Unified derivation of phase-field models for alloy solidification from a grand-potential functional

In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid, with a unique local composition. In the second, the interface is seen as a mixture of two phases that each retain their macroscopic properties, and a separate concentration field for each phase is introduced. It is shown here that both types of models can be obtained by the standard variational procedure if a grand-potential functional is used as a starting point instead of a free-energy functional. The dynamical variable is then the chemical potential instead of the composition. In this framework, a complete analogy with phase-field models for the solidification of a pure substance can be established. This analogy is then exploited to formulate quantitative phase-field models for alloys with arbitrary phase diagrams. The precision of the method is illustrated by numerical simulations with varying interface thickness.Comment: 36 pages, 1 figur

Dynamics of gas bubble growth in a supersaturated solution with Sievert's solubility law

This paper presents a theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution. We study systems where gas molecules completely dissociate in the solvent into two parts, thus making Sievert's solubility law valid. We show that the difference between Henry's and Sievert's laws for chemical equilibrium conditions causes the difference in bubble growth dynamics. Assuming that diffusion flux is steady we obtain a differential equation on bubble radius. Bubble dynamics equation is solved analytically for the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop. We also obtain conditions of diffusion flux steadiness. The fulfillment of these conditions is studied for the case of nucleation of water vapor bubbles in magmatic melts.Comment: 22 pages, 3 figure

Direct Observation of Martensitic Phase-Transformation Dynamics in Iron by 4D Single-Pulse Electron Microscopy

The in situ martensitic phase transformation of iron, a complex solid-state transition involving collective atomic displacement and interface movement, is studied in real time by means of four-dimensional (4D) electron microscopy. The iron nanofilm specimen is heated at a maximum rate of ∼10^(11) K/s by a single heating pulse, and the evolution of the phase transformation from body-centered cubic to face-centered cubic crystal structure is followed by means of single-pulse, selected-area diffraction and real-space imaging. Two distinct components are revealed in the evolution of the crystal structure. The first, on the nanosecond time scale, is a direct martensitic transformation, which proceeds in regions heated into the temperature range of stability of the fcc phase, 1185−1667 K. The second, on the microsecond time scale, represents an indirect process for the hottest central zone of laser heating, where the temperature is initially above 1667 K and cooling is the rate-determining step. The mechanism of the direct transformation involves two steps, that of (barrier-crossing) nucleation on the reported nanosecond time scale, followed by a rapid grain growth typically in ∼100 ps for 10 nm crystallites

Molecular Dynamics Simulation of Solvent-Polymer Interdiffusion. I. Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t^{1/2}, which is expected for Fickian type of diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.Comment: 17 pages and 7 figure

Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries

In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction-diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelled droplet.Comment: This document is the revised version of arXiv:0912.1288v

Diffusion Coefficients of a Highly Nonideal Ternary Liquid Mixture: Cyclohexane–Toluene–Methanol

To better understand diffusion phenomena in highly nonideal ternary liquid mixtures, cyclohexane–toluene–methanol is studied by equilibrium molecular dynamics (EMD) simulation. Intradiffusion and Maxwell–Stefan (MS) diffusion coefficients, being strictly kinetic properties, are predicted by EMD over the entire composition range at ambient conditions. The thermodynamic contribution to the Fick diffusion coefficients is studied with an excess Gibbs energy model. Predictive results from the combination of these two approaches are in convincing agreement with experimental Fick diffusion coefficient data. Different aspects determining the composition dependence of diffusion coefficients, such as their behavior at the binary limits, hydrogen bonding, and stability criteria, are discussed. While the intradiffusion coefficients exhibit only a weak composition dependence, the MS diffusion coefficients are strongly affected by the nonideality of the present mixture. Fick diffusion coefficients reveal pronounced diffusive coupling effects and are mainly governed by the thermodynamic contribution, especially in the vicinity of the miscibility gap

The effect of the regular solution model in the condensation of protoplanetary dust

