Publications of Kai Nordlund

Equilibrium concentrations of self-interstitial atoms and divacancies have been determined in Cu by molecular dynamics computer simulations using embedded atom potentials. Near the melting temperature these concentrations are both $\sim 10^{-6}$. Owing to the higher mobility of the interstitial atoms, however, they contribute more to diffusion. In perfect, or pulse-heated crystals, spontaneous Frenkel pair production results in even higher interstitial concentrations.

Phys. Rev. Lett. 80 (1998) 4201

Electron-phonon coupling in energetic collision cascades is believed to greatly enhance the cooling rate of heat spikes in many metals. Previous studies have not been able to conclusively determine the magnitude of the coupling, however. By directly comparing ion beam mixing experiments and molecular dynamics simulations of collision cascades in Ni, Pd and Pt, metals in which the coupling is believed to be most important, we show that the influence of electron-phonon coupling on mixing can be no more than about 30 %, roughly an order of magnitude less than the most widely used models predict.

Phys. Rev. B. (Rapid comm.) 57 (1998) 13965

We study ion beam mixing of metallic bilayer interfaces using classical molecular dynamics simulations of 5 keV collision cascades in the vicinity of Co/Cu and Ni/Cu (111) interfaces. We find that the production of vacancies and interface roughening is asymmetrical. On average, more Cu is introduced into the Co or Ni parts than vice versa, and more vacancies are produced in the Cu, indicative of an inverse Kirkendall effect in collision cascades. The effect is explained by the difference in melting points leading to different recrystallization rates of the two materials.

Phys. Rev. B 59 (1999) 20.

Ion irradiation is a common technique of materials processing, as well as being relevant to the radiation damage incurred in nuclear reactors. Early models of the effects of ion irradiation typically assumed that particles undergo two-body elastic collisions, like billiard balls colliding in three dimensions. Later descriptions invoked such phenomena as localization of kinetic energy, thermalization and localized melting. In all these descriptions, the displacement of atoms is chaotic in that slight variations in the ion's trajectory produce completely different, unpredictable sets of atomic displacements. Here we report molecular-dynamics simulations of high-energy self-bombardment of copper and nickel, in which we see collective displacements of atoms. The high pressures developed in collision cascades centred well below the surface can cause a coherent displacement of thousands of atoms, over tens of atomic planes, in a shear-induced slip motion towards the surface. The mechanism leads to a significant increase in damage production near the surface, characterized by well-ordered islands of adsorbed atoms. Our findings suggest an explanation for some features of radiation damage, as well as for differences between ion and neutron irradiation.

Nature 398, 49 - 51 (1999) © Macmillan Publishers Ltd.

Preprint of publication not available due to copyright restrictions.

For an accurate prediction of penetration depths of energetic ions in materials, especially in crystal channels, a realistic electronic stopping model is needed. Usually simulation codes employing the binary collision approximation are used and the electronic stopping is calculated from either a spherically symmetric or uniform charge distribution. By using molecular dynamics and calculating the electronic stopping from a 3D charge distribution without using any free parameters, we obtain accurate range distributions on a realistic physical basis. Our electronic stopping model is based on the Brandt--Kitagawa (BK) [W. Brandt and M. Kitagawa, Phys. Rev. B 25 5631(1982)] theory, in which the electronic stopping of a heavy ion is the electronic stopping of a proton scaled by the square of the effective charge. We first test the model for hydrogen, to determine whether or not a basis exists for the scaling hypothesis, and then for other ions. The results are compared with experimental range profiles and show good agreement, much better than that achieved by using standard (nonlocal) electronic stopping models. Our model has a sound physical basis, no free parameters and can be used for all ion-target--combinations.

Phys. Rev. B 62 (2000) 3109.

The erosion of carbon by intensive hydrogen bombardment has been recently shown to decrease sharply at very high fluxes (~ 10¹⁹ ions/cm²s). This effect can not be explained by standard sputtering or erosion models, yet understanding it is central for selection of fusion reactor divertor materials, and formulation of sputtering models for high-flux conditions. Using molecular dynamics computer simulations we now show that the effect is due to the buildup of a high hydrogen content at the surface, leading to a shielding of carbon atoms by the hydrogen.

