Incommensurate Ones Research Articles

Robustness of structural superlubricity beyond rigid models

Structural superlubricity is a theoretical concept stating that the friction force is absent between two rigid, incommensurate crystalline surfaces. However, elasticity of the contact pairs could modify the lattice registry at interfaces by nucleating local slips, favoring commeasure. The validity of structural superlubricity is thus concerned for large-scale systems where the energy cost of elastic distortion to break the lattice registry is low. In this work, we study the size dependence of superlubricity between single-crystal graphite flakes. Molecular dynamics simulations show that with nucleation and propagation of out-of-plane dislocations and strained solitons at Bernal interfaces, the friction force is reduced by one order of magnitude. Elastic distortion is much weaker for non-Bernal or incommensurate ones, remaining notable only at the ends of contact. Lattice self-organization at small twist angles perturbs the state of structural superlubricity through a reconstructed potential energy surface. Theoretical models are developed to illustrate and predict the interfacial elastoplastic behaviors at length scales beyond those in the simulations. These results validate the rigid assumption for graphitic superlubricity systems at microscale, and reveal the intrinsic channels of mechanical energy dissipation. The understandings lay the ground for the design of structural superlubricity applications.

Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of positive nonlinearity

We study the landscape of solutions of the coherent quantum states in a ring-shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical solutions in the absence of lattice are used as a starting point, and the transformation of those solutions is mapped as the lattice is introduced and strengthened. This approach allows a simple classification of all the solutions into states with periods commensurate or incommensurate with the lattice period and those with or without nodes. Their origins are traced to the primary dispersion curve and the swallowtail branches of the lattice-free spectrum. The commensurate states tend to remain delocalized with increasing lattice depth, whereas the incommensurate ones may be localized. The symmetry and stability properties of the solutions are examined and correlated with branch energies. The crucial importance of rotation is highlighted by its utility in continuously transforming solutions and accessing in a finite ring with a few sites the full spectrum of nonlinear Bloch waves on an infinite lattice.

Incommensurate grain boundary in silicon and the silver-ratio sequence

A scheme is proposed to solve the structure of incommensurate interfaces, starting from high-resolution images of electron microscopy, supplemented by adapted simulation techniques and complemented by theoretical tools. Direct silicon bonding is a way to produce artificial interfaces, in particular incommensurate ones. We focus on a technology-driven tilt grain boundary in silicon. While the Fibonacci sequence, linked to the golden ratio, is a prototype of the quasicrystalline structures, a silver-ratio sequence allows us to analyze this incommensurate interface. The four-fold coordination of the Si atoms is kept at the interface.

Structural and dielectric characteristics of Ba3Ln3Ti5Nb5O30 (Ln = La, Nd, Sm) filled tungsten bronze ceramics

In the present work, the structural, dielectric and relaxor ferroelectric properties were investigated for Ba3Ln3Ti5Nb5O30 (Ln = La, Nd, Sm) ceramics. The filled tungsten bronze phase with space group P4/mbm was confirmed for all compositions, while a small amount of secondary phase was detected in Ba3Nd3Ti5Nb5O30 and Ba3Sm3Ti5Nb5O30. The typical relaxor ferroelectric behaviors were observed: a broad peak of dielectric constant shifting to higher temperatures and decreasing its magnitude with increasing frequency and the frequency dispersion obeying the Vogel-Fulcher relationship. The P-E (polarization-electric field) hysteresis loops were obtained for Ba3Ln3Ti5Nb5O30 (Ln = La, Nd, Sm) ceramics at low temperatures. The nanoscale ferroelectric 180° domains with strip-like shape were observed in the paraelectric matrix at room temperature, where the commensurate structural modulations were determined in the domains and incommensurate ones were determined in the matrix. The significant differences were determined between the present ceramics and Ba4Ln2Ti4Nb6O30 and Ba5LnTi3Nb7O30 because of the different distribution patterns of A1 and A2 cations.

