Rigid Lattices Research Articles

On the possibility of observing chaotic motion of cold atoms in rigid optical lattices

The possibility of experimental observation of chaotic motion of cold atoms in a one-dimensional rigid optical lattice without any modulation of its parameters and additional impact is demonstrated theoretically and numerically. This effect of deterministic chaos arises near the optical resonance due to the nonlinear coupling of electronic and mechanical degrees of freedom in the atom. In a certain range of resonance detunings, at each crossing of the lattice-forming standing wave node by the atom, the atomic dipole moment changes pseudorandomly in a step-like manner, accompanied by an appropriate change in the atom momentum. This leads to the effect of chaotic wandering of atoms, possessing the properties of the classical deterministic chaos, namely, to the exponential sensitivity of atomic trajectories to small variations of the initial conditions and/or the control parameters. With time, part of atoms from the initial cloud changes the direction of their motion to the opposite one, which can be detected in a real experiment. Numerical experiments with lithium atoms with the spontaneous emission taken into account show that by varying the laser radiation intensity (normalised detuning of resonance) in the rigid optical lattice, one can implement the transition from the regular regime of the atomic motion to the chaotic wandering in a real experiment.

Exact mean field concept to compute defect energetics in random alloys on rigid lattices

In modern materials science modeling, the evolution of the energetics of random alloys with composition are desirable input parameters for several meso-scale and continuum scale models. When using atomistic methods to parameterize the above mentioned concentration dependent function, a mean field theory can significantly reduce the computational burden associated to obtaining the desired statistics in a random alloy. In this work, a mean field concept is developed to obtain the energetics of point-defect clusters in perfect random alloys. It is demonstrated that for a rigid lattice the concept is mathematically exact. In addition to the accuracy of the presented method, it is also computationally efficient as a small box can be used and perfect statistics are obtained in a single run. The method is illustrated by computing the formation and binding energy of solute and vacancy pairs in FeCr and FeW binaries. Also, the dissociation energy of small vacancy clusters was computed in FeCr and FeCr-2%W alloys, which are considered model alloys for Eurofer steels. As a result, it was concluded that the dissociation energy is not expected to vary by more than 0.1eV in the 0–10% Cr and 0–2% W composition range. The present mean field concept can be directly applied to parameterize meso-scale models, such as cluster dynamics and object kinetic Monte Carlo models.

Classification of epitaxy in reciprocal and real space: rigid versus flexible lattices.

Early investigations of epitaxy focused on inorganic adsorbates consisting of atoms or few-atom molecules, where commensurate registries are predominantly encountered. Expanding such studies to larger (organic) molecules has revealed hitherto unknown types of epitaxy with coherence between adlayer and substrate lattices in just one direction. Here we review recent contributions to the fundamental understanding and modeling of epitaxy. By sorting the ideas brought forward in the literature and amending some basic algebraic considerations a universal scheme for the classification of lattice epitaxy is presented. Ultimately, the occurrence of the different types of epitaxy is made plausible by easy-to-grasp energetic arguments.

Light-induced atomic elevator in optical lattices

It is shown how an atomic elevator that can elevate falling cold atoms in a vertical optical lattice can be created. The effect appears near resonance owing to the nonlinear interaction between the electronic and mechanical degrees of freedom of an atom, which is responsible for its random walk in rigid optical lattices without any modulation and additional action. Numerical experiments involving spontaneous emission demonstrate that random walk of atoms and light-induced atomic elevator can be observed in a real experiment.

ChemInform Abstract: Influence of Guest Molecules on the Crystal Lattice Structure and Porous Structure Characteristics of Coordination Polymers

AbstractReview: 30 refs.

Soft Crystals in Flatland: Unraveling Epitaxial Growth.

Thin film epitaxy typically invokes a superposition of a pair of rigid two-dimensional lattices with a well-defined orientation governed by some form of commensurism. A report by Meissner et al. in this issue of ACS Nano demonstrates that the organization of organic molecules on substrates may not be that simple, as static distortion waves involving miniscule shifts of atomic positions from substrate lattice points can lead to orientations of a molecular film that cannot be described by often used models. Herein, we provide some highlights of epitaxy, with a focus on configurations that reflect the delicate balance between intermolecular interactions within a molecular film and molecule-substrate interactions. Although geometric models for explaining and predicting epitaxial configurations can be used to guide synthesis of materials, their use must recognize energetic factors and the possibility of more complex, and possibly less predictable, interface structures.