Phys. Rev. B (Rapid commun.) 60 (1999) 14005.

Since extrinsic stacking faults can form during post-implantation annealing of Si, understanding their properties is important for reliable control of semiconductor manufacturing processes. We demonstrate how grazing-incidence X-ray scattering methods can be used as a non-destructive means for detecting extrinsic stacking faults in Si. Atomistic analysis of diffuse intensity streaks is used to determine the size of the faults, the minimum size at which the streak pattern in the scattering will be visible, and the magnitude of atomic displacements in the center of the stacking fault.

Appl. Phys. Lett. 76 (2000) 846

Diffuse X-ray scattering is a powerful means to study the structure of defects in crystalline solids. The traditional analysis of diffuse X-ray scattering experiments relies on analytical and numerical methods which are not well suited for studying complicated defect configurations. We present here an atomistic simulation method by which the diffuse X-ray scattering can be calculated for an arbitrary finite-sized defect in any material where reliable interatomic force models exist. We present results of the method for point defects, defect clusters and dislocations in semiconductors and metals, and show that surface effects on diffuse scattering, which might be important for the investigation of shallow implantation damage, will be negligible in most practical cases. We also compare the results with X-ray experiments on defects in semiconductors to demonstrate how the method can be used to understand complex damage configurations.

J. Appl. Phys. 88 (2000) 2278-.

It has long been clear that vacancies are usually the most abundant defect in equilibrium in most dense, close-packed metals. However, some important effects, such as the observed deviation of the diffusion coefficient from pure Arrhenius behaviour, can not be explained by invoking only a single vacancy. The most common explanation to the deviations is that also divacancies, and possibly even trivacancies, play a significant role. However, some evidence also indicate that interstitials could play a significant role. In this article, we review some recent work and our computer simulation results on this issue. Both the reviewed work and simulations point in the direction that the interstitial could be of major importance close to the melting temperature and during rapid heating. The results also strongly support the Granato model of liquids and solids.

Defect and Diffusion in Metals - Annual Retrospective 2000 ( invited review paper )

Preprint of publication not available, but see the PRL on the same topic.

Defect formation in compound semiconductors such as GaAs under ion irradiation is not as well understood as in of Si and Ge. We show here how a combination of ion range calculations and molecular dynamics computer simulations can be used to predict the atomic-level damage structures produced by MeV ions. The results show that the majority of damage produced in GaAs both by low-energy self-recoils and 6 MeV He ions is in clusters, and that a clear majority of the isolated defects are interstitials. Implications of the results to suggested applications are also discussed.

J. Appl. Phys. 90 (2000) 1710.

Recent experiments on irradiated carbon nanotubes evidence that ion bombardment gives rise to their amorphization and dramatic dimensional changes. Using an empirical potential along with molecular dynamics, we study structure and formation probabilities of atomic-scale defects produced by low-dose irradiation of nanotubes with Ar ions. For this, we simulate impact events over a wide energy range of incident ions. We show that the maximum damage production occurs for a bombarding ion energy of about 600 eV, and that the most common defects produced at all energies are vacancies, which at low temperatures are metastable but long-lived defects. Employing the tight-binding Green's function technique, we also calculate STM images of irradiated nanotubes. We demonstrate that irradiation-induced defects may be detected by STM and that isolated vacancies may look like bright spots in atomically-resolved STM images of irradiated nanotubes.

Phys. Rev. B. 63 (2001) 245405

It has recently become clear that electron irradiation can recrystallise amorphous zones in semiconductors even at very low temperatures, and even when the electron beam energy is so low that it can not induce atomic displacements by ballistic collisions. We study the mechanism of this effect using classical molecular dynamics augmented with models describing the breaking of covalent bonds induced by electronic excitations. We show that the bond-breaking allows geometric rearrangement at the crystal-amorphous interface which can induce recrystallisation in silicon without any thermal activation.