Simple theory of low-temperature thermal conductivity in single- and double-walled carbon nanotubes

Low-temperature phonon thermal conductance (PTC) of any 1D system increases proportionally to the temperature. However, here we show that in single- and double-walled carbon nanotubes (CNTs), starting from 3--6 K, the PTC increases faster than the linear function, since the low-frequency modes of dispersion curves, which do not tend to zero together with the wave vector, are excited. To develop the PTC theory, we combine the Landauer's ballistic approach with the simple continuous model proposed for the calculation of the low-frequency phonon spectra of both free nanotubes and those interacting with an environment. The approach obtained is valid not only for commensurate double-walled CNTs, but also for incommensurate ones. The temperature-dependent relation between the PTC of double-walled CNT and those of its constituent SWNTs is obtained and discussed. The low-temperature heat transfer in bulk materials originated from CNTs is also considered and the upper limit of thermal conductivity of such materials is determined. We argue that the ideal material consisting of CNTs can challenge diamond only when the mean length of its defect-free nanotubes reaches at least one hundred of micrometers.

A collection of magnetic structures with cif-like files as a database seed

We report the release within the Bilbao Crystallographic server [1] of a webpage providing detailed quantitative information on a representative set of published magnetic structures. Under the name of MAGNDATA (www.cryst.ehu.es/magndata) more than 140 entries are available. Each magnetic structure has been saved making use of magnetic symmetry, i.e. Shubnikov magnetic groups for commensurate structures, and magnetic superspace groups for incommensurate ones. This ensures a unified communication method and a robust and unambiguous description of both atomic positions and magnetic moments. The origin and main crystallographic axes of the parent phase are usually kept, with the cost of often using a non-standard setting for the magnetic symmetry. The magnetic point group is also given, so that the allowed macroscopic tensor properties can be derived. The fact that magnetic structures are being described according to various methods, often with ambiguous information, has forced an elaborate interpretation and transformation of the original data. For this purpose the freely available internet tools MAXMAGN [1] and ISODISTORT [2] have been our essential tools. Most of the analyzed structures happen to possess maximal magnetic symmetries within the constraints imposed by the magnetic propagation vector, and the relevant model could be derived in a straightforward manner using MAXMAGN [1]. In a few cases a lower symmetry is realized, but then it corresponded to one isotropy subgroup of one or several irreducible representations (irreps) of the paramagnetic grey space group, and ISODISTORT [2] could be applied to model the structure. Although the structure description is done using magnetic groups, the active irrep(s) are also given in most cases. The entries of the collection can be retrieved in a cif-like format, which is supported by internet tools as STRCONVERT [1] and ISOCIF [2], the visualization program VESTA [3], and some refinement programs (JANA2006, FULLPROF). Each entry also includes Vesta files that allow the visualization of a single magnetic unit cell.

Molecular dynamics characterization of the contact between clean metallic surfaces with nanoscale asperities

We use molecular dynamics (MD) simulations to characterize the tensile strength of contacts formed between various clean platinum surfaces with nanoscale asperities. Both commensurate contacts between (001) and (111) surfaces and incommensurate (001) ones are considered over a wide range of asperity sizes. In cyclic closing and opening, fresh asperities that form contacts for the first time show significant plastic deformation; this leads to a reduction in the effective contact area during the first few cycles, after which steady state is achieved both in terms of contact size and the pull-out force necessary to open the contacts. As is the case for commensurate surfaces [H. Kim and A. Strachan, Phys. Rev. Lett. 104, 215504 (2010)], the strength of the metallic bridges that form in incommensurate contacts exhibit strong size effects; their strength increases with decreasing size until a length of \ensuremath{\sim}5 nm, below which weakening is observed. Commensurate contacts lead to stronger bridges than incommensurate ones but only during the initial closing events; after steady state is achieved, commensurate and incommensurate (001) surfaces lead to bridges of similar strengths.

