Based on a recent result showing that the net Coulomb potential in condensed ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summation over the r−1 Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pairwise, spherically truncated r−1 summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple method is developed that achieves charge neutralization wherever the r−1 pair potential is truncated. This enables the extraction of the Coulomb energy, forces, and stresses from a spherically truncated, usually charged environment in a manner that is independent of the grouping of the pair terms. The close connection of our approach with the Ewald method is demonstrated and exploited, providing an efficient method for the simulation of even highly disordered ionic systems by direct, pairwise r−1 summation with spherical truncation at rather short range, i.e., a method which fully exploits the short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, such as free surfaces and grain boundaries.

The mechanical behaviour of nanocrystalline materials (that is, polycrystals with a grain size of less than 100 nm) remains controversial. Although it is commonly accepted that the intrinsic deformation behaviour of these materials arises from the interplay between dislocation and grain-boundary processes, little is known about the specific deformation mechanisms. Here we use large-scale molecular-dynamics simulations to elucidate this intricate interplay during room-temperature plastic deformation of model nanocrystalline Al microstructures. We demonstrate that, in contrast to coarse-grained Al, mechanical twinning may play an important role in the deformation behaviour of nanocrystalline Al. Our results illustrate that this type of simulation has now advanced to a level where it provides a powerful new tool for elucidating and quantifying--in a degree of detail not possible experimentally--the atomic-level mechanisms controlling the complex dislocation and grain-boundary processes in heavily deformed materials with a submicrometre grain size.

Molecular-dynamics simulations have recently been used to elucidate the transition with decreasing grain size from a dislocation-based to a grain-boundary-based deformation mechanism in nanocrystalline f.c.c. metals. This transition in the deformation mechanism results in a maximum yield strength at a grain size (the 'strongest size') that depends strongly on the stacking-fault energy, the elastic properties of the metal, and the magnitude of the applied stress. Here, by exploring the role of the stacking-fault energy in this crossover, we elucidate how the size of the extended dislocations nucleated from the grain boundaries affects the mechanical behaviour. Building on the fundamental physics of deformation as exposed by these simulations, we propose a two-dimensional stress-grain size deformation-mechanism map for the mechanical behaviour of nanocrystalline f.c.c. metals at low temperature. The map captures this transition in both the deformation mechanism and the related mechanical behaviour with decreasing grain size, as well as its dependence on the stacking-fault energy, the elastic properties of the material, and the applied stress level.

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It is demonstrated that stability criteria derived using elastic stiAness coefticients which govern stressstrain relations at finite deformation give quantitative predictions of crystal instability, as observed in direct molecular dynamics simulations. With the aid of such analysis we show that instabilities can be triggered in succession; as a consequence, the limit of metastability in the superheating of a defect-free crystal can be predicted.

Elastic stability criteria are derived for homogeneous lattices under arbitrary but uniform external load.These conditions depend explicitly on the applied stress and reduce, in the limit of vanishing load, to the criteria due to Born, involving only the elastic constants of the crystal. By demonstrating the validity of our results through a comparison of the analysis of an fcc lattice under hydrostatic tension with direct moleculardynamics simulation, we show that crystal stability under stress (ideal strength) is not a question only of material property, and that even qualitative predictions require the inclusion of the effects of applied stress. General implications of our endings, as well as relevance to stability phenomena in melting, polymorphism, crack nucleation, and solid-state amorphization, are discussed.

Based on the manner in which large Coulomb terms with opposite signs cancel each other at long range, it is proposed that most ionic-crystal surfaces undergo a simple zero-temperature reconstruction, a prediction validated by computer simulation of surfaces in rocksalt-structured materials. PACS numbers: 61.50. -f, 68.35.MdThe classic Madelung problem, i.e. , the divergence associated with the r ' term in the Coulomb potential of condensed systems [1],and its consequences for the physics of ionic crystals and liquids have received considerable attention throughout this century. The mathematical problems associated with the handling of conditionally convergent series have led to computationally expensive summation methods which, based mostly on Ewald's solution [2], are now in common use for the simulation of ionic materials. These problems have also given rise to a widespread belief that certain "typically ionic" phenomena, such as the long-range charge ordering in ionic liquids or the space-charge effects at ionic surfaces and interfaces, are a consequence of the long-ranged Coulomb interactions.However, as evidenced, for example, byEvjen's solution [3,4] and by extensive simulations of ionic liquids [5], in many instances Coulombic effects seem to cancel almost completely at long range. Here, by describing a direct solution to the Madelung problem involving shell-wise lattice summation over dipolar molecules with integral ionic charges, we demonstrate that the effective Coulomb potential in a perfect ionic crystal at zero temperature decreases as r . In contrast with earlier direct-summation solutions [6-9], this approach obviously requires a polarization correction [10] to obtain the correct Madelung constant. It has the advantage, however, of avoiding (i) the assumption that the basis molecule must have at least a vanishing dipole [6] or even higher multipole moments [7-9] and (ii) the assignment of fractional ionic charges to the summation unit [2,7,8]. These simplifications are shown to lead naturally to the prediction, illustrated here for the case of materials with the NaCl structure, that most ionic-crystal surfaces should be reconstructed at zero temperature.The main difficulty in the evaluation of Madelung's constant by direct summation arises from the fact that all shells of the erystaI lattice are charged and that, therefore, it is virtually impossible to terminate the summation in a way that renders the system as a whole neutral [4].As illustrated in Fig. 1, this problem may be simply overcome by summing over neutral shells of molecules, i.e. , shells of the Bravais lattice with subsequent attachment of the neutral basis molecule (such as NaCI, with charges q). This results in the generation of two identical, oppositely charged crystal lattices displaced relative to each other by the basis vector b. The total "molecular" Coulomb energy F.~, '~o f some ion i at the origin is then given by =~int '+Z &in(e (&. ), +q -q FIG. I. Dipolar shells of a Bravais lattice (schematic).where the first term represe...

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