Phys. Rev. B 64 (2001) 125313

We are studying ion irradiation induced amorphization in Si, Ge and GaAs using molecular dynamics simulations. Although high-energy recoils produce defects and amorphous pockets, we show that low-energy recoils (about 5 - 10 eV) can lead to a significant component of athermal recrystallization of pre-existing damage. For typical experimental irradiation conditions this recrystallization is, however, not sufficient to fully recrystallize larger amorphous pockets, which grow and induce full amorphization. We also examine the coordination and topological defect structures in Si, Ge and GaAs observed in the simulations, and find that these structures can explain some experimentally observed features found in amorphous semiconductors. For irradiated amorphous GaAs, we suggest that long (about 2.8 Å) and weak Ga-Ga bonds, also present in pure Ga, are produced during irradiation.

Phys. Rev. B 65 (2002) 165329

Using classical molecular-dynamics simulations we examine the formation of craters during 0.4-100-keV Xe bombardment of Au. Our simulation results, and comparison with experiments and simulations of other groups, are used to examine to what extent analytical models can be used to predict the size and properties of craters. We do not obtain a fully predictive analytical model (with no fitting parameters) for the cratering probability, because of the difficulty in predicting the probability of cascades splitting into subcascades, and the relation of the heat spike lifetime and energy density. We do, however, demonstrate that the dependence of the crater size on the incident ion energy can be well understood qualitatively in terms of the lifetime of the heat spike and the cohesive energy of the material. We also show that a simple energy density criterion cannot be used to predict cratering in a wide ion energy range because of the important role of the heat spike lifetime in high-energy cascades. The cohesive energy dependence differs from that obtained for macroscopic cratering (observed, e.g., in astrophysics) because of the crucial role of melting in the development of heat spikes.

Phys. Rev. B, 64, 235426 (2001)

Using empirical-potential and tight-binding models, we study the structure and stability of atomic-scale irradiation-induced defects on walls of carbon nanotubes. Since atomic vacancies are the most prolific but metastable defects which appear under low-dose, low temperature ion irradiation, we model the temporal evolution of single vacancies and vacancy-related defects (which isolated vacancies can turn into) and calculate their lifetimes at various temperatures. We further simulate scanning-tunneling microscopy (STM) images of irradiated nanotubes with the defects, employing for this the tight-binding Green's function technique. Our simulations demonstrate that the defects live long enough at low temperatures to be detected by STM and that different defects manifest themselves in STM images in different ways, all of which makes it possible to detect and distinguish the defects experimentally.

J. Vac. Sci. Techn. 20 (2001) 728.

311 defects are extended, rod-like defects which play a central role in the processing of Si during integrated circuit manufacturing. Diffuse x-ray scattering techniques provide a non-destructive means to detect defects in solids. However, to date there has been no knowledge of what the x-ray scattering pattern from 311 defects looks like. Using a recently introduced fully atomistic modeling scheme, I calculate the diffuse x-ray scattering patterns from 311 defects. The results demonstrate how 311 defects can be detected, how the main varieties of 311 defect can be distinguished, and how both the defect width and length can be derived from the scattering.

J. Appl. Phys. 91 (2002) 2978

Molecular dynamics has been successful in predicting range profiles for ions implanted into crystalline materials in the dose regime where it can be approximated that changes in the sample structure do not affect the profiles. Many experimental distributions are, however, strongly dose-dependent due to the amorphization of the crystalline material. This has so far been taken into account only in some binary-collision-approximation calculations with a damage build-up model that depends on the probability for the amorphization to occur at a certain depth. We present here a fast molecular dynamics model for predicting range profiles of ions in crystalline Si. The model includes cumulative damage build-up, where the amorphization states are taken from molecular dynamics simulations of cascade damage. The method can be used to predict profiles for any material. We used silicon because of the large amount of experimental data available. No free parameters were used. Comparison of results to a wide range of experiments show very good agreement.