Flexible 2D Crystals of Polycyclic Aromatics Stabilized by Static Distortion Waves.

The epitaxy of many organic films on inorganic substrates can be classified within the framework of rigid lattices which helps to understand the origin of energy gain driving the epitaxy of the films. Yet, there are adsorbate–substrate combinations with distinct mutual orientations for which this classification fails and epitaxy cannot be explained within a rigid lattice concept. It has been proposed that tiny shifts in atomic positions away from ideal lattice points, so-called static distortion waves (SDWs), are responsible for the observed orientational epitaxy in such cases. Using low-energy electron diffraction and scanning tunneling microscopy, we provide direct experimental evidence for SDWs in organic adsorbate films, namely hexa-peri-hexabenzocoronene on graphite. They manifest as wave-like sub-Ångström molecular displacements away from an ideal adsorbate lattice which is incommensurate with graphite. By means of a density-functional-theory based model, we show that, due to the flexibility in the adsorbate layer, molecule–substrate energy is gained by straining the intermolecular bonds and that the resulting total energy is minimal for the observed domain orientation, constituting the orientational epitaxy. While structural relaxation at an interface is a common assumption, the combination of the precise determination of the incommensurate epitaxial relation, the direct observation of SDWs in real space, and their identification as the sole source of epitaxial energy gain constitutes a comprehensive proof of this effect.

Reaction Rate Constants of CH4(ads) ⇌ CH3(ads) + H(ads) on Ni(111): The Effect of Lattice Motion.

Methane dissociation on metal surfaces is of great commercial importance. The dissociation and recombination rate constants of CH4 on Ni(111) are calculated using the quantum instanton approach with the path integral Monte Carlo method. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically to reveal the effects of lattice motion and quantum tunneling. For the dissociation of CH4, the rates have the smallest value on the rigid lattice, while they possess the largest value on the quantum lattice. For instance, at 300 K, the rates on the classical and quantum lattices are 5 and 12 times larger than that on the rigid lattice, respectively. The curve of the Arrhenius plot for the dissociation rates on the rigid lattice demonstrates that the quantum tunneling effect of the ruptured H atom is remarkable, while the nearly invariable dissociation rates at low temperatures on the quantum lattice confirm that the thermally assisted tunneling should be dominant at low temperatures. For the recombination of CH4, the quantum lattice still has rates that are much larger than that of the rigid lattice. For instance, the ratio of the recombination rates on the quantum and rigid lattices is 12 at 300 K. The quantum tunneling effect seems to play a minor role in the recombination rates on the rigid lattice; however, the thermally assisted tunneling is still very significant for the recombination process.

Influence of Guest Molecules on the Crystal Lattice Structure and Porous Structure Characteristics of Coordination Polymers

The influence of guest molecules, including the solvent, on the structure of porous coordination polymers (PCP) and, as a consequence, their adsorption properties is analyzed. It was suggested that the nature of the solvent can predetermine the selectivity of PCP adsorption only when the solvent acts as a template in the formation of such a polymer. In contrast to PCP with rigid crystal lattices, the characteristics of PCP with labile lattices and their adsorption properties depend significantly on the nature of guest molecules.

Synthesis and efficient blue-emitting of Eu2+-activated borate fluoride BaAlBO3F2

Eu2+-doped borate fluoride BaAlBO3F2 was synthesized by the conventional high temperature solid state reaction. The crystal phase formations were confirmed by X-ray powder diffraction (XRD) measurements and the structure refinement. The photoluminescence (PL) excitation and emission spectra, and the decay curves were investigated. Eu2+-doped BaAlBO3F2 phosphor can be efficiently excited by near-UV light and presents narrow blue luminescence band centered at 450nm. The maximum absolute quantum efficiency (QE) of BaAlBO3F2:0.05Eu2+ phosphor was measured to be 76% excited at 398nm light at 300K. The thermal stability of the blue luminescence was evaluated by the luminescence decays as a function of temperature. The phosphor shows an excellent thermal stability with high thermal activation-energy on temperature quenching effects because of the rigid crystal lattices.

