Graeme Ackland

Development of new interatomic potentials appropriate for crystalline and liquid iron

Two procedures were developed to fit interatomic potentials of the embedded-atom method (EAM) form and applied to determine a potential which describes crystalline and liquid iron. While both procedures use perfect crystal and crystal defect data, the first procedure also employs the first-principles forces in a model liquid and the second procedure uses experimental liquid structure factor data. These additional types of information were incorporated to ensure more reasonable descriptions of atomic interactions at small separations than is provided using standard approaches, such as fitting to the universal binding energy relation. The new potentials (provided herein) are, on average, in better agreement with the experimental or first-principles lattice parameter, elastic constants, point-defect energies, bcc–fcc transformation energy, liquid density, liquid structure factor, melting temperature and other properties than other existing EAM iron potentials.

Computer simulation of point defect properties in dilute Fe-Cu alloy using a many-body interatomic potential

Abstract The behaviour of copper atoms in dilute solution in α-iron is important for the microstructural changes that occur in ferritic pressure vessel steels under fastneutron irradiation. To investigate the properties of atomic defects that control this behaviour, a set of many-body interatomic potentials has been developed for the Fe—Cu system. The procedures employed, including modifications to ensure suitability for simulating atomic collisions at high energy, are described. The effect of copper on the lattice parameter of iron in the new model is in good agreement with experiment. The phonon properties of the pure crystals and, in particular, the influence of the instability of the metastable, bcc phase of copper that precipitates during irradiation are discussed. The properties of point defects have been investigated. It is found that the vacancy has lower formation and migration energy in bcc copper than in α-iron, and the self-interstitial atom has very low formation energy in this phase of coppe...

Simple N-body potentials for the noble metals and nickel

Abstract Using the approach of Finnis and Sinclair, N-body potentials for copper, silver, gold and nickel have been constructed. The total energy is regarded as consisting of a pair-potential part and a many body cohesive part. Both these parts are functions of the atomic separations only and are represented by cubic splines, fitted to various bulk properties. For the noble metals, the pair-potentials were fitted at short range to pressure-volume relationships calculated by Christensen and Heine so that interactions at separations smaller than that of the first-nearest neighbours can be treated in this scheme. Using these potentials, point defects, surfaces (including the surface reconstructions) and grain boundaries have been studied and satisfactory agreement with available experimental data has been found.

An improved N-body semi-empirical model for body-centred cubic transition metals

Abstract The recently published semi-empirical potentials of Finnis and Sinclair for the metals V, Nb, Ta, Mo and W appear to give unphysical results for properties involving small interatomic separation. This is remedied by adding to the potentials cores fitted to electron gas calculations on dimers. The adjusted potentials are shown to predict a more realistic pressure-volume relationship. Interstitial formation energies are calculated for various configurations, using quenched molecular dynamics and static relaxation. Some preliminary results on interstitial migration are presented.

Structure and elasticity of MgO at high pressure

Abstract The structural and elastic properties of MgO periclase were studied up to 150 GPa with the first-principles pseudopotential method within the local density approximation. The calculated lattice constant of the B1 phase over the pressure range studied is within 1% of experimental values. The observed B1 phase of MgO was found to be stable up to 450 GPa, precluding the B1-B2 phase transition within the lower mantle. The calculated transition pressure is less than one-half of the previous pseudopotential prediction but is very close to the linearized augmented plane-wave result. All three independent elastic constants, c11, c12, and c44, for the B1 phase are calculated from direct computation of stresses generated by small strains. The calculated zero-pressure values of the elastic moduli and wave velocities and their initial pressure dependence are in excellent agreement with experiments. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 15 GPa and then increasing from 15 to 150 GPa. Longitudinal and shear-wave velocities were found to vary by 23 and 59%, respectively, with propagation direction at 150 GPa. The character of the anisotropy changes qualitatively with pressure. At zero pressure longitudinal and shear-wave propagations are fastest along [111] and [100], respectively, whereas above 15 GPa, the corresponding fast directions are [100] and [110]. The Cauchy condition was found to be strongly violated in MgO, reflecting the importance of noncentral many-body forces.