Nucl. Instr. Meth. Phys. Res. B. 195 (2002) 269-280

Ion irradiation of individual carbon nanotubes deposited on substrates may be used for making metallic nanowires and studying effects of disorder on the electronic transport in low-dimensional systems. In order to understand the basic physical mechanisms of radiation damage production in supported nanotubes, we employ molecular dynamics and simulate ion impacts on nanotubes lying on different substrates, such as platinum and graphite. We show that the defect production depends on the type of the substrate and the damage is higher for metallic heavy-atom substrates than for light-atom substrates, since in the former case sputtered metal atoms and backscattered recoils produce extra damage in the nanotube. We further study the behavior of defects upon high-temperature annealing and demonstrate that, although ions may severely damage nanotubes in a local region, the nanotube carbon network has a unique ability to heal such a strong localized damage due to defect migration and dangling bond saturation. We also show that after annealing the residual damage in nanotubes is independent of the substrate type. We predict pinning of nanotubes to substrates through nanotube-substrate bonds which appear near irradiation-induced defects.

Phys. Rev. B 65 (2002) 164523.

Employing both quantum-mechanical and empirical force models, we use molecular dynamics simulations to obtain sticking cross-sections for CH₃ radical chemisorption on unsaturated sites on carbon surfaces. Effects of the local atomic neighbourhood on the chemisorption were examined in order to compare the results with experiments. Our results show that the chemisorption of a CH₃ radical onto a dangling bond is highly affected by the neighbourhood of the unsaturated carbon atom sites. Notably, sticking cross sections of totally bare dangling bond sites at the surface and sites partly shielded by neighbouring methyl groups were observed to differ by two orders of magnitude, (15.3 ± 1.7) Ų and (0.2 ± 0.1) Ų, respectively.

J. Appl. Phys. 93, 1826 (2003)

Doping is a widely used method to enhance the properties of materials. Despite the recently increased understanding of the mechanisms of chemical erosion by low-energy hydrogen ions, the effect of doping on these types of processes is still not well understood. We study the erosion of Si-doped (0 -- 30 at.\%) carbon under 20 eV deuterium irradiation using molecular dynamics simulations. We show that the chemical sputtering of carbon decreases with increasing Si concentration. The reasons for the reduced sputtering yield lie in the longer Si--C interaction lengths and efficient dynamic rebonding of hydrocarbon species.

J. Appl. Phys. 92 (2002) 2216

Molecular dynamics has proven to be succesful in calculating range profiles for low energy (keV) ions implanted into crystalline materials. However, for high fluences the structure of the material changes during the impl antation process. The crystalline material becomes amorphized, which changes the range profiles. This damage build-up process has usually been taken into account with probabilities for changing the crystal structure during the simulation, and typically only BCA methods have been used. We present a fast MD method that simulates the damage build-up process in silicon, without bringing any free parameters to the simulation. Dama ge accumulation during the implantation is simulated by changing the material structure in front of path of the incoming ion. The amorphization l evel at each depth is proportional to the nuclear deposited energy in that depth region. The amorphization states are obtained from MD simulations of cascade dam age. Silicon was used as a target material because of the large amount of experimental data available. Comparison with the simulations show a go od agreement for a wide range of experiments.

Nucl. Instr. Meth. Phys. Res. B 202 (2003) 132.

Using classical molecular dynamics method we have studied the burrowing mechanis m of Co nanoclusters on a Cu substrate. We found that there are primarily two different mechanisms for the burrowing, depending on the configuration of the cluster after thermal deposition. Deposited clusters with an epitaxial configuration will burrow through vacancy migration a long the Co-Cu interface, and non-aligned clusters burrow through disordered motion of atoms. The re-alignment of the non-aligned c lusters was found to be due to a collective rotational movement of the whole cluster during the burrowing process. We discuss these res ults and perform a comparison with experimental and previously simulated results.

Phys. Rev. B 67 (2002) 075415

Recent experiments have shown that when gold atom clusters bombard copper with an energy of 10 keV/atom, the mean range of the gold atoms is independent of the cluster size, but the straggling (broadening) of the depth distribution is an increasing function of the cluster size. The same set of experiments did not show this effect when the target was amorphous Si. Using molecular dynamics computer simulations we have studied this effect by simulating Au cluster bombardment of Cu and Si with energies 1 -- 10 keV/atom. We found that in Cu, the mean range is not fully independent of the cluster size, but the dependence on cluster size is so weak it is hard to observe experimentally. On the other hand, we found a strong enhancement of the straggling in Cu, but not Si, in agreement with the experiments. By following the time dependence of the straggling we show that this is due to the massive heat spike effects which are present in Cu but not Si.

