Kinetic temperature and charge of a dust grain in weakly ionized gas-discharge plasmas

Analytical relations are given for estimating the energy of the stochastic motion of an individual dust grain heated by electrostatic ion oscillations in a weakly ionized gas-discharge plasma. Dust grain charging processes are analyzed, and an empirical approximation is obtained for the ion current to the grain surface. The processes are simulated under conditions similar to those of laboratory experiments on dusty plasmas. It is found that the kinetic temperature of a dust grain heated by electrostatic ion oscillations in a gas-discharge plasma can exceed the background gas temperature.     

Cycloid motions of grains in a dust plasma

Hypocycloid and epicycloid motions of irregular grains(pine pollen) are observed for the first time in a dust plasma in a two-dimensional(2D) horizontal plane. These cycloid motions can be regarded as a combination of a primary circle and a secondary circle. An inverse Magnus force originating from the spin of the irregular grain gives rise to the primary circle.Radial confinement resulting from the electrostatic force and the ion drag force, together with inverse Magnus force, plays an important role in the formation of the secondary circle. In addition, the cyclotron radius is seen to change periodically during the cycloid motion. Force analysis and comparison experiments have shown that the cycloid motions are distinctive features of an irregular grain immersed in a plasma.     

Attractive potential around a thermionically emitting microparticle

We present a simulation study of the charging of a dust grain immersed in a plasma, considering the effect of thermionic electron emission from the grain. It is shown that the orbit motion limited theory is no longer reliable when electron emission becomes large: screening can no longer be treated within the Debye-Huckel approach and an attractive potential well can form, leading to the possibility of attractive forces on other grains with the same polarity. We suggest to perform laboratory experiments where emitting dust grains could be used to create nonconventional dust crystals or macromolecules.     

非均匀磁场尘埃等离子体中颗粒的复杂运动

本文研究了在非均匀磁场尘埃等离子体中不规则尘埃颗粒的复杂运动, 包括圆滚运动、尖头圆滚运动、圆周运动以及波浪运动等. 放置在电极上的圆柱形磁铁的主要作用是改变鞘层的径向分布, 进而对颗粒产生径向约束, 使尘埃颗粒悬浮于圆柱形磁铁周围, 其磁场并不足以磁化颗粒使其做圆滚运动. 通过与球形尘埃颗粒的对比实验发现, 圆滚运动是不规则尘埃颗粒在等离子体中特有的一种运动. 我们提出了一种新的机理: 由于不规则颗粒的自旋而引起的横向反Magnus力对颗粒的圆滚运动起了重要的作用. 文中通过受力分析定性地对实验中观察到的非球形颗粒的各种运动给出了合理的解释.     

Low-dimensionality energy landscapes: Magnetic switching mechanisms and rates

In this paper we propose a new method for the study and visualization of dynamic processes in magnetic nanostructures, and for the accurate calculation of rates for such processes. The method is illustrated for the case of switching of a grain of an exchange-coupled recording medium, which switches through domain wall nucleation and motion, but is generalizable to other rate processes such as vortex formation and annihilation. The method involves calculating the most probable (lowest energy) switching path and projecting the motion onto that path. The motion is conveniently visualized in a two-dimensional (2D) projection parameterized by the dipole and quadrupole moment of the grain. The motion along that path can then be described by a Langevin equation, and its rate can be computed by the classic method of Kramers [4]. The rate can be evaluated numerically, or in an analytic approximation—interestingly, the analytic result for domain-wall switching is very similar to that obtained by Brown in 1963 for coherent switching, except for a factor proportional to the domain-wall volume. Thus in addition to its lower coercivity, an exchange-coupled medium has the additional advantage (over a uniform medium) of greater thermal stability, for a fixed energy barrier.     

Diffusion generated motion for grain growth in two and three dimensions

An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grain boundaries are zero-level sets of signed distance functions. Curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains. Hundreds of thousands of grains can be simulated using a small number of signed distance functions (in this work, 32 in two dimensions and 64 in three dimensions are more than sufficient) using modest computational hardware.     

