Length-scale Fluctuations Research Articles

Garnet zoning patterns record multiple processes of chemical transfer during subduction

Subduction is the principal mechanism by which volatiles are transferred from the Earth's surface to its interior. In garnets from eclogites and blueschists formed within the subduction setting, fine-scale, oscillatory elemental zoning is a common feature, sometimes considered to record open-system fluid exchange during prograde metamorphism. We present oxygen isotope data for garnets with such zoning from five exhumed subduction zone complexes. Short length scale fluctuations in elemental and oxygen isotope zoning (which are themselves spatially decoupled) cannot be linked to open-system fluid exchange during garnet crystallization in all samples; these data do not provide evidence for a genetic relationship between elemental oscillations and fluid fluxing. However, garnets from one setting do provide clear evidence for syn-growth ingress of elementally and isotopically buffering fluids, a process that operated simultaneously with the formation of elemental oscillations. Our findings indicate multiple mechanisms of chemical transfer operate at the grain–rock scale during subduction, and that some subduction zone rocks may experience only limited interaction with external prograde fluids. These results are consistent with a picture of highly heterogenous volatile transfer during subduction, and suggest that some proportion of the fluid inventory inherited at shallow depths may be transferred to sub-arc depths.

Renormalized one-loop theory of correlations in disperse polymer blends.

Polymer blends are critical in many commercial products and industrial processes and their phase behavior is therefore of paramount importance. In most circumstances, such blends are formulated with samples of high dispersity, which have generally only been studied at the mean-field level. Here, we extend the renormalized one-loop theory of concentration fluctuations to account for blends of disperse polymers. Analyzing the short and long length-scale fluctuations in a consistent manner, various measures of polymer molecular weight and dispersity arise naturally in the free energy. Thermodynamic analysis in terms of moments of the molecular weight distribution(s) provides exact results for the inverse susceptibility and demonstrates that the theory is not formally renormalizable. However, physically motivated approximations allow for an "effective" renormalization, yielding (1) an effective interaction parameter, χe, which depends directly on the sample dispersities (i.e., Mw/Mn) and leaves the form of the mean-field spinodal unchanged, and (2) an apparent interaction parameter χa that depends on higher-order dispersity indices, for instance Mz/Mw, and characterizes the true limits of blend stability accounting for long-range off-critical fluctuations. We demonstrate the importance of dispersity on several example systems, including both "toy" models that may be realized in computer simulation and more realistic industrially relevant blends. We find that the effects of long-range fluctuations are particularly prominent in blends where the component dispersities are mismatched, especially when there is a small quantity of the high-dispersity species. This can be understood as a consequence of the shift in the critical concentration(s) from the monodisperse value(s).

Germanium-based nearly hyperuniform nanoarchitectures by ion beam impact

We address the fabrication of nano-architectures by impacting thin layers of amorphous Ge deposited on SiO2 with a Ga+ ion beam and investigate the structural and optical properties of the resulting patterns. By adjusting beam current and scanning parameters, different classes of nano-architectures can be formed, from elongated and periodic structures to disordered ones with a footprint of a few tens of nm. The latter disordered case features a significant suppression of large length scale fluctuations that are conventionally observed in ordered systems and exhibits a nearly hyperuniform character, as shown by the analysis of the spectral density at small wave vectors. It deviates from conventional random fields as accounted for by the analysis of Minkowski functionals. A proof of concept for potential applications is given by showing peculiar reflection properties of the resulting nano-structured films that exhibit colorization and enhanced light absorption with respect to the flat Ge layer counterpart (up to one order of magnitude at some wavelength). This fabrication method for disordered hyperuniform structures does not depend on the beam size. Being ion beam technology widely adopted in semiconductor foundries over 200 mm wafers, our work provides a viable pathway for obtaining disordered, nearly-hyperuniform materials by self-assembly with a footprint of tens of nanometers for electronic and photonic devices, energy storage and sensing.

Vibrational spectral dynamics and ion-probe interactions of the hydrogen-bonded liquids in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

We investigate ion-probe interactions within the molecular liquid, examine dynamics, and interpret the vibrational spectral dynamics of the mixtures of ionic liquid, 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [EMIm][NTf2] with the probes of varying alkyl chain length – HOD, methanol-d4, ethanol-d6. Structural analysis depicts pronounced interactions of the oxygen atom of HOD with the corresponding anionic oxygen site rather than the hydrogen atom located at the two-position of the imidazolium ring. Our computed frequency distribution for each of the probes in IL exhibits similarity with the experimental linear FT-IR spectrum. We further performed the orientational anisotropy calculations; the ion reorientation plays a significant role in determining the transport properties in ILs. The results of rotational anisotropy of the O-D bond vector reflect the hydrogen bond length-scale fluctuations and collective reorientation associated with the complete structural reorganization of the probe modes. Our findings in this study agree well with the earlier experimental and simulation studies.

