Diatomic Lattice Research Articles

Anharmonic gap mode in a one-dimensional diatomic lattice with nearest-neighbor Born-Mayer-Coulomb potentials and its interaction with a mass-defect impurity.

Both stationary and moving intrinsic anharmonic gap modes are generated in a perfect one-dimensional diatomic chain. Within the rotating-wave approximation, the eigenfrequency, eigenvector, and energy of such a localized packet can be found from differential-difference equations. A connection between the anharmonic system treated here and the harmonic one is that since the effective force constants are determined by the eigenvector of the particular localized mode, they can be viewed as renormalized force constants in a harmonic lattice. For the diatomic chain the even-parity anharmonic mode is unstable against conversion to an odd-parity mode while the odd-parity mode shows long term stability, in contrast with the result found earlier for a monatomic chain. Part of the mean energy of the odd-parity gap mode is associated with kinetic and potential terms of the ac vibration while the rest resides in a localized dc distortion of the lattice. Strongly localized gap modes can be approximated by the dynamics of a triatomic molecule. For larger vibrational amplitudes and associated dc distortions, the potential for the gap mode becomes double valued and the rotating-wave approximation fails. When the interaction of intrinsic gap modes with stationary anharmonic mass defect impurity modes is examined in numerical simulation studies, a variety of scattering results are found depending on the mass defect magnitude and the site in the diatomic chain. Two important features of the trajectories are that the gap mode is trapped at the mass defect when the vibrational frequencies of the moving mode and the anharmonic defect mode are near resonance and that the scattering is elastic when the frequencies are far apart.

Gap solitons in damped and parametrically driven nonlinear diatomic lattices.

Considerable theoretical progress has been made in the study of gap solitons in nonlinear periodic media and anharmonic diatomic lattices. In this paper we investigate the soliton excitations in a damped and parametrically driven nonlinear diatomic lattice. An experiment for observing gap solitons is suggested.

Erratum: Strongly localized gap solitons in diatomic lattices

Erratum: Strongly localized gap solitons in diatomic lattices

Collective excitations in a three-dimensional diatomic Penrose lattice

We present detailed investigations of the vibrational modes in a three-dimensional diatomic Penrose lattice. The vibrational densities of states are calculated using a recursion technique. These spectra show an apparently branched structure, we classify the branches by means of the same convention as used for crystals. The acoustic branches appear to be smooth and continuous and exhibit a linear feature near zero frequency, while the optical-like branches display a rich structure. The results demonstrate that the density of states in the acoustic branches can be attributed to the phonon and the fracton-like excitations and that in the optical-like branches to some localized vibrational modes.

Irreversibility and Interatomic Potentials in One-dimensional Lattice Models

Abstract Since the computational work on the relaxation process toward the equilibrium state by Fermi, Pasta, and Ulam (FPU) [1], the stochastic behaviors in one dimensional lattice models have been studied by many physicists numerically and theoretically. The objective of those studies is to understand the origin of thermodynamical properties from the microscopic particle motions which are determined by the deterministic equations of motion. In the FPU work, since the given energy was too small and anharmonicity was too weak, thermodynamic irreversibility phenomena, which lead to the equipartition of energy among modes, were not observed. Many studies after this work confirmed the existence of the threshold for the chaotic motions [2] [3]. However, the relation of the chaotic motion in the system with many degrees of freedom to the thermodynamical properties is not well understood [4]. The steady lattice thermal conduction in one dimensional lattice poses an interesting problem in this; respect. A clear linear internal temperature gradient was not observed in the FPU model [5], while it was observed in the the ding-a-ling model by Casati et al. [6] and the diatomic Toda lattice (DTL) by Mokross and Büttner [7]. Recently, the system size dependence of the coefficient of thermal conductivity has been studied [8][9] and the Fourier's law of heat conduction is begining to be confirmed in the DTL.

Stationary Anharmonic Gap Modes in a One-Dimensional Diatomic Lattice with Quartic Anharmonicity

Stationary anharmonic localized modes with eigenfrequencies appearing in the gap between the optic and acoustic frequency bands are studied for a one-dimensional diatomic lattice with hard or soft quartic anharmonicity. A systematic analytical scheme using the lattice Green's function method combined with the rotating-wave approximation and its improved version is developed on the one hand, and extensive numerical experiments have been made on the other. The eigenfrequencies and profile functions of anharmonic gap modes are obtained both analytically and numerically. Good quantitative agreement between the theoretical result and the experimental ones is obtained for both of the gap modes due to the hard and soft quartic anharmonicity. It is shown that the spatial localization of the latter is much more pronounced than that of the former.

