Common Neighbor Analysis Research Articles

Molecular dynamics characterization of icosahedral short range order in undercooled copper

The stability of undercooled simple metals is still an intriguing problem for materials science and technology. There is not consensus on the role played by the icosahedral short range order during undercooling. The scenario is even less clear for undercooled metals under external pressure. Extensive molecular dynamics simulations, based on an empirical tight-binding interatomic potential, are performed to explain experimental results recently obtained on liquid and undercooled liquid copper. A common neighbour analysis is used to fully characterize the icosahedral short range order in both undercooled and liquid systems. Moreover, the effect of pressure on icosahedral short range order, is addressed and rationalized. External pressure increases the probability to find atomic bonds with icosahedral symmetry both in the liquid and in the undercooled copper.

Dynamical study of metallic clusters using the statistical method of time series clustering

We perform common neighbor analysis on the long-time series data generated by isothermal Brownian-type molecular dynamics simulations to study the thermal and dynamical properties of metallic clusters. In our common neighbor analysis, we introduce the common neighbor label (CNL) which is a group of atoms of a smaller size (than the cluster) designated by four numeric digits. The CNL thus describes topologically smaller size atomic configurations and is associated an abundance value which is the number of “degenerate” four digits all of which characterize the same CNL. When the cluster is in its lowest energy state, it has a fixed number of CNLs and hence abundances. At nonzero temperatures, the cluster undergoes different kinds of atomic activities such as vibrations, migrational relocation, permutational and topological isomer transitions, etc. depending on its lowest energy structure. As a result, the abundances of CNLs at zero temperature will change and new CNLs with their respective new abundances are created. To understand the temperature dependence of the CNL dynamics, and hence shed light on the cluster dynamics itself, we employ a novel method of statistical time series analysis. In this method, we perform statistical clustering at two time scales. First, we examine, at given temperature, the signs of abundance changes at a short-time scale, and assign CNLs to two short-time clusters. Quasi-periodic features can be seen in the time evolution of these short-time clusters, based on which we choose a long-time scale to compute the long-time correlations between CNL pairs. We then exploit the separation of correlation levels seen in these long-time correlations to extract strongly-correlated collections of CNLs, which we will identify as effective variables for the long-time cluster dynamics. It is found that certain effective variables show subtleties in their temperature dependences and these thermal traits bear a delicate relation to prepeaks and main peaks seen in clusters Ag 14, Cu 14 and Cu 13Au 1. We therefore infer from the temperature changes of effective variables and locate the temperatures at which these prepeaks and principal peaks appear, and they are evaluated by comparing with those deduced from the specific heat data.

Influences of Strain Rate on Copper Nanowire in Tension

This study uses molecular dynamics simulations with an embedded-atom method (EAM) potential to investigate the effects of strain rate on a copper wire in tension at the nanoscale. By averaging the atomic stresses over the entire system, the stress-strain curves for the nanowire were predicted. The results show that an elastic region clearly exists in the early deformation of the copper nanowire and the elastic modulus is about two times of the value measured at the macroscale. The yield stress of the nanowire increases with the strain rate. Moreover, the evolution of the crystal structure was investigated in terms of the radial distribution function and the local atomic order was also examined by the common neighbour analysis. The dislocations and recrystallization processes inside the nanowire have been observed. The simulated results reveal the process of the fracture of copper nanowire in tension.

Phase transition in nanocrystalline iron: Atomistic-level simulations

Abstract Molecular dynamics simulations, along with the modified analytic embedded atom method, have been employed to study the bcc → fcc phase transition of nanocrystalline iron. The Gibbs free energies of bulk fcc and bcc iron phases are calculated as a function of temperature, and used to determine the bulk phase-transition temperature. Furthermore, the transformation temperature in the nanocrystalline iron, with a mean grain size of 3 nm, is determined to be 975 ± 25 K using the bond-order parameter method. The radial-distribution function and common neighbor analysis are used to understand the phase structure of the nanocrystalline iron and the evolution of local atomic structure. The snapshots of a two atomic layer thick slice provide a visible scenario of structural evolution during phase transition.