Centripetal Thinking in Curriculum Studies

After years of generating divergent approaches to scholarship, cast mostly as reactions against a historical orthodoxy, the curriculum studies community is now looking at a new dialectic—one marked by a physics that pull ideas inward toward some centripetal center. The tension between looking for unifying ideas as they articulate with a multiplicity of incommensurate ones has, in fact, marked the nature of most scholarly thinking. Isaiah Berlin personified such a tension in his use of the Greek aphorism, “The fox knows many things, but the hedgehog knows one big thing.” In recent years, the curriculum field has been dominated by foxes, who have resisted any attempt to even consider the role of hedgehog. But several projects have recently been launched in the field that might signal a new age for curriculum studies, as a new dialogue has been opened that considers possibilities of finding some semblance of canon or disciplinarity in the field. The search for canon or disciplinarity is less likely to yield a hard‐and‐fast verifiable outcome as much as an inconclusive discussion. But, as Plato reminds us, such a discussion is precisely the point because the knowing of canon is doing the knowing of canon.

Spin correlations in electron-doped high- [formula omitted] superconductor

Spin correlations in the electron-doped Pr 1 - x LaCe x CuO 4 have been investigated by neutron-scattering and muon rotation/relaxation measurements. The low-enegy spin correlations were found to be in commensurate with the wide superconducting phase, unlike the incommensurate ones in the hole-doped La 2 - x Sr x CuO 4 . No enhancement of the magnetic order by impurity-doping and applying magnetic fields was observed, although the superconductivity is effectively suppressed, compared to that in the hole-doped system. Distinct impurity and magnetic field effects between the static spin correlation in the electron-doped system and those in the hole-doped systems suggest the different magnetic ground state in the two systems.

Molecular dynamics study of radial pressure transmission in multiwalled carbon nanotubes

The pressure response of multiwalled carbon nanotubes (MWCNTs) to the radial hydrostatic pressure is studied by using constant pressure molecular dynamics simulations for finite systems. The inner tube is effectively protected by the outer tube against the external pressure. The pressure transmission efficiency of MWCNTs depends upon both the size and morphology combination of the tubes. The larger the tube is, the higher the pressure transmission efficiency will be. The pressure transmission in commensurate MWCNTs is more efficient than that in incommensurate ones. Based on the present simulations, an experimental method is suggested for measuring the pressure transmission efficiency of MWCNTs.

Integrable correlated electron model with next-nearest-neighbour interactions

The exactly solvable model of supersymmetric t - J chains (STJC) of correlated electrons with next-nearest-neighbour (NNN) interactions is proposed and studied. The model with interactions between nearest neighbours and NNN interactions in one chain can also be considered as a two-chain model with zigzag-like coupling between the chains. The NNN interaction (coupling between chains) causes the onset of additional Dirac seas for low-lying charge and/or spin excitations. These Dirac seas change the low-energy (conformal) behavior of the model. The filling of those seas depends on the values of the NNN coupling (interactions between chains), external magnetic field and applied voltage. We identify the new ground state phases which appear due to the NNN as incommensurate ones. The NNN coupling in the incommensurate phases induces spontaneous magnetization and/or spontaneous filling of the Dirac sea for charge excitations (“spontaneous charge ordering”). The onset of this order implies a first order quantum phase transition driven by the field with hysteresis phenomena.

Phase correlation of cortical rhythms at different frequencies: higher-order spectral analysis of multiple-microelectrode recordings from cat and monkey visual cortex