Development of an interatomic potential for phosphorus impurities in α-iron

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.We present the derivation of an interatomic potential for the iron phosphorus system based primarily on {\it ab initio} data. Transferrability 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.

Elastic instabilities in crystals from ab initio stress - strain relations

Pressure-induced elastic instabilities are investigated in the prototypic ionic and covalent solids (MgO, CaO, and Si) using generalized elastic stability criteria based on the elastic stiffness coefficients which are determined directly from stress - strain relations. From first-principles computer simulations of the instabilities, we demonstrate the validity and importance of the generalized criteria relative to the conventional criteria in describing the crystal stability under hydrostatic pressure in relation to the real structural transformations. We examine systems for which the two phases can be related by a simple deformation, and in all cases we show that the generalized elastic stiffness coefficient associated with that deformation softens toward the transition. The shear stability criterion bounds the first-order B1 - B2 phase transition pressure from above and below in MgO and CaO, suggesting a wide pressure regime of metastability, whereas the tetragonal shear stability criterion predicts precisely the second-order rutile-to- transition in . The high-pressure elastic behaviour of diamond structure Si is studied in detail. A tetragonal shear instability corresponding to its transformation to the -Sn structure should occur in diamond structure Si at a pressure of 101 GPa, compared to the experimental value of 9 to 13 GPa for the transition pressure.

Development of an interatomic potential for the simulation of phase transformations in zirconium

In recent years, some 30 studies have been published on the molecular dynamics (MD) of zirconium, primarily of its twinning deformation and response to radiation damage. Its low thermal neutron absorption makes it uniquely suited for the latter application. Surprisingly, currently used interatomic potentials do not encapsulate the unique properties of Zr, namely its high stacking-fault energy, anomolous self-diffusion, melting and phase transformation under temperature and pressure (or alloying). Ab initio calculations have shown deficiencies in the description of point defects, both vacancies and interstitials, using existing interatomic potentials, deficiencies that can now be rectified by refitting. Here, we show the calculation of phase transitions self-consistently and present a potential for Zr that correctly reproduces the energetics of our extended database of ab initio configurations and high-temperature phase transitions. The potential has an analytic many-body form, making it suitable for existing large-scale MD codes. We also present a best-fit potential for the hcp structure and its defects.

Semi-empirical calculation of solid surface tensions in body-centred cubic transition metals

Abstract We present calculations of surface tension (surface stress γ)for the body-centred cubic (b.c.c.) metals V, Nb, Ta, Mo and W made using simple empirical N-body potentials obtained by Finnis and Sinclair (1984). Results for several crystal faces are evaluated and compared with the corresponding surface energies σ. Although there is a broad correlation between the calculated tensions and energies for different metals, and the two quantities are of a similar order of magnitude, they differ from one another by a factor of up to 2. Variant potentials for molybdenum were constructed to test the sensitivity of the results; negative surface tensions were found in some cases and shown to be a symptom of metastability of the b.c.c. structure.

Point-defect and threshold displacement energies in Ni3Al I. Point-defect properties

Abstract The energy and volume change associated with the creation of point defects in Ni3Al have been calculated by computer simulation using a modified version of the many-body potentials of Vitek, Ackland and Cserti. The potentials have been adjusted to provide a better description of the interaction between atoms at separations inside the normal nearest-neighbour spacing. This region is important for interstitial properties and the interaction of atoms in displacement events associated with radiation damage. The properties of point defects in the pure metals Al and Ni are in good agreement with known values. For Ni3Al, the properties of the Ni defects are very close to those found by Caro, Victoria and Averback with the embedded-atom potentials for Ni3Al of Foiles and Daw, and the most stable interstitial, in particular, is the Ni-Ni⟨100⟩ dumbbell centred on a Ni site in the {100} planes which contain only Ni atoms. For the Al and antisite defects, however, the model used here gives different results....