Monatomic Chains Research Articles

Periodic Solutions of Wave Propagation in a Strongly Nonlinear Monatomic Chain and Their Novel Stability and Bifurcation Analyses

Abstract A modified incremental harmonic balance (IHB) method is used to determine periodic solutions of wave propagation in discrete, strongly nonlinear, periodic structures, and solutions are found to be in a two-dimensional hyperplane. A novel method based on the Hill’s method is developed to analyze stability and bifurcations of periodic solutions. A simplified model of wave propagation in a strongly nonlinear monatomic chain is examined in detail. The study reveals the amplitude-dependent property of nonlinear wave propagation in the structure and relationships among the frequency, the amplitude, the propagation constant, and the nonlinear stiffness. Numerous bifurcations are identified for the strongly nonlinear chain. Attenuation zones for wave propagation that are determined using an analysis of results from the modified IHB method and directly using the modified IHB method are in excellent agreement. Two frequency formulae for weakly and strongly nonlinear monatomic chains are obtained by a fitting method for results from the modified IHB method, and the one for a weakly nonlinear monatomic chain is consistent with the result from a perturbation method in the literature.

Stretching-controlled structural evolution in phosphorene: Transferable and tunable twinning nanoarchitecture for construction of monatomic chains

Stretching-controlled structural evolution in phosphorene: Transferable and tunable twinning nanoarchitecture for construction of monatomic chains

Lattice dynamics and elastic waves scattering by surrogate atoms in quasi-one dimensional atomic assemblies

An analytical and numerical formalism is developed to study the influence of the various positions of substitution atoms B on the scattering and transmission vibration modes in quasi-1D monatomic structures A. The matching technique is employed to calculate the dynamical properties and transmittance spectra of two substituted atomic sites. The theoretical formalism gives a complete description of the lattice dynamics and the vibration-waves propagation in the presence of the impurity sites. Numerical calculations are performed for three different positions of the two substituted atoms B in the low-dimensional structure consisting of double monatomic parallel chains. First, we examine the position where the two B atoms are adjacent in the y-direction, afterwards, we place the two sites side by side in the x-direction. Lastly, the two sites are placed in oblique configuration. The obtained results show that phonons associated to the inhomogeneous structures are strongly dependent on the scattering frequency, elastic force parameters and the position of the atomic substituted sites. In the three considered positions, the presence of the B atoms gives rise to localized vibration effects. The fluctuations observed in the vibration spectra are related to resonances due to the coherent coupling between travelling phonons and the localized vibration modes in the neighborhood of the impurity sites.

The Memory Function of an Impurity in Mass and Hooke Constant in a Diatomic Chain

The memory function of an impurity with different mass and Hooke constant in a classical diatomic chain is studied by means of the recurrence relations method. The Laplace transform of the memory function has two pairs of resonant poles and three branch cuts. The poles contribute a cosine and the cuts contribute acoustic and optic branches, which are expressed as a convolution of a difference of two sines and an expansion of even-order Bessel functions. The expansion coefficients are integrals of Jacobian elliptic function sn(u) along the real axis in a complex u+iv plane for the acoustic branch, and integrals of nd(v) along a contour parallel to the imaginary axis of the plane for the optical branch, respectively. Different special cases are discussed in detail. It shows that a perfect monatomic or diatomic chain and such a chain with a mass impurity share the same memory function except for a constant factor, and that the pole contribution exists only if the impurity has both different mass and Hooke constant.

Manipulating the Spin Orientation of Co Atoms Using Monatomic Cu Chains.

Harnessing the spin of single atoms is at the heart of quantum information nanotechnology based on magnetic concepts. By attaching single Co atoms to monatomic Cu chains, we demonstrate the ability to control the spin orientation by the atomic environment. Due to spin-orbit coupling (SOC), the spin is tilted by ≈58° from the surface normal toward the chain as evidenced by inelastic tunneling spectroscopy. These findings are reproduced by density functional theory calculations and have implications for Co atoms on pristine Cu(111), which are believed to be Kondo systems. Our quantum Monte Carlo calculations suggest that SOC suppresses the Kondo effect of Co atoms at chains and on the flat surface. Our work impacts the fundamental understanding of low-energy excitations in nanostructures on surfaces and demonstrates the ability to manipulate atomic-scale magnetic moments, which can have tremendous implications for quantum devices.