Short length scale fluctuations in lattice growth models

Fluctuations of interfaces produced by lattice growth models scale as those of stochastic equations at distances r much larger than the lattice constant a. However, those equations may be derived from the short range interactions through renormalization, which suggests that universal properties may also be observed in short scale fluctuations of the lattice models. We first investigate this question in interfaces with preset exact power law structure factors by expanding the autocovariance function, which is shown to scale as r2α+constant at distances as small as r∼5a (α is the roughness exponent). Next we perform numerical simulations of lattice models in five universality classes, in one and two dimensions, and calculate the autocovariance function and the fluctuation of a local average height in their growth regimes, where finite-size effects are negligible. In cases of normal roughening with α>0, those quantities also scale as affine functions of r2α in distances from a to ∼10a, in contrast with the usual expectation that such relation is applicable only in the hydrodynamic limit. In a model with super-roughening in the Mullins–Herring class, similar relation is applicable with the local roughness exponent in one and two dimensions. In cases with α≤0, the fits of those functions diverge in the zero distance limit, in the same form as the one-point fluctuations of the corresponding stochastic equations. Finally, we study competitive models with crossovers in the roughness evolution and show that, at any given time, short and long range fluctuations scale with the exponent α of the dominant universality class at that time. Thus, short range correlations at long times do not keep a memory on the short time kinetics. These results reinforce the connection between discrete and continuous growth models by showing that their short range fluctuations have related properties.

Anomalous stress fluctuations in athermal two-dimensional amorphous solids.

We numerically study the local stress distribution within athermal, isotropically stressed, mechanically stable, packings of bidisperse frictionless disks above the jamming transition in two dimensions. Considering the Fourier transform of the local stress, we find evidence for algebraically increasing fluctuations in both isotropic and anisotropic components of the stress tensor at small wave numbers, contrary to recent theoretical predictions. Such increasing fluctuations imply a lack of self-averaging of the stress on large length scales. The crossover to these increasing fluctuations defines a length scale ℓ_{0}, however, it appears that ℓ_{0} does not vary much with packing fraction ϕ, nor does ℓ_{0} seem to be diverging as ϕ approaches the jamming ϕ_{J}. We also find similar large length scale fluctuations of stress in the inherent states of a quenched Lennard-Jones liquid, leading us to speculate that such fluctuations may be a general property of amorphous solids in two dimensions.

Order-by-disorder near criticality inXYpyrochlore magnets

We consider a system of spins on the sites of a three-dimensional pyrochlore lattice of corner-sharing tetrahedra interacting with a predominant effective $xy$ exchange. In particular, we investigate the selection of a long-range ordered state with broken discrete symmetry induced by thermal fluctuations near the critical region. At the standard mean-field theory (s-MFT) level, in a region of the parameter space of this Hamiltonian that we refer to as $\Gamma_5$ region, the ordered state possesses an accidental $U(1)$ degeneracy. In this paper, we show that fluctuations beyond s-MFT lift this degeneracy by selecting one of two states (so-called $\psi_2$ and $\psi_3$) from the degenerate manifold, thus exposing a certain form of order-by-disorder (ObD). We analytically explore this selection at the microscopic level and close to criticality by elaborating upon and using an extension of the so-called TAP method, originally developed by Thouless, Anderson and Palmer to study the effect of fluctuations in spin glasses. We also use a single-tetrahedron cluster-mean-field theory (c-MFT) to explore over what minimal length scale fluctuations can lift the degeneracy. We find the phase diagrams obtained by these two methods to be somewhat different since c-MFT only includes the shortest-range fluctuations. General symmetry arguments used to construct a Ginzburg-Landau theory to lowest order in the order parameters predict that a weak magnetic moment, $m_z$, along the local $\langle 111 \rangle$ (${\hat z}$) direction is generically induced for a system ordering into a $\psi_2$ state, but not so for $\psi_3$ ordering. Both E-TAP and c-MFT calculations confirm this weak fluctuation-induced $m_z$ moment. Using a Ginzburg-Landau theory, we discuss the phenomenology of multiple phase transitions below the paramagnetic phase transition and within the $\Gamma_5$ long-range ordered phase.

