Radial-fluctuation-induced stabilization of the ordered state in two-dimensional classical clusters

Melting of two-dimensional (2D) clusters of classical particles is studied using Brownian dynamics and Langevin molecular dynamics simulations. The particles are confined either by a circular hard wall or by a parabolic external potential and interact through a dipole or a screened Coulomb potential. We found that, with decreasing strength of the interparticle interaction, clusters with a short-range interparticle interaction and confined by a hard wall exhibit a reentrant behavior in its orientational order.     

Brownian dynamics simulations of a cubic haematite particle suspension with a more effective treatment of steric layer interactions

We have proposed a new repulsive layer model for describing the interaction between steric layers of coated cubic particles. This approach is an effective technique applicable to particle-based simulations such as a Brownian dynamics simulation of a suspension composed of cubic particles. 3D Brownian dynamics simulations employing this repulsive interaction model have been performed in order to investigate the equilibrium aggregate structures of a suspension composed of cubic haematite particles. It has been verified that Brownian dynamics employing the present steric interaction model are in good agreement with Monte Carlo results with respect to particle aggregate structures and particle orientational characteristics. From the viewpoint of developing a surface modification technology, we have also investigated a regime change in the aggregate structure of cubic particle in a quasi-2D system by means of Brownian dynamics simulations. If the magnetic particle–particle interaction strength is relatively strong, in zero applied magnetic field the particles aggregate in an offset face-to-face configuration. As the magnetic field strength is increased, the offset face-to-face structure is transformed into a more direct face-to-face contact configuration that extends throughout the whole simulation region.     

Equilibrium states and quasi-static magnetization switching of a multilayer structure

The equilibrium orientations of magnetic moments that correspond to various values and directions of the biasing field are found in a set of magnetic films with cubic crystalline anisotropy and uniaxial induced anisotropy. The films are coupled by exchange interaction of the antiferromagnetic type. Field intervals are established where noncollinear and bistability states causing orientational phase transitions and hysteresis exist. Ninety degree magnetization switching (per switching cycle) of the magnetic moments of the films, as well as an orientational phase transition of bifurcation character, is discovered. Hysteresis loops for 180° in-plane magnetization switching are constructed.     

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)     

Order-disorder component in the phase transition mechanism of 18O enriched strontium titanate

Ti and Sr nuclear magnetic resonance spectra of 18O enriched SrTiO3 (STO-18) provide direct evidence for Ti disorder already in the cubic phase and show that the ferroelectric transition at T(C)=24 K occurs in two steps. Below 70 K rhombohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below T(C). This shows that the elusive ferroelectric transition in STO-18 is indeed connected with local symmetry lowering and implies the existence of an order-disorder component in addition to the displacive soft mode one. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric state of STO-16 as well. The concentration of the rhombohedral clusters is, however, not high enough to allow for percolation.     

3D Monte Carlo simulations on the aggregate structures of a suspension composed of cubic hematite particles

In the previous study, from the viewpoint of surface modification technology, we considered a quasi-2D suspension in thermodynamic equilibrium in order to investigate the characteristics of magnetic cubic particles on a material surface. The present study has been expanded to include 3D Monte Carlo simulations of a suspension of magnetic cubic particles in order to discuss a regime change in the structures of cubic particle aggregates. We attempt to elucidate the dependence of a regime change in the aggregate structures on a variety of factors. The main results obtained here are summarised as follows. If the magnetic interaction strength is sufficiently large, closely packed clusters are formed by repeat and expansion of a cluster unit composed of eight particles, which may be the most preferred configuration as it gives rise to a minimum energy. A regime change in the internal structure of aggregates appears in a narrow range with increasing magnetic interaction strength. As the applied magnetic field strength is increased, closely packed clusters collapse and are transformed into wall-like clusters that are formed along the magnetic field direction. An increase in the volumetric fraction of particles induces a regime change from thick chain-like clusters to the formation of wall-like clusters.     

Dynamic magnetization reversal and bistable states in antiferromagnetic multilayer structures

The dynamic behavior of the magnetization under a transverse microwave field is investigated in a system of magnetic layers with cubic crystallographic anisotropy coupled through interlayer antiferromagnetic exchange interaction. An orientational phase transition is found to occur as the microwave field frequency and amplitude are varied. It is established that there is a frequency range in which several steady-state regimes of precession of magnetic moments exist. The limits of this range can be efficiently controlled both by varying the strength of the bias magnetic field and the amplitude of the microwave field.     

