Monte Carlo computer experiments on critical phenomena and metastable states

Ising and Heisenberg models are studied by the Monte Carlo method. Several hundred up to 60 000 spins located at two- and three-dimensional lattices are treated and various boundary conditions used to elucidate various aspects of phase transitions. Using free boundaries the finite size scaling theory is tested and surface properties are derived, while the periodic boundary condition or the effective field-like ‘self-consistent’ boundary condition are used to derive bulk critical properties. Since Monte Carlo averages can be interpreted as time averages of a stochastic model, ‘critical slowing down of convergence’ occurs. The critical dynamics is investigated in the case of the single spin-flip kinetic Ising model. Also non-equilibrium relaxation processes are treated, e.g. switching on small negative fields the magnetization reversal and nucleation processes are studied. The metastable states found can be understood in terms of a scaling theory and the droplet model. Using a spin exchange model the phase separation kinetics of a binary alloy is simulated.     

Size, shape and structure dependent cohesive energy and phase stability of metallic nanocrystals

A model to account for the size, shape and structure dependent cohesive energy of metallic nanocrystals is developed in this contribution. It is predicted that the cohesive energy of nanocrystals decreases with decreasing the crystal size in specific shape, and decreases with increasing the shape factor in specific size. Furthermore, the model can be applied to predict the size and shape dependent phase stability of nanocrystal. To take Cr nanocrystal as an example, we found that there exists FCC structure for Cr crystal (the bulk structure is BCC) when the crystal size is small enough, and critical size of phase transition ranges from 249 to 824 atoms due to crystal shape variation, which is consistent with the corresponding experimental results.     

熔渣颗粒碰壁的相变沉积热过程模拟

离心粒化方法在高温熔渣余热回收方面具有结构紧凑、能耗低、得到的渣粒粒径小等优势。但受到粒化仓空间限制,会出现高温熔融渣粒碰撞、黏附在壁面的现象,影响装置运行的稳定性。本文针对该问题建立了熔融渣粒碰撞壁面的三维对称模型,结合VOF(流体体积)方法和凝固/融化模型来模拟熔渣动态形变和凝固换热过程。模拟得到,两个同粒径熔融渣粒在壁面上相继沉积会出现碰撞、铺展、回缩、飞溅、稳定的动态行为。进一步,讨论了熔渣初始温度和冷却风速对其形变和凝固换热的影响。结果表明,熔渣初始温度越小,铺展因数越小,凝固所需时间延长。而冷却风速(1~3 m/s)对熔渣碰壁过程中的铺展形变和换热的影响都很微小。     

Phase diagrams of decomposing nanoalloys

The thermodynamics of nucleation and decomposition in small isolated particles are considered. There exist three possibilities: phase separation, prohibition of decomposition and a metastable state. We investigate the peculiarities of phase diagrams related to depletion of the nanosize parent phase even at the nucleation stage. For small particles the equilibrium diagram becomes split (and shifted and size dependent). Concentration, size and temperature hystereses take place. Size-dependent ‘critical supersaturation’, increasing with decreasing size, has been analysed.     

Laser-induced condensation in colloid—polymer mixtures

We study a mixture of hard sphere colloidal particles and non-adsorbing polymers exposed to a plane wave external potential which represents a three-dimensional standing laser field. With computer simulations and density functional theory we investigate the structure and phase behaviour using the simple Asakura-Oosawa model. For varying laser wavelength λ we monitor the emergence of structure in response to the external field, as measured by the amplitude of the oscillations in the one-body density distribution. Between the ideal gas limit for small λ and the bulk limit of large λ there is a non-monotonic crossover that is governed by commensurability of λ and the colloid diameter. The theoretical curves are in good agreement with simulation results. Furthermore, the effect of the periodic field on the liquid-vapour transition is studied, a situation that we refer to as laser-induced condensation. Above a threshold value for λ the theoretical phase diagram indicates the stability of a ‘stacked’ fluid phase, which is a periodic succession (in the beam direction) of liquid and vapour slabs. This partially condensed phase causes a splitting of the liquid-vapour binodal leading to two critical and a triple point. All our predictions should be experimentally observable for colloid-polymer mixtures in an optical resonator.     