Reversibly Assembled Cellular Composite Materials

We introduce composite materials made by reversibly assembling a three-dimensional lattice of mass-produced carbon fiber-reinforced polymer composite parts with integrated mechanical interlocking connections. The resulting cellular composite materials can respond as an elastic solid with an extremely large measured modulus for an ultralight material (12.3 megapascals at a density of 7.2 milligrams per cubic centimeter). These materials offer a hierarchical decomposition in modeling, with bulk properties that can be predicted from component measurements and deformation modes that can be determined by the placement of part types. Because site locations are locally constrained, structures can be produced in a relative assembly process that merges desirable features of fiber composites, cellular materials, and additive manufacturing.

Remarks on a conjecture of Chabauty

The Chabauty conjecture for connected nilpotent Lie groups has been proved by S. P. Wang. We show that one reasoning flaw has infiltrated the proof. We therefore give a new proof of the validity of Chabauty's conjecture in this setup. More generally, we shall prove that the Chabauty conjecture is true for rigid lattices and Zariski dense lattices of connected solvable Lie groups. In particular, the Chabauty conjecture holds for solvable Lie groups of (R)-type.

A novel algorithm to model the influence of host lattice flexibility in molecular dynamics simulations: Loading dependence of self-diffusion in carbon nanotubes

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.

NANOSCALE PROPERTIES OF FRICTION AND LUBRICATION AT SOLID INTERFACES WITH LUBRICANTS

Nanoscale frictional phenomena at a solid interface with a lubricant layer are studied numerically. We use a model which consists of two rigid substrate lattices with surface impurities and a lubricant lattice, where the upper substrate is driven by an external force. From the analysis of velocity–velocity correlations, it is found that surface randomness due to impurities cause a correlated lubrication dynamics in the lubricant layer. Such correlation is not observed for clean interfaces. We discuss effects of surface randomness on lubrication dynamics of the lubricant.

Non-rigidity Degree of a Lattice and Rigid Lattices

Voronoi defines a partition of the cone of positive semidefinite n -ary formsPn into L -type domains. Each L -type domain is an open polyhedral cone of dimensionk , 1 ≤k≤n(n+ 1)2, where n is the number of variables and dimension of the corresponding lattice. We define a non-rigidity degree of a lattice as the dimension of the L -type domain containing the lattice. We prove that the non-rigidity degree of a lattice equals the corank of a system of equalities connecting norms of minimal vectors of cosets of 2 L in L. A lattice of non-rigidity degree 1 is called rigid. A lattice is rigid if any of its sufficiently small deformations distinct from a homothety changes its L -type. Using the list of 84 zone-contracted Voronoi polytopes inR5given by Engel [8], we give a complete list of seven five-dimensional rigid lattices.

Kinetic Monte Carlo simulations of cascades in Fe alloys

ABSTRACTThe Pressurized Water Reactor vessel steels are embrittled by neutron irradiation. Among the solute atoms, copper play an important role in the embrittlement and different Cu-rich defects have been experimentally observed to form. We have investigated by Kinetic Monte Carlo (KMC) on rigid lattices the evolution of the primary damage. Since the point defects created by the displacement cascades have very different kinetics, their evolution is tracked in two steps. In a first step, we have studied their recombination in the cascade region and the formation of interstitial clusters using “object diffusion”. The parameters of this model are based on MD simulations, or on first principles calculations. In a second part, we have investigated the subsequent evolution of the primary damage with a model based on a vacancy jump mechanism. These simulations which rely on an adapted EAM potential show the formation of copper rich defects. Some of the potential's predictions that played a key role in the model were checked by ab initio calculations. The defects obtained from these simulations, subsequent to the primary damage created by displacement cascades, exhibit similarities with the ones observed by atom probe. The influence of temperature and Cu content on the final damage was investigated.

