 9 s, and several important issues for the general understanding have been identified.