Long Range Order for Lattice Dipoles

We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as expected by spin wave theory. The proof is based on reflection positivity methods. In particular, we demonstrate a previously unproven conjecture on the dispersion relation of the spin waves, first proposed by Fröhlich and Spencer, which allows one to apply infrared bounds for estimating the long distance behavior of the spin-spin correlation functions.     

Quasi-2D Monte Carlo simulations of the regime change in the aggregates of magnetic cubic particles on a material surface

We have investigated the aggregate structure of a suspension composed of magnetic particles with a cubic geometry by means of Monte Carlo simulations. From the viewpoint of application to the technology of surface modification, we have considered a quasi-two-dimensional suspension in thermodynamic equilibrium. As the magnetic interaction strength is increased, the effects of the thermal energy are reduced and the particles tend to aggregate together. These aggregates of cubic particles are not chain-like, but are designated as closely packed clusters. An applied magnetic field tends to enhance the formation of clusters along the field direction but does not significantly regularise the internal structure of the cluster. This is mainly due to the preference of a face-to-face contact configuration for the alignment of particles with cubic geometry. The regime of the internal structure of aggregates has a significant effect on the characteristics of the alignment of the magnetic moments with regard to the external magnetic field direction. Our simulations indicate that larger closely packed clusters are formed with increasing volumetric fraction, whereas the internal structure of the closely packed clusters is not found to be significantly influenced by the change in the volumetric fraction.     

The influence of atomic impurities on the orientational transitions in localized monolayer films of diatomic molecules adsorbed on crystalline surfaces

The orientational ordering in localized films consisting of a mixture of diatomic and mono-atomic particles and formed on the (100) face of a cubic crystal is considered. It is demonstrated that the presence of atomic impurities influence the formation of orientationally ordered states. In particular, it is shown that even a simple mean-field theory leads to a qualitatively correct picture of changes in orientational properties in the film when the molar ratio of spherically symmetric particles increases.     

Dynamical clustering of counterions on flexible polyelectrolytes

Molecular dynamics simulations are used to study the spatiotemporal dynamics of charge fluctuations around a polyelectrolyte molecule at charge densities above and below the classic counterion condensation threshold. Surprisingly, the counterions form weakly interacting clusters which exhibit slowly decaying short range orientational order. Local charge fluctuations create energy fluctuations at the order of k_(B)T that is sufficient to affect the polyelectrolyte interaction with an approaching ligand molecule. The predictions of the classical theory appear to be appropriate only over much longer time scales.     

Structural properties of complex (dusty) plasma upon crystallization and melting

A change in the local order of a bounded complex (dusty) plasma in the process of its crystallization and melting has been examined by molecular dynamics simulations. The dynamics of microparticles is considered in the framework of a Langevin thermostat, the pair interaction between charged particles is described by a screened Coulomb potential (Yukawa potential) with the hard wall potential as a confinement. It has been shown that the beginning of the crystallization of such a system is accompanied by the formation of clusters with the hexagonal close packed (hcp) structure; a noticeable number of these clusters are then transformed to the face centered cubic (fcc) phase. A plasma crystal formed after crystallization consists of the metastable hcp phase, fcc clusters, and a small number of clusters with a body centered cubic (bcc) crystal lattice. Beginning with a certain threshold value of the thermostat temperature, the number of fcc/bcc clusters decreases sharply with increasing temperature, which is an important signature of the beginning of the melting of the plasma crystal.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Interfacial reaction rates and free energy of cubic clusters

A new formulation of interfacial reaction rates for clusters in binary alloys is presented. It accounts for the matrix structure and the topological properties of the clusters at the atomic scale. It is shown that the probabilities per unit time that a solute atom be captured or released by a cluster are functions not only of the partition function but also of a transition function. The principles of calculation of these functions are general but only the case of cubic clusters is treated here (results can be used for L₁₂ clusters in fcc matrices). Exact calculations have been done for small clusters (size<10), followed by a Monte-Carlo sampling method for intermediate sizes as a function of temperature and interaction energy (a material characteristic). Finally, it is shown that generic results can be extrapolated at higher cluster size in a large range of temperature and/or interaction energy.     