Development of a method to determine Burgers vectors from atomistic data

Large-scale molecular dynamics simulations have been widely used to investigate the mechanical behaviour of materials. But complex datasets, involving the positions of millions of atoms, generated during the simulations make quantitative data analysis quite a challenge. This paper presents a novel method to determine not only dislocations in the crystal, but also to quantify their Burgers vectors. This is achieved by combining geometrical methods to determine the atoms lying in the dislocations cores, like for example the common neighbour analysis or the bond angle analysis, with the slip vector analysis. The first methods are used to filter out the atoms lying in undisturbed regions of the crystal; the latter method yields the relative slip of the remaining atoms and thus indicates the Burgers vector of those atoms lying in the dislocation cores. The validity of the method is demonstrated here on a single edge dislocation in a relatively small sample. Furthermore a way will be sketched how this analysis can be used to determine densities of statistically stored and geometrically necessary dislocations, respectively. Hence, this method can be expected to provide valuable input for strain gradient plasticity models.

Onset of failure in argon by the effect of a shockwave: A molecular dynamics study

Molecular dynamic simulations of shockwaves in solid argon were performed. The simulation cell contains 51,840 atoms at 5 K interacting by means of a pairwise potential. The shockwave itself was introduced explicitly in the simulation by a piston hitting the sample from one side of the simulation box, at speeds ranging from 1.2 to 1.3 times the speed of sound in solid argon at the chosen density. In order to characterize the sample in terms of both structural and dynamic properties, we determine the density and temperature profiles according the advance of the shockwave, evaluating, for different slabs, the pair–distribution function, coordination number as well as performing a common neighbor analysis for the atoms. Our simulations reproduce the experimental Hugoniot curve and show how the material is break due to rarefaction waves. The picture that emerges is that when the shockwave starts, a local melting is produced in a region of the sample. Then, as the shockwave travels through the sample, a high density disordered phase is identified. When the piston stops, a rarefaction wave develops, producing a large tensile stress, which finally causes the failure of the sample.

Geometry of Slow Structural Fluctuations in a Supercooled Binary Alloy

The liquid structure of a glass-forming binary alloy is studied using molecular dynamics simulations. The analysis employs the geometrical approach of Frank and Kasper to establish that the supercooled liquid contains extended clusters characterized by the same short range order as the crystal. The steep increase in the heat capacity on cooling is directly coupled to the growing fluctuations of the Frank-Kasper clusters. The relaxation of particles in the clusters dominates the slow tail of the self-intermediate scattering function.

Orientation-dependent mechanical properties of Au nanowires under uniaxial loading

Using molecular dynamics simulations with the quantum corrected Sutton–Chen type many-body potential, we have investigated the mechanical responses of Au nanowires along the [1 0 0], [1 1 0], and [1 1 1] crystallographic orientations under compression and tension. The main focus of this work is the orientation-dependent effects on the mechanical properties. The common neighbor analysis method is used to investigate the structural evolution and deformation mechanism of Au nanowires. The simulation results show that the Young’s modulus is strongly dependent on nanowire’s orientation. Under tension, all the oriented nanowires yield via the activities of Shockley partial dislocations, and their plastic deformation is accommodated by partial dislocation activities without twining. Under compression, the [1 0 0] nanowire presents the same yield mechanism together with the deformation twins occurring in its plastic deformation, however, for the [1 1 0] and [1 1 1] nanowires, the buckling instability preferentially occurs, followed by full dislocation activities to carry the plastic deformation without partial dislocations involved. The deformation behaviors indicate that the predication of the Schmidt factor based on bulk single crystal is valid for Au nanowires under compression but not under tension. Our study also shows that the [1 1 0] Au nanowire exhibits a better ductibility, while the [1 1 1] Au nanowire possesses excellent overall mechanical properties.

