Self-Organization in a Granular Medium by Internal Avalanches

Internal avalanches of grain displacements can be created inside a granular material kept in a bin in two ways: (i) by removing a randomly selected grain at the bottom of the bin; and (ii) by breaking a stable arch of grains clogging a hole at the bottom of the bin. Repeated generation of such avalanches leads the system to a steady state. It is relevant to ask whether this state is a critical state, as in self-organized criticality (SOC). We review here some recent studies of this problem using cellular automata and hard-disc models.     

Collective effects in grain boundary migration

In situ high-resolution transmission electron microscopy is used to study grain boundary structure and kinetics in bicrystalline Au films at elevated temperature. We report the first direct evidence for the existence of cooperative atomic motion in grain boundary migration. Certain nanoregions at grain boundaries, typically involving up to several hundred atoms, are found to switch back and forth between neighboring grains. Reversible structural fluctuations at temperatures near 0.5T(m) and above have been discovered in [110] and [001] tilt, as well as in general grain boundaries.     

Correlations and aggregate statistics in granular packs

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Vorono? cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.     

Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission     

Fluctuations in granular media

Dense slowly evolving or static granular materials exhibit strong force fluctuations even though the spatial disorder of the grains is relatively weak. Typically, forces are carried preferentially along a network of "force chains." These consist of linearly aligned grains with larger-than-average force. A growing body of work has explored the nature of these fluctuations. We first briefly review recent work concerning stress fluctuations. We then focus on a series of experiments in both two- and three-dimension [(2D) and (3D)] to characterize force fluctuations in slowly sheared systems. Both sets of experiments show strong temporal fluctuations in the local stress/force; the length scales of these fluctuations extend up to 10(2) grains. In 2D, we use photoelastic disks that permit visualization of the internal force structure. From this we can make comparisons to recent models and calculations that predict the distributions of forces. Typically, these models indicate that the distributions should fall off exponentially at large force. We find in the experiments that the force distributions change systematically as we change the mean packing fraction, gamma. For gamma's typical of dense packings of nondeformable grains, we see distributions that are consistent with an exponential decrease at large forces. For both lower and higher gamma, the observed force distributions appear to differ from this prediction, with a more Gaussian distribution at larger gamma and perhaps a power law at lower gamma. For high gamma, the distributions differ from this prediction because the grains begin to deform, allowing more grains to carry the applied force, and causing the distributions to have a local maximum at nonzero force. It is less clear why the distributions differ from the models at lower gamma. An exploration in gamma has led to the discovery of an interesting continuous or "critical" transition (the strengthening/softening transition) in which the mean stress is the order parameter, and the mean packing fraction, gamma, must be adjusted to a value gamma(c) to reach the "critical point." We also follow the motion of individual disks and obtain detailed statistical information on the kinematics, including velocities and particle rotations or spin. Distributions for the azimuthal velocity, V(theta), and spin, S, of the particles are nearly rate invariant, which is consistent with conventional wisdom. Near gamma(c), the grain motion becomes intermittent causing the mean velocity of grains to slow down. Also, the length of stress chains grows as gamma-->gamma(c). The 3D experiments show statistical rate invariance for the stress in the sense that when the power spectra and spectral frequencies of the stress time series are appropriately scaled by the shear rate, Omega, all spectra collapse onto a single curve for given particle and sample sizes. The frequency dependence of the spectra can be characterized by two different power laws, P proportional, variant omega(-alpha), in the high and low frequency regimes: alpha approximately 2 at high omega; alpha<2 at low omega. The force distributions computed from the 3D stress time series are at least qualitatively consistent with exponential fall-off at large stresses. (c) 1999 American Institute of Physics.     

Re-exchange of Fe and Cu at the interface in sintered Nd–Fe–B magnets: A method to eliminate Fe precipitation at grain boundaries

According to the decoupling hypothesis for magnetic grains, the coercivity in sintered Nd–Fe–B magnets is increased after Cu doping, which is due to the formation of non-magnetic grain boundaries. However, this method partially fails, and ferromagnetic Fe-segregation occurs at the grain boundary. We discovered both experimentally and through calculation that the Fe content at the grain boundaries can be tuned across a wide range by introducing another element of Ag. Segregated Fe at high temperature at the grain boundary re-dissolves into Nd₂Fe₁₄B grains during annealing at low temperature. Both configurable and magnetic entropies contribute a large driving force for the formation of nonmagnetic grain boundaries. Almost zero Fe content could be achieved at the grain boundaries of sintered Nd–Fe–B magnet.     