The convection of large and intermediate scale fluctuations in a turbulent mixing layer

The convection velocity of large and intermediate scale velocity fluctuations in a nominally two-dimensional planar mixing layer, and its dependence upon the length scale, is explored by carrying out particle image velocimetry (PIV) experiments. A “global” convection velocity, containing the convection of all the length scales present in the flow, is produced by examining the autocorrelation functions between velocity fluctuations in successive PIV records across the mixing layer. This “global” convection velocity is found to be similar to the mean flow, although fluctuations on the low speed side of the mixing layer on average convect at speeds greater than the mean and fluctuations on the high speed side of the mixing layer are observed to convect at speeds less than the mean. Scale specific convection velocity profiles are then produced by examining the phase difference between the spectral content specific to one wavenumber in streamwise velocity fluctuation traces in successive PIV records, offset by time τ. Probability density functions (pdfs) are produced of this phase difference, which is subsequently converted into a convection displacement, and these show that the convection of single length scale fluctuations exhibits a significant variance, particularly so for larger scale fluctuations and in the high speed side of the mixing layer. Convection velocity profiles are produced from these pdfs using both the mean convection distance and the modal convection distance. It is observed that the convection velocity is relatively insensitive to the length scale of the fluctuations considered, particularly when the mean convection distance is used. A slight sensitivity to length scale is, however, observed for convection velocities based on the modal convection distance. This dependence is primarily observed in the high speed side of the mixing layer, in which smaller length-scale fluctuations convect more quickly than larger length-scale fluctuations. It is also observed that the magnitude of the fluctuation itself affects the convection velocity with larger magnitude fluctuations convecting less rapidly than lower magnitude ones at the largest length scales investigated with this behaviour being reversed at more intermediate length scales.

Hybrid lipids increase nanoscale fluctuation lifetimes in mixed membranes

A recently proposed ternary mixture model is used to predict fluctuation domain lifetimes in the one phase region. The membrane is made of saturated, unsaturated, and hybrid lipids that have one saturated and one unsaturated hydrocarbon chain. The hybrid lipid is a natural linactant which can reduce the packing incompatibility between saturated and unsaturated lipids. The fluctuation lifetimes are predicted as a function of the hybrid lipid fraction and the fluctuation domain size. These lifetimes can be increased by up to three orders of magnitude compared to the case of no hybrids. With hybrid, small length scale fluctuations have sizable amplitudes even close to the critical temperature and, hence, benefit from enhanced critical slowing down. The increase in lifetime is particularly important for nanometer scale fluctuation domains where the hybrid orientation and the other lipids composition are highly coupled.

Relaxation of surface steps after thermal quenches: A numerical study within the terrace-step-kink model

We study the out-of-equilibrium relaxation of surface steps after thermal quenches using numerical simulations of the terrace-step-kink model for a vicinal surface. We analyze both single and interacting steps in a situation where the temperature is suddenly changed at a given quench time. We focus on a physically relevant range of temperatures and show that the relaxation of the roughness is compatible with a power-law behavior with an effective relaxation exponent close to γ = 1/2 in all cases. This value is consistent with a one-dimensional Edwards-Wilkinson equation. In particular, this means that, although the case of interacting steps is effectively a two-dimensional system, its relaxation is dominated by short length-scale fluctuations, where steps are not interacting.

Universal sequence of ordered structures obtained from mesoscopic description of self-assembly

Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived by a systematic coarse-graining procedure. For particles interacting with spherically symmetric potentials of arbitrary form, the grand-thermodynamic potential consists of two terms. The first term is associated with microscopic length-scale fluctuations, and has the form of the standard density functional. The second term is associated with mesoscopic length-scale fluctuations, and has the form known from the statistical field theory. For the correlation function between density fluctuations in mesoscopic regions, a pair of equations similar to the Ornstein-Zernicke equation with a new closure is obtained. In the special case of weak ordering on the mesoscopic length scale, the theory takes a form similar to either the Landau-Ginzburg-Wilson (LGW) or the Landau-Brazovskii (LB) field theory, depending on the form of the interaction potential. Microscopic expressions for the phenomenological parameters that appear in the Landau-type theories are obtained. Within the framework of this theory, we obtain a universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close-packing density. The sequence of phases agrees with experimental observations and with simulations of many self-assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short-range attraction long-range repulsion potential, we find the bicontinuous gyroid phase ( Ia3d symmetry) that may be related to a network-forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.