Nonlinear theory of resonant beam-plasma interaction: Nonrelativistic case

Analytic and numerical methods are used to study the nonlinear dynamics of the resonant interaction between a dense nonrelativistic electron beam and a plasma in a spatially bounded system. Regimes such as collective (Raman) and single-particle (Thomson) Cherenkov effects are considered. It is shown that in the first case, the motion of both the beam and plasma electrons exhibits significant nonlinearities. However, because of the weak coupling between the beam and the plasma, the nonlinear dynamics of the instability can be studied analytically and it can be strictly shown that saturation of instability is caused by a nonlinear shift of the radiation frequency and loss of resonance. In the second case, the nonlinear instability dynamics can only be studied numerically. In this regime, at low beam densities significant nonlinearity is only observed in the motion of the beam electrons while the plasma remains linear and saturation of the instability is caused by trapping of beam electrons in the field of the beam-excited plasma wave.     

Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux Balance

Previous considerations of dust acoustic waves is demonstrated to be inconsistent ‐ the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self‐consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 – 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter‐grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Grain Boundary Dynamics: A Novel Tool for Microstructure Control

The reaction of grain boundaries to a wide spectrum of forces is reviewed. Curvature, volume energy and mechanical forces are considered. The boundary mobility is strongly dependent on misorientation, which is attributed to both grain boundary structure and segregation. In magnetically anisotropic materials grain boundaries can be moved by magnetic forces. For the first time a directionality of boundary mobility is reported. Flat boundaries can also be moved by mechanical forces, which sheds new light on microstructure evolution during elevated temperature deformation. Curvature driven and mechanically moved boundaries can behave differently. A sharp transition between the small and large angle boundary regime is observed. It is shown that grain boundary triple junctions have a finite mobility and thus, may have a serious impact on grain growth in fine grained materials. The various dependencies can be utilized to influence grain boundary motion and thus, microstructure evolution during recrystallization and grain growth.     

Grain boundary,triple junction and quadruple point mobility controlled normal grain growth

Reduction in stored free energy provides the thermodynamic driving force for grain and bubble growth in polycrystals and foams. Evolution of polycrystalline networks exhibit the additional complication that grain growth may be controlled by several kinetic mechanisms through which the decrease in network energy occurs. Polyhedral boundaries, triple junctions (TJs), and quadruple points (QPs) are the geometrically distinct elements of three dimensional networks that follow Plateau’s rules, provided that grain growth is limited by diffusion through, and motion of, cell boundaries. Shvindlerman and co-workers have long recognized the kinetic influences on polycrystalline grain growth of network TJs and QPs. Moreover, the emergence of interesting polycrystalline nanomaterials underscored that TJs can indeed influence grain growth kinetics. Currently there exist few detailed studies concerned either with network distributions of grain size, number of faces per grain, or with ‘grain trajectories’, when grain growth is limited by the motion of its TJs or QPs. By contrast there exist abundant studies of classical grain growth limited by boundary mobility. This study is focused on a topological/geometrical representation of polycrystals to obtain statistical predictions of the grain size and face number distributions, as well as growth ‘trajectories’ during steady-state grain growth. Three limits to grain growth are considered, with grain growth kinetics controlled by boundary, TJ, and QP mobilities.     

Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma

Viscoelastic vortical fluid motion in a strongly coupled particle system has been observed experimentally. Optical tracking of particle motion in a complex plasma monolayer reveals high grain mobility and large scale vortex flows coexistent with partial preservation of the global hexagonal lattice structure. The transport of particles is superdiffusive and ascribed to Lévy statistics on short time scales and to memory effects on the longer scales influenced by cooperative motion. At these longer time scales, the transport is governed by vortex flows covering a wide spectrum of temporal and spatial scales.     

Collective motion of atoms in grain boundary migration of a bcc metal

Molecular dynamics simulations of grain boundary (GB) migration of a bcc metal, tungsten, have been carried out. The GB is of asymmetrical ? 110? tilt type. Detailed examinations of atomic processes in the migration, show that the GB migration consists mainly of GB dislocation glides. Furthermore, each motion of a GB dislocation involves a cooperative motion of about three atoms on each of the atomic planes perpendicular to the tilt axis, leading to their realignment from the receding grain to the advancing grain. This collective motion is not synchronized in all of the atomic planes, but appears to be in two or three adjacent planes, suggesting a kink mechanism for glides of the GB dislocations.     

Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry

We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation, a multiple scale analysis leads to an analytical equation of motion for the boundary that shares many properties with that of a crystalline solid. We find that defect motion is generically opposed by a pinning force that arises from nonadiabatic corrections to the standard amplitude equations. The magnitude of this force depends sharply on the misorientation angle between adjacent domains: the most easily pinned grain boundaries are those with a low angle (typically 4 degrees < or =theta;< or =8 degrees ). Although pinning effects may be small, they can be orders of magnitude larger than those present in smectic phases.     

The Effect of Triple Junctions on Grain Boundary Motion and Grain Microstructure Evolution

The theory of steady state motion of grain boundary sytems with triple junctions and the main features of such systems are considered. A special technique of in-situ observations and recording of triple junction motion is introduced, and the results of experimental measurements on Zn tricrystals are discussed. It is shown, in particular, that the described method makes it possible to measure the triple junction mobility. It was found that the measured shape of a moving half-loop with a triple junction agrees with theoretical predictions. A transition from triple junction kinetics to grain boundary kinetics was observed. This means that triple junctions can drag boundary motion. It is demonstrated that the microstructural (granular) evolution is slowed down by triple junction drag for any n-sided grain. The second consequence pertains to six-sided grains. For a boundary system with dragging triple junctions there is no unique dividing line between vanishing and growing grains with respect to their topological class anymore, like n = 6 in the Von Neumann-Mullins relation.     

Faceting of a moving grain boundary and its effect on the kinetic properties of grain boundaries

The motion of an individual half-loop grain boundary in zinc is studied experimentally. A correlation is revealed between the half-loop’s mobility and the change in the shape of its structural elements (curved segments, facets, and grain boundary edges). A hysteresis is observed on the temperature dependence curve of grain boundary mobility. The results from investigating grain boundary migration accompanied by faceting inside zinc bicrystals indicate that unsteady grain boundary motion occurs upon high-temperature isothermal annealing. The unsteady motion is due to the considerable difference between the mobility of a facet and that of the curved part of a grain boundary.     

Effects of boundary inclination and boundary type on shear-driven grain boundary migration

A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low Σ) and general (non-Σ) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-Σ boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For Σ5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.     

Grain growth and collective migration of grain boundaries during plastic deformation of nanocrystalline materials

A theoretical model is proposed for the collective migration of two neighboring grain boundaries (GBs) in a nanocrystalline material under applied elastic stress. By analyzing the change in the energy of the system, it is shown that GBs can remain immobile or migrate toward each other depending on the values of the applied shear stress and misorientation angles. The process of GB migration can proceed either in a stable regime, wherein the GBs occupy equilibrium positions corresponding to a minimum of the energy of the system under relatively small applied stress, or in an unstable regime, wherein the motion of GBs under relatively high stress is accompanied by a continuous decrease in the system energy and becomes uncontrollable. The stable migration of GBs leads to a decrease of the grain bounded by them at the cost of growth of the neighbor grains and can result in complete or partial annihilation of the GBs and the collapse of this grain. Unstable migration leads either to annihilation of GBs or to passage of them through each other, which can be considered as the disappearance of the grain and nucleation and growth of a new grain.     

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.     

Sheath motion in a capacitively coupled radio frequency discharge

The sheath motion in a capacitively coupled RF discharge is highly nonlinear. The voltage waveform on a cylindrical probe placed in the sheath region is measured as a function of position and time. A circuit model of the probe-discharge system relates the observed probe voltage to the sheath motion. The equations derived from this circuit model are solved numerically with varying nonlinear sheath motions; the resulting waveforms are compared with the experimental observations to determine the actual sheath motion. The time-varying plasma potential is also determined, indirectly, from the comparison. The authors also report observation of oscillations related to the plasma frequency, whose peak harmonic component can be calculated from a single plasma model. These oscillations can be a useful plasma diagnostic for determining plasma density. The presence of these high-frequency oscillations may significantly enhance the rate of stochastic heating of electrons