Nickel-based superalloys are widely deployed in high-pressure compressors and turbine rotors in various aeroengines. Developing advanced processing strategies is essential to boost the service performance of the alloy. In this work, molecular dynamics simulations based on the modified analytical embedded-atom method are performed to investigate the uniaxial tensile behaviors of γ/γ′ nanowires (NWs). The cross-sectional sizes of NWs range from 1.416 to 4.249 nm, and the simulation temperatures vary from 100 to 700 K. Cross-sectional size and temperature serve as key factors for surface activity, which in turn exerts a significant influence on the mechanical properties. The results obtained demonstrate that the mechanical properties increase exponentially with increasing cross-sectional size but decrease linearly with the rising temperature. Surface activity, including surface energy and surface thickness, acts as the driving force for dislocation or slip nucleation and is regulated by size and temperature. The critical size threshold for the transition of deformation mechanisms from crystal slip to twin formation is approximately 2.75 nm, as the size and temperature have a synergistic effect on the surface energy. The coupled effect of size, temperature, and surface, each of which imposes distinct regulatory roles, respectively, collectively governs the deformation behavior and mechanisms of NWs. In small NWs, deformation is primarily dominated by dislocation glide. By contrast, in larger NWs, plastic deformation is dominated by twin-mediated plasticity that impedes the dislocation movement and lattice glide. The study reveals the coupled size–temperature–surface effects on the deformation behaviors, which provides a theoretical foundation for the design of superalloys used in extreme environments.

结合改进型嵌入原子势函数,利用分子动力学模拟 Ni/Ni3Al纳米线在单轴拉伸应变条件下的形变过程,研究其内在机制.结果表明:Ni/Ni3Al纳米线的形变过程分为弹性、塑性形变两个阶段.在弹性形变阶段,其应力随着形变量变化呈线性关系,通过拟合发现其弹性模量约等于 120 GPa,明显低于相应的块体材料结果.在此基础上,重点分析纳米孔洞对 Ni/Ni3Al纳米线形变行为的影响,发现纳米孔洞的存在有效地破坏合金材料内部的微观结构,使得晶格位错交割无法形成,导致晶格滑移比较容易产生,从而降低合金纳米线的弹性模量等.

By using the tight-binding model and the eigen-equation method, both the dipole and quadrupole modes of the plasmon in one-dimensional system arc studied. The modulation effects of the external field, the size of system and the number of electrons on these two modes arc investigated. The results show that, the modes of the plasmon can be controlled by the external field, a symmetrical electric potential field only excites the quadrupole mode, and an anti-symmetrical electric potential field only excites the dipole mode. Based on the size effect of plasmon, the increase of the length of one-dimensional system can reduce the plasmon frequency and enhance the excitation intensity. Based on the charge accumulation effect of plasmon, the increase of the number of electrons before half filling can increase the frequency and excitation intensity of plasmon. Moreover, the excitation intensity of plasmon is symmetric with respect to the half-filling electron number since the excitations of electrons and holes arc equivalent. As for the size effect of plasmon, the results calculated by the eigen-equation method can be well fitted by those obtained by the random phase approximation method.

Molecular dynamics (MD) simulation is employed to investigate the release behavior of helium and its effect on the mechanical properties of palladium (Pd) nanowire. The results indicate that the helium atom can assemble easily to form a helium bubble, which effectively degrade the mechanical properties of Pd nanowire as the bubble size increases. Then, the development propensities of the helium bubble pressure is discussed with the helium atoms continuously releasing, which shows that the relationship between the pressure and the volume of the helium bubble is in well agreement with the description of the state equation. On the basis, it is further found that the release rate of helium has a tight connection with the variation of the bubble pressure in nanowire. Finally, the inherent mechanism of helium releasing from the Pd nanowire is analyzed in detail.

In the paper, molecular dynamics simulation with the modified analytical embedded atom method (MAEAM) is applied to study the size effect on the elastic properties of the B2-NiAl nanofilm. The simulation results indicate that there is a critical thickness, which is about 5.38 nm, to distinguish the size dependence of the elastic properties of the nanofilm. On the one hand, these properties, such as the averaged cohesive energy and the bulk modulus, change evidently as the size is smaller than the critical thickness and the change tendency is tightly controlled by the surface atom composition. On the other hand, as the nanofilm size exceeds the critical one, the calculated values of the elastic properties are almost independent of the film thickness. Relatively, the bulk modulus magnitude of the nanofilm is apparently larger than that of the corresponding bulk material. Finally, the inherent mechanisms of the size impacting on the elastic properties of the B2-NiAl nanofilm have been discussed in more detail. The strengthening effect of the bulk modulus results from the smaller multilayer relaxation of the interlayer distance as compared to those of the bulk materials.

