Dynamics Of Phase Boundaries Research Articles

Density Gradient Model in Spherically Symmetric Formulation and Its Explicit-Implicit Dissipative Discretization for the Study of Phase Boundary Dynamics

Density Gradient Model in Spherically Symmetric Formulation and Its Explicit-Implicit Dissipative Discretization for the Study of Phase Boundary Dynamics

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is—at present—no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469: 111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argon-methane mixtures in several space dimensions. To our knowledge, such compressible two-phase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

Phase boundary dynamics of bubble flow in a thick liquid metal layer under an applied magnetic field

Dynamic neutron radiography is used to observe the effect of a transverse magnetic field on argon bubbles rising through a thick layer of liquid gallium without interactions with the container walls.

(Adiabatic) phase boundaries in a bistable chain with twist and stretch

Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli.

Cyclic Supersaturation and Triple Phase Boundary Dynamics in Germanium Nanowire Growth

Video-rate environmental transmission electron microscopy of Au-catalyzed chemical vapor deposition of Ge nanowires shows that growth kinetics are linked to an oscillatory behavior at the liquid−solid interface near the triple phase boundary (TPB), where the nanowire surface consists of an oblique facet. A nanowire growth cycle starts by preferential Ge precipitation at the TPB, which increases the wetting angle and Ge supersaturation of the liquid AuGe catalyst. With a continuously rising Ge supersaturation, the kinetic barrier for Ge bilayer nucleation falls until step nucleation occurs. Subsequent step flow creates a (111)-type plane at the nanowire growth front and hence rapidly decreases the Ge supersaturation in the catalyst. This leads to the destabilization and partial dissolution of the Ge initially stored in the rough TPB area, i.e., completes the growth cycle. The results and arguments are general and based on few system specific assumptions, therefore may be applicable to other nanowire systems, and are relevant to general nucleation and liquid−solid interface dynamics in dimensionally confined systems.

Shocks versus kinks in a discrete model of displacive phase transitions

We consider dynamics of phase boundaries in a bistable one-dimensional lattice with harmonic long-range interactions. Using Fourier transform and Wiener-Hopf technique, we construct traveling wave solutions that represent both subsonic phase boundaries (kinks) and intersonic ones (shocks). We derive the kinetic relation for kinks that provides a needed closure for the continuum theory. We show that the different structure of the roots of the dispersion relation in the case of shocks introduces an additional free parameter in these solutions, which thus do not require a kinetic relation on the macroscopic level. The case of ferromagnetic second-neighbor interactions is analyzed in detail. We show that the model parameters have a significant effect on the existence, structure, and stability of the traveling waves, as well as their behavior near the sonic limit.

Phase boundary dynamics: transitions between ordered and disordered lipid monolayers

Based on a general thermodynamical theory of mass and momentum, we propose and investigate a new phase field model for small transition layers between two spatially separated phases with intersecting free energy functions. We use a phase fraction, that only depends on the ratio of the two density components. From the phase field model we derive conditions for the sharp interface velocity and density jumps. The general model is motivated by and applied to the dynamics of lipid monolayers, which appear as surfactant on the strongly expanded and compressed thin water film of lung alveoli. While the \emph{liquid condensed ordered phase} (LC) of a flat lipid monolayer is characterized by high viscosity and limited compressibility, the \emph{liquid expanded disordered phase} (LE) is dominated by diffusion and high compressibility. In order to perform the asymptotic transition layer analysis at moving phase boundaries, a new nonlinear free energy interpolation model is proposed whose excess energy, in comparison to standard linear interpolations, contains an energy hump that has to be surpassed in a permissive transition from one phase to the other. This leads to a unique density jump condition in the case that the ordered phase is extending, whereas in the retracting case the jump densities are not restricted. The transition profiles and the resulting interface speed are numerically determined for a typical example by solving the nonlinear degenerate ODE-system. In a simplified 1-dimensional situation with low Reynolds number, the approximative macroscopic system of differential equations with moving sharp interface is numerically solved and interpreted in application to surfactant monolayers in lung alveoli.