About the influence of lattice vibrations on the diffusion of methane in a cation-free LTA zeolite

The influence of lattice vibrations on the diffusion of methane in a cation-free zeolite of structure Type LTA is examined. It is shown that contrary to earlier published results the self-diffusion coefficients obtained with flexible and with rigid lattices are practically the same. This finding is true over a wide range of temperatures and for different interaction parameters. The reason why earlier papers did not state this independence of D on the lattice vibrations is explained.

Curing reactions and modeling of silicone-carbon resins

New silicone-carbon resins have been made, based on four- or five-membered cyclosiloxanes, cyclopentadiene dimer (DCPD), and cyclopentadiene trimer (TCPD). The monomers are first polymerized to a B-stage resin, and then heated at higher temperatures to cure. In this work, the curing reaction of this silicone-carbon resin (which leads to network formation) is simulated using two approaches. In the first approach (stochastic model), all the available functional groups (olefin and silyl hydride) are allowed to react with each other with equal probability. This gives the kinetically controlled, liquidlike, diffusion-free limit. Extrapolation of the model to reactions where diffusion may play a role can be made by including molecular weight dependence in the rates. This dependence on the molecular weight can be scaled to fit the experimental data. In the second approach a percolation model is used. In the extreme case, this model corresponds to the solid-state reaction between silicone-carbon resin molecules on 2-dimensional or 3-dimensional rigid lattices. Relaxation of this geometric constraint can be made by providing a larger reacting distance between the reactants. Computer programs have been written for 2- and 3-dimensional lattices. Illustrative examples are given for these approaches. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 1557–1573, 1997

Simulation of atomic zinc luminescence in rare gas solids: A localized pair potentials approach

The luminescence spectroscopy of atomic zinc isolated in the solid rare gases (Zn/RG) is compared with theoretical predictions obtained from the sum of diatomic Zn⋅RG and RG⋅RG pair potentials. In particular the existence of pairs of emission bands, both of which are assigned to the same gas phase electronic transition, is examined with the use of diatomic pair potentials to simulate the potential energy surfaces of the Jahn–Teller active vibrational modes of Zn in the solid rare gases Ar, Kr, and Xe. Simulations of the solid state Zn/RG luminescence are developed from a consideration of the excited state Zn(1P1)⋅RGn van der Waals cluster species in the gas phase. The maximum binding energy of the Zn(1P1)⋅RGn clusters is found in the Zn⋅RG4 cluster having a square planar structure at the energy minimum. Based on the results of the cluster calculations, lattice distortions which led to a dominant interaction between the Zn atom and four of its host atoms were sought to simulate the solid state luminescence. Two such vibronic modes were identified; one a lattice mode in which four rare gas atoms contract on a single plane toward the Zn atom, referred to as the waist mode, and the other a motion of the Zn atom toward an octahedral interstitial site of the lattice, the body mode. Energy calculations of these modes were carried out for rigid and relaxed rare gas lattices allowing identification of the high energy emission bands in the Zn/RG systems as arising from the waist mode, while the lower energy bands are associated with the body mode. The model also rationalizes the differences exhibited in the time-resolved behavior of the pairs of singlet emission bands in the Zn/Ar and Zn/Kr systems, whereby the lower energy band of a given system shows a risetime of a few hundred picoseconds while the higher energy band exhibits direct feeding. The steep gradient calculated on the waist mode, feeding the high energy band, and the flat gradient found on the body mode, feeding the lower energy emission, are consistent with the existence of a risetime in the latter and its absence in the former. The close agreement found between theory and experiment indicates the validity of using pair potentials in analysis of matrix zinc spectroscopy and thereby indicates that the luminescence is controlled by localized guest–host interactions.

Direct Observation of Vortex Dynamics in Superconducting Films with Regular Arrays of Defects

The microscopic mechanism of the matching effect in a superconductor, which manifested itself as the production of peaks or cusps in the critical current at specific values of the applied magnetic field, was investigated with Lorentz microscopy to allow direct observation of the behavior of vortices in a niobium thin film having a regular array of artificial defects. Vortices were observed to form regular and consequently rigid lattices at the matching magnetic field, at its multiples, and at its fractions. The dynamic observation furthermore revealed that vortices were most difficult to move at the matching field, whereas excess vortices moved easily.