In this paper the molecular dynamics (MD) technique and the modified analytic embedded atom method (MAEAM) are applied to study the influence of size and surface condition of the nanofilm on the elastic properties of B2-NiAl, The elastic properties of the bulk NiAl alloy and the size dependence of the surface energy of nanofilms are first calculated. It is found that the calculated results of the elastic properties are consistent with those from experiments and theories; and the surface energy, which is barely influenced by the thickness, is controlled by the surface atomic composition. On this basis, our investigations are mainly focused on the relationship between the elastic properties of nanofilms and their thickness. The obtained results indicate that the elastic properties of the nanofilm may change exponentially with the increasing thickness, which can also be regulated by the surface atomic composition. Furthermore, the inherent mechanism of the thicknes and surface that affects this relationship is analyzed in detail, showing that the surface atomic composition and the deviation of interplanar spacing in nanofims are two major factors for determining the thickness dependence of the elastic properties. These are in good agreement with the previous theoretical and experimental studies.

In this paper molecular dynamics (MD) method and the modified analytical embedded atom model (MAEAM) are used to investigate the size effect on the elastic properties of Ni, Al and V nanowires and the role the free surface plays. For convenience of comparison, the elastic properties of these corresponding perfect bulk materials are also studied. Results obtained indicate that the calculated values of the elastic properties of these perfect materials are in good agreement with those previously given theoretical and experimental ones. But the calculated bulk moduli of the nanowires, which are lower than those of the prefect materials, increase exponentially with increasing size of the nanowire and are nearly close to a constant (180.20 GPa for the Ni nanowire, 83.98 GPa for the Al nanowire and 162.48 GPa for the V nanowire). Meanwhile, the surface energy of the nanowire decreases exponentially with the increase of its size and reaches a minimal value (1.84 J·m-2 for the Ni nanowire, 0.77 J·m-2 for the Al nanowire, and 1.71 J·m-2 for the V nanowire), which is consistent with the corresponding bulk material. And the critical value of the size, which has a distinct effect on the elastic properties and the surface energy, is about 5.0 nm for all nanowires. On this basis, the free surface dependence of the elastic properties of these metallic nanowires and the inherent mechanisms are further discussed by exploring the size effect on the surface energies of Ni, Al and V nanowires and their distribution characteristics, showing that the free surface plays a more and more important role in the diminution of the elastic properties of nanowires as the size decreases. The mode of the surface impacting on the elastic properties of nanowire is described as follows:The surface first reduces the compressional stress of the internal core region of nanowires and then the reduced compressional stress results further in the decrease in the elastic properties of nanowires.

The molecular dynamics (MD) simulation and the modified analytical embedded-atom method (MAEAM) were used to study the influence of a He atom on the movement of the edge dislocation in Ni. First, the calculated Burgers vector distribution shows that the equilibrium dissociation distance (Ded) and the stacking fault energy (Esf) between two partial edge dislocations are about 25.95 Å and 108 mJ/m2, respectively. Then, the obtained formation energies (Ef) of a He atom at some different sites demonstrate that the He atom is attracted and repelled in the tension and compression regions, respectively. And the He–dislocation interaction reveals that an interstitial He atom plays a more significant role in the dislocation movement than a substitutional He atom. Finally, it is found that the movement of an interstitial He atom is apparent as the first partial dislocation bypasses and the edge dislocation offers fast-diffusion path for the migration of a He atom.

Molecular dynamics (MD) together with the modified analytical embedded atom method (MAEAM) is employed to study the alloying elements (Re, Ru, Co, and Ta) dependence of the elastic properties of L12-Ni3Al. The investigations indicate that the calculated elastic properties of Ni3Al are in reasonable agreement with the previous results. The substituting formation energies of the alloying elements in Ni3Al are calculated to determine the site preference. It is found out that Re, Ru, and Ta atoms prefer to occupy the Al sites, and the Co atom prefers to occupy the Ni site. Based on Re, Ru, and Ta substituting the 1st, 2nd, 3rd, and 4th nearest-neighbor atoms, we ascertain that the substituting manners of these alloying elements have a decisive effect on the bulk modulus and the local crystal lattice of Ni3Al. Moreover, for Re, the bonding interaction plays a predominant role in the improvement in the bulk modulus of Ni3Al, whereas the size effect of Ru and Ta on the improvement in the bulk modulus is more obvious. Finally, the potential reasons of which the alloying elements enhance the bulk modulus are discussed in details.