Crystallographic preferred orientation produced by diffusional creep of harzburgite: Effects of chemical interactions among phases during plastic flow

Experimental deformation experiments have been conducted on fine‐grained, two‐phase aggregates of olivine and orthopyroxene to investigate the role of grain and phase boundary sliding on rheology and fabric development. A suite of large‐strain (γ ≥ 1) general shear experiments conducted at T = 1200°C and P = 1.6 GPa on aggregates ranging from 65 to 0 vol % orthopyroxene, to characterize the evolution of fabric, were complemented by small‐strain axial compression experiments at T = 1200°C and P = 0.3 GPa, to better constrain the rheology. Microstructural and rheological data suggest that deformation of these two‐phase aggregates in the diffusion creep regime occurs via interface‐reaction‐controlled diffusion creep that is accompanied by extensive migration of olivine‐orthopyroxene phase boundaries. The resulting rheologies suggest that olivine + orthopyroxene composites are weaker than the olivine end‐member at the conditions tested. Physically, this behavior arises because long‐range, i.e., grain‐scale, diffusion of Si4+ is unnecessary in these pseudobinary two‐phase aggregates. We further demonstrate that interface‐controlled diffusion creep leads to strong crystallographic preferred orientations (CPO) of the component minerals, which develops in the near absence of dislocation activity. The CPO formed in these anhydrous, low‐stress experiments has the olivine a axis aligned perpendicular to the flow direction (“type B” fabric) argued by some to be the unique result of deformation under conditions of high differential stress and high water fugacity. Phase boundary dynamics, thus, are argued as a significant factor in the accumulation of strain in polyphase aggregates.

Multi‐phase field systems with anisotropic surface energies

AbstractThe dynamics of phase boundaries in multi‐phase systems has been studied with a focus on interfacial energy contributions. A diffuse interface model based on the phase field methodology has been derived which, in the sharp interface limit, is related to a classical description with moving hypersurfaces modeling the phase boundaries. A nontrivial task in the case of multiple phases is to let the surface energies enter the equations of the diffuse interface model in the right way. A gradient potential and a multi‐well potential of obstacle type are presented that allow for a wide class of surface anisotropies. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computation of dynamical phase transitions in solids

This paper deals with the dynamics of phase boundaries in a nonlinear elastic two-phase material. We consider the elasticity system in 1D and the equations of anti-plane shear motion in 2D, where effects of viscosity and capillarity are neglected. These first-order conservation laws allow to represent phase boundaries as shock-like sharp interfaces. However, in contrast to what is known for homogeneous materials, the entropy inequality does not select a unique solution, and an additional criterion, the so-called kinetic relation, is required. Based on a scheme introduced by Hou, Rosakis and LeFloch [T. Hou, Ph. Rosakis, P.G. LeFloch, A level-set approach to the computation of twinning and phase-transition dynamics, J. Comput. Phys. 150 (1999) 302–331] we focus on the numerical solution of a specific model system. Using a level-set technique to enforce the kinetic relation on the discrete level leads to a reformulation of the original system in the form of a system of conservation laws coupled to a Hamilton–Jacobi equation for each phase boundary. The numerical method for the reformulated system is constructed for unstructured meshes (in 2D), and a self-adaptive algorithm is introduced. In the 1D-case we show that the reformulated system has a solution that corresponds to exact dynamical phase boundaries of the elasticity system which obey the kinetic relation. To validate the method in 2D, we present computations on the interaction of a plane wave with a phase boundary. The efficiency of the adaptation mechanism is demonstrated by an example showing the development of microstructures by twinning.

Structure and dynamics of dense monolayers of no adsorbed on Rh(111) in equilibrium with the gas phase in the Torr pressure range.

Using scanning tunneling microscopy, we show the phase transition between new structures of NO on Rh(111) in equilibrium with the gas phase near 300 K, in the Torr pressure range. Two phases with (2 x 2) and (3 x 3) periodicity transform into each other as the pressure and temperature change around the equilibrium P-T line. By measuring P and T at coexistence, we determined the heat of adsorption in the (3 x 3) structure. From the phase boundary dynamics, the activation energy barrier between phases were estimated. The results demonstrate that unique information can be obtained from high-pressure and high-temperature studies.