Influence of the size and shape of free nanoparticles on the local changes in the lattice parameter and on the structural stability of body-centered cubic zirconium and iron

The influence of the shape and size of nanocrystals on the lattice relaxation of body-centered cubic metals (zirconium, iron) at a constant temperature has been investigated using the molecular dynamics method with the many-body interatomic interaction potential obtained in terms of the embedded-atom model. The calculations have been performed for isolated clusters with sizes ranging from 2.5 to 17 nm for zirconium and from 2 to 14 nm for iron. It has been demonstrated that, in free zirconium and iron particles, the relaxation of the lattice constant along the [100], [010], and [001] directions has an oscillatory character. Irrespective of the size of the zirconium and iron particles, the equilibrium distances between atoms at the center of cubic clusters are minimum compared to those observed in near-surface layers and the equilibrium value of the lattice parameter for the bulk sample. In spherical clusters, the region of a maximum contraction corresponds to a depth approximately equal to 0.2 particle diameter from the surface. An increase in the size of both cubic and spherical clusters leads to a decrease in the deviation of the local lattice parameter from the equilibrium value for the bulk sample. It has been established that the size and shape of the cluster substantially affect the temperature and mechanism of the structural transformation from the body-centered cubic phase into the hexagonal close-packed phase.     

Domain structure of (011) crystalline garnet ferrite plates

The domain structure in (011) crystalline garnet ferrite plates is studied with allowance for induced uniaxial anisotropy and two-constant cubic anisotropy. It is shown that the inclusion of the second constant of cubic anisotropy greatly affects the orientational phase diagram and also the topology of magnetic inhomogeneities in a given magnet. It is found, in particular, that 180°non-Bloch domain walls may appear in a certain range of combined anisotropy constants, causing a continuous change in the wall orientation.     

Simulated Cu–Zr glassy alloys: the impact of composition on icosahedral order

The structural properties of the simulated Cu_αZr_1-α glassy alloys are studied in the wide range of the copper concentration to clarify the impact of the composition on the number density of the icosahedral clusters. Both bond orientational order parameters and Voronoi tessellation methods are used to identify these clusters. Our analysis shows that abundance of the icosahedral clusters and the chemical composition of these clusters are essentially nonmonotonic versus and demonstrate local extrema. That qualitatively explains the existence of pinpoint compositions of high glass-forming ability observing in Cu Zr alloys. Finally, it has been shown that Voronoi method overestimates drastically the abundance of the icosahedral clusters in comparison with the bond orientational order parameters one.     

Largest Lyapunov exponent in molecular systems. II: Quaternion coordinates and application to methane clusters

We present a numerical procedure for extracting Lyapunov characteristic exponents from classical molecular-dynamics simulations of molecular systems. The theoretical frame chosen to describe the orientational degrees of freedom is the quaternions scheme. We apply the method to small methane clusters. Two different model potentials are used to investigate the role of internal molecular motion on the nonlinear dynamics, and several parameters are calculated to study the thermodynamics and chaotic dynamics of these clusters. Evidence is found for a solidlike to plasticlike phase transition occurring with the release of the orientational degrees of freedom, at low temperatures below the melting point. The largest Lyapunov exponent increases significantly during this transition, but it exhibits no particular variation during melting.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Quantum charge density fluctuations and the phase transition in Ce

We have calculated the quantum quadrupolar interaction due to charge density fluctuations of localized 4f-electrons in Ce by taking into account the angular dependence, the degeneracy of the localized 4f -orbitals and the spin-orbit coupling. The calculated crystal field of 4 f electronic states is in good agreement with neutron diffraction measurements. We show that orientational ordering of quantum quadrupoles drives a phase transition at K which we assign with the transformation. In the phase the centers of mass of the Ce atoms still form a face centered cubic lattice. The theory accounts for the first order character of the transition and for the cubic lattice contraction which accompanies the transition. The transition temperature increases linearly with pressure. Our approach does not involve Kondo spin fluctuations as the significant process for the phase transition. Received 19 October 1998