We utilize a chemical equilibrium code in order to study the condensation process which occurs in protoplanetary discs during the formation of the first solids. The model specifically focuses on the thermodynamic behaviour on the solid species assuming the regular solution model. For each solution, we establish the relationship between the activity of the species, the composition and the temperature using experimental data from the literature. We then apply the Gibbs free energy minimization method and study the resulting condensation sequence for a range of temperatures and pressures within a protoplanetary disc. Our results using the regular solution model show that grains condense over a large temperature range and therefore throughout a large portion of the disc. In the high temperature region (T > 1400 K) Ca-Al compounds dominate and the formation of corundum is sensitive to the pressure. The mid-temperature region is dominated by Fe(s) and silicates such as Mg2SiO4 and MgSiO3 . The chemistry of forsterite and enstatite are strictly related, and our simulations show a sequence of forsterite-enstatite-forsterite with decreasing temperature. In the low temperature regions (T < 600 K) a range of iron compounds and sulfides form. We also run simulations using the ideal solution model and see clear differences in the resulting condensation sequences with changing solution model In particular, we find that the turning point in which forsterite replaces enstatite in the low temperature region is sensitive to the solution model. Our results show that the ideal solution model is often a poor approximation to experimental data at most temperatures important in protoplanetary discs. We find some important differences in the resulting condensation sequences when using the regular solution model, and suggest that this model should provide a more realistic condensation sequence.Comment: MNRAS: Accepted 2011 February 16. Received 2011 February 14; in original form 2010 July 2

Statics and Dynamics of Colloid-Polymer Mixtures Near Their Critical Point of Phase Separation: A Computer Simulation Study of a Continuous AO Model

We propose a new coarse-grained model for the description of liquid-vapor phase separation of colloid-polymer mixtures. The hard-sphere repulsion between colloids and between colloids and polymers, which is used in the well-known Asakura-Oosawa (AO) model, is replaced by Weeks-Chandler-Anderson potentials. Similarly, a soft potential of height comparable to thermal energy is used for the polymer-polymer interaction, rather than treating polymers as ideal gas particles. It is shown by grand-canonical Monte Carlo simulations that this model leads to a coexistence curve that almost coincides with that of the AO model and the Ising critical behavior of static quantities is reproduced. Then the main advantage of the model is exploited - its suitability for Molecular Dynamics simulations - to study the dynamics of mean square displacements of the particles, transport coefficients such as the self-diffusion and interdiffusion coefficients, and dynamic structure factors. While the self-diffusion of polymers increases slightly when the critical point is approached, the self-diffusion of colloids decreases and at criticality the colloid self-diffusion coefficient is about a factor of 10 smaller than that of the polymers. Critical slowing down of interdiffusion is observed, which is qualitatively similar to symmetric binary Lennard-Jones mixtures, for which no dynamic asymmetry of self-diffusion coefficients occurs.Comment: 42 pages, 17 figures, submitted to J. Chem. Phy

Hydrogen charging in nickel and iron and its effect on their magnetic properties

The current study was undertaken to explore the possibility of detecting hydrogen cavitation in magnetic materials through magnetic propertymeasurements. It is known that dissolved hydrogen in a material causes microvoids. These voids may affect the structure‐sensitive magnetic properties such as coercivity and remanence. In this study, hydrogen was introduced into nickel and iron by two processes, namely thermal charging and cathodic charging. The effect on the magnetic properties was measured. In addition, the variation of the magnetic properties with porosity was studied

Glycerol monolaurate prevents mucosal SIV transmission

Although there has been great progress in treating human immunodeficiency virus 1 (HIV-1) infection1, preventing transmission has thus far proven an elusive goal. Indeed, recent trials of a candidate vaccine and microbicide have been disappointing, both for want of efficacy and concerns about increased rates of transmission2–4. Nonetheless, studies of vaginal transmission in the simian immunodeficiency virus (SIV)–rhesus macaque (Macacca mulatta) model point to opportunities at the earliest stages of infection in which a vaccine or microbicide might be protective, by limiting the expansion of infected founder populations at the portal of entry5,6. Here we show in this SIV–macaque model, that an outside-in endocervical mucosal signalling system, involving MIP-3α (also known as CCL20), plasmacytoid dendritic cells and CCR5+ cell-attracting chemokines produced by these cells, in combination with the innate immune and inflammatory responses to infection in both cervix and vagina, recruits CD4+ T cells to fuel this obligate expansion. We then show that glycerol monolaurate—a widely used antimicrobial compound7with inhibitory activity against the production of MIP-3α and other proinflammatory cytokines8—can inhibit mucosal signalling and the innate and inflammatory response to HIV-1 and SIV in vitro, and in vivo it can protect rhesus macaques from acute infection despite repeated intra-vaginal exposure to high doses of SIV. This new approach, plausibly linked to interfering with innate host responses that recruit the target cells necessary to establish systemic infection, opens a promising new avenue for the development of effective interventions to blockHIV-1 mucosal transmission