A microscopic derivation of macroscopic sharp interface problems involving phase transitions

Macroscopic free boundary problems involving phase transitions (e.g., the classical Stefan problem or its modifications) are derived in a unified way from a Hamiltonian based on a general set of microscopic interactions. A Hamiltonian of the form ℋ + ∑x,x′J(x−x′)ϕ(x)ϕ(x′) leads to differential equations as a result of Fourier transforms. Expanding the Fourier transform ofJ in powers ofq (the wave number), one can truncate the series at anarbitrary orderM, and thereby obtainMth-order differential equations. An asymptotic analysis of these equations in various scalings of the physical parameters then implies limits which are the standard macroscopic models for the dynamics of phase boundaries.

Theory of q-soliton and phase boundary dynamics in a (2+1)-dimensional O(3)-antiferromagnet

The classical antiferromagnet is studied in the approximation of a continuous (2+1)-dimensional O(3)-model supplemented by a system of phase slip boundaries. Antiferromagnetic ordering at T > 0 is supposed to be destroyed by dynamic effects of the q-soliton plasma on the phase boundary network. Dynamic effects are studied via Lorentz invariance of the action, where phason speed c replaces the light speed. A qualitative theory of the action of translating and rotating q-solitons and mobile phase boundaries as well as a quantization of these objects is developed.

Conserved-phase field system: Implications for kinetic undercooling.

A model is proposed to study the dynamics of phase boundaries using a conserved order parameter. A relation between the temperature and the curvature, surface tension, and velocity is derived and compared with the analogous system of equations using a nonconserved order parameter. The kinetic-undercooling term is altered, thereby changing the stability properties of an interface.

Amorphous-crystalline boundary dynamics in cw laser crystallization

Two theoretical descriptions have been developed for the phase-boundary dynamics during crystallization of amorphous films by scanning with the slit image of a cw energy beam. The first reduces the problem to the solution of a one-dimensional integral equation, which allows a choice of initial conditions. Depending on the background temperature, numerical solutions yield either periodic or runaway motion of the amorphouscrystalline ($a\ensuremath{-}c$) boundary, as observed in experiments on scanned laser crystallization of thin films of $a$-Ge on fused-silica substrates. The calculations give a semiquantitative fit to the experimental results for the spatial periodicity observed in the crystallized films as a function of background temperature. Profiles of film temperature as a function of distance from the laser image at successive times have been computed for both the periodic and runaway cases. The model qualitatively explains many of the effects observed during scanned cw laser crystallization, including periodic fluctuations in light emission. The second theoretical description is a more exact two-dimensional treatment applicable only to cases of steady-state motion of the $a\ensuremath{-}c$ boundary, which can rigorously handle heat flow into the substrate. This treatment has been used to calculate the boundary velocity during steady-state runaway. The dependence of this velocity on background temperature and on film and substrate thermal properties and thickness has been determined from the theory. At the minimum background temperature required for runaway the calculated value of the steady-state velocity ${v}_{\mathrm{ac}}$ is $\ensuremath{\sim}140$ cm/sec for the case of a Ge film 0.3-\ensuremath{\mu}m thick on a fused-silica substrate 1-mm thick. Experimental values for ${v}_{\mathrm{ac}}$ lie in the range 100-300 cm/sec. However, comparison of the theory with experiment suggests the presence of a thermal barrier between substrate and film, which would modify the theoretical results for ${v}_{\mathrm{ac}}$. A class of laser-guided steady-state solutions has been obtained for which the boundary velocity is equal to the laser scanning velocity but lower than the boundary velocity for uncontrolled runaway.

Measurement of Phase Boundary Dynamics During Scanned Laser Crystallization of Amorphous Ge Films

ABSTRACTTwo techniques have been used to measure the velocity of the amorphous-crystalline boundary during scanned laser crystallization of amorphous Ge films on fused-silica substrates. Values in the vicinity of 200 cm sec-1 have been measured by both methods. The results obtained by the first technique, an optical transmission method, confirm our theoretical model for the periodic motion of the boundary. The measurements made by the second technique, which is based on an examination of the structural features obtained at laser scanning rates up to about 600 cm sec-1 , show the boundary velocity to be rather insensitive to film thickness and background temperature. Controlled crystallization is expected to require stability of the laser beam power.