Size effect on alloying ability and phase stability of immiscible bimetallic nanoparticles

In the present paper, the surface and size effects on the alloying ability and phase stability of immiscible alloy nanoparticles have been studied with calculating the heats of formation of Au-Pt alloy nanoparticles from the single element nanoparticles of their constituents (Au and Pt) with a simple thermodynamic model and an analytic embedded atom method. The results indicated that, besides the similar compositional dependence of heat of formation as in bulk alloys, the heat of formation of alloy nanoparticles exhibits notable size-dependence, and there exists a competition between size effect and compositional effect on the heat of formation of immiscible system. Contrary to the positive heat of formation for bulk-immiscible alloys, a negative heat of formation may be obtained for the alloy nanoparticles with a small size or dilute solute component, which implies a promotion of the alloying ability and phase stability of immiscible system on a nanoscale. The surface segregation results in an extension of the size range of particles with a negative heat of formation. The molecular dynamics simulations have indicated that the structurally and compositionally homogeneous AuPt nanoparticles tend to form a core-shell structure with temperature increasing.     

Dynamical dipole and quadrupole response properties of small metallic particles: Random phase approximation and the modified spherical infinite barrier model

The self-consistent electrostatic response of small metallic spherical particles is studied in the random phase approximation and using the electronic wave functions in the infinite barrier model, with the size of the effective positive background adjusted to minimize the electrostatic energy of the system. The multipole susceptibilities and the numerical results are presented for the dipole (L = 1) and quadrupole (L = 2) cases. The spectra, showing both surface and several bulk plasmon peaks and the electron-hole excitations are discussed and analyzed in terms of their associated density fluctuations. The results are compared with the recent calculation of the same physical properties, based on the self-consistent field Kohn-Sham method.     

Raman scattering from gas-evaporated silicon small particles

Raman scattering measurements are reported on silicon small particles prepared by gas-evaporation technique. The crystalline structure is also observed for the sample having 70 A particles in average size. Four resolved component modes with Gaussian distribution function are identified with the three usual modes (LA, TO and allowed-TO) and a new surface mode. The surface mode of silicon particle, whose relative integrated intensity decrease with an increase of the particle size, is presented for the first time.     

Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems

We extend previous computations of mechanical stability of atomic microclusters to the realm of statistical thermodynamics, obtaining thermodynamic functions for small, solid-like Van der Waals clusters of less than some 100 atoms possessing non-crystalline structures of ‘polytetrahedral’ type. These are shown to be almost invariably at a thermodynamic advantage over alternative lattice structures of the same number of atoms, at least for the Lennard-Jones potential in the harmonic-oscillator/rigid-rotor approximation. The dependence of thermodynamic functions upon cluster size appears to be essentially monotonic in the number of internal degrees of freedom; although there are certain exceptional structures, particularly with icosahedral symmetry, there proves to be little evidence for the occurrence of ‘magic numbers’ for stability at any temperature and within the size-range considered. Particular attention is given to the heat capacity of model systems in relation to their vibrational spectra. The Debye T ³ law appears reasonably well obeyed at low temperatures with no evidence for the existence of either ‘soft modes’ or distinct surface contributions.

The results for the free energy of formation of minimal clusters ΔG _f are then applied to the computation of nucleation rates in terms of the Becker-Döring-Volmer-Zeldovitch quasi-equilibrium theory. Gibbsian behaviour in the form of a maximum in the curve of ΔG _f versus size is observed with a critical nuclear size at realistic temperatures and pressures of the order of that predicted by macroscopic liquid-drop theories. These figures and those derived for nucleation rate and critical supersaturation appear remarkably insensitive to the details of the model used, in particular to the distinction between ‘microcrystalline’ and ‘amorphous’ atomistic models.