Strongly localized gap solitons in diatomic lattices.

It is shown that strongly localized discrete gap solitons may exist in a diatomic chain of particles interacting via a harmonic and a quartic anharmonic potential. In the framework of the rotating-wave approximation, several types of such nonlinear modes are found in the limit of large nonlinearity.

Nonlinear lattices and gap solitons

Strong similarities between the properties of nonlinear diatomic lattices, recently explored by Kivshar and Flytzanis [Phys. Rev. A 46, 7972 (1992)], and those of periodic nonlinear optical structures are elucidated.

Anharmonic gap modes in a perfect one-dimensional diatomic lattice for standard two-body nearest-neighbor potentials.

Two-body potentials of the Toda, Born-Mayer, Lennard-Jones, and Morse type are used in a one-dimensional diatomic lattice to demonstrate both analytically and numerically that stable anharmonic gap modes are a general feature of these perfect lattices. Associated with each vibrational mode is a localized dc lattice expansion, which forms an integral part of this dynamical configuration.

Optical and Acoustic Branches in the Vibrational Spectrum of a Diatomic Penrose Lattice

Vibrational densities of states for a diatomic Penrose lattice are calculated. They show apparently acoustic and optical branches. The acoustic branches appear smooth and continuous, while the optical branches are peakrich and have some small gaps. Detailed analysis shows that the density of states in the acoustic branches is attributed to the phonons and the fracton-like excitations and that in the optical branches due to some localized vibrational modes.

Quasisolitons on a diatomic chain at room temperature.

We have studied analytically and numerically a nonlinear diatomic lattice with a cubic nearest-neighbor interaction potential. Our system is a one-dimensional chain of pairs of atoms interacting through a ``hard'' interaction, each pair being bound to the neighboring pairs by a ``soft'' interaction. This is a simple model for hydrogen-bonded molecular chains, like the spines in an \ensuremath{\alpha} helix. We have used a multiple-scale reductive perturbative technique to transform the equations of motion, and derived a nonlinear Schr\"odinger equation describing the time evolution of localized solitonic excitations. We have also derived analytically, following the method introduced by Zakharov and Shabat, the thresholds for the creation of solitons when the chain is initially excited by a square wave, which is a model of a generic localized excitation. We have performed afterwards several molecular-dynamics simulations at zero temperature. We have found that localized solitonlike excitations can propagate along the chain without being significantly altered; if the initial excitation has a square-wave shape, it evolves into a solitonlike excitation also traveling along the chain. However, if the initial excitation is excessively broad it tends to disperse in a way similar to a linear system; on the other hand, if the excitation is too narrow it may become pinned at the initial position. Finally, we have repeated our simulations in presence of thermal disorder corresponding to temperatures ranging up to 300 K. We have found that the thermal vibrations not only do not destroy the solitonlike excitations, but do not even alter in any significant way their propagation along the molecular chain.

Gap solitons in diatomic lattices.

We consider a nonlinear diatomic lattice of the Klein-Gordon type composed of particles with two different masses. The linear spectrum of this model exhibits a gap, which is proportional to the mass difference in addition to the natural gap stipulated by a nonlinear substrate potential. We analyze the coupled nonlinear excitations of such a diatomic chain which have a similar origin as the well-known gap solitons appearing in nonlinear (e.g., optical) systems with a spatial periodicity. We also describe dark-profile localized structures with a frequency lying below the gap. In the limit when the gap disappears, i.e., for the case of a monoatomic chain, the gap solitons do not exist but instead there exist localized structures of a distinct type created by the nonlinearity-induced symmetry breaking between two equivalent eigenmodes of the lattice, the so-called self-supporting gap solitons.

Phonon self-energy to the fourth order: An application to an anharmonic diatomic linear lattice.

