Qualitative evaluation of the effect of morphology,spatial distribution and coherent interfaces on the coarsening kinetics and size distribution of particles during Ostwald ripening

ABSTRACT

By exploiting the simple structure of the recently developed Multi-Particle model of Ostwald ripening based on pairwise interactions, the effect of extra factors affecting the coarsening process, such as the morphology of particles, the topology of their spatial distribution and the presence of elastic fields surrounding coherent precipitates, is analysed from a qualitative viewpoint.

Two observables disclose the presence of deviations with respect to the behaviour of a system of spherical and incoherent precipitates: the absolute value of the kinetic coarsening constant, together with its evolution with the volume fraction, and the shape of the asymptotic particle size distribution (PSD) for a given volume fraction of second phase.

By using a parametrised ‘rounded cube’ ideal solid it is shown that, as the shape of precipitates flattens, the coarsening constant decreases reaching in some condition values as low as about 20% that of a system of spheres with the same fraction.

Consequently, the curve of the relative kinetic constant with the volume fraction has a slower increase above 0.7 compared to spherical particles and this permits to explain accurately the experimental data on dense systems in the whole range of volume fractions.

It is also shown how the shape of the PSD is influenced by regular arrangements of particles in the space and by interfacial stresses in the matrix surrounding coherent precipitates. In both cases the model predicts a sharpening of the PSD, whose shape tends to become more symmetrical and somehow similar to that of the classical LSW theory.     

Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion

Dislocation climb mobilities, assuming vacancy bulk diffusion, are derived and implemented in dislocation dynamics simulations to study the coarsening of vacancy prismatic loops in fcc metals. When loops cannot glide, comparison of the simulations with a coarsening model based on the line tension approximation shows good agreement. Dislocation dynamics simulations with both glide and climb are then performed. Allowing for glide of the loops along their prismatic cylinders leads to faster coarsening kinetics, as direct coalescence of the loops is now possible.     

Two-dimensional coarsening kinetics of reconstruction domains: GaAs(001)-beta(2 x 4)

We study the nonconserved coarsening kinetics of a reconstructed semiconductor surface. The domain size evolution is obtained in situ by time-resolved surface x-ray diffraction. The system exhibits four equivalent domain types with two nonequivalent types of domain boundaries. Small domains are prepared by molecular beam epitaxy deposition of one GaAs layer. We find the correlation lengths of the domain size distribution to depend on time as l is proportional to t(0.42+/-0.05) in the half-order reflections and l is proportional to t(0.22+/-0.05) in the quarter-order reflections. The fraction of the higher energy domain boundaries increases as lnt.     

Dislocation glasses: aging during relaxation and coarsening

The dynamics of dislocations is reported to exhibit a range of glassy properties. We study numerically various versions of 2D edge dislocation systems, in the absence of externally applied stress. Two types of glassy behavior are identified (i) dislocations gliding along randomly placed, but fixed, axes exhibit relaxation to their spatially disordered stable state; (ii) if both climb and annihilation are allowed, irregular cellular structures can form on a growing length scale before all dislocations annihilate. In all cases both the correlation function and the diffusion coefficient are found to exhibit aging. Relaxation in case (i) is a slow power law, furthermore, in the transient process (ii) the dynamical exponent z approximately 6, i.e., the cellular structure coarsens relatively slowly.     

Hysteresis and elastic interactions of microasperities in dry friction

Velocity independent dry friction of a slider upon a base is due to an hysteretic response of relative displacement to a tangential driving force F. We show that the purely elastic model for multistability considered in a previous publication is in no way essential: multistability arises just as well from adhesion. We emphasize the physical consequences of multistability for dynamic/static, a.c./d.c. friction. When the slider is moved from rest by an amount the transition from the zero force static configuration to dynamic behaviour is progressive, spreading on a range equal to the width of the hysteresis cycle. When is small, an elastic restoring force ensues, in agreement with observations. The competition of that elastic pinning with bulk elasticity generates a screening length which we believe is the natural size of Burridge Knopoff blocks. We then study the effect of elastic interactions between asperities: it is weak for dilute asperities, but its long range makes it important. In lowest order the interaction mediated displacement of a given asperity has logarithmically divergent fluctuations: they become comparable to the asperity radius when the slider size reaches another characteristic “Larkin length”, which for dilute micronic asperities is exponentially large. We give arguments suggesting that individually monostable asperities display collective multistability on scales larger than . For individually multistable sites we show that elastic interactions give rise to cascade processes in which the spinodal jump of a given asperity triggers the jump of others. We estimate the size of these cascades that should show up in the noise spectrum. Received: 3 February 1998 / Accepted: 19 March 1998     

Deformed tensor interactions in deuteron elastic and inelastic scattering

The various forms of tensor potentials present in deuteron elastic and inelastic scattering on a deformed target nucleus are derived using a folding model for the deuteron-nucleus interaction. Approximate expressions for the radial dependence of the deformed tensor interactions parametrized with the derivatives of Woods-Saxon potentials are obtained and discussed for the case of a rotational nucleus.     