Phys. Rev. B 68 (2003) 035419

Recent experiments on ion irradiation of heavy metals such as gold and silver have shown that very unusual surface configurations can be produced by the irradiation. Typically, the surface damage has the shape of a crater, similar to those produced by meteorite impacts. The crater shapes are, however, often highly asymmetric and can show extended adatom ridges extending far from the crater well. Using molecular dynamics simulations we show how such exotic atom arrangements are produced. We describe atomic bridges over a crater and illustrate a slingshot-like effect which can propel atom clusters far from an impact position to produce isolated adatom islands.

Nucl. Instr. Meth. Phys. Res. B 206, 189 (2003).

An analytical bond-order potential for GaN is presented that describes a wide range of structural properties of GaN as well as bonding and structure of the pure constituents. For the systematic fit of the potential parameters reference data are taken from total energy calculations within the density functional theory if not available from experiments. Although long-range interactions are not explicitly included in the potential, the present model provides a good fit to different structural geometries including defects and high pressure phases of GaN.

Journal of Physics: Condensed Matter 15 (2003) 5649.

Non-molecular solid nitrogen, metastable even at zero pressure and low temperature, was recently manufactured by Eremets et al. [Nature 411 (2001) 173] and investigated with respect to its pressure stability. In this study we present analytical potential molecular dynamics simulations that allow reproducing all the stages of the experiment. The bonding structure and energetics of the N polymeric state obtained from the dynamical simulations are verified to be reasonable using a plane wave {\it ab initio} method. We predict that the metastable low-pressure phase has predominantly 3-folded bonded atoms in a disordered configuration. The energy accumulated in the metastable phase is about 1 eV/atom.

Europhysics Letters 65 (2004) 400

Recent experiments have shown that when gold atom clusters bombard copper with an energy of 10 keV/atom, the mean range of the gold atoms is independent of the cluster size, but the straggling (broadening) of the depth distribution is an increasing function of the cluster size. The same set of experiments did not show this effect when the target was amorphous Si. Using molecular dynamics computer simulations we have studied this effect by simulating Au cluster bombardment of Cu and Si with energies 1 -- 10 keV/atom. We found that in Cu, the mean range is not fully independent of the cluster size, but the dependence on cluster size is so weak it is hard to observe experimentally. On the other hand, we found a strong enhancement of the straggling in Cu, but not Si, in agreement with the experiments. By following the time dependence of the straggling we show that this is due to the massive heat spike effects which are present in Cu but not Si.

Phys. Rev. B 68, 035419 (2003).

We have used molecular dynamics methods to study the accumulation of damage d uring ion beam irradiation of GaN. First we analyzed individual recoils between 200 eV and 10 keV. We found that the spatial average of the threshold displacement energy was high and much less damage was produced in GaN than in Si, Ge or GaAs cascades. Most of the damage was in isolated point defects or small clusters, which enhanc es the damage recombination probability. Ion beam amorphization was simulated by starting successive 400 eV or 5 keV reco ils in initially perfect crystal. The development of volume, energy and ring statist ics, as well as segregation of compounds was followed through the process. The simul ations show that the amorphization begins with single defects and formation of long weak Ga-Ga bonds in the distort ed lattice. We also observe that nitrogen gas is produced during prolonged irradiation, in agreement with experimental observations. We recognize two reasons for the high amorphization dose of GaN, the high threshold displacement energy (about a factor of 5) and in-cascade recombin ation (about a factor of 1-2).

Phys. Rev. B 68, 184104 (2003)

Using molecular dynamics simulations combined with kinetic Monte Carlo methods w e have studied the evolution of copper nanoclusters on a copper (100) surface. We have developed a method for relaxing the clusters into a suitable configurati on for input into the kinetic Monte Carlo method using molecular dynamics. Using kinetic Monte Carlo methods we have simulated the evolution of clusters wi th sizes of 22 -- 2045 atoms at temperatures of 220 -- 1020 K. We found that the Cu clusters on the surface will be reduced to one monolayer if given enough time to relax, and that this process shows an Arrhenius behaviour. In this article we present the relaxation method we developed and our observatio ns for the evolution of the clusters.