In classical EEG analysis rhythms with different frequencies occuring at separable regions and states of the brain are analysed. Rhythms in different frequency bands have often been assumed to be independent and their occurrence was interpreted as a sign of different functional operations. Independence has scarcely proved because of conceptual and computational difficulties. It is, on the other hand, probable that different rhythmic brain processes are coupled because of the broad recurrent connectivity among brain structures. We therefore set out to find interactions among rhythmic signals at different frequencies. We were particularly interested in interactions between lower frequency bands and γ-activities (30–90 Hz), because the latter have been analysed in our laboratory in great detail and had properties suggesting their involvement in perceptual feature linking. Fast oscillations occurred synchronized in a stimulus-specific way in the visual cortex of cat and monkey. Their presence was often accompanied by lower frequency components at considerable power. Such multiple spectral peaks are known from many cortical and subcortical structures. Despite their well known occurrence, coupling among different frequencies has not been established, apart from harmonic components. For the present investigation we extended existing analytical tools to detect non-linear correlations among signal pairs at any frequency (including incommensurate ones). These methods were applied to multiple microelectrode recordings from visual cortical areas 17 and 18 of anesthetized cats and V1 of awake monkeys. In particular, we assessed non-linear correlations by means of higher order spectral analysis of multi-unit spike activities (MUA) and local slow wave field potentials (LFP, 1–120 Hz) recorded with microelectrodes. Non-linear correlations among signal components at different frequencies were investigated in the following steps. First, the frequency content of short (≈250 ms) sliding window signal epochs was analyzed for simultaneously occurring rhythms of significant power at different frequencies. This was done by a newly developed method derived from the trispectrum using separate averaging of the products of short-epoch power spectra for any possible combination of frequency pairs. Second, non-linear (quadratic) phase coupling between different frequencies was assessed by the methods of bispectrum and bicoherence. We found phase correlations at different frequencies in the visual cortex of the cat and monkey. These couplings were significant in about 60% of the investigated MUA and LFP recordings, including several cases of coupling among incommensurate (i.e. non-harmonic) frequencies. Significant phase correlations were present: (1) within the γ-frequency range; (2) between γ- and low frequency ranges (1–30 Hz, including α- and β-rhythms); and (3) within the low frequency range. Phase correlations depended, in most cases, on specific visual stimulation. We discuss the possible functional significance of phase correlations among high and low frequencies by including proposals from previous work about potential roles of single-frequency rhythms of the EEG. Our suggestions include: (1) visual feature linking across different temporal and spatial scales provided by coherent oscillations at high and low frequencies; (2) linking of visual cortical representations (high frequencies) to subcortical centers (low frequencies) like the thalamus and hippocampus; and (3) temporal segmentation of the sustained stream of incoming visual information into separate frames at different temporal resolutions in order to prevent perceptual smearing due to shifting retinal images. These proposals are, at present, merely speculative. However, they can, in principle, be proved by microelectrode recordings from trained behaving animals. © 1997 Elsevier Science B.V.

Structure and dynamics of rare-gas layers on pt(111)

The structural behavior of rare-gas monolayers on the (111)-surfaces of Ag and of Pt is radically different. On Ag the adlayers show a uniform behavior, they are all “floating” incommensurate. This corresponds to a laterally perfectly flat holding potential; the substrate structure is evidenced only in the alignment of the hexagonal adlayers with the substrate. In contrast, on Pt the adlayers exhibit a great variety of phases and phase transitions. In particular for Xe-adlayers, the phases range from “locked” commensurate and high order commensurate to various “floating” incommensurate ones. Temperature and coverage changes induce first and second order as well as symmetry breaking and conserving transitions between these phases. This fascinating plurality of phases and phase transitions is due to a delicate balance between the adatomadatom interaction and the corrugation of the Pt holding potential. This corrugation is thus, in the case of Pt, by no means negligible; its average value - as deduced from direct measurements - is larger than 30 meV, i.e. 10 % of the holding potential. The lattice dynamics of these rare-gas layers on Pt(111) accessible via the perpendicular modes as observed so far in He inelastic scattering appears to be much less sensitive to the corrugation of the holding potential. All the features predicted by assuming a completely uncorrugated holding potential, i.e. almost dispersionless monolayer mode, leakage into the bulk around \\ ̄ gG and hybridization with the substrate Rayleigh wave have been confirmed in detail by high resolution He Spectroscopy of Ar, Kr and Xe adlayers on Pt(111). No frequency difference between the Einstein oscilations of the commensurate and incommensurate Xe-layers could be detected so far showing that, in spite of the corrugation, the perpendicular curvature of the holding potential does not vary significantly along the surface. Substantial differences are expected for the in-plane adlayer modes.

Microscopic model for incommensurate crystal phases

As a model for a crystal with an incommensurate phase we studied a linear chain of classical particles interacting by harmonic forces between up to third neighbors and anharmonic nearest-neighbor forces. Such a system has an infinite number of stable equilibrium configurations, among which there are incommensurate ones. The system has translational invariance and consequently acoustic phonons. Other excitations may be identified as phasons and amplitudons. In a mean-field approximation the model exhibits a soft mode, a transition to an (in general) incommensurate phase, which develops via discommensurations to a superstructure at a lock-in transition.