Table of contents

See the PDF file for the text of this editorial.

Fusion reactors create extreme conditions for structures close to the plasma. It seems unlikely that materials currently being considered can meet all performance requirements under such conditions. We explore the possibility of separating functionality in composite structures to overcome this barrier. To this end, several suggestions of directions are made for the search for such materials. In particular, we note some of the new materials that have become available only in the last two decades. Those discussed include the use of diamond-like carbon coatings, nano-structured materials, layered structures, stacked structures, and viscous coatings, including more complex carbon composite materials. Materials modelling will be an important component in the search for viable materials. However, the extreme conditions and the nature of the radiation damage demand extensions both to molecular dynamics and to the much-used Norgett–Robinson–Torrens model. We identify some of the relevant condensed matter challenges for modelling and materials testing in the fusion context, including the relevance of spallation source neutron testing to fusion materials evaluation.

We combine theoretical and experimental results to study percolation-driven transport phenomena in an irradiated material. We show that whereas the first transition takes place at the value of amorphous fraction , the second transition corresponds to the percolation of depleted phase. The knowledge of the radius of depletion sphere of the isolated damaged region allows one to predict the radiation dose at which the second percolation transition takes place, with dramatic increase in transport.

We present the derivation of an interatomic potential for the iron–phosphorus system based primarily on ab initio data. Transferability in this system is extremely problematic, and the potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Some preliminary molecular dynamics calculations show that P strongly affects point defect migration.

The theoretical basis of density functional pseudopotential methods for determining the properties of defects in semiconductors is given. The formalism is applied to a single illustrative defect, the carbon interstitial in silicon, which has been identified by electron paramagnetic resonance, vibrational mode spectroscopy, photoluminescence and deep-level transient spectroscopy. The theory is shown to largely account for the properties of the defect.

The dynamics of a soft sphere model glass, studied by molecular dynamics, is investigated. The vibrational density of states divided by ω² shows a pronounced boson peak. Its shape is in agreement with the universal form derived for soft oscillators interacting with sound waves. The excess vibrations forming the boson peak have mainly transverse character. From the dynamic structure factor in the Brillouin regime pseudo dispersion curves are calculated. Whereas the longitudinal phonons are well defined up to the pseudo zone boundary the transverse ones rapidly get over-damped and go through the Ioffe–Regel limit near the boson peak frequency. In the high q regime constant-ω scans of the dynamic structure factor for frequencies around the boson peak are clearly distinct from those for zone boundary frequencies. Above the Brillouin regime, the scans for the low frequency modes follow closely the static structure factor. This still holds after a deconvolution of the exact harmonic eigenmodes into local and extended modes. Also the structure factor for local relaxations at finite temperatures resembles the static one. This semblance between the structure factors mirrors the collective motion of chain-like structures in both low frequency vibrations and atomic hopping processes, observed in the earlier investigations.

The usual way of minimizing the total energy of a planar boundary between two crystals by relaxing the atomic positions is inefficient, because it does not exploit the physical insight that forces are localized near the interfaces or surfaces. I introduce a simple change of variables, which leads to much faster and more accurate relaxation in such systems. In general the method is formulated for three-dimensional monoclinic supercells with sides (a,b,c), subject to periodic boundary conditions. If the crystals fill space the method exploits the stress tensor in the supercell to adjust its side c, where the boundary lies in the (a,b) plane, but the stress tensor is not required for a slab of finite thickness, which would be simulated by including a vacuum layer in the supercell. In either case the number of conjugate gradient steps required to relax the atomic positions does not increase with the thickness of the system. The power of this method is demonstrated by calculations on one-dimensional chains, both finite and infinite, using a pair potential to calculate the energy, forces and stresses.

Phase transformations in 2xxx series aluminium alloys (Al–Cu–Mg) are investigated with an off-lattice atomistic kinetic Monte Carlo simulation incorporating the effects of strain around misfitting atoms and vacancies. Atomic interactions are modelled by Finnis–Sinclair potentials constructed for these simulations. Vacancy diffusion is modelled by comparing the energies of trial states, where the system is partially relaxed for each trial state. No special requirements are made about the description of atomic interactions, making our approach suitable for more fundamentally based models such as tight binding if sufficient computational resources are available. Only a limited precision is required for the energy of each trial state, determined by the value of k_BT. Since the change in the relaxation displacement field caused by a vacancy hop decays as 1/r³, it is sufficient to determine the next move by relaxing only those atoms in a sphere of finite radius centred on the moving vacancy. However, once the next move has been selected, the entire system is relaxed.

Simulations of the early stages of phase separation in Al–Cu with elastic relaxation show an enhanced rate of clustering compared to those performed on the same system with a rigid lattice.

Segregation of the cation substitution defects Ba²⁺, Sr²⁺, Ce⁴⁺ and Zr⁴⁺ to the stable low index surfaces of UO₂ has been predicted using atomistic simulation techniques. While Ce⁴⁺ and Zr⁴⁺ substitute simply for U⁴⁺, charge compensation in the form of oxygen vacancies is required in the case of Ba²⁺ and Sr²⁺. Three surfaces are considered: (110), (111) and (100). Although the (111) and (110) are perfect cleaved surfaces, the (100) necessarily incorporates a series of surface defects to neutralize the inherent dipole. The segregation energies of these cations depend strongly on the surface to which the segregation is proceeding. Furthermore, it is also a function of the orientation of the segregating defect cluster with respect to the surface and, in the case of the (100) dipolar surface, the configuration of the surface defects.