界面润湿性及固相体积分数对颗粒粗化动力学影响的相场法研究

利用多相场模型模拟了液-固两相体系中固相颗粒的粗化过程, 分析了界面润湿性及固相体积分数对粗化指数、粗化速率及颗粒尺寸分布的影响.结果表明, 不同固相体积分数下粗化指数基本不变, 但粗化速率常数及尺寸分布与固相体积分数及界面润湿性密切相关.在完全润湿条件下, 随着固相体积分数的增加, 粗化速率常数逐渐增大; 而非完全润湿条件下, 随着固相体积分数的增加, 粗化速率常数增大速度变缓, 且当润湿性较低、 固相分数较大时, 粗化速率常数还将随体积分数的增加而下降. 此外, 模拟结果表明各种润湿条件下颗粒的尺寸分布均随着固相分数增加而变宽, 分布峰值降低, 但非完全润湿条件下峰值下降变缓.模拟结果为理解不同实验观测结果之间的分歧提供了依据. 关键词： 粗化 相转变 相场法 润湿性     

Anharmonic interactions of elastic and orientational waves in one-dimensional crystals

Planar oscillations of a chain of dumbbell-shaped particles possessing three degrees of freedom are studied. This system models the dynamics of quasi-one-dimensional crystals consisting of elongated anisotropic molecules. A system of nonlinear differential equations describing the anharmonic interaction of the elastic and orientational waves in the lattice, corresponding to different degrees of freedom of the particles, is constructed assuming a cubic interparticle interaction potential. It is shown that in the low-frequency approximation the system obtained is equivalent to the equations of the moment theory of elasticity, widely employed for describing nonlinear and dispersion properties of layered crystals and phase transformations in alloys. Some types of three-wave collinear interactions are investigated, suggesting the possibility of exciting orientational waves in organic crystals because of their nonlinear interaction with acoustic waves. Fiz. Tverd. Tela (St. Petersburg) 39, 137–144 (January 1997)     

Electrostatically driven granular media: phase transitions and coarsening

We report the experimental and theoretical study of electrostatically driven granular material. We show that the charged granular medium undergoes a hysteretic phase transition from the immobile condensed state (granular solid) to a fluidized dilated state (granular gas) with a changing applied electric field. In addition we observe a spontaneous precipitation of dense clusters from the gas phase and subsequent coarsening-coagulation of these clusters. Molecular dynamics simulations show qualitative agreement with experimental results.     

Dynamics of coarsening foams: accelerated and self-limiting drainage

The evolution of a foam is determined by drainage flow of the continuous (liquid) phase and coarsening (aging) of the dispersed phase (gas bubbles). Free-drainage experiments with slow- and fast-coarsening gases show markedly different dynamics and elucidate the importance of the coupling of the two effects. Strong coarsening leads to drainage times that are shorter (accelerated drainage) and independent of the initial liquid content (self-limiting drainage). A model incorporating the physics of both drainage and diffusive coarsening shows quantitative agreement with experiment.     

First-principles calculations of structural stability,elastic, dynamical and thermodynamic properties of SiGe,SiSn, GeSn

A first-principles calculations, based on the norm-conserving pseudopotentials and the density functional theory (DFT) and the density functional perturbation theory (DFPT) as implemented in the ABINIT code, have been performed to investigate the structural stability, elastic, lattice dynamic and thermodynamic properties of the ordered SiGe, SiSn and GeSn cubic alloy in zinc-blende (B3) structure. The calculated lattice parameters and bulk modulus agree with the previous results. The second-order elastic constants have been calculated and other related quantities such as the Young’s modulus, shear modulus, anisotropy factor are also estimated. We also obtain the data of lattice dynamics and the temperature dependent properties currently lacking for SiGe, SiSn and GeSn. Findings are also presented for the temperature-dependent behaviors of some thermodynamic properties such as the internal energy, Helmholtz free energy, entropy and heat capacity.     

