Pair Interaction Model Research Articles

Controlled capillary assembly of magnetic Janus particles at fluid-fluid interfaces.

Capillary interactions can be used to direct assembly of particles adsorbed at fluid-fluid interfaces. Precisely controlling the magnitude and direction of capillary interactions to assemble particles into favoured structures for materials science purposes is desirable but challenging. In this paper, we investigate capillary interactions between magnetic Janus particles adsorbed at fluid-fluid interfaces. We develop a pair-interaction model that predicts that these particles should arrange into a side-side configuration, and carry out simulations that confirm the predictions of our model. Finally, we investigate the monolayer structures that form when many magnetic Janus particles adsorb at the interface. We find that the particles arrange into long, straight chains exhibiting little curvature, in contrast with capillary interactions between ellipsoidal particles. We further find a regime in which highly ordered, lattice-like monolayer structures form, which can be tuned dynamically using an external magnetic field.

Shape phase transition in the odd Sm nuclei: effective order parameter and odd–even effect**Supported by National Natural Science Foundation of China (11375005, 11005056, 11175078, 11405080)

Some binding energy related quantities serving as effective order parameters have been used to analyze the shape phase transition in the odd Sm nuclei. It is found that the signals of phase transition in the odd Sm nuclei are greatly enhanced in contrast to the even Sm nuclei. A further analysis shows that the transitional behaviors related to pairing in the Sm nuclei can be well described by the mean field plus pairing interaction model, with a monotonic decrease in the pairing strength G.

Simulation of Atomic Diffusion in the Fcc NiAl System: A Kinetic Monte Carlo Study

The atomic diffusion in fcc NiAl binary alloys was studied by kinetic Monte Carlo simulation. The environment dependent hopping barriers were computed using a pair interaction model whose parameters were fitted to relevant data derived from electronic structure calculations. Long time diffusivities were calculated and the effect of composition change on the tracer diffusion coefficients was analyzed. Our results indicate that this variation has noticeable impact on the atomic diffusivities. A clear reduction in the mobility of both Ni and Al is demonstrated with increasing Al content. Examination of the pair interaction between atoms was carried out for the purpose of understanding the predicted trends.

Phase transitions of boron carbide: Pair interaction model of high carbon limit

Boron Carbide exhibits a broad composition range, implying a degree of intrinsic substitutional disorder. While the observed phase has rhombohedral symmetry (space group R3¯m), the enthalpy minimizing structure has lower, monoclinic, symmetry (space group Cm). The crystallographic primitive cell consists of a 12-atom icosahedron placed at the vertex of a rhombohedral lattice, together with a 3-atom chain along the 3-fold axis. In the limit of high carbon content, approaching 20% carbon, the icosahedra are usually of type B11 Cp, where the p indicates the carbon resides on a polar site, while the chains are of type C–B–C. We establish an atomic interaction model for this composition limit, fit to density functional theory total energies, that allows us to investigate the substitutional disorder using Monte Carlo simulations augmented by multiple histogram analysis. We find that the low temperature monoclinic Cm structure disorders through a pair of phase transitions, first via a 3-state Potts-like transition to space group R3m, then via an Ising-like transition to the experimentally observed R3¯m symmetry. The R3m and Cm phases are electrically polarized, while the high temperature R3¯m phase is nonpolar.

Simulation of Diffusion in FCC NiFe Binary Alloys Using Kinetic Monte Carlo Method

The use of the atomistic kinetic Monte Carlo method was explored to examine the vacancy-mediated diffusion in fcc NiFe binary alloy. Relevant energetic and kinetic parameters were calculated from density functional theory, and these were used to parametrize a pair interaction model for determination of environment-dependent diffusion barriers. Kinetic Monte Carlo simulations were performed to compute the tracer diffusivities as functions of composition and temperature. Calculations for pure Ni and for Ni with dilute amount of Fe yielded results that compare well with experiments. With increasing amount of Fe, the model predicts a slight reduction in the diffusivity of Fe. This trend was examined on the basis of the neighbor pair interactions between atoms.

Symmetries of 2-Lattices and Second Order Accuracy of the Cauchy--Born Model

We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multispecies pair interaction models, we construct a new stored energy density, using shift gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys.

