Short-range Atomic Interactions Research Articles

Simulations of primary damage in a High Entropy Alloy: Probing enhanced radiation resistance

High Entropy Alloys (HEA) attract attention as possible radiation resistant materials, a feature observed in some experiments that has been attributed to several unique properties of HEA, in particular to the disorder-induced reduced thermal conductivity and to the peculiar defect properties originating from the chemical complexity. To explore the origin of such behavior we study the early stages (less than 0.1 ns), of radiation damage response of a HEA using molecular dynamics simulations of collision cascades induced by primary knock-on atoms (PKA) with 10, 20 and 40 keV, at room temperature, on an idealized model equiatomic quinary fcc FeNiCrCoCu alloy, the corresponding “Average Atom” (AA) material, and on pure Ni. We include accurate corrections to describe short-range atomic interactions during the cascade. In all cases the average number of defects in the HEA is lower than for pure Ni, which has been previously used to help claiming that HEA is radiation resistant. However, simulated defect evolution during primary damage, including the number of surviving Frenkel Pairs, and the defect cluster size distributions are nearly the same in all cases, within our statistical uncertainty. The number of surviving FP in the alloy is predicted fairly well by analytical models of defect production in pure materials. All of this indicates that the origin of radiation resistance in HEAs as observed in experiments may not be related to a reduction in primary damage due to chemical disorder, but is probably caused by longer-time defect evolution.

Fortran and C programs for the time-dependent dipolar Gross–Pitaevskii equation in an anisotropic trap

Many of the static and dynamic properties of an atomic Bose–Einstein condensate (BEC) are usually studied by solving the mean-field Gross–Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank–Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x–y and x–z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas–Fermi approximations. Program summaryProgram title: (i) imag1dZ, (ii) imag1dX, (iii) imag2dXY, (iv) imag2dXZ, (v) imag3d, (vi) real1dZ, (vii) real1dX, (viii) real2dXY, (ix) real2dXZ, (x) real3dCatalogue identifier: AEWL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWL_v1_0.htmlProgram obtainable from: CPC Program Library, Queens University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 111384No. of bytes in distributed program, including test data, etc.: 604013Distribution format: tar.gz

Atomistic-to-continuum multiscale modeling with long-range electrostatic interactions in ionic solids

We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that make these materials of critical importance. Examples include solid electrolytes that conduct current through the motion of charged point defects, and complex oxide ferroelectrics that display multifunctionality through the motion of domain wall defects. Therefore, it is important to understand the structure of defects and their response to electrical and mechanical fields. A central hurdle, however, is that interactions in ionic solids include both short-range atomic interactions as well as long-range electrostatic interactions. Existing atomistic-to-continuum multiscale methods, such as the Quasicontinuum method, are applicable only when the atomic interactions are short-range. In addition, empirical reductions of quantum mechanics to density functional models are unable to capture key phenomena of interest in these materials.To address this open problem, we develop a multiscale atomistic method to coarse-grain the long-range electrical interactions in ionic crystals with defects. In these settings, the charge density is rapidly varying, but in an almost-periodic manner. The key idea is to use the polarization density field as a multiscale mediator that enables efficient coarse-graining by exploiting the almost-periodic nature of the variation. In regions far from the defect, where the crystal is close-to-perfect, the polarization field serves as a proxy that enables us to avoid accounting for the details of the charge variation. We combine this approach for long-range electrostatics with the standard Quasicontinuum method for short-range interactions to achieve an efficient multiscale atomistic-to-continuum method. As a side note, we examine an important issue that is critical to our method, namely the dependence of the computed polarization field on the choice of unit cell. Potentially, this is fatal to our coarse-graining scheme; however, we show that consistently accounting for boundary charges leaves the continuum electrostatic fields invariant to choice of unit cell.

Dipolar Bose–Einstein condensate soliton on a two-dimensional optical lattice

Using a three-dimensional mean-field model we study one-dimensional dipolar Bose–Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose–Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301].

Lattice statics Green's function for a semi-infinite crystal

The lattice statics Green's function describes the linear response of displacement to the application of a force on a crystal lattice. From a macroscopic point of view, the crystal lattice behaves like an anisotropic elastic body. Therefore, the lattice statics Green's function must approach the elastic Green's function for large distances from the point at which the force is applied. The lattice used in calculating the lattice Green's function should have the elastic constants corresponding to the crystal and a symmetrical stress tensor in the continuum elastic limit. In order to satisfy these conditions, three-body forces are introduced. The Green's function for the infinite lattice with short-range atomic interaction is calculated immediately by translational symmetry. The Green's function for the defective lattice is derived from the Dyson equation. The definitive Green's function for the semi-infinite lattice is presented.

Growing perfect quasicrystals.

We present an approach for aggregating Penrose tiles to form a defect-free, 2D pentagonal quasicrystal tiling. Contrary to conventional wisdom, defect-free quasiperiodic tilings can be constructed by use of local rules alone. The results provide new insights as to how materials with only short-range atomic interactions can grow large, nearly perfect quasicrystal grains.

Symmetry and a similarity transformation for perturbation theory of short-range atomic interactions

Di-atomic molecules possess a peculiar symmetry. Considerations based on it are used in an attempt to extend Byers-Brown's perturbation treatment of short range atomic interactions. Example of a soluble model is treated briefly.

Perturbation theory for short-range atomic interactions. I. Numerical results

Numerical results for various perturbation series for atomic interactions at short range are presented for the energy, dipole moment, and dipole polarizability of one−electron diatomics. Although third−order energy results are accurate at short range, there is appreciable error in the other property values. The convergence of the series is considered in a companion paper.

Van Vleck perturbation treatment of short-range atomic interactions in H2+ and HeH++

A modified version of Van Vleck perturbation theory, the distinguishable electron method, is applied to short-range diatomic interactions in H2+ and HeH++. Starting with united-atom wavefunctions φoa and φob at two centers, a and b, as two degenerate states, each wavefunction is corrected to first order in charge-shifting perturbations, Zb(1/ra−1/rb) and Za(1/rb−1/ra), where Zi is the nuclear charge and ri is the electron-nucleus distance. The final molecular wavefunction, correct to first order in charge-shifting perturbation, is then obtained by solving a secular equation; this is facilitated by making use of molecular symmetry and electron-nucleus cusp conditions. For a one-electron diatomic molecule the wavefunction Ψ to first order in charge-shifting perturbation is shown to have the form Ψ = (Za/Z) [φoa+λZbf(ξ, η, Z, R)] + (Zb/Z)[φob+λZaf(ξ, −η, Z, R)], where Z is the sum of nuclear charges, λ is the ordering parameter, and f is a function of Z, R, and confocal elliptic coordinates defined by ξ = (ra+rb)/R and η = (ra−rb)/R. Application of the method to the ground states of H2+ and HeH++ gives better convergence than do the one-center calculations. The total energies evaluated to second order compare favorably with exact values for R < 1.0 a. u. in the case of H2+ and for R < 0.75 a. u. in the case of HeH++. The physical interpretation of the charge-shifting processes is discussed and the method is compared with that of Byers-Brown and Power.