Interaction between the nucleon and muon currents in elastic neutrino-nucleon interactions

The spin relations of neutrino-nucleon interaction with the formation of a muonv(V) N N are investigated within the framework of the two-component and four-component theories of two neutrinos under the assumption of a point neutrino. The difference between the predictions of the two theories is identified. It is shown that the four-component theory of two neutrinos, unlike the two-component theory, accommodates the V + A variant of interaction between the muon current (v) and the barion current.The authors are grateful to Prof. A. A. Sokolov and to R. Sh. Yakh'yaev for evaluating the results.     

On the various impact of chemical composition and elastic strain in SiGe nanoscale islands to the diffuse X-ray scattering

High-resolution X-ray diffraction in combination with kinematical scattering simulations based on finite element calculations for the elastic strain field has been utilized to investigate the chemical composition of SiGe/Si(0 0 1) Stranski–Krastanov islands. Therefore, the intensity distribution in the vicinity of the symmetric (0 0 4) reflection has been three dimensionally measured and compared with respective simulations. Around an asymmetrical reflection, e.g. Si(1 1 3), the impact of lateral and vertical strain tensor components on the diffraction pattern decouples. This allows to distinguish between tetragonally distorted regions at the island bottom and elastically relaxed unit cells of cubic shape at the island apex in accordance with finite element calculations. Artificially switching off and on the various scattering abilities of silicon and germanium in otherwise equivalent simulations yields practically no difference in the resulting scattering. Thus, at X-ray energies far from absorption edges, the diffuse scattering is dominated by elastic strain which is caused by the chemical profile.     

Many-atom interactions in the theory of higher order elastic moduli: A general theory

The total potential energy of a crystal U({r _ik }) as a function of the vectors r _ik connecting centers of equilibrium positions of the ith and kth atoms is assumed to be represented as a sum of irreducible interaction energies in clusters containing pairs, triples, and quadruples of atoms located in sites of the crystal lattice A2: U({r _ik }) ≡ Σ _N=1 ⁴ E _N ({r _ik }). The curly brackets denote the “entire set.” A complete set of invariants {I _j ({r _ik })} _N , which determine the energy of each individual cluster as a function of the vectors connecting centers of equilibrium positions of atoms in the cluster E _N ({r _ik }) ≡ E _N ({I _j ({r _ik })} _N ), is obtained from symmetry considerations. The vectors r _ik are represented in the form of an expansion in the basis of the Bravais lattice. This makes it possible to represent the invariants {I _j ({r _ik })} _N in the form of polynomials of integers multiplied by τ ₂ ^m . Here, τ₂ is one-half of the edge of the unit cell in the A2 structure and m is a constant determined by the model of interaction energy in pairs, triples, and quadruples of atoms. The model interaction potential between atoms in the form of a sum of the Lennard-Jones interaction potential and similarly constructed interaction potentials of triples and quadruples of atoms is considered as an example. Within this model, analytical expressions for second-order and third-order elastic moduli of crystals with the A2 structure are obtained.     

Nonlinear interactions of acoustic modes in ferromagnets near magnetoacoustic resonance: Effective elastic constants

The magnetoelastic contribution ΔĈ ₍₃₎ to the effective third-order elastic constants Ĉ ₍₃₎ ^ef is determined; it describes the additional elastic anharmonicity induced by nonlinear spin-spin and spin-phonon interactions in ferromagnets. In the vicinity of magnetoacoustic resonance, this anharmonicity can be manifested in three-frequency elastic wave interactions, producing magnetoacoustic mode-frequency transformation effects. It is shown that these effects are magnified in resonance as the result of a huge increase (by several orders of magnitude) in the dynamic elastic constants ΔĈ ₍₃₎. Quantitative estimates are obtained for yttrium iron garnet. Fiz. Tverd. Tela (St. Petersburg) 40, 2080–2084 (November 1998)     

Feshbach resonances in the 6Li-40K Fermi-Fermi mixture: elastic versus inelastic interactions

We present a detailed theoretical and experimental study of Feshbach resonances in the ⁶Li-⁴⁰K mixture. Particular attention is given to the inelastic scattering properties, which have not been considered before. As an important example, we thoroughly investigate both elastic and inelastic scattering properties of a resonance that occurs near 155?G. Our theoretical predictions based on a coupled channels calculation are found in excellent agreement with the experimental results. We also present theoretical results on the molecular state that underlies the 155?G resonance, in particular concerning its lifetime against spontaneous dissociation. We then present a survey of resonances in the system, fully characterizing the corresponding elastic and inelastic scattering properties. This provides the essential information to identify optimum resonances for applications relying on interaction control in this Fermi-Fermi mixture.