Van der Waals interaction as a summable asymptotic series

The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients ${C}_{2k}$ of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density $\ensuremath{\rho}$ with outer radius $R$ and thickness $t$. The result is ${C}_{2k}=\ensuremath{-}{c}_{k}(t/R)\sqrt{4\ensuremath{\pi}\ensuremath{\rho}}{[{(2R)}^{2}]}^{k}$. The ${c}_{k}$ approach a limiting constant value, so the infinite series for the van der Waals interaction at separation $d$, $\ensuremath{-}{C}_{6}/{d}^{6}\ensuremath{-}{C}_{8}/{d}^{8}\ensuremath{-}\ensuremath{\cdots}$, can be summed analytically, diverging only for $d\ensuremath{\le}2R$. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with $R$ fixed by the true static dipole polarizability. Once $t/R$ is fixed, all the higher coefficients are determined by just ${C}_{6}$ and ${C}_{8}$. Finally, we compare the exact ${C}_{2k}$ to those from a pair interaction model, which works for solid spheres ($t=R$) but not for fullerenes.

Defect and solute properties in dilute Fe-Cr-Ni austenitic alloys from first principles

We present results of an extensive set of first-principles density functional theory calculations of point defect formation, binding, and clustering energies in austenitic Fe with dilute concentrations of Cr and Ni solutes. A large number of possible collinear magnetic structures were investigated as appropriate reference states for austenite. We found that the antiferromagnetic single- and double-layer structures with tetragonal relaxation of the unit cell were the most suitable reference states and highlighted the inherent instabilities in the ferromagnetic states. Test calculations for the presence and influence of noncollinear magnetism were performed but proved mostly negative. We calculate the vacancy formation energy to be between 1.8 and 1.95 eV. Vacancy cluster binding was initially weak at 0.1 eV for divacancies but rapidly increased with additional vacancies. Clusters of up to six vacancies were studied and a highly stable octahedral cluster and stacking fault tetrahedron were found with total binding energies of 2.5 and 2.3 eV, respectively. The $\ensuremath{\langle}100\ensuremath{\rangle}$ dumbbell was found to be the most stable self-interstitial with a formation energy of between 3.2 and 3.6 eV and was found to form strongly bound clusters, consistent with other fcc metals. Pair interaction models were found to be capable of capturing the trends in the defect cluster binding energy data. Solute-solute interactions were found to be weak in general, with a maximal positive binding of 0.1 eV found for Ni-Ni pairs and maximum repulsion found for Cr-Cr pairs of $\ensuremath{-}$0.1 eV. Solute cluster binding was found to be consistent with a pair interaction model, with Ni-rich clusters being the most stable. Solute-defect interactions were consistent with Ni and Cr being modestly oversized and undersized solutes, respectively, which is exactly opposite to the experimentally derived size factors for Ni and Cr solutes in type 316 stainless steel and in the pure materials. Ni was found to bind to the vacancy and to the $\ensuremath{\langle}100\ensuremath{\rangle}$ dumbbell in the tensile site by 0.1 eV and was repelled from mixed and compressive sites. In contrast, Cr showed a preferential binding to interstitials. Calculation of tracer diffusion coefficients found that Ni diffuses significantly more slowly than both Cr and Fe, which is consistent with the standard mechanism used to explain radiation-induced segregation effects in Fe-Cr-Ni austenitic alloys by vacancy-mediated diffusion. Comparison of our results with those for bcc Fe showed strong similarity for pure Fe and no correlation with dilute Ni and Cr.

Simple concentration-dependent pair interaction model for large-scale simulations of Fe-Cr alloys

This work is motivated by the need for large-scale simulations to extract physical information on the iron-chromium system that is a binary model alloy for ferritic steels used or proposed in many nuclear applications. From first-principles calculations and the experimental critical temperature we build a new energetic rigid lattice model based on pair interactions with concentration and temperature dependence. Density functional theory calculations in both norm-conserving and projector augmented-wave approaches have been performed. A thorough comparison of these two different ab initio techniques leads to a robust parametrization of the Fe-Cr Hamiltonian. Mean-field approximations and Monte Carlo calculations are then used to account for temperature effects. The predictions of the model are in agreement with the most recent phase diagram at all temperatures and compositions. The solubility of Cr in Fe below 700 K remains in the range of about 6 to 12%. It reproduces the transition between the ordering and demixing tendency and the spinodal decomposition limits are also in agreement with the values given in the literature.

How simple rules determine pedestrian behavior and crowd disasters

With the increasing size and frequency of mass events, the study of crowd disasters and the simulation of pedestrian flows have become important research areas. However, even successful modeling approaches such as those inspired by Newtonian force models are still not fully consistent with empirical observations and are sometimes hard to calibrate. Here, a cognitive science approach is proposed, which is based on behavioral heuristics. We suggest that, guided by visual information, namely the distance of obstructions in candidate lines of sight, pedestrians apply two simple cognitive procedures to adapt their walking speeds and directions. Although simpler than previous approaches, this model predicts individual trajectories and collective patterns of motion in good quantitative agreement with a large variety of empirical and experimental data. This model predicts the emergence of self-organization phenomena, such as the spontaneous formation of unidirectional lanes or stop-and-go waves. Moreover, the combination of pedestrian heuristics with body collisions generates crowd turbulence at extreme densities--a phenomenon that has been observed during recent crowd disasters. By proposing an integrated treatment of simultaneous interactions between multiple individuals, our approach overcomes limitations of current physics-inspired pair interaction models. Understanding crowd dynamics through cognitive heuristics is therefore not only crucial for a better preparation of safe mass events. It also clears the way for a more realistic modeling of collective social behaviors, in particular of human crowds and biological swarms. Furthermore, our behavioral heuristics may serve to improve the navigation of autonomous robots.