The general status of atomistic nucleation theory is critically examined in the light of these and similar results.     

On the Instabilities of the Collisionless and Non-Magnetized Active Plasmas

Spontaneously excited instabilities in a uniform, collisionless and non-magnetized active plasma are studied, under the assumption that the polarisability of its active constituent is due to transitions of only one optical electron between two inversely populated energy levels. The attention is focused on non-resonant situations in which the modal frequencies of the excited waves differ significantly from the frequency of coherent electromagnetic radiation arising due to the presence of the active constituent. The longitudinal (‘acoustic’) waves in both low and high phase velocity domains, as well as the transverse (‘optical’) waves, are investigated. It is shown that the instabilities excited are most frequently aperiodical, and appear within, a comparatively large wavelength range. Their amplitude increments are evaluated. Under certain particular conditions, specified in the paper, the instabilities turn out to be periodical and to appear in very narrow wavelength bands only. Their modal frequencies and amplitude increments are also evaluated.     

Generalized bond-energy model for cohesive energy of small metallic particles

A generalized bond-energy model has been developed to calculate the cohesive energy of nanoparticles by considering the different contributions of face-, edge- and corner-atoms. The model is adapted for metallic particles in a large size range from several atoms to infinity, studying their morphology, phase stability and melting point, etc.     

Particle size effects on Wulff constructions

The equilibrium structure of small particles is analysed by minimising the total surface energy of atomistic clusters. Large deviations from the bulk Wulff construction are identified for fairly large (~10 nm) particles due to sphere packing corrections. These act as additional edge terms which can be significantly larger than the true edge terms. For a simplified fcc model, it is shown that the fraction of (100) surface drops markedly as the particle size drops because of these packing effects. This can lead to very large particle size effects for a face sensitive catalytic reaction. It is also pointed out that these packing corrections link very small (< 100 atom) cluster to very large particles.     

Rough Lennard-Jones molecules

A heuristic model for pseudospherical molecules is proposed. The model interaction consists of a simple Lennard-Jones potential with an added intermolecular torque which depends on the relative ‘surface velocity’ of colliding particles. Certain unphysical features of the related rough hard sphere model can be avoided in a natural way. Mean squared forces and mean squared torques may be calculated directly from the Lennard-Jones pair correlation function. Results of molecular dynamics calculations on 108-particle rough Lennard-Jones systems are presented.     

Alkali atom chemisorption on small metal particles

A quantum mechanical model of ionic chemisorption on small metal particles is presented. The model takes into account the size dependence of the metal electronic properties and treats ionic and covalent bond contributions in a selfconsistent fashion. The binding energy and the charge at the adatom are found to be strongly size dependent.     

Fabrication and simulation of glass micromachining using CO2 laser processing with PDMS protection

An efficient synthesis route for highly luminescent silicon nanocrystal (Si-nc) films is presented. Si-ncs in the films are synthesized in the gas phase by using an argon-silane radio-frequency dielectric-barrier discharge (RF-DBD) plasma. The size of Si-ncs is well tunable by changing the resident time. The resulting Si-nc films with different oxidation degree exhibit emission across the full visible spectrum. Structural and optical characterization indicates that the red-to-green luminescence from big particles show quantum confinement effect (QCE), while this effect disappears in blue luminescence from small ones. A model is presented to explain this result. In this model, the radiative process in big particles is Band-to-Band recombination, in which surface states have a negligible impact on the QCE, while the blue emission from small Si-ncs is due to the Band-to-Bound recombination, in which surface state plays an important role, resulting in the disappearance of QCE. Additionally, obvious double-exponential decay from midsize particles is observed, in which the two kinds of recombination may coexist.     