X-ray scattering study of two length scales in the critical fluctuations ofCuGeO3

The critical fluctuations of ${\mathrm{CuGeO}}_{3}$ have been measured by synchrotron x-ray scattering, and two length scales are clearly observed. The ratio between the two length scales is found to be significantly different along the a axis, with the a axis along the surface normal direction. We believe that such a directional preference is a clear sign that random surface strains, especially those caused by dislocations, are the origin of the long length scale fluctuations.

Shear induced fluctuations and fluctuation-length transition in the quasiflexible polymer in a solution of a hydrogen-bond enhancing solvent

Dynamics of cellulose diacetate (a typical polysaccharide) in N,N-dimethylacetamide (a hydrogen-bond enhancing solvent) at 27 °C was investigated in a shear field of velocity gradient γ=0–5.3 s−1 through dynamic light scattering under circular Couette flow. The polymer mass concentration was set around the crossover of dilute and semidilute regimes. Growth of extra-large length-scale fluctuations and their transitions with shear were detected, which were originated by the long-ranged interaction, or the hydrogen bond, operating on the OH and CO groups in the glucose residues of cellulose acetates via high electronegative solvent. Two modes of fluctuations with fast and slow decay rates Γf and Γs were induced and each Γ value changed stepwise and linearly with γ, respectively. The decay rate distribution, which was estimated from the electric-field time correlation function expressed in the KWW-type of stretched exponential decay form g(1)(t)=A exp[−(t/τ)β] with β the index of decay rate distributions, was changed from 1/2 (one-sided stable distribution) to 3/2 (Holtzmark distribution) around γ=0.8–1 s−1 for the fast mode, while β=2 (Gaussian, or the sharpest distribution) over the full range of 0.40<γ<5.3 s−1 for the slow mode. The usual Cauchy distribution (β=1) at γ=0 (the quiescent state) was destroyed above a threshold γ*=0.033 s−1. At γ*<γ<0.2 s−1, fluctuations of various length-scale modes (0<β<1/2) were created but finally converged to two modes of fixed β(=1/2, 3/2, 2) at γ>0.4 s−1. In addition, oscillatory feature was conspicuous in g(1)(t) at every γ of 0.40<γ<5.3 s−1 and periodic fluctuations became remarkable in the scattered intensity IVv at γ>3.7 s−1, which may come from the competition between shear flow distortion and the Brownian diffusion of polymer chain in solution and can be grasped qualitatively by the initial stage of spinodal decomposition under the control of long-ranged attractive interactions.

Effect of Side Chain Rigidity on the Elasticity of Comb Copolymer Cylindrical Brushes: A Monte Carlo Simulation Study

We report the results of a Monte Carlo simulation study of isolated comb copolymer cylindrical brushes. The conformational characteristics of molecules consisting of a flexible backbone densely grafted with side chains strongly depend on the rigidity of the side chains, which is exemplified by using both fully flexible and totally rigid side chains. The short length scale fluctuations of the backbone are not affected by the presence of rigid rod side chains, whereas flexible side chains induce local stretching of the backbone. However, at the large length scale, the persistence length λ of the cylindrical brush is considerably larger for rigid rod side chains than for flexible side chains. Moreover, for rigid side chains the ratio between the persistence length λ and the diameter D of the brush increases approximately linearly as a function of the rod length L, thus supporting the possibility of lyotropic behavior. In contrast to this, in the case of flexible side chains, λ/D is approximately independent of the side chain length M.

Scanning single-electron transistor microscopy: Imaging individual charges

We describe the single-electron transistor scanning electrometer (SETSE), a novel scanned probe microscope capable of mapping static electric fields and charges with submicron (100 nm) spatial resolution and fractional electron charge sensitivity (0.01 e). The active sensing element of the SETSE is a single-electron transistor fabricated at the end of a sharp glass tip. Images of the surface electric fields of a GaAs/AlGaAs heterostructure sample taken before and after brief exposures to light show individual photoionized charge sites as well as 100 nm length scale fluctuations in the dopant and surface charge distribution. We also describe SETSE images and measurements of depleted regions, local capacitance, band bending, and work functions at submicron length scales on the surface of this model semiconductor device.