A model of a long Josephson junction described by a nonlocal governing fluxon equation, assuming Newtonian dissipation, is presented and studied analytically as well as numerically. From a ballistic trial solution for a steadily moving 2π phase difference kink based on an exact limiting form, observables such as the lower critical field for the appearance of Josephson vortices, the vortex magnetic field, the microscopic voltage across the tunnel layer, and the macroscopic voltage across the junction itself are derived and assessed for nonlocal effects. The current–voltage characteristic of the junction due to a regular array of Josephson vortices moving uniformly along it predominantly exhibits monostability when nonlocality is weak and dissipation high; however, a transition to bistability and associated formation of filaments of different current densities can occur when nonlocality is strong and dissipation low.

The development of the HADES code by Michael Norgett in the 1970s enabled, for the first time, the routine simulation of point defects in inorganic solids at the atomic scale. Using examples from current research we illustrate how the scope and applications of atomistic simulations have widened with time and yet still follow an approach readily identifiable with this early work. Firstly we discuss the use of the Mott–Littleton methodology to study the segregation of various isovalent cations to the (00.1) and (01.2) surfaces of haematite (α-Fe₂O₃). The results show that the size of the impurities has a considerable effect on the magnitude of the segregation energy. We then extend these simulations to investigate the effect of the concentration of the impurities at the surface on the segregation process using a supercell approach. We consider next the effect of segregation to stepped surfaces illustrating this with recent work on segregation of La³⁺ to CaF₂ surfaces, which show enhanced segregation to step edges. We discuss next the application of lattice dynamics to modelling point defects in complex oxide materials by applying this to the study of hydrogen incorporation into β-Mg₂SiO₄. Finally our attention is turned to a method for considering the surface energy of physically defective surfaces and we illustrate its approach by considering the low index surfaces of α-Al₂O₃.

We discuss how two techniques, based on (1) lattice statics/lattice dynamics simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of oxide mixtures at zero and high pressure. The lattice statics/lattice dynamics calculations involve a full free energy structural optimization of each of a number of configurations, followed by thermodynamic averaging. Strategies for generating a suitable set of configurations are discussed. We compare results obtained by random generation with those obtained using radial distribution functions or explicit symmetry arguments to obtain approximate or exact weightings respectively for individual configurations. The Monte Carlo simulations include the explicit interchange of cations and use the semigrand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parametrization. Agreement between the two techniques is better at high pressures where anharmonic terms are smaller. We compare in detail the use of each technique for properties such as enthalpies, entropies, volume and free energies of mixing at zero and high pressure and thus calculation of the phase diagram. We assess the vibrational contributions to these quantities and compare results with those in the dilute limit. The techniques are illustrated throughout using MnO–MgO and should be readily applicable to more complicated systems.

This paper describes a computer modelling study of the F⁻ and OH⁻ forms of topaz, Al₂SiO₄(OH,F)₂. A potential model is developed, and used to calculate the perfect lattice and defect properties of both forms of the mineral. Excellent agreement between experimental and calculated phonon frequencies is obtained. Predictions are made of the probable intrinsic defect structure and of the location of dopant ions incorporated in ion implantation.

Computer modelling techniques based on density functional theory are applied to modelling the structures and energies of key defect species in microporous aluminosilicates. We focus on dehydroxylation and dehydrogenation reactions of 'hydroxyl nest' defects (silicon vacancies saturated by hydroxyl groups). Our calculations chart the mechanisms and energetics of the transformation of these defects, which are introduced during the synthesis and processing of these materials.

An aspherical ion model (AIM) is constructed for lithium oxide, Li₂O. The model incorporates both many-body polarization and short-range ion distortion effects. A procedure for extracting the required model parameters by fitting to results from a series of electronic structure calculations is described. The model is tested with respect to both static and dynamic properties. The experimentally observed Cauchy violation in the elastic constants and phonon frequencies are well reproduced as is the onset temperature for superionic behaviour in the Li⁺ sublattice. The system is shown to display a peak in the heat capacity as a function of temperature. The correlated and uncorrelated ion dynamics are studied and the origin of the respective solid- and liquid-state Haven ratios is rationalized.

Hybrid spin unrestricted Hartree–Fock density functional theory (UHF-DFT) calculations of Li_xNi_1−xO indicate that within the range of exact exchange for which the electronic structures of the associated point defects, , and are insulating, is a largely inert defect with negligible effect on the electronic, magnetic and excitonic properties of the NiO host lattice. Over this range of exact exchange the free hole, , is essentially d⁸L in nature, or O⁻ in chemical terms, with strong spatial and spin polaronic character. The differences in the electronic properties of the free, , and bound, , hole, notably the d⁸L–d⁹ gap, are minimal so that their separate identification would seem to be unlikely.

We report a study of the atomic and electronic structure, along with spin densities and energetics, of the primary intrinsic defects in silver chloride in their neutral and charged forms. We have correctly predicted the dominance of the cation Frenkel defect. In agreement with recent studies we have found that both the neutral and charged silver interstitial defects adopt a split-interstitial geometry, with the conventional body-centred interstitial found to be a transition state. We propose that the split-interstitial structure forms four-membered chains which can migrate through the crystal by a knock-on mechanism. We have also studied the structures of the cation and anion vacancies, and seen little relaxation, except on formation of an F-centre, where there is an unusually strong contraction of the nearest-neighbour cations towards the vacant site, which has been proposed to be an ion-size effect.