Lattice Discreteness Research Articles

Experimental study of intrinsic localized mode mobility in a cyclic, balanced, 1D nonlinear transmission line.

Mobile intrinsic localized modes (ILMs) in balanced nonlinear capacitive-inductive cyclic transmission lines are studied by experiment, using a spatiotemporal driver under damped steady-state conditions. Without nonlinear balance, the experimentally observed resonance between the traveling ILM and normal modes of the nonlinear transmission line generates lattice drag via the production of a lattice backwave. In our experimental study of a balanced running ILM in a steady state, it is observed that the fundamental resonance can be removed over extended, well-defined driving frequency intervals and strongly suppressed over the complete ILM driving frequency range. Because both of these nonlinear capacitive and inductive elements display hysteresis our observation demonstrates that the experimental system, which is only partially self-dual, is surprisingly tolerant, regarding the precision necessary to eliminate the ILM backwave. It appears that simply balancing the cell dual nonlinearities makes the ILM envelope shape essentially the same at the two locations in the cell, so that the effective lattice discreteness seen by the ILM nearly vanishes.

Current Transients in Graphene Electronics under Single‐Particle Irradiation

Low‐dimensional materials hold great promise in next‐generation electronics. However, the performance of such devices is susceptible to external perturbations such as irradiation due to the high exposure of constituent atoms to the environment. Herein, real‐time time‐dependent density‐functional theory at the tight‐binding level extended to open systems for electrons and Ehrenfest dynamics for ions is developed and used to explore the effects of single‐H irradiation on graphene electronics. The results show that the peak current displays distinct energy and site dependences, which are largely different from the dependences of the stopping powers. Charge‐density analysis shows that the current transients are driven by delocalized plasmonic excitation, in contrast to localized electronic excitation, which plays a crucial role in the stopping power. The site dependence of the transient current is determined by the electron density at the irradiation site and the ionic charges. These findings highlight the roles of lattice discreteness and electronic structures of materials, which have been overlooked in previous studies based on theoretical formulations and semiempirical models. Using the insights gained from the calculations and the dataset constructed under typical space‐irradiation conditions, the device responses of graphene nanoelectronics are modeled, laying the ground for device design in the space environment.

Controlling and visualizing fracture of 2D crystals by wrinkling

Shaping two-dimensional (2D) crystals with well-defined edges along specific directions remains technically challenging due to the intrinsic lattice discreteness and anisotropy in their fracture toughness. The patterns of crystal cleavage are determined by the fracture resistance and loading conditions, and usually display kinking features. We show that the fracture of single-crystalline 2D films (MoS2, MoTe2, graphene) can be controlled by mechanically-induced wrinkles, and the distortion of their profiles can visualize the distorted local strain state near the crack tip. In thin samples with stretch-induced wrinkles, the elastic driving force with effective anisotropy steers crack propagation, resulting in straight edges following the corrugation profile. In contrast, thick samples remain flat under stretch for their elevated bending resistance, and the cracks advance with sawtooth patterns following the zigzag motif. The experimental findings are explained by wrinkling-induced elastic anisotropy, which dominates over fracture anisotropy. The control of fracture in 2D crystals can be applied to fabricate micro- and nanostructures for their applications in electromechanical and optoelectronic devices.

Study on lattice discreteness effect on superdislocation core properties of Ni3Al by improved semi-discrete variational Peierls-Nabarro model

Nickel-based superalloys (NBSAs) serve as hot-end component materials of aero engines. NBSAs generally consist of γ and γ′ phases, the γ′ phase (i.e. Ni3Al) presents anomalous yield strength and non-Schmid effect, influencing the mechanical behaviors of NBSAs significantly. These phenomena are closely related to the ⟨110⟩{111} superdislocations. In the present work, based on the quasiharmonic density functional theory (DFT), the improved semi-discrete variational Peierls-Nabarro (SVPN) model is employed to systematically investigate the properties of such superdislocations, in terms of dislocation density distribution, splitting distance (i.e., anti-phase boundary APB, super-lattice intrinsic stacking fault SISF and complex stacking fault width CSF), total energy, Peierls stress and so on. It is found that the predicted superdislocation characters, especially the Peierls stress, are in good agreement with previous experimental results, considering the lattice discreteness effect. This implies that the lattice discreteness plays an important role in the total dislocation energy and Peierls stress, which has however been ignored in previous studies. Although such superdislocation may have several possible core configurations, the dissociation of four 1/6⟨112⟩ Shockley partials separated by two CSFs and an APB may be more energetically favorable at both 300 K and 1200 K. In addition, the superdislocation properties with such the core structure may be easily affected by applied stress. The present work provides an improved SVPN model with consideration of lattice discreteness to describe the superdislocation properties in Ni3Al, which may be helpful for understanding the plastic deformation behavior of the γ′ phase and NBSAs.