Molecular Dynamics Simulation of Deformation Mechanism and Mechanical Properties in Au Cluster

Inelastic deformation of gold (Au) cluster is investigated by using molecular dynamics (MD) simulations. We performed compression and unloading test by computer simulation, where two silicon (Si) plates approach each other and push single Au cluster of 4 nm, 8 nm or 12 nm diameter in between. The potential function we utilized for Au-Au interaction is an embedded atom method (EAM) type proposed by Cai et al. for intermetallic alloys. On the other hand, the interactions between Si and Au atoms are developed on the Lennard-Jones framework by assessing the interaction force obtained by the AFM experiment. By using common neighbor analysis (CNA) suitably used in crystalline structures, initial f.c.c. structure once decreases in compression, but is then recovered in unloading. From stress-strain curves, it is understood that these nano-sized Au clusters possess tremendously large recovery strain in unloading after compression. The large recovery strain is estimated at 10% in average. Smaller cluster tends to show larger recovery strain depending on temperature. The large recovery strain may lead to the possibility of superelastic response of the Au cluster. The present paper also discusses the cause of large recovery appeared in whole shape and clarifies the mechanism of characteristic rearrangement of atoms. By compression, stacking faults are introduced inside the cluster, and then twin deformation occurs with crystalline rotation. In unloading, large recovery strain is obtained.

Atomistic Simulation on the Relation between Amorphization and Crystalline Transformation in Ni-Ti Alloy

Ni-Ti alloys are typical shape-memory materials. It is suggested that the atomic-scale phase transformation between martensite and austenite crystalline phases is responsible for such function. However, it is reported that these alloys sometimes show also amorphization together with nanocrystal under severe deformation. The mechanism of amorphization should compete against martensitic (crystalline) transformation (MT). This study focuses on the atomistic relation between amorphization and MT in Ni-Ti alloys. Molecular dynamics simulation is performed by using our simplified potential built on the MEAM framework. The change in crystalline state is identified and traced mainly by developing common neighbor analysis (CNA) method. Under amorphization from B2 cubic structure, the characteristic topological change in CNA cluster around a transforming atom is detected. By applying simple shear in periodic specimen, it is found that the martensite phases appear first then amorphous phases are formed. The nucleation of amorphous phases is strongly dependent on choice of shear plane, e.g. {100}, {110} or {111} plane. When the shear direction does not match to the orientation of inherent slip system, amorphous phase is nucleated with relative ease and remains for a long time. It is recognized that dislocation slip (plastic deformation), MT and amorphization are closely related in atomic scale. The direction of phase transition is mostly B2(austenite)→B19'(martensite)→amorphous, except for the case of {111} shear plane which possesses pre-amorphous structures. It is found that the pre-amorphous is once formed and then disappears, preceding martensite phase or principal and later formation of amorphous phase.

Atomic structure and diffusion in Cu60Zr40 metallic liquid and glass: molecular dynamics simulations

Temperature effects on the structural evolution and diffusivity of Cu60Zr40 in the liquid and glassy states were studied by molecular dynamics simulations using the Finnis–Sinclair potential. The pair distribution functions and common-neighbor analysis were used to investigate the structural variations. It is found that the amount of pentagonal bipyramids increases sharply in a short temperature range of about 200 K above the glass transition temperature Tg, leading to the increasing of the icosahedral cluster centered by Cu atom and larger Kasper polyhedral cluster centered by Zr atom. The mean square displacement and the self part of the van Hove function were calculated to evaluate the relaxation and transport properties. The cage effect is found to appear at 1100 K. The mode-coupling theory equation is more suitable than the Vogel–Fulcher–Tammann equation to describe the change in diffusivity in the liquid state. The critical temperature Tc, a predicted glass transition temperature in mode-coupling theory, for Cu60Zr40 glass former is 1008.2 K. At temperatures near Tc, there is a dynamic crossover. In supercooled liquid state, the dynamic heterogeneity is detected. The comparison of the activation enthalpies of the two components shows that the small atoms transport faster obeying the size effect.

