Solid-liquid Interface Motion Research Articles

Kinetics of solid-liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon.

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal-liquid interface featuring an increase up to a maximum at 10-30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson-Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Thermal performance of shell and tube latent heat storage unit: Comparative assessment of horizontal and vertical orientation

Abstract A comparative thermal performance assessment is reported for vertical and horizontal orientation of shell and tube type Latent Heat Storage Unit (LHSU) using stearic acid (melting point of 55.7–56.6 °C) as Phase Change Material (PCM) and water as Heat Transfer Fluid (HTF). Total 45 thermocouples are used in radial, axial and angular directions to measure the temperature distribution in the PCM. In horizontal LHSU, temperature in the upper half of the horizontal diametric plane reaches the melting point faster due to natural convection. As a result, the upper half melts earlier than the lower half. In order to demonstrate the motion of solid-liquid interface, liquid fraction contours are presented. For vertical LHSU, melting front moves in a conical fashion around the vertical plane with faster melting at upper axial locations. Experimental analysis suggests that horizontal LHSU is better for part load operation as compared to vertical LHSU, as it requires lesser time to melt half of the PCM mass. Energy storage/retrieval rate during melting and solidification is also compared for both the LHSU configurations.

The Effect of a Magnetic Field on the Melting of Gallium in a Rectangular Cavity

ABSTRACTThe role of magnetic field and natural convection on the solid–liquid interface motion, flow, and heat transfer during melting of gallium on a vertical wall is reported in this paper. The classical geometry consisting of a rectangular cavity with uniform but different temperatures imposed at two opposite side walls, insulated top, and bottom walls is considered. The magnetic field is imposed in the horizontal direction. A numerical code is developed to solve for natural convection coupled to solid–liquid phase transition and magnetic effects. The corresponding streamlines and isotherms predicted by the numerical model serve to visualize the complicated flow and temperature field. The interplay between the conduction and convection modes of heat transfer stimulated by the combination of the buoyancy-driven flow and the Lorentz force on the fluid due to the magnetic field are studied. The results show that the increase of Rayleigh number promotes heat transfer by convection, while the increase of Hartmann number dampens the strength of circulating convective currents and the heat transfer is then mainly due to heat conduction. These results are applicable in general to electrically conducting fluids and we show that magnetic field is a vital external control parameter in solid–liquid interface motion.

Non parabolic interface motion for the 1-D Stefan problem: Dirichlet boundary conditions

Over a finite 1-D specimen containing two phases of a pure substance, it has been shown that the liquid-solid interface motion exhibits parabolic behavior at small time intervals. We study the interface behavior over a finite domain with homogeneous Dirichlet boundary conditions for large time intervals, where the interface motion is not parabolic due to finite size effects. Given the physical nature of the boundary conditions, we are able to predict exactly the interface position at large time values. These predictions, which to the best of our knowledge, are not found in the literature, were confirmed by using the heat balance integral method of Goodman and a non-classical finite difference scheme. Using heat transport theory, it is shown as well, that the temperature profile within the specimen is exactly linear and independent of the initial profile in the asymptotic time limit. The physics of heat transport provides a powerful tool that is used to fine tune the numerical methods. We also found that in order to capture the physical behavior of the interface, it was necessary to develop a new non-classical finite difference scheme that approaches asymptotically to the predicted interface position. We offer some numerical examples where the predicted effects are illustrated, and finally we test our predictions with the heat balance integral method and the non-classical finite difference scheme by studying the liquid-solid phase transition in aluminum.

Melting inside a horizontal cylindrical capsule

The role of natural convection on solid-liquid interface motion during constrained melting within a horizontal cylindrical capsule was investigated. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid-liquid phase change. Flow patterns for different Rayleigh numbers are presented. The resulting melt shapes and the temperature in the PCM provide conclusive evidence of the importance of natural convection on heat transfer in the melt region.