Journal of Physics: Condensed Matter (2004), accepted for publication

We employ a theoretical model to calculate mechanical characteristics of macroscopic mats and fibers of single-walled carbon nanotubes. We further investigate irradiation-induced covalent bonds between nanotubes and their effects on the tensile strength of nanotube mats and fibers. We show that the stiffness and strength of the mats can be increased at least by an order of magnitude, and thus small-dose irradiation with energetic particles is a promising tool for making macroscopic nanotube materials with excellent mechanical characteristics.

Physical Review Letters 93, 215503 (2004)

A reactive interatomic potential based on an analytic bond-order scheme is devel oped for the ternary system W-C-H. The model combines Brenner's hydrocarbon potential with parameter sets for W-W, W-C and W-H interactions and is adjusted to materials properties of reference structures with different local atomic coor dinations including tungsten carbide, W-H molecules as well as H dissolved in bulk W. The potential has been tested in various scenarios, like surface, defect, and me lting properties, none of which were considered in the fitting. The intended area of application is simulations of hydrogen and hydrocarbon inte ractions with tungsten, that have a crucial role in fusion reactor plasma-walls. Furthermore, this study shows that the angular dependent bond-order scheme can b e extended to second-nearest neighbour interactions, which are relevant in bcc metals. Moreover, it provides a possibly general route for modeling metal carbides.

Journal of Applied Physics, accepted for publication (2005)

We have developed a two-band model of Fe-Cr, fitted to properties of the ferro-magnetic alloy. Fitting many-body functionals to the calculated mixing enthalpy of the alloy and the mixed interstitial binding energy in iron, our potential reproduces changes in sign of the formation energy as function of Cr concentration. When applied in Kinetic Monte Carlo simulations, the potential correctly predicts decomposition of initially random Fe-Cr alloys into the $\alpha$-prime phase as function of Cr concentration.

Physical Review B 72 (2005) 214119.

Recent work has shown that atom motion in liquids is not completely homogeneous, but that stringlike cooperative motion can be used to explain several properties of liquids. We now show that with increasing concentration the properties of interstitial atoms in crystalline materials smoothly approach and eventually completely match the properties of the string atoms in liquids. In terms of the interstitialcy theory of liquids and solids, the strings are direct manifestations of interstitials.

Europhys. Lett. 71 (2005) 625.

Numerous experiments have shown that low-energy H ions and neutrals can erode amorphous carbon at ion energies of 1-10 eV, where physical sputtering is impossible, but at erosion rates which are clearly higher than those caused by thermal ions. In this paper we will first review our computer simulation work providing an atom-level mechanism for how this erosion occurs, and then present some new results for H and He bombardment of tungsten carbide and amorphous hydrogenated silicon, which indicate the mechanism can be of importance in a wide range of covalently bonded materials. We also discuss how the presented mechanism relates to previously described abstraction and etching mechanisms.

Pure and Applied Chemistry 78 (2005) 1203-1212

We study the initial state of irradiation damage in WC, an alloy with a large mass difference between the constituents, using molecular dynamics computer simulations. We find that a vast majority of the resulting isolated defects are carbon. Moreover, an in-cascade defect recombination effect even more pronounced than that known previously to occur in metals is observed. Both effects are shown to be related to the high formation energy of W defects.

Phys. Rev. B (Rapid comm.) 74 (2006) 140103

Using large-scale atomistic simulations, we show that the macroscopic cratering behavior emerges for projectile impacts on Au at projectile sizes between 1,000--10,0000 Au atoms at impact velocities comparable to typical meteoroid velocities. In this size regime, we detect the compression of material in Au nanoparticle impacts similar to that observed for hypervelocity macroscopic impacts. The simulated crater volumes agree with the values calculated using the macroscopic crater size scaling law, in spite of a downwards extrapolation over more than fifteen orders of magnitude in terms of the impactor volume. The result demonstrate that atomistic simulations can be used as a tool to understand the strength properties of materials in cases where only continuum models have been possible before.

Phys. Rev. Lett. 101 (2008) 027601, and cover of issue 2.