Pressure effects on icosahedral short range order in undercooled copper

There is not a wide consensus on the role played by the icosahedral short range order on the stability of undercooled simple metals. The scenario is even less clear for undercooled metals under external pressure. Classical molecular dynamics simulations are performed to explain experimental results recently obtained on liquid and undercooled liquid copper under pressure. The atomic configurations are characterized by a common neighbor analysis to reveal the icosahedral short range order and its relation with external pressure. External pressure increases the probability to find atomic bonds with icosahedral symmetry both in the liquid and in the undercooled copper.

Long time scale simulation of a grain boundary in copper

A general, twisted and tilted, grain boundary in copper has been simulated using the adaptive kinetic Monte Carlo method to study the atomistic structure of the non-crystalline region and the mechanism of annealing events that occur at low temperature. The simulated time interval spanned 67 μs at 135 K. Similar final configurations were obtained starting from different initial structures: (i) by bringing the two grains into contact without any intermediate layer, and (ii) by inserting an amorphous region between the grains. The results obtained were analyzed with a radial distribution function and a common neighbor analysis. Annealing events leading to lowering of the energy typically involved concerted displacement of several atoms—even as many as 10 atoms displaced by more than half an Ångström. Increased local icosahedral ordering is observed in the boundary layer, but local HCP coordination was also observed. In the final low-energy configurations, the thickness of the region separating the crystalline grains corresponds to just one atomic layer, in good agreement with reported experimental observations. The simulated system consists of 1307 atoms and atomic interactions were described using effective medium theory.

Structural study of Co and Au nanoclusters landed onto Cu

The process in which nanoclusters of Co and Au at low energy (<1eV/atom) impinge on a substrate of Cu (001) has been studied by molecular-dynamics (MD). Particularly our interest is focussed on the crystalline structure of the clusters and on whether the epitaxy is achieved. The atomic interactions are calculated by means of a many-body potential based on the second momentum approximation of tight-binding scheme.The size of the clusters ranges from a few tens to a few hundreds of atoms. Techniques such as the analysis of grains, the calculation of epitaxy factor and the common neighbour analysis (CNA) are methods of analysis, used in this work, capable to determine the crystalline orientation and resemblance of the clusters to the substrate once they have been deposited on it. The number of atoms with fcc structure is explicitly calculated. The high values found, for large clusters, corroborate that part of the original structure of the cluster remains intact.The results obtained can be summarized as follows: whenever epitaxy requires an expansion of the cluster structure to fit the substrate, the process is more effective than the opposite in which a compression is required. The size of the cluster plays an opposite role in the epitaxial process, i.e. the effectiveness to get epitaxy diminishes for large sizes.

Development of an EAM potential for zinc and its application to the growth of nanoparticles

In the context of the investigation of particle formation, a potential model by means of the embedded atom method is developed for the hexagonal close packed metal zinc. This type of model includes many-body interactions caused by delocalised electrons in metals. The effective core charge as function of the distance is calculated here by an integral over the electron distribution function rather than fitting it to experimental data. In addition, the dimer potential is included in the parameterisation because we focus on the formation of nanoparticles from the vapour phase. With this potential model, the growth of zinc clusters consisting of 125 to 1000 atoms is investigated, which takes place at elevated temperatures in a liquid-like cluster state. The growing clusters are embedded in an argon carrier gas atmosphere which regulates the cluster temperature. The average thermal expansion of the clusters and the different lattice constants are analysed. For the determination of the cluster structure, the common-neighbour analysis method is extended to hexagonal close packed surface structures. During growth, small clusters with less than approximately 60 atoms develop transient icosahedral structure before transforming into hexagonal close-packed structure. The surface of the clusters exhibits a transformation from planes with high surface energy to the most stable ones. Besides ambiguous surface structures the final clusters are almost completely in an hexagonal close packed structure.