Hierarchical unit cell employing a nonlinear energy sink for passive, low-pass amplitude filtering of acoustic waves

In this letter we present a hierarchical unit cell incorporating a nonlinear energy sink (NES) that functions as a low-pass amplitude filter. The hierarchical unit cell is composed of an outer and inner mass coupled by essentially nonlinear springs. Other than its nonlinear coupling to the outer mass, the inner mass is otherwise unconstrained and thus acts as an NES. Using numerical simulations, we show that the nonlinear unit cell passively filters incident waves as a function of their amplitude. The resonator is inactive at low amplitudes, permitting waves to pass. At high amplitudes, the NES activates and its resonant behavior reflects incident waves. Consequently, the unit cell effectively operates as an amplitude limiter for specific signal frequency and amplitude ranges. Notably, the passing of low-amplitude incident energy while bypassing the nonlinearity results in very little distortion in transmitted signals. We analytically investigate this behavior further using a harmonic balance method. The analysis supports the transmission filtering behavior as well as the activation of the nonlinear energy sink. Lastly, we design and construct the nonlinear unit cell and perform tests using incident and transmitted waveguides composed of monatomic chains. Both the nonlinear unit cell and monatomic chains are assembled using steel masses and additively-manufactured springs. We test the fabricated filter using low and high amplitude signals and observe amplitude filtering at various excitation frequencies that document strong agreement with numerical simulations and the analytical model. The ability to passively reflect high amplitude waves, and transmit low amplitude waves with minimal distortion, may inspire new devices for hearing protection, or for isolating and protecting sensitive equipment and instruments.

Mechanical tensile behavior-induced multi-level electronic transport of ultra-thin SiC NWs

Mechanical tensile behavior and its influence on electron transport are especially appealing for ultra-thin SiC Nanowires (NWs). Our studies theoretically show that ultra-thin SiC-[100] NWs in different diameters possess much better plasticity than SiC NWs in large scales and exhibit non-traditionally multiple-fluctuating stress-strain curves due to the chain-by-chain fracture of NWs. Noticeably, NWs possesses almost the same fracture stain and the corresponding stress decreases with diameter. Influenced by the strain, ultra-high transmission coefficients appear (exceed 1) and stable electron transmission can be kept in some strain range for all sizes of SiC NWs. An obvious increase of transmission peaks occurs in the thinnest SiC atomic chain at larger strains while the strain has almost no effect on the number of transmission peaks for other thicker SiC NWs. The generation of monatomic chains would weaken the electron transport of thicker SiC NWs. Internally, C elements and p-orbital contribute more in electron transport and stretching strains have almost no effect on such contribution assignments. This work provides stronger support for applications of ultra-thin SiC-[100] NWs in nano-piezoelectric devices and nanoelectronics in mechanically disturbed environments, and an effective way to strengthen electron transport of NWs.

The deformation of the icosahedral gold 13-atom cluster

As a building block, the icosahedral gold 13-atom cluster has attracted much attention for many years. In this paper, the tensile and compressive deformation of the icosahedral gold 13-atom cluster are investigated and some interesting results different from bulks and nanowires are obtained. It is found that the elastic strain limits of the cluster are much larger than those of the gold bulks and the nanowires. Within the elastic strain limit, the loading force–strain relationship is not linear. And the stiffness coefficient decreases with increasing strain under the tensile loading, and increases with increasing strain under the compressive loading. Under the influence of temperature, the loading force and the stiffness coefficient decrease with the increasing temperature at the same strain. The elastic strain limit and the break-up strain are also reduced as the temperature rises. Although the bulks and nanowires cannot return to their original configurations when they are in a plastic state, however, the calculation shows that the cluster can return spontaneously to its original icosahedral structure even if the cluster has been at plastic deformation when the loading is released above a certain temperature. A monatomic chain is formed when the cluster is close to rupture. The interatomic distance and the tensile force for the monatomic chain are consistent with the experimental data.