Influence of charging current fluctuations on the grain velocity distribution in weakly-ionized plasmas

The distribution function of dust particles immersed in a weakly-ionized plasma is calculated with regard to electron and ion absorption by grains and fluctuations of grain-charging currents. The dust-particle energy is shown to undergo abrupt changes due to specific velocity dependence of the grain friction coefficient and stochastic character of grain charging. Their effect can crucially influence the state of the grain. This model can give some indication concerning the possibility of structure formation and melting of a dusty crystal structure. The hysteresis in the transition from the one-peak distribution function to twin-peak distribution function can be observed with changing of plasma parameters.     

Huge fluctuations in weight measurements at the bottom of a two-dimensional vertical sheet of grains

Weight measurements at the bottom of a quasi-2D vertical sheet of static cohesionless grains are carried out. The grains are held between two coaxial cylinders. This peculiar setup allows us to set either periodic or fixed lateral boundary conditions. Huge relative fluctuations in weight measurements appear in case of fixed lateral walls. This may be related to some indetermination in the mobilization state of friction forces on lateral walls. This argument would hold for any piling, but would lead to huge fluctuations in 2D systems only, because of averaging effects in 3D.     

Velocity correlations in dense granular flows observed with internal imaging

We show that the velocity correlations in uniform dense granular flows inside a silo are similar to the hydrodynamic response of an elastic hard-sphere liquid. The measurements are made using a fluorescent refractive-index-matched interstitial fluid in a regime where the flow is dominated by grains in enduring contact and fluctuations scale with the distance traveled, independent of flow rate. The velocity autocorrelation function of the grains in the bulk shows a negative correlation at short time and slow oscillatory decay to zero similar to simple liquids. Weak spatial velocity correlations are observed over several grain diameters. The mean square displacements show an inflection point indicative of caging dynamics. The observed correlations are qualitatively different at the boundaries.     

Measurement of the charging of individual dust grains in a plasma

An experiment is described for investigating the charging of dust grains in a plasma. The apparatus is a double plasma device into which single dust grains are dropped from the top. The dust charge is detected and measured by a sensitive electrometer attached to a Faraday cup on the bottom. Experiments with electrons from the emissive filaments but without plasma indicate that the grains charge to approximately the filament potential for filament bias voltages smaller in absolute value than -70 V. The charge is of order 10⁶ electrons for SiC grains 30-150 μm in diameter. At higher bias voltage the charge is reduced due to secondary emission. The charge on grains increases with grain size and is nearly independent of the filament emission current. With plasma in the device, the grains charge both positively and negatively     

Effect of radiative cooling on collapsing charged grains

The effect of the radiative cooling of electrons on the gravitational collapse of cold dust grains with fluctuating electric charge is investigated. We find that the radiative cooling as well as the charge fluctuations, both, enhance the growth rate of the Jeans instability. However, the Jeans length, which is zero for cold grains and nonradiative plasma, becomes finite in the presence of radiative cooling of electrons and is further enhanced due to charge fluctuations of grains resulting in an increased threshold of the spatial scale for the Jeans instability.     

Velocity correlations in dense granular flows

Velocity fluctuations of grains flowing down a rough inclined plane are experimentally studied. The grains at the free surface exhibit fluctuating motions, which are correlated over a few grain diameters. The characteristic correlation length is shown to depend on the inclination of the plane and not on the thickness of the flowing layer. This result strongly supports the idea that dense granular flows are controlled by a characteristic length larger than the particle diameter.     

A model of grain refinement and strengthening of Al alloys due to cold severe plastic deformation

This paper presents a model which quantitatively predicts grain refinement and strength/hardness of Al alloys after very high levels of cold deformation through processes including cold rolling, equal channel angular pressing (ECAP), multiple forging (MF), accumulative roll bonding (ARB) and embossing. The model deals with materials in which plastic deformation is exclusively due to dislocation movement within grains, which is in good approximation the case for many metallic alloys at low temperature, for instance aluminium alloys. In the early stages of deformation, the generated dislocations are stored in grains and contribute to overall strength. With increase in strain, excess dislocations form and/or move to new cell walls/grain boundaries and grains are refined. We examine this model using both our own data as well as the data in the literature. It is shown that grain size and strength/hardness are predicted to a good accuracy.     