Effect Of Natural Convection On Directional Solidification Of Pure Metal

AbstractThe paper is focused on the modeling of the directional solidification process of pure metal. During the process the solidification front is sharp in the shape of the surface separating liquid from solid in three dimensional space or a curve in 2D. The position and shape of the solid-liquid interface change according to time. The local velocity of the interface depends on the values of heat fluxes on the solid and liquid sides. Sharp interface solidification belongs to the phase transition problems which occur due to temperature changes, pressure, etc. Transition from one state to another is discontinuous from the mathematical point of view. Such process can be identified during water freezing, evaporation, melting and solidification of metals and alloys, etc.The influence of natural convection on the temperature distribution and the solid-liquid interface motion during solidification of pure copper is studied. The mathematical model of the process is based on the differential equations of heat transfer with convection, Navier-Stokes equation and the motion of the interface. This system of equations is supplemented by the appropriate initial and boundary conditions. In addition the continuity conditions at the solidification interface must be properly formulated. The solution involves the determination of the temporary temperature and velocity fields and the position of the interface. Typically, it is impossible to obtain the exact solution of such problem. The numerical model of solidification of pure copper in a closed cavity is presented, the influence of the natural convection on the phase change is investigated. Mathematical formulation of the problem is based on the Stefan problem with moving internal boundaries. The equations are spatially discretized with the use of fixed grid by means of the Finite Element Method (FEM). Front advancing technique uses the Level Set Method (LSM). Chorin’s projection method is used to solve Navier-Stokes equation. Such approach makes possible to uncouple velocities and pressure. The Petrov-Galerkin formulation is employed to stabilize numerical solutions of the equations. The results of numerical simulations in the 2D region are discussed and compared to the results obtained from the simulation where movement of the liquid phase was neglected.

Unsteady Growth ofBaB2O4Single Crystal from High-Temperature Solution

Two-dimensional growth ofBaB2O4single crystal from high-temperature solution was performed, and the motion of solid-liquid interface was observed in real time by differential interference microscopy. Results show that the solid-liquid interface exhibits the morphology of a vicinal face where steps with height of several microns are observed. The measurements of growth rate V and step propagating velocityυshow that both V andυfluctuate by up to 40∼50% of their average values, respectively, under constant external conditions. Such intrinsic fluctuations with time interval of the order of one second is mainly the result of step bunching, which has been confirmed by the gradual decrease of step spacing when approaching the edge of the growing interface. Besides above fluctuations, a longer-period oscillation of V (period interval of 4∼5 seconds) is obtained for relatively rapid growth, which is triggered by the periodical alteration of step propagating directions.

In Situ Fast Temperature Measurement of Silicon Thin Films during the Excimer Laser Annealing

The formation and growth mechanism of polysilicon grains in thin films via laser annealing of amorphous silicon thin films are studied. The complete understanding of the mechanism is crucial to improve the thin film transistors used as switches in the active matrix liquid crystal displays. To understand the recrystallization mechanism, the temperature history and liquidsolid interface motion during the excimer laser annealing of 50-nm thick amorphous and polysilicon films on fused quartz substrates are intensively investigated via in-situ time-resolved thermal emission measurements, optical reflectance and transmittance measurements at near infrared wavelengths. The front transmissivity and reflectivity are measured to obtain the emissivity at the 1.52 μm wavelength of the probe IRHeNe laser to improve the accuracy of the temperature measurement. The melting point of amorphous silicon is higher than that of crystalline silicon of 1685 K by 100-150 K. This is the first direct measurement of the melting temperature of amorphous silicon thin films. It is found that melting of polysilicon occurs close to the melting point of crystalline silicon. Also the optical properties such as reflectance and transmittance are used to determine the melt duration by the detecting the difference of the optical properties of liquid silicon and solid silicon.

Growth of NaBi(WO4)2 Dendrite and Mechanism

The solid–liquid interface motion of NaBi(WO4)2 (NBWO) meltcrystal growth is observed in an in situ system, in which the wholeprocesses of interface transition from flat interface and cellular todendrite are visualized. The spacing of the dendrite under smallertemperature gradient turns out to be larger than that under largertemperature gradient, which is found to be sensitive to the temperaturedistribution. The mechanism of dendrite growth of NBWO is studied basedon the model of the growth units of anion coordination polyhedra. The{ 001} face has two apex links, so it shows higher stability and hashigh growth rate and forms the arm of dendrite, whereas the { 010} facehas only one apex link, and thus shows relative slower growth rate andfirstly forms the branches.

High-Quality Poly-Si Crystallization Technology Based on Laser-Induced Melting and Resolidification Dynamics of Si Thin Films.