Large length-scale fluctuations at the spin-Peierls transition in CuGeO3.

We report a detailed synchrotron x-ray-scattering study of the structural fluctuations near the spin-Peierls transition in CuGe${\mathrm{O}}_{3}$. Below the transition temperature ${T}_{\mathrm{SP}}$, the superlattice peak profile is resolution limited and the peak intensity, which is proportional to the order parameter squared, is well described by a simple power law, ${(1\ensuremath{-}\frac{T}{{T}_{\mathrm{SP}}})}^{2\ensuremath{\beta}}$. The fitted value of $\ensuremath{\beta}$, 0.33(3), agrees quantitatively with previously reported results from neutron-diffraction measurements. Above the transition temperature ${T}_{\mathrm{SP}}$, pretransitional lattice fluctuations are observed within about 1 K above ${T}_{\mathrm{SP}}$. The length scale of these fluctuations is about an order of magnitude larger than that characterizing the bulk critical fluctuations. The line shape of these large length-scale fluctuations is consistent with a Lorentzian-squared form. The measured critical exponents associated with the large length-scale fluctuations are $\ensuremath{\nu}=0.56(9)$, and $\overline{\ensuremath{\gamma}}=2.0(3)$. Similar large length-scale fluctuations have been observed at the structural transitions in some perovskites and the magnetic transitions in holmium and terbium. We suggest that in CuGe${\mathrm{O}}_{3}$ the large length-scale fluctuations reflect the disconnected susceptibility originating from random field Ising-type local defects.

X-ray- and neutron-scattering measurements of two length scales in the magnetic critical fluctuations of holmium.

The short-ranged correlations associated with magnetic ordering in the rare-earth antiferromagnet holmium have been characterized in high-resolution x-ray- and neutron-scattering studies. For temperatures within about 2 K above ${\mathit{T}}_{\mathit{N}}$, the short-ranged magnetic fluctuations exhibit two length scales, instead of the single one expected in an ideal system. Well above ${\mathit{T}}_{\mathit{N}}$, the shorter of the two length scales exhibits power-law behavior consistent with normal critical fluctuations; the line shape in momentum space is well described by a Lorentzian, and the measured critical exponents are \ensuremath{\nu}=0.54\ifmmode\pm\else\textpm\fi{}0.04 and \ensuremath{\gamma}=1.24\ifmmode\pm\else\textpm\fi{}0.15. The longer of the two length scales is well described by a squared-Lorentzian line shape, and exhibits a power-law temperature dependence. Both the shorter and the longer length-scale fluctuations are approximately spatially isotropic. We propose that the longer length-scale fluctuations are related to random strain fields which are localized at or near the sample surfae. These results are reminiscent of behavior observed at the cubic-to-tetragonal structural phase transitions of some perovskite materials.

Generic features of late-stage crystal growth.

A cell dynamical system model, which realistically incorporates diffusion, is developed to study various aspects of late-stage crystal growth. The algorithm is computationally efficient, allowing the development of complex spatial structures to be studied, and is motivated by renormalization group considerations. We establish the existence of an asymptotic dense branching morphology and relate it to diffusion-limited aggregation. Our findings indicate that the radius of a dense-branching structure grows linearly with time, despite being diffusion controlled, in agreement with experimental observations of the growth of spherulites. A clear morphological transition from kinetic-effect-dominated growth to surface-tension-dominated growth is observed, marked by a difference in the way growth velocity scales with undercooling. We also study the evolution of interfacial instability and find scaling behavior for the interface power spectra, indicating the nonlinear selection of a unique length scale, insensitive to short length-scale fluctuations.

Detection of tides on the patagonian shelf by the seasat satellite radar altimeter: An initial comparison

The detection of tides on the Patagonian shelf off Argentina by the SEASAT satellite radar altimeter is reported. The satellite data was obtained during two passes of the satellite over the shelf on August 1 and August 4, 1978, and compared with empirical estimates of the tidal elevation along the satellite ground tracks based on coastal tide gage data, an estimate of tidal variation over the shelf, and the tidal prediction equations of Shureman (1958). Good agreement was observed between the satellite data of sea surface height with respect to a standard ellipsoid and the empirical estimate for the near-shore pass, with agreement degraded slightly for the pass further off shore. It is concluded that the generally good agreement found demonstrates the applicability of satellite radar altimeter data to the determination of tides and that small length scale fluctuations in the geoid are minor along the two ground tracks.