The charge state of conducting fine-dispersed systems in an insulating matrix

The influence of fluctuations in the number of Fermi particles on the charge state of fine-dispersed metallic grains in an insulating matrix is investigated. It is suggested that the system of grains does not form a tunnel medium and that charge transfer between metallic elements of the composite occurs due to thermal excitations of electrons over barriers. As follows from a calculation of the grand partition function, the average charge of the ith grain is a nonlinear function of the potential V _i of the conductor.     

A phase-field model for elastically anisotropic polycrystalline binary solid solutions

A phase-field model for modeling the diffusional processes in an elastically anisotropic polycrystalline binary solid solution is described. The elastic interactions due to coherency elastic strain are incorporated by solving the mechanical equilibrium equation using an iterative-perturbation scheme taking into account elastic modulus inhomogeneity stemming from different grain orientations. We studied the precipitate interactions among precipitates across a grain boundary and grain boundary segregation–precipitate interactions. It was shown that the local pressure field from one coherent precipitate influences the shape of precipitates in other grains. The local pressure distribution due to primary coherent precipitates near the grain boundary leads to inhomogeneous solute distribution along the grain boundary, resulting in non-uniform distribution of secondary nuclei at the grain boundary.     

Absence of an abrupt phase change from polycrystalline to amorphous in silicon with deposition temperature.

Using fluctuation electron microscopy, we have observed an increase in the mesoscopic spatial fluctuations in the diffracted intensity from vapor-deposited silicon thin films as a function of substrate temperature from the amorphous to polycrystalline regimes. We interpret this increase as an increase in paracrystalline medium-range order in the sample. A paracrystal consists of topologically crystalline grains in a disordered matrix; in this model the increase in ordering is caused by an increase in the grain size or density. Our observations are counter to the previous belief that the amorphous to polycrystalline transition is a discontinuous disorder-order phase transition.     

Bardeen-Cooper-Schrieffer theory of finite-size superconducting metallic grains

We study finite-size effects in superconducting metallic grains and determine the BCS order parameter and the low energy excitation spectrum in terms of the size and shape of the grain. Our approach combines the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements, and corrections to the BCS mean field. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we observe shell effects when, e.g., a small change in the electron number leads to large changes in the energy gap.     

The deformation of B4C particle in the B4C/2024Al composites after high velocity impact

In the present work, B₄C/2024Al composites with volume fraction of 45% were prepared by a pressure infiltration method. The microstructure of the crater bottom of B₄C/2024Al composite after impact was characterized by transmission electron microscope (TEM), which indicated that recovery and dynamic recrystallization generated in Al matrix, and the grain size distribution was about from dozens of nanometer to 200 nm. Furthermore, the plastic deformation was observed in B₄C ceramic, which led to the transformation from monocrystal to polycrystal ceramic grains. The boundary observed in this work was high-angle grain boundary and the two grains at the boundary had an orientation difference of 30°.     

Effect of granularity and inhomogeneity in excess conductivity of YBa2Cu3O7−δ+xBaTiO3 superconductor

Synthesis of polycrystalline YBCO+xBaTiO₃ (x=1.0, 2.5, 5.0) superconductor has been done and the effects of granularity and inhomogeneities due to inclusions of nano-BaTiO₃ in excess conductivity are reported in this work. The phase formation, texture and grain alignments were analyzed through XRD and SEM techniques. SEM results reveal that the grain size is reduced and morphology is improved with the incorporation of nano-BaTiO₃ particles. Superconducting order parameter fluctuation (SCOPF) studies on the electrical conductivity were investigated from the resistivity vs. temperature data in the experimental domain relatively above T_c. Log(Δσ) vs. log(ε) plots show that the 2D to 3D crossover temperature (T_LD) that demarcates dimensional nature of fluctuation inside the grains is influenced by BaTiO₃ incorporation in YBCO matrix. An upward shift of T_LD in the mean field region has been observed as a consequent dominance of 3D region with increase in 1 wt% BaTiO₃ in the composites as compared to higher inclusions. It has been analyzed that microscopic inhomogeneities produced as a result of diffusion of a fraction of Ti ions into the grains affect fluctuations in the excess conductive region. The interplay of microscopic inhomogeneities produced inside the grains and mesoscopic inhomogeneities in the grain boundaries on the excess conductivity has been explained in terms of thermal fluctuations for the composites.