Coordination-dependent bond energies derived from DFT surface-energy data for use in computations of surface segregation phenomena in nanoclusters

Theoretical computations of alloy surface phenomena, such as elemental segregation, within atomic pair-interaction models, necessitate the use of reliable bond energies as input. This work introduces the idea to extract the coordination dependence of bond energies from density-functional theory (DFT) computed surface energy anisotropy. Polynomial functions are fitted to DFT data reported recently for surface energies of pure Pt, Rh and Pd. Compared to other approaches, the proposed method is highly transparent, and is expected to yield better insight into the origin of alloy segregation phenomena at surfaces of bulk and nanoclusters. Reference to this paper should be made as follows: Polak, M. and Rubinovich, L. (2011) 'Coordination-dependent bond energies derived from DFT surface-energy data for use in computations of surface segregation phenomena in nanoclusters', Int. J. Nanotechnol., Vol. 8, Nos. 10/11/12, pp.898-906.

A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D

For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially guarantee a one-to-one correspondence between atomistic solutions and QNL-QC solutions. The analysis is based on consistency error estimates in negative norms, novel a priori and a posteriori stability estimates, and a quantitative inverse function theorem.

Adsorption of Pt on Ni(111) surface: introduction of an effective pair interaction model

By means of potentials derived from the second-moment approximation to the tight-binding model, isolated Pt adatom properties on the vicinal Ni (997) surface are investigated. The comparison with the Ni adsorption on the vicinal Pt(997) shows that the fcc and hcp sites are energetically very close. A promising effective pair interaction model is developed in order to study the surface diffusion of Pt adatoms in the presence of an adisland on Ni(111) which will be very useful to understand the growth phenomena in kinetic calculations.

New exact solutions of the standard pairing model for well-deformed nuclei

A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which the eigenvalues and corresponding eigenstates can be obtained progressively. This new approach draws upon an observation that the original one- plus two-body problem in a $k$-particle Hilbert subspace can be mapped onto a one-body grand hard-core boson picture that can be solved step by step with a simple Bethe ansatz known from earlier work. Based on this new procedure, it is further shown that the extended pairing model for deformed nuclei [Feng Pan, V. G. Gueorguiev, and J. P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)] is similar to the standard pairing model with the first step approximation, in which only the lowest energy eigenstate of the standard pure pairing interaction part is taken into consideration. Our analysis shows that the standard pairing model with the first step approximation displays similar pair structures of the first few exact low-lying states of the model, which, therefore, provides a link between the two models.

Theoretical study of the Ni growth on Pt stepped surfaces

We have investigated the growth of Ni on Pt stepped surfaces with (1 1 1) terraces by means of potentials derived from the second moment approximation in a tight-binding model. The activation energies associated to these processes are determined. The Schwoebel barriers of Ni atoms descending steps of Pt stepped surfaces are calculated for different kinds of straight steps (A and B steps) differing by the orientation of the ledge. In addition, we study the diffusion of Ni adatoms at fcc or hcp sites in the presence of small adislands on the terraces, in the vicinity of the A and B steps. We show that a good estimate of the potential wells and diffusion barriers could be given by introducing a lateral effective pair interaction model, the interactions extending up to the next nearest neighbors. Finally, we have carried out Kinetic Monte-Carlo simulations to investigate the Ni wire formation at Pt step edges and the influence of the exchange processes in the alloy formation.