The elastic properties and energy characteristics of Au nanowires: an atomistic simulation study

This paper have performed molecular static calculations with the quantum corrected Sutten–Chen type many body potential to study size effects on the elastic modulus of Au nanowires with [100], [110] and [111] crystallographic directions, and to explore the preferential growth orientation of Au nanowires. The main focus of this work is the size effects on their surface characteristics. Using the common neighbour analysis, this paper deduces that surface region approximately consists of two layer atoms. Further, it extracts the elastic modulus of surface, and calculate surface energy of nanowire. The results show that for all three directions the Young's modulus of nanowire increases as the diameter increases. Similar trend has been observed for the Young's modulus of surface. However, the atomic average potential energy of nanowire shows an opposite change. Both the potential and surface energy of [110] nanowire are the lowest among all three orientational nanowires, which helps to explain why Au nanowires possess a [110] preferred orientation during the experimental growth proceeds.

Molecular dynamics study of the hcp–bcc phase transformation in nanocrystalline zirconium

Abstract The hcp – bcc phase transformation in nanocrystalline zirconium with an initial grain size of about 7 nm is studied by means of molecular dynamics simulations based on an analytic embedded atom method. The radial distribution function, the fraction of different type atoms differentiated by the common neighbor analysis method and snapshots of a slice through the simulation cell with relaxation time are all used to describe the hcp – bcc phase transformation process in nanocrystalline zirconium. The results indicate that the new phase of bcc structure zirconium first appears in the grain boundary regions, and then the interphase boundary migrates from the bcc to hcp phase, finally the grain of pure bcc phase grows. In addition, the critical temperature of phase transformation for nanocrystalline zirconium is determined as 1225 ± 25 K, which is somewhat higher than the experimental value of 1136 K for conventional zirconium.

The deformation mechanism of nanofilm with void under tensile loading: An atomistic simulation study

In this paper, we employ molecular static approach with quantum corrected Sutten-Chen many-body potential to study the mechanical behavior of nickel nanofilm during uniaxial loading, and investigate its microstructure by common neighbor analysis methods. The simulated results show that the existence of void significantly weakens the Young’s modulus and yield stress of nanofilm; with the increased strain, the shape of void changes from circular into elliptical, and the void is eventually entirely closed. The plastic deformation of nanofilm is characterized by {111} glide associated with Shockley partial dislocations, resulting in the formation of stacking faults.

Size-dependent effects on equilibrium stress and strain in nickel nanowires

Using molecular static calculations with the quantum corrected Sutten-Chen-type many-body potential, we have studied the stress and strain characteristics in nickel nanowires along [100], [110], and [111] crystallographic orientations under the equilibrium state. The main focus of this work is the size-dependent effects on these characteristics above. We deduce from the common neighbor analysis that surface region approximately consists of two layer atoms. Further, we extract the equilibrium characteristics in both surface and core regions of nanowires. The results show that with increasing diameter, the equilibrium stress and strain which are compressive decrease sharply in the core region, while the surface tensile stress starts to increase, and gradually trends to a nonzero constant. Due to much larger compressive stress and smaller modulus, the core of [100] nanowire endures larger compressive strain than that of [110] and [111] nanowires.

Local order in undercooled liquid metals: A tight binding molecular dynamics approach

We use constant (zero) pressure molecular dynamics based on a semi-empirical tight binding model to simulate the structures of liquid Ni, Cu, Pd and Au in the stable and undercooled states. We compare our data with the available experiments (neutron scattering for Ni, EXAFS for Pd). We analyze the structure in terms of Voronoi polyhedra and use the neighbors defined by this analysis to perform a Common Neighbors Analysis. We show that a small but significant difference in the number of bonds with five common neighbors exists between undercooled Ni and the other elements. We question the possible experimental observation of such a difference and its relevance to the issue of the existence of an icosahedral short range order in the liquid.