A theoretical investigation of glide dislocations in BN/AlN heterojunctions

Glide dislocations with periodic pentagon-heptagon pairs are investigated within the theory of one-dimensional misfit dislocations in the framework of an improved Peierls–Nabarro (P–N) equation in which the lattice discreteness is fully considered. We find an approximate solution to handle misfit dislocations, where the second-order derivative appears in the improved P–N equation. This result is practical for periodic glide dislocations with narrow width, and those in the BN/AlN heterojunction are studied. The structure of the misfit dislocations and adhesion work are obtained explicitly and verified by first-principles calculations. Compared with shuffle dislocations, the compression force in the tangential direction of glide dislocations has a greater impact on the normal direction, and the contributions of the normal displacement to the interfacial energy cannot simply be ignored.

Topological wave energy harvesting in bistable lattices

In this paper, we present an input-independent energy harvesting mechanism exploiting topological solitary waves. This class of medium transforming solitons, or transition waves, entails energy radiation in the form of trailing phonons in discrete bistable lattices. We observe numerically and experimentally that the most dominant frequencies of these phonons are invariant to the input excitations as long as transition waves are generated. The phonon energy at each unit cell is clustered around a single invariant frequency, enabling input-independent resonant harvesting with conventional energy transduction mechanisms. The presented mechanism fundamentally breaks the link between the unit cell size and the metamaterial’s operating frequencies, offering a broadband solution to energy harvesting that is particularly robust for low-frequency input sources. We further investigate the effect of lattice discreteness on the energy harvesting potential, observing two performance gaps and a topological wave harvesting pass band where the potential for energy conversion increases almost monotonically. The observed frequency-invariant phonons are intrinsic to the discrete bistable lattices, enabling broadband energy harvesting to be an inherent metamaterial property.

Lattice-based J integral for a steadily moving dislocation

According to continuum theory and the conservation theorem, the J integral represents the net translational force acting on a defect and, specifically, it is equivalent to the Peach–Koehler force for dislocation. In this study, we newly derive the J integral to quantify driving force on a uniformly moving dislocation with considering its core-induced dynamic behaviors. Using both molecular dynamics simulation and lattice dynamics theory based on atomic chain model, we prove that radiation drag and self-stress asymmetry during the dislocation motion, which are generated by lattice discreteness, make the newly derived J integral depend on the distance from the dislocation core, which is lumped into resistance to the dislocation motion. Finally, we show that the J integral converges to the Peach–Koehler force as the resistance term disappears for a stationary dislocation.

Modification of the Peierls–Nabarro model for misfit dislocation**Project supported by the National Natural Science Foundation of China (Grant No. 11874093).

For a misfit dislocation, the balance equations satisfied by the displacement fields are modified, and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al. This second-order derivative describes the lattice discreteness effect that arises from the surface effect. The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls–Nabarro equation in which the effect of discreteness is fully taken into account. As an application, the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.

Interpolation method for pair correlations in classical crystals

Effects of anharmonicity on the pair correlation function of classical crystals are studied. The recently proposed shortest-graph approach using the Gaussian representation of the individual correlation peaks (the peak width is determined by the length of the shortest graph connecting a given pair of particles) is further improved, to account for anharmonic corrections due to finite temperatures and hard-sphere-like interactions. Two major effects are identified, leading to a modification of the correlation peaks at large or short distances: (i) the peaks at large distances, well described by Gaussians, should be calculated from the finite-temperature phonon spectra; (ii) at short distances, the correlation peaks deviate significantly from the Gaussian form due to the lattice discreteness. We propose the analytical interpolation method, based on the shortest-graph approach, which includes both effects. By employing the molecular dynamics simulations, the accuracy of the method is verified for three- and two-dimensional crystals with the Yukawa, inverse-power-law, and pseudo-hard-sphere pair interactions. The capabilities of the method are demonstrated by calculating the phase diagram of a three-dimensional Yukawa system.

Shape change and Peierls barrier of dislocation

Shape change and Peierls barrier of dislocation are investigated theoretically in the framework of the improved Peierls-Nabarro model in which the lattice discreteness is considered fully. We found that the dislocation will become narrow as it moves from the energy valley to the barrier top. An expression for the Peierls barrier is proposed based on our calculations without the rigid translation assumption. The results enable us to relate the Peierls stress to the bulk properties of crystals directly and can be easily used in the evaluation of material plasticity.

Soliton mobility in disordered lattices.

We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schrödinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from a deviation from integrability, which is due to randomness for the AL model, and both randomness and lattice discreteness for the NLS lattice. The statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size. The usefulness of this effective potential in studying soliton dynamics is demonstrated numerically. Furthermore, we propose two ways to enhance soliton transport in the presence of disorder: one is to use specific realizations of randomness, and the other is to consider a specific soliton pair.

Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials.

In this paper we develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. The proposed approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. Due to the presence of the short-range repulsive component in the potential, the interparticle distances in the lattice kinks with high energy are limited by physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with the single velocity and single energy, which are independent on the excitation conditions. The unique average velocity of the supersonic kinks on the periodic substrate potential we relate with the kink amplitude of the relative particle displacements, which is determined by the interatomic distance corresponding to the minimum of the total, interparticle plus substrate, lattice potential. The found kinks are ultradiscrete and can be described with the "magic wave number" q=2π/3a, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the observed supersonic kinks, with basically two particles moving at the same time, allows the detailed interpretation of their double-kink structure, which is not possible for the multikinks without an account for the lattice discreteness. Analytical calculations of the displacement patterns and energies of the supersonic kinks are confirmed by numerical simulations. The computed energy of the found supersonic kinks in the considered realistic lattice potential is in a good agreement with the experimental evidence for the transport of localized energetic excitations in silicate mica crystals between the points of ^{40}K recoil and subsequent sputtering.

Stationary polarons in discrete molecular chains

Properties of the large acoustic polarons in discrete molecular chains have been investigated within the adiabatic approximation. It turns out that practically all the polaron features are determined by the single parameter-coupling constant which represents the ratio between the small polaron binding energy and the electron bandwidth. Three different types of stationary solutions were found corresponding to weak, intermediate, and strong coupling limits, respectively. In the weak coupling regime, that is, for the values of coupling constant exceeding the limit of the applicability of continuum approximation but lower than the critical one ( ), we observe symmetric bond-centered solution corresponding to the polaron positioned in the middle between the adjacent lattice sites. When coupling constant overgrows, this critical value transition toward the site-centered state occurs. It takes place continuously through the intermediate asymmetric state whose position gradually approaches lattice site as coupling constant increases. One of the main consequences of the lattice discreteness is the emergence of the periodic potential, Peierls-Nabarro potential relief, through which polarons have to pass to transfer along the chain. The conditions for the polaron propagation are formulated in terms of the threshold velocity. © 2012 Wiley Periodicals, Inc.

Continuous description of lattice discreteness effects in front propagation

Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propagation leads in a discrete description to different conclusions that in the case of its, respectively, continuous description, and also that the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that we have denominated Peierls-Nabarro drift, which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurcation diagram. Numerical simulations of the discrete equation show quite good agreement with the phenomenological description.

Atomistic and multiscale analyses of brittle fracture in crystal lattices

Applicability of the Griffith criterion [A. A. Griffith, Philos. Trans. R. Soc. London, Ser. 221, 163 (1920); S. Zhang, S. L. Meilke, R. Khare, D. Troya, R. S. Ruoff, G. C. Schatz, and T. Belytschko, Phys. Rev. B 71, 115403 (2005)] for predicting the onset of crack extension in crystal lattices is systematically evaluated using atomistic and multiscale simulations with a focus on the effects of crack size and lattice discreteness. An atomistic scheme is developed to determine the true Griffith load defined by the thermodynamic energy balance of crack extension for both finite-sized and semi-infinite crack models. For a model monolayer lattice, we identify a characteristic crack length (about ten lattice spacings) below which the Griffith fracture stress markedly overestimates the true Griffith load. Through a stability analysis of crack-tip bond separation, the athermal (nonthermally activated) loads of instantaneous fracture are determined, thereby yielding the estimated lattice trapping range. Our simulations show that the strength of lattice trapping depends on the interaction range of the interatomic force fields. Using the reaction pathway exploration method, we determine the minimum energy paths of bond breaking and healing at a crack tip, giving a more precise estimate of the lattice trapping range. The activation energy barriers governing the rate of kinetic crack extension are extracted from the minimum energy paths. Implications concerning the distinction between the athermal and Griffith fracture loads are discussed. Based on these results, a general criterion is established to predict the onset of crack growth in crystal lattices. In addition to taking into account the lattice trapping effect, this criterion is applicable to a large spectrum of crack sizes.

Existence of multisite intrinsic localized modes in one-dimensional Debye crystals

The existence of highly localized multisite oscillatory structures (discrete multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an inverse dispersion law is proven and their linear stability is investigated. The results are applied in the description of vertical (transverse, off-plane) dust grain motion in dusty plasma crystals, by taking into account the lattice discreteness and the sheath electric and/or magnetic field nonlinearity. Explicit values from experimental plasma discharge experiments are considered. The possibility for the occurrence of multibreathers associated with vertical charged dust grain motion in strongly coupled dusty plasmas (dust crystals) is thus established. From a fundamental point of view, this study aims at providing a rigorous investigation of the existence of intrinsic localized modes in Debye crystals and/or dusty plasma crystals and, in fact, suggesting those lattices as model systems for the study of fundamental crystal properties.