The liquid-solid interface motion and the temperature history of thin Si films during short pulse ( 200 K) followed by spontaneous nucleation into fine-grained material is observed. Lateral crystal growth is induced by fluence distribution leading to spatial control of partial/complete melting. However, growth length is limited by the triggering of spontaneous nucleation in supercooled liquid Si and lateral solidification velocity is measured to be about 7.0 m/s. To enhance the lateral growth, the pulse-duration-controlled solid-state laser is utilized. This sequential crystal growth is found to extend over 10 μm in the lateral direction. The validity of the method is confirmed by superior TFT characteristics of high field-effect mobility (n-ch μ > 460 cm2/Vs) with low threshold voltage deviation (Vth: σ < 0.07 V).

In-situ Observation of Laser-induced Melting and Resolidification Dynamics of Si Thin Films

The liquid-solid interface motion and the temperature history of thin Si films during short pulse (FWHM = 25 ns) excimer laser annealing are observed by in-situ diagnostics. Substantial supercooling (> 200 K) followed by spontaneous nucleation into fine-grained material is observed. Lateral crystal growth is limited by the triggering of spontaneous nucleation in supercooled liquid Si, and the lateral solidification velocity is measured to be about 7.0 m/s. To enhance the lateral growth, the pulse-duration-controlled solid-state laser is utilized. This sequential crystal growth is found to extend over 5 μm in the lateral direction. The validity of the method is confirmed by superior TFT characteristics of high field-effect mobility (n-ch μ > 460 cm2/Vs).

Extended thermodynamical analysis of a motion of the solid-liquid interface in a rapidly solidifying alloy

On the basis of extended irreversible thermodynamics @D. Jou, J. Casas-Vazquez, and G. Lebon, Rep. Prog. Phys. 51, 1005 ~1988!; 62, 1035 ~1999!# an analysis of the solid-liquid interface motion is presented. In addition to the formalism of the classic irreversible thermodynamics of Onsager and Prigogine, a space of independent thermodynamic variables is extended by introducing the solute diffusion flux in consistency with the extended thermodynamic approach to local nonequilibrium processes. Considering the rapid solidification front motion, when the crystal growth velocity is of the order or even greater than the speed for solute diffusion, a local nonequilibrium at the solid-liquid interface and inside bulk liquid is adopted by the model. Taking into account the solute diffusive speed at the phase interface and the finite speed of solute diffusive propagation in bulk system, the equations for thermodynamical fluxes, conjugated driving forces, the Gibbs free energy change on solidification, and liquidus line slope are derived. A discussion of the outcomes predicted by the present model and a comparative analysis of the model predictions with experimental data are made.

Inverse method with heat and entropy transport in solidification processing of materials

An inverse formulation is presented for phase change heat transfer with applications in materials processing such as casting solidification. The scheme predicts the proper transient boundary conditions in order to achieve a prescribed solid–liquid interface motion, as well as corresponding desired interface characteristics (i.e. planar interface). In addition to heat transfer, the model considers entropy transport for effective enhancement of the overall formulation. In particular, the second law of thermodynamics is applied in a corrective manner to support stable computations in the event of non-physical numerical results, such as numerical oscillations. Both heat and entropy transport models are implemented in a control-volume-based finite element formulation of the phase change governing equations. Numerical results are presented for sample problems in order to examine the performance of the inverse algorithm. These results indicate promising performance and good agreement with available analytic solutions. In the application problems, numerical stability is achieved with entropy based corrections of computations during solidification.

Model for isothermal pattern formation of growing crystals in undercooled binary alloys

Using the model of local non-equilibrium solidification, which takes into account deviations from local thermodynamical equilibrium at the interface and bulk phases, a model for pattern formation of crystals in isothermal undercooled binary alloys is presented. The model equations describe the kinetics of the liquid-solid interface motion and local non-equilibrium solute diffusion in the liquid phase. For the self-consistency of the model, we have also taken into account the solute trapping at the interface and deviation of the liquidus line from its equilibrium value using local non-equilibrium diffusion. A main feature of the model equations is the inclusion of crystal growth velocities which are of the order of the diffusion speed in the bulk liquid. This allows one to describe rapid solidification in deeply undercooled alloys. To solve numerically the problem of the growth of crystals and obtain their morphology, an approximation for the model differential equations is formulated using the finite-difference technique.