On the derivation of linear elasticity from atomistic models

We derive linear elastic energy functionals from atomistic models as a -limit when the number of atoms tends to infinity, respec tively, when the interatomic distances tend to zero. Our approach generalizes a recent result of Braides, Solci and Vitali (2). In particular, we study mass spring models with full nearest and next-to-nearest pair interactions. We also consider boundary value problems where a part of the boundary is free. 1. Introduction. The passage from discrete atomic models to continuum theories is an active area of current research in continuum mechanics. For elastic systems one usually refers to the Cauchy-Born rule to obtain macroscopic energy densities from atomistic interaction functionals. The Cauchy-Born rule states that - roughly speaking - each individual atom follows the macroscopic deformation gradient and in particular does not take into account fine scale oscillations on the microscopic scale. For a two-dimensional mass spring model, the validity of the Cauchy-Born rule for deformations close to a rigid motion has been proved by Friesecke and Theil in (8). Their result has been generalized to arbitrary dimensions by Conti, Dolzmann, Kirchheim and Muller in (3). If the deformation gradients are very close to SO(d), the set of orientation pre- serving rigid motions, then we expect linear elasticity theory to apply. This relation has been made rigorous by Dal Maso, Negri and Percivale who derive the energy functional of linear elasticity as a -limit of nonlinear el asticity for small displace- ments in (5). (See also the author's article (10) for a strong convergence result for the associated minimum problems.) Recently it has been noted that one can derive linear elasticity functionals directly from certain atomistic pair potentials: For a special class of pair interaction models Braides, Solci and Vitali prove -convergence of the discre te energy functionals to the energy functional of an associated continuum linear elasticity energy functional (see (2)). In this set-up one has to deal with two small parameters e and δ measuring the typical interatomic distance and the local distance of the deformations from the set of rigid motions, respectively. The aim of the present article is to extend these results in three directions. Firstly, we will drop the assumption that atoms are allowed to interact only along

Ion–water cluster free energy computer simulation using some of most popular ion–water and water–water pair interaction models

The bicanonical Monte-Carlo method allows effective computer simulation of free energy, entropy as well as internal energy of ion molecular clusters. The advantages of this method have been exploited to test how much adequately frequently applied pair interaction models reproduce not only energetics, but also statistical properties of the investigated ion–water clusters. In present paper, the series of reproductions of mass spectroscopy data on stepwise binding Gibbs energy, enthalpy and entropy of Ion(H 2O) n , n = 1 ÷ 6 clusters for a set of monovalent ions has been carried out with the help of bicanonical Monte-Carlo technique. Each reproduction from the series has been performed using one of pair interaction ion–water plus water–water models, the experimental data on free energy, entropy as well as internal energy of ion molecular clusters. Based on the result of the simulations, the quantitative analysis of the investigated pair interaction models accuracy has been accomplished. The accuracy of the pair interaction ion–water plus water–water models has been compared with the accuracy of the one of polarizable models taking into account polarization of ions and water molecules explicitly.

Determination of low-temperature interfacial energies from a pair interaction model

The chemical contribution to the energy of coherent interfaces is calculated from a pair interaction model, which represents an extension of the model presented by Becker in 1938. Nearest neighbour interaction is assumed, and entropy contributions are not considered. Concentration dependence of the pair interaction energies, as well as a change of crystal structure and/or a breakdown of long-range order at the interface are taken into account in the presented model. As examples, the interfacial energy is evaluated for coherent Cu–Co, Fe–Ag, and Cu–Cu 4Ti interfaces. The necessary interaction parameters can be derived from the thermodynamic functions of the system determined experimentally or by thermodynamic calculations, e.g., by using the CALPHAD method.

Influence of short-range adatom-adatom interactions on the surface diffusion of Cu on Cu(111)

The EAM potential set up by Mishin et al. [Phys. Rev. B 63 224106 (2001)] is used to study some elementary processes in the homoepitaxy of $\mathrm{Cu}$ on $\mathrm{Cu}(111)$. After having checked its ability to reproduce surface physical quantities, this potential is applied to an investigation of the energetics, the vibrations and the surface diffusion of ${\mathrm{Cu}}_{N}$ close-packed adislands $(1\ensuremath{\leqslant}N\ensuremath{\leqslant}7)$. In each case we determine the most stable configurations, the corresponding activation barriers, the local vibrational spectra, and the Vineyard prefactors. In particular it is found that, at room temperature, dimers and trimers are still very mobile and move by concerted jumps much faster than tetramers while heptamers can be considered as immobile. The very good agreement of our results with scanning tunneling microscopy observations justifies the use of Mishin et al. potential for treating surface diffusion. This allowed us to study in details the influence of the lateral atomic environment of the adatoms along its diffusion path. An effective lateral pair interaction model is set up which is able to predict the existence of a saddle point along the path and to give a very good estimation of the activation barrier height. This model will be very useful in kinetic Monte Carlo simulations of homoepitaxial growth of $\mathrm{Cu}(111)$.

Pairing correlations and transitions in nuclear systems

We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We describe recent experimental evidence that points to a relation between pairing and phase transitions (or transformations) in finite nuclear systems. A simple pairing interaction model is used in order to study and classify an eventual pairing phase transition in finite fermionic systems such as nuclei. We show that systems with as few as ∼ 10 – 16 fermions can exhibit clear features reminiscent of a phase transition.