Ferromagnetic shape memory alloys: A theoretical approach

The interaction of crystallographic twin boundaries with an external magnetic field as a mechanism for shape deformation is analyzed theoretically and applied to the alloy Ni2MnGa. A defect, modeled as a Gaussian strain distribution interacting elastically with the twin boundary, is localized in one of the two variants bordering the twin boundary. Micromagnetic equations are used to determine the magnetization angles throughout the variants as well as the equilibrium positions of the twin boundary. These values of the magnetization angle are now incorporated into equations governing the time dependence of the twin boundary motion. The minimum velocity to maintain twin boundary motion in the presence of defects is determined as a function of defect strength and applied field. The results show, among others, a resistance to twin boundary motion due to lattice discreteness and a large but temporary reduction in twin boundary velocity during the interaction between the localized pulse and the defect. Finally, a distribution of stress-related defects is postulated and the relative elongation of the material as a function of the applied magnetic field is obtained. Further, experimental results on the temperature dependence of the magnetic anisotropy and magnetization, as well as the effects of random thermal fluctuations, are included in our micromagnetic equations. The upper limit to the magnetic field driving force then becomes a function of the temperature dependence of the anisotropy. We show that the random thermal energy input is critical to overcoming stress-related obstacles to twin boundary motion.

Feature Article: Influence of the lattice discreteness on magnetic ordering in nanostructures and nanoarrays

AbstractThe cover picture shows an artist's view of magnetic, single domain, in‐plane magnetized islands (courtesy of M. Bode) superimposed with the schematic representation of corresponding magnetostatic multipolar moments. The islands possess shape‐dependent distributions of uncompensated “magnetic” charges and, hence, different multipolar moments (see Section 4 of the Feature Article [1]). The moments are imaged as equipotential surfaces of charge distributions corresponding to conventional spherical harmonics. Positive charged surfaces are red, the negative ones green. The disc‐shaped nanodots with a height equal to a diameter possess only dipolar terms, the elongated elliptic islands have a strong octopolar contribution, while the islands of even more elongated or complicated shape possess superposition of different multipoles.Elena Vedmedenko is a research scientist of the Institute for Applied Physics at the University of Hamburg. Among other scientific topics her research activity concerns theoretical aspects of nanomagnetism. In 2005 Elena Vedmedenko was awarded the Hertha‐Sponer Prize of the German Physical Society for achievements in this area.The issue also contains a special section on “Metamaterials – Optical Elements for the 21st Century” with papers presented at the DPG Summer School held in Bad Honnef, Germany, in September 2006.

Influence of the lattice discreteness on magnetic ordering in nanostructures and nanoarrays

AbstractThe article attempts to analyze the effect of lattice discreteness on the magnetic ordering in nanostructures and nanoarrays. The discussion starts with a basic introduction of the theoretical methods for the description of the magnetic ordering. Next it is shown that the discrete nature of an atomic lattice may lead to the size‐driven reorientation of magnetization in nanoparticles, i.e., the magnetization direction can be changed by shrinking the lateral size, keeping the thickness fixed. It is demonstrated that in finite nanomagnets the shape anisotropy can be divided into the discrete and continuum contributions. Then the orientation of magnetic domain walls in low‐symmetry objects is discussed. It is shown theoretically that in nanomagnets of monolayer thickness the mechanism of the orientation of domain walls is different from that of bulk systems and is mainly determined by the discreteness of the atomic lattice and the exchange energy. In the last part the theoretical study of magnetostatically interacting nanoarrays is presented. Special attention is paid to the influence of the underlaying lattice symmetry and the higher order multipolar terms on the magnetic ordering. It is demonstrated that the multipole‐multipole interactions lead to an enhancement/decrease of the coercivity in arrays with in‐plane/out‐of‐plane magnetization, respectively. In each section of the manuscript the agreement between the theory and recent experimental results is analyzed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Role of lattice discreteness on brittle fracture: Atomistic simulations versus analytical models

By means of thorough atomistic simulations an energy-based theory, named quantized fracture mechanics, is commented and validated. This approach modifies continuum linear elastic fracture mechanics by introducing the hypothesis of discrete crack propagation, taking into account the discreteness of the crystal lattice. We investigate at an atomistic level the crack energy resistance for a matrix of silicon carbide with an isolated crack, and the effect on the stress at the crack tip due to a second phase particle. In both cases our results show that, while atomistic simulations provide the most basic level of understanding of mechanical behavior in nanostructured brittle materials, quantized fracture mechanics is able to effectively incorporate the main lattice-related feature, thus enlarging the realm of continuum modeling.