Experimental realization of an additively manufactured monatomic lattice for studying wave propagation

Increasing interest in wave propagation in phononic systems and metamaterials motivates the development of experimental designs, measurement techniques, and fabrication methods for use in basic research and classroom demonstrations. The simplest phononic system, the monatomic chain, exhibits rich physics such as dispersion and frequency-domain filtering. However, a limited number of experimental studies showcase monatomic chains for macroscale observation of phonons. Herein, we discuss the design, fabrication, and testing of monatomic lattices as enabled by three-dimensional (3D) printing. Using this widely available technology, we provide design guidelines for realization of a monatomic chain composed of 3D printed serpentine springs and press-fitted cylindrical masses. We also present measurement techniques that record propagating waves and algorithms for the experimental determination of dispersion behavior.

Nonlinear hierarchical unit cell for passive, amplitude-dependent filtering of acoustic waves

In this letter we propose a nonlinear hierarchical unit cell for use in passive, amplitude-dependent filtering of acoustic energy transmission. Analogous to unit cell designs which filter on frequency using bandgaps, the nonlinear hierarchical unit cell filters on amplitude with minimal waveform distortion. Numerical simulations of wave propagation in a mechanical chain employing the proposed unit cell predict nearly zero transmission of energy at low amplitudes, and nearly perfect energy transmission at large amplitudes. We hypothesize that the amplitude-dependent transmission behavior results from the nonlinear unit cell locking at high amplitudes, and thus acting as a single mass. When this single mass has the same weight as the other masses in the chain, near-perfect transmission is possible. We investigate this behavior further through a nonlinear analysis using a harmonic balance method to predict wave transmission through the nonlinear unit cell. The analysis confirms the transmission behavior and the rigid body hypothesis at large amplitudes. To validate the simulated and analysis results, we design and construct a monatomic chain using steel masses and additively-manufactured serpentine springs, to include a specially-designed nonlinear spring in the hierarchical unit cell. We then document amplitude-dependent filtering in the experiment for multiple frequencies, with strong agreement documented between measured results and simulation. In addition, high-speed camera images of the hierarchical cell verify the hypothesized locking behavior at large amplitudes. We believe the ability to passively select transmission based on a signal’s amplitude, with minimal resulting distortion, may open new opportunities in wave control and filtering, and new approaches for conceiving wave-based devices.

The Role of Quadruple Bonding in the Electron Transport through a Dimolybdenum Tetraacetate Molecule.

A dimolybdenum tetraacetate (Mo2(O2CCH3)4) molecule is embedded between two electrodes formed by semi-infinite 1D monatomic chains of lithium, aluminum, and titanium atoms. Electron transport through the Mo2(O2CCH3)4 molecule is calculated. The role of quadrupole bonding in the transport properties of the studied systems is analyzed.

Magnetic ground state of supported monatomic Fe chains from first principles

A new computational scheme is presented based on a combination of the conjugate gradient and the Newton–Raphson method to self-consistently minimize the energy within local spin-density functional theory, thus to identify the ground state magnetic order of a finite cluster of atoms. The applicability of the new ab initio optimization method is demonstrated for Fe chains deposited on different metallic substrates. The optimized magnetic ground states of the Fe chains on Rh(111) are analyzed in details and a good comparison is found with those obtained from an extended Heisenberg model containing first principles based interaction parameters. Moreover, the effect of the different bilinear spin–spin interactions in the formation of the magnetic ground states is monitored. In case of Fe chains on Nb(110) spin-spiral configurations with opposite rotational sense are found as compared to previous spin-model results which hints on the importance of higher order chiral interactions. The wavelength of the spin-spiral states of Fe chains on Re(0001) was obtained in good agreement with scanning tunneling microscopy experiments.