Using molecular dynamics, nudged elastic band and modified analytic embedded atom methods, the diffusion behaviors of Pd adatom on stepped Pd(001) surface have been investigated. Lower than 975 K, Pd adatom just hops along the perfect [110]-direction step. The diffusion dynamics equation is derived from the Arrhenius law between 875 and 975 K, and the corresponding migration energy and prefactor are 0.76 eV and 5.2 × 10− 2 cm2/s respectively, which shows that they adhere to the step in case of adatom moving to the step. The adatom diffuses across the perfect step with an Ehrlich–Schwoebel barrier of 0.09 eV by exchange mechanism. Our calculations show the kink at step can markedly decrease the static energy barrier across the step with a negative Ehrlich–Schwoebel barrier, and it contributes to form layer-by-layer growth model in the epitaxial experiment. Our calculations show that the kink can also markedly improve the adatom's mass transport of interlayer, contributing to the formation of the compact film. Lastly, a quantitative result at 300 K shows that the kink affects tremendously the diffusion mobility of adatom near it, which indicates that the kink plays a key role in the formation of the compact and uniform film on Pd(001) surface in an epitaxial growth experiment.

Using molecular dynamics and modified analytic embedded atom methods, the atomic self-diffusion dynamics behaviors relevant to 2D crystal growth on Ni(111) surface have been studied between 150 and 600K. On perfect Ni(111) surface, the activation energy and prefactor are 0.058±0.001eV and 4.2×10−4cm2/s between 150 and 350K, and 0.082±0.003eV and 7.8×10−4cm2/s from 400 to 600K. Ni adatom just hops along the directions of close-packed steps on stepped Ni(111) surface, the corresponding activation energies and prefactors are 0.188±0.002eV and (3.8–4.4)×10−3cm2/s along the direction of A-type step, 0.140±0.001eV and (1.1–1.2)×10−3cm2/s along the direction of B-type step, and both fitting lines of Arrhenius law intersect at Tc=420–440K. Our results show that the atomic growth dynamics under nonequilibrium conditions is gradually dominated by the prefactor with increasing temperature. In addition, the shape-change of the 2D nanometer-size island has been discussed on stepped Ni(111) surface in different temperature range.

The size dependence of the mechanical properties of Ni/Ni3Al nanowires (NWs) was investigated with molecular dynamics (MD) simulations. The results indicated that the surface energy σ increased, and bulk modulus B and B/G ratio decreased with increasing the inverse of the nanowire perimeter of the NWs. The extrapolated values of surface energy σ0 were 2.100 J/m2 and 1.956 J/m2 for the samples with surface atoms of pure Ni atoms and mixture of Ni and Al atoms, respectively. The size dependence of the bulk modulus was in good agreement with the prediction of the Birch-Murnaghan equation and the surface shell softening the bulk modulus. Finally, the B/G ratio indicated that the ductility/brittleness behaviors of the NWs depended mainly on the energy distributions of the surface shell, and the mechanisms of the ductility/brittleness of the NWs were studied in detail.

By means of molecular dynamics (MD) and the modified analytic embedded-atom method (MAEAM), we investigate the effect of the gamma'-phase volume fraction (gamma'-VF) on the apparent interface energy, the critical thickness of the interface transition region (ITR) and the binding mechanism of the gamma/gamma' interface. The results indicate that the apparent interface energy increases linearly with the ITR width increasing. Then, by extrapolating the ITR width Delta l to zero, we can obtain the interface energy which is equal to the limiting value of the apparent interface energy. The volume fraction of the gamma'-phase has no influence on the interface energy and the critical thickness of the ITR. The interface energy is in reasonable agreement with the previous results and the critical value of the ITR width is about 1.7 nm which also agrees well with the experimental and theoretical ones. Finally, the gamma'-VF dependence of the apparent interface energy and the interface separation of the ITR with about 1.7 nm thickness are analyzed in more detail. The results reveal that the crystalline configuration of Ni-base superalloy (NBSA) with (60-70%) gamma'-VF is the stablest, which is similar to the previous investigations. (C) 2012 Elsevier B.V. All rights reserved.

Molecular dynamics (MD) and modified analytical embedded atom method (MAEAM) are used to study the effect of the cross-sectional shape on the nanowire (NW) premelting. The results indicate that the premelting phenomenon occurs far below the melting point. The temperature dependence of mean square displacement (MSD) shows that the shape effect on the premelting phenomenon is obvious. Based on the detailed analysis of the atomic configuration, the premelting activation energy (PAE), and the shape factor, we have further found that the cross-sectional shape has an important effect on the premelting mechanism of the NW.

Molecular dynamics and the modified analytical embedded atom potential are employed to study the size effect of a V nanowire (NW) on the melting behaviour. It is found that the melting temperature of the NW and its latent heat of fusion are much lower than those of the bulk, and depend strongly on the size. The calculated self-diffusion coefficient indicates that the premelting phenomenon first occurs at the surface and then spreads inwards with increasing temperature. The activation energy Q of the shell decreases as the reciprocal of the diameter increases. The lower activation energy indicates that premelting and melting can take place more easily. Finally, some representative snapshots on the temperature dependence of the cross-section atomic structure reveal that the melting mechanism of a large-sized NW is quite different from that of a small-sized one. For large-sized NWs (>4.0 nm), the surface plays a dominant role in the melting process, which is made up of two stages, i.e. gradual premelting and rapid melting. For small-sized NWs (<3.0 nm), the melting results mainly from the anharmonic effect of crystal lattice vibration, and the surface melting is barely noticeable. When the diameter size of the NWs ranges from 3.0 to 4.0 nm, both foregoing factors have an influence on the melting behaviour, which indicates that the critical diameter of the NW with a different melting mechanism is about 3.0 nm.