Steps on surfaces: experiment and theory

The properties of steps in thermal equilibrium are described in the context of prediction of the stability and evolution of nanostructures on surfaces. Experimental techniques for measuring the appropriate step parameters are described, and simple lattice models for interpreting the observations are reviewed. The concept of the step chemical potential and its application to the prediction of step motion (and therefore surface mass transport) is presented in depth. Examples of the application of this step-continuum approach to experimental observations of evolution of surface morphology are presented for morphological phase transitions, the decay of metastable structures, and the spontaneous evolution of metastable structure due to kinetic instabilities.     

The robustness in dynamics of out of equilibrium bidirectional transport systems with constrained entrances

Macroscopic and microscopic long-distance bidirectional transfer depends on connections between entrances and exits of various transport mediums. Persuaded by the associations, we introduce a small system module of Totally Asymmetric Simple Exclusion Process including oppositely directed species of particles moving on two parallel channels with constrained entrances. The dynamical rules which characterize the system obey symmetry between the two species and are identical for both the channels. The model displays a rich steady-state behavior, including symmetry breaking phenomenon. The phase diagram is analyzed theoretically within the mean-field approximation and substantiated with Monte Carlo simulations. Relevant mean-field calculations are also presented. We further compared the phase segregation with those observed in previous works, and it is examined that the structure of phase separation in proposed model is distinguished from earlier ones. Interestingly, for phases with broken symmetry, symmetry with respect to channels has been observed as the distinct particles behave differently while the similar type of particles exhibits the same conduct in the system. For symmetric phases, significant properties including currents and densities in the channels are identical for both types of particles. The effect of symmetry breaking occurrence on the Monte Carlo simulation results has also been examined based on particle density histograms. Finally, phase properties of the system having strong size dependency have been explored based on simulations findings.     

Smoothed particle hydrodynamics and magnetohydrodynamics

This paper presents an overview and introduction to smoothed particle hydrodynamics and magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several ‘urban myths’ regarding SPH, in particular the idea that one can simply increase the ‘neighbour number’ more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the ndspmhd SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.     

Amplitude Instability in Two-Dimensional Hexagonal Clusters

The conditions for the formation of amplitude instabilities in two-dimensional Yukawa systems consisting of seven charged particles have been investigated. An analytical approach to searching for a criterion of the development of such instabilities based on the determination of the inflection point of a system’s potential energy when the particles deviate from their equilibrium positions is considered. The results obtained are compared with the melting criteria for extended two-dimensional systems.     

On turbulent chemical explosions into dilute aluminum particle clouds

We use a hybrid two-phase numerical methodology to investigate the flow-field subsequent to the detonation of a spherical charge of TNT with an ambient distribution of a dilute cloud of aluminum particles. Rayleigh–Taylor instability ensues on the contact surface that separates the inner detonation products and the outer shock-compressed air due to interphase interaction, which grows in time and results in a mixing layer where the detonation products afterburn with the air. At early times, the ambient particles are completely engulfed into the detonation products, where they pick up heat and ignite, pick up momentum and disperse. Subsequently, as they disperse radially outwards, they interact with the temporally growing Rayleigh–Taylor structures, and the vortex rings around the hydrodynamic structures results in the clustering of the particles by also introducing local transverse dispersion. Then the particles leave the mixing layer and quench, yet preserve their hydrodynamic ‘footprint’ even until much later; due to this clustering, preferential heating and combustion of particles is observed. With a higher initial mass loading in the ambient cloud, larger clusters are observed due to stronger/larger hydrodynamic structures in the mixing layer – a direct consequence of more particles available to perturb the contact surface initially. With a larger particle size in the initial cloud, clustering is not observed, but when the initial cloud is wider, fewer and degenerate clusters are observed. We identify five different phases in the dispersion of the particles: (1) engulfment phase; (2) hydrodynamic instability-interaction phase; (3) first vortex-free dispersion phase; (4) reshock phase; and (5) second vortex-free dispersion phase. Finally, a theoretical Buoyancy-Drag model is used to predict the growth pattern of the ‘bubbles’ and is in agreement with the simulation results. Overall, this study has provided some useful insights on the post-detonation explosive dispersal of dilute aluminum particle clouds.