Study of the transport properties of cobalt atomic contact under mechanical strain in a nitrogen atmosphere

Achieving an efficient spin-filter effect and large magneto-resistance in molecular junctions is very important in spintronics. By employing the non-equilibrium Green's function formalism combined with the density functional theory, this study investigated the atomic structures and spin-resolved transport properties of molecular junctions consisting of nitrogen (N2) sandwiched between two cobalt (Co) electrodes with different crystal lattices as a function of stretching distance. In the case of face-centred cubic Co electrodes, our calculations showed that the transport properties depend strongly on the stretching process, which changes the contact between the N2 and Co electrodes. Specifically, the maximum spin polarization is due to the configuration of N2 molecules sitting in parallel with the protruding Co atoms. Furthermore, the Co dxz,yz orbitals interact with the N px,y orbitals, which contribute to the high transmission coefficient at the Fermi level for spin-down electrons. Meanwhile, the Co s-dz2 hybridization orbitals, which interact weakly with the N p orbitals, contribute to the small transmission coefficient at the Fermi level. This can also be verified by the molecular junction model adopting simple monatomic Co chain electrodes, which also show a perfect spin-filter effect and achieve an ideal magnetoresistance. In contrast, in the case of hexagonal Co electrodes, the spin-filter effect disappears. However, the effect appears again by adding one more Co atom to the central point contact. Our findings show that the spin-resolved electronic transport of molecular junctions depends on the stretching process and the nature of the electrodes, which can help in the future design of molecular devices based on the spin degree of freedom.

Excitonic-insulator instability and Peierls distortion in one-dimensional semimetals

The charge density wave instability in one-dimensional semimetals is usually explained through a Peierls-like mechanism, where the coupling of electrons and phonons induces a periodic lattice distortion along certain modes of vibration, leading to a gap opening in the electronic band structure and to a lowering of the symmetry of the lattice. In this work, we study two prototypical Peierls systems: the one-dimensional carbon chain and the monatomic hydrogen chain with accurate ab initio calculations based on quantum Monte Carlo and hybrid density functional theory. We demonstrate that in one-dimensional semimetals at $T=0$, a purely electronic instability can exist independently of a lattice distortion. It is induced by spontaneous formation of low energy electron-hole pairs resulting in the electronic band gap opening, i.e., the destabilization of the semimetallic phase is due to an excitonic mechanism.

Superior electron transport of ultra-thin SiC nanowires with one impending tensile monatomic chain

The effect of the tensile strain on the electron transport are studied theoretically for ultra-thin SiC Nanowires (NWs) with different diameters. Results show that these NWs exhibit distinctive and non-traditional stress-strain curves, characterized by multistage fluctuations. The tension greatly affects the electron transport. The strongest transmission appears when the wire is stretched to the near-emergence of the monatomic chain in the necking place (especially for thicker SiC NWs) which suppresses the electron transport, essentially originating from localized transmission eigenstates and pathways. This work provides an approach to enhance the electron transport and strong backing in promising applications of nanoelectronics and nano-piezoelectric devices for ultra-thin SiC NWs.

Perturbation analysis of nonlinear evanescent waves in a one-dimensional monatomic chain.

This paper investigates evanescent waves in one-dimensional nonlinear monatomic chains using a first-order Lindstedt-Poincaré approach. Perturbation approaches applied to traveling waves in similar chains have predicted weakly nonlinear phenomena such as dispersion shifts and amplitude-dependent stability. However, nonlinear evanescent waves have received sparse attention, even though they are expected to serve a critical role in nonlinear interface problems. To aid in their analysis, the nonlinear evanescent waves are categorized herein as either complete or transitional evanescent waves. Complete evanescent waves, including linear evanescent waves, attenuate to zero amplitude in the far field. Transitional evanescent waves, only occurring in softening systems, attenuate to a nontrivial amplitude in the far field, regardless of the initial amplitude, resulting in a saturation effect. For both cases, the presented perturbation approach reveals that the imaginary wave number in the evanescent field is a function of space, rather than a constant value as in its linear counterpart. It also reveals that hardening and softening nonlinearity slow and accelerate the near-field decay, respectively. The predictions obtained from the perturbation approach are verified using numerical simulations with both initial-condition and boundary-continuous excitation, documenting strong agreement.

Acoustic bandgaps in polyatomic chains of 3D-printed resonators

Acoustic bandgaps are ranges of frequencies in a medium at which sound cannot propagate. The classical model often used in solid-state physics is that of a 1D chain of masses and springs, the analysis of which can predict the speed of sound in a material, its dispersive nature, and any forbidden sound frequencies. We use a lumped parameter model for the acoustic inertance and compliance of pipes and cavities to create 1D monatomic, diatomic, and triatomic chains that demonstrate these acoustic bandgaps experimentally. The ease of 3D-printing these devices means that this method can be used to explore bandgap engineering in acoustic systems for low-frequency applications and used as a simple platform for creating acoustic analogs of the solid-state physical problem. Furthermore, it allows us to explore novel polyatomic behavior (e.g., tetratomic and pentatomic) and could ultimately find use as filters for experiments requiring miniaturized acoustic isolation.