The modified analytical embedded atom method (MAEAM) has been used to study the cross-sectional shape dependence of the melting of vanadium nanowire (NW). The results indicate that the effect of the shape on the melting behavior is apparent. For the prefect crystal, the calculated thermodynamic properties including the melting temperature and the latent heat of melting, which are evidently higher than those of the NWs, are in good agreement with the previously corresponding value. For NWs, by monitoring the temperature dependence of the potential energy and heat capacity, the melting temperature of Tr-, Te-, and Cr-NW has been accurately determined to be 1730 K, 1790 K, and 1760 K, respectively. The melting temperature discrepancy of NWs predicates that the shape effect is prominent. On the basis of the obtained melting point of NW, we study the temperature dependence of the atomic fraction of all shells to explore the effect of cross-sectional shape on the melting behavior. Compared with the melting transition of three NWs, it is found that the melting behavior of triangular nanowire (Tr-NW) with the relatively larger shape factor is significantly different from that of other shape NW. Finally, the cross-sectional shape dependent melting mechanism of NWs is further studied by displaying the atomic snapshots at some given temperatures.

By means of molecular dynamics (MD) simulations, the melting mechanism of thin W(111) and W(110) planes with free surfaces has been studied with the modified analytic embedded-atom method (MAEAM). Firstly, the results obtained by calculating the temperature dependence of mean square displacement (MSD) indicate that the influence of surface and anharmonic effect on the microstructure and properties of planes are significant and the vibration of atoms locating in the surface region is anisotropic. Then, according to providing further investigation into the temperature dependence of the atomic density function (ADF) and structural factor (SF) of the given atomic planes, it is found that the melting mechanisms and processes of both membranes are different. For the W(111) plane, the free surface plays an important role in the melting transition. The W(111) plane entirely becomes disordering at 3700 K which is in agreement with the calculated melting temperature. The fitted relation between the fraction of the disordered atom and the temperature demonstrates that the premelting-melting transition temperature is about 3550 K. Instead, the W(110) plane is melted when the temperature reaches 4000 K, which is so-called superheating. And the melting transition of this plane relies strongly on the anharmonic effect.

In this paper, we use molecular dynamics (MD) simulations and a modified analytic embedded-atom method to investigate the edge dislocation movement without imposed strain at 0 K. The obtained results indicate that the straight lines of the partial dislocations always preserve their original shapes and are parallel to each other during the simulation process. According to the energy of each atom, the positions of both partial dislocation cores are determined. Then the velocities in the period of the relaxation process are investigated in detail. The MD simulations reveal that the MD relaxation time dependence of the edge dislocation mobility is divided into two parts. First, during the initial period ranging from 0 to 6 ps, the relative velocity of the dislocation movement lineally increases with the incremental relaxation time. Second, in the latter period from 6 ps to the end of the simulated process the velocity decreases exponentially as the MD simulation time evolves.

分析大学物理教学中的微积分思想方法及其一些重要概念,说明了用微积分解决物理问题的一般步骤,以及如何选取微元及在微元内如何建模,并举例说明了利用微积分的知识解决几类较为重要的物理问题.

Using molecular dynamics, nudged elastic band and modified analytic embedded atom methods, the self-diffusion dynamics properties of palladium atomic clusters up to seven atoms on the Pd (1 1 1) surface have been studied at temperatures ranging from 300 to 1000 K. The simulation time varies from 20 to 75 ns according to the cluster sizes and the temperature ranges. The heptamer and trimer are more stable than the other neighboring clusters. The diffusion coefficients of the clusters are derived from the mean square displacement of the cluster's mass-center, and the diffusion prefactors D(0) and activation energies Ea are derived from the Arrhenius relation. The activation energy of the clusters increases with the increasing atom number in the clusters, especially for Pd(6) to Pd(7). The analysis of trajectories shows the noncompact clusters diffuse by the local diffusion mechanism but the compact clusters diffuse mainly by the whole gliding mechanism, and some static energy barriers of the diffusion modes are calculated. From Pd(2) to Pd(6), the prefactors are in the range of the standard value 10(-3) cm(2) s(-1), and the prefactor of Pd(7) cluster is 2 orders of magnitude greater than that of the single Pd adatom because of a large number of nonequivalent diffusion processes. The heptamer can be the nucleus in the room temperature range according to nucleation theory.