Thermal transport in melting and recrystallization of amorphous and polycrystalline Si thin films

The liquid–solid interface motion and temperature history of thin Si films during excimer laser annealing are observed by in situ experiments combining time-resolved (∼1 ns) electrical conductance, optical reflectance/transmittance at visible and near-IR wavelengths and thermal emission measurements. For laser energy densities causing partial melting, the maximum temperature remains close to the melting point of amorphous silicon (a-Si). When complete melting occurs, substantial supercooling is observed, followed by spontaneous nucleation. These phase transformations are consistent with the recrystallized poly-Si morphologies. It is also found that the melting of poly-Si occurs close to the melting point of crystalline silicon. This temperature is higher than the melting point of a-Si by about 100–150 K.

Melting and resolidification dynamics of a-Si and poly-Si thin films during excimer laser annealing

ABSTRACTThe liquid-solid interface motion and the temperature history of thin Si films during excimer laser annealing are observed by in-situ experiments combining time-resolved (∼Ins) electrical conductance, optical reflectance/transmittance at visible and near-IR wavelength, and thermal emission measurements. The existence of partial and complete melting regimes is elucidated. In the partial melting regime, the maximum temperature remains close to the melting point of aSi, since the laser energy is consumed on the latent heat of phase-change. In the complete melting regime, substantial supercooling, followed by homogeneous nucleation is observed. These phase transformations are consistent with the recrystallized poly-Si morphologies.

Theory of Scholte, leaky Rayleigh, and lateral wave excitation via the laser-induced thermoelastic effect

The analysis of the laser-induced thermoelastic excitation of acoustic waves propagating along a plane interface between two elastic media is presented. The general solution for the interface motion is derived. The detailed description of the liquid–solid interface motion caused by the photoexcited leaky Rayleigh, Scholte and lateral wave in the liquid is given both in frequency and time domain. The presented theory predicts that laser-induced thermoelastic stresses in the liquid and the solid can contribute in phase to the excitation of a Scholte wave and that the lateral wave excitation is suppressed when the light penetration depth and Scholte wave penetration depth in the liquid are equal. The obtained analytical solutions provide necessary theoretical background for the optimization of the laser-induced generation of interface waves in experiments.

Performance indicators for solar pipes with phase change storage

Performance indicators for a solar pipe system in which solar radiation is stored as latent heat of a phase changing material are proposed. These performance indicators are aimed at serving as a yardstick by which such multivariables systems are evaluated. The indicators are the melt and solidification times obtained for standardized systems and conditions. These indicator enable the comparison between the suitability of systems with different materials and configurations to store and release thermal energy. The indicators are obtained from numerical solutions of the nonlinear heat conduction problem of the axisymmetric liquid-solid interface motion within the solar pipe. Longitudinal dimension required for the determination of the solidification time is added by an axial superposition of axisymmetric sections. This simplified approach enables a simple numerical solution for an otherwise complicated problem. Estimates of performance characteristics that are based on a simplified model and realistic materials point to the practical potential of solar pipe utilization.

Simulation of porosity reduction in random structures

We describe an algorithm for computing the motion of a solid-liquid interface in 2D, which is applicable to geological pressure solution or to pressure sintering. The backward motion (toward the solid) of the interface is due to dissolution of the solid, and the forward motion (away from the solid) is due to the inverse process of reprecipitation. The interface velocity is assumed proportional to the difference between the solubility of the solid and the concentration of the solution. The former is dependent upon stress (the phenomenon of “pressure solution”), so our algorithm must also keep track of the stress. We use a Lagrangian grid, with constant-stress periodic boundary conditions. The method has been applied to porosity reduction in sandstone. It is applicable to other interface-following problems, such as freezing, if the motion is slow enough that heat transport is not rate-limiting.

EXPERIMENTAL STUDIES OF MELTING PHENOMENA FROM A CONSTANT HEAT FLUX VERTICAL PLATE

This paper reports experimental studies on the melting phenomena of phase-change material (PCM) when constant heat flux is applied to the PCM in a rectangular enclosure. Heat transfer from a vertical heating plate, solid-liquid interface motion, and temperature distributions in the PCM during the complete melting process have been investigated. The transient melting phenomena is described in terms of the Fourier number multiplied by the modified Stephan number, i.e., Fo Ste*. The result of the study reveals that at Fo Ste* + 0.6, the natural-convection mode in the liquid phase of the PCM becomes dominant, and the ratio of the melted PCM volume to the initial volume is likely to be constant in the tested range