Moving window techniques to model shock wave propagation using the concurrent atomistic–continuum method

Atomistic methods have successfully modeled different aspects of shock wave propagation in materials over the past several decades, but they suffer from limitations which restrict the total runtime and system size. Multiscale methods have been able to increase the length and time scales that can be modeled but employing such schemes to simulate wave propagation and evolution through engineering-scale domains is an active area of research. In this work, we develop two distinct moving window approaches within a Concurrent Atomistic–Continuum (CAC) framework to model shock wave propagation through a one-dimensional monatomic chain. In the first method, the entire CAC system travels with the shock in a conveyor fashion and maintains the shock front in the middle of the overall domain. In the second method, the atomistic region follows the shock by the simultaneous coarsening and refinement of the continuum regions. The CAC and moving window frameworks are verified through dispersion relation studies and phonon wave packet tests. We achieve good agreement between the simulated shock velocities and the values obtained from theory with the conveyor technique, while the coarsen-refine technique allows us to follow the propagating wave front through a large-scale domain. This work showcases the ability of the CAC method to accurately simulate propagating shocks and also demonstrates how a moving window technique can be used in a multiscale framework to study highly nonlinear, transient phenomena.

Hybrid Bandgaps in Mass-coupled Bragg Atomic Chains: Generation and Switching

In this work, without introducing mass-in-mass units or inertial amplification mechanisms, we show that two Bragg atomic chains can form an acoustic metamaterial that possesses different types of bandgaps other than Bragg ones, including local resonance and inertial amplification-like bandgaps. Specifically, by coupling masses of one monatomic chain to the same masses of a diatomic or triatomic chain, hybrid bandgaps can be generated and further be switched through the adjustment of the structural parameters. To provide a tuning guidance for the hybrid bandgaps, we derived an analytical transition parameter (p-value) for the mass-coupled monatomic/diatomic chain and analytical discriminants for the mass-coupled monatomic/triatomic chain. In our proposed mass-coupled monatomic/triatomic chain system, each set of analytical discriminants determines a hybrid bandgap state and a detailed examination reveals 14 different bandgap states. In addition to bandgap switching, the analytical p-value and discriminants can also be used as a guide for designing the coupled-chain acoustic metamaterials. The relations between the mass-coupled monatomic/triatomic chain system and a three-degree-of-freedom (DOF) inertial amplification system further indicate that the band structure of the former is equivalent to that of the latter through coupling masses by negative dynamic stiffness springs.

Fundamental frequency analysis of endohedrally functionalized carbon nanotubes with metallic nanowires: a molecular dynamics study.

The endohedral functionalization of carbon nanotubes (CNTs) with nanowires (NWs), i.e., NWs@CNTs, has been the center of attention in a lot of research due to the applications of NWs@CNTs in nanoelectronic devices, heterogeneous catalysis, and electromagnetic wave absorption. To this end, based on the classical molecular dynamics (MD) simulations, the effect of four pentagonal structures of encapsulated metallic nanowires (mNWs), namely the eclipsed pentagon (E), the deformed staggered pentagon (Ds), staggered pentagon (S), and staggered pentagonal structure without the monatomic chain passing through the centers of the parallel pentagons (R) configurations on the vibrational behavior of CNTs, is investigated. Also, the effects of geometrical parameters such as length and radius of CNTs on the natural frequencies of simulated models are explored. The results illustrate that by increasing the length, the natural frequency of pure CNTs and mNWs@CNTs decreases. In a similar length, mNWs@CNTs possess lower natural frequencies compared to the pure CNTs. According to the results, the highest and lowest natural frequencies are calculated by inserting the S structure of sodium NW and Ds structure of aluminum NW inside their proper armchair CNT, i.e., Na-S NW@ (9,9) CNT and Al-Ds NW@ (7,7) CNT, respectively.