Various contributions responsible for phonon-frequency shifts and widths to the fourth order in the anharmonic perturbation are reformulated and expressed in a computationally suitable form. Numerical calculations of these expressions have also been made for the case of a diatomic linear lattice. Some useful results relating to the expressions for self-energy and to the diatomic linear lattice are presented. The numerical results indicate the relative importance of various contributions. The importance of decay of phonons for width calculations accounting for various decay mechanisms is also pointed out.

Self-Localized Mode in a Diatomic Nonlinear Lattice

Vibrations of a perfect one-dimensional diatomic lattice which has quartic anharmonicity are investigated by computer simulation. We obtain a stationary localized mode which has the s-like symmetry. This self-localized mode appears above the optical band of the corresponding linear lattice.

Undamping of Localized Mode Vibrations in a Nonlinear Diatomic Lattice

Unharmonic vibrations of a one-dimensional diatomic lattice which has a mass impurity are investigated by computer simulation. We obtain stable localized mode vibrations for symmetric potentials.

Thermal conductivity in one-dimensional quasi-periodic Toda lattices

The authors investigate the thermal conductivity in one-dimensional quasi-periodic Toda lattice by means of the molecular dynamics technique. The lattice consists of two kinds of atom with different masses which are arranged according to the Fibonacci sequence. The temperature profile exhibits exponential behaviour as does the diatomic Toda lattice presented in their previous paper. The thermal conductivity is evaluated by separating the ballistically propagating part from the total heat flow. Heat conduction in the Toda lattice with quasi-periodic mass distribution in found to obey Fourier's law. The resultant thermal conductivity is inversely proportional to local temperature and the magnitude is reduced remarkably in comparison with that of the diatomic Toda lattice.

SOLITON-LIKE PHONON LOCALIZED MODES IN DIATOMIC NONLINEAR LATTICE CHAIN

We have studied the localization of multivibrational states in diatomic nonlinear lattice chain. A simple model Hamiltonian presented here describes a system containing two kinds of phonons. The equations of motion for these boson operators are two partial differential equations with nonlinear coupling in long-wave approximation. With the help of the method of multiple scales, these equations are reduced to the nonlinear Schrödinger equation. It is shown that soliton-like phonon localized modes, multi-phonon localized modes can exist. The possibility of observing the gap solitons (phonon localized modes in the frequency gap) in diatomic nonlinear lattice chain is predicted.

Mechanical stability of simple planar lattices.

Elastic constants of simple two-dimensional structures, monatomic square, monatomic hexagonal, and diatomic square, have been calculated with different pairwise atom-atom potentials of the general form V(r)=-A/${\mathit{r}}^{\mathit{n}}$+B/${\mathit{r}}^{\mathit{m}}$, with different A, B, n, and m parameters. The general conditions for the potential parameters have been found to assure stability of the lattices. It is shown that the monatomic square structure can never be stable with the parameters used. On the other hand, the hexagonal monatomic lattice is always stable. Only in the case of the diatomic square lattice does the stability depend on the actual values of the potential parameters. These results explain why in the majority of atomic crystals the (001) surfaces are reconstructed, rough, or stepped, and not planar square.

Temperature-dependent thermal conductivity in low-dimensional lattices

The validity of Fourier's law is investigated by taking account of the temperature dependence of the thermal conductivity for the one- and two-dimensional diatomic lattices. The thermal conductivity is found to be proportional to the inverse of temperature for both the one- and two-dimensional lattices. Fourier's law is confirmed by excluding the nondiffusive or ballistic energy flow from the total energy current.

Ion channeling studies of C + irradiated TiC single crystals

TiC 0.83 crystals have been irradiated in a random direction at room temperature to 5 × 10 15/cm 2 with 350 keV C + ions. Depth profiles of displaced atoms from the carbon and titanium sublattices have been extracted from 1.25 MeV D + backscattering energy spectra and proton energy spectra produced by the 12C(d,p) 13C nuclear reaction, respectively, by comparison of the undamaged and damaged areas oriented along the 〈110〉 direction. The experimental data have been analyzed using a dechanneling theory for diatomic lattices developed in the present study. The profiles obtained for the displaced Ti- and C-atoms are compared with the simulated profiles obtained using a Monte Carlo practice transport code. The results suggests that the threshold displacement energy is different for Ti- and C-sublattices: the displacement energy for the C-sublattices is smaller than that of the Ti-sublattices in TiCo 0.83 crystals.