Eutectic alloy microstructure: atomic force microscopy analysis

The exciting microstructures found in several eutectic alloys are a result of a cooperative growth, which is connected to the atomic transfer in the melt ahead the solid/liquid interface. In a eutectic system, the growth of solid phases depends on the simultaneous rejection of constituents to the liquid phase, which causes adjustments of the melt composition and hence, mass transport by diffusion normal to the growth direction. Generally, eutectic microstructures are examined by using optical (OM) and scanning electron microscopy (SEM). While OM may not provide the necessary resolution, the eutectic microstructure may present three-dimensional features, as a result of etching, which is not always possible to be observed by SEM. As an alternative, this paper describes the use of atomic force microscopy (AFM) in understanding micro-scale feature of a eutectic microstructure. For such a purpose, directionally solidified samples of a Ni–Al–V lamellar eutectic, a Ni–Al–Mo fibrous eutectic and a Ni–Al–Nb three-phase eutectic were examined. The results obtained provided a new picture of multi-phase microstructures and allows one to understand their new characteristics.     

Solidification of a semitransparent planar layer subjected to radiative and convective cooling

This work deals with the analysis of solidification of a semi-transparent planar layer subjected to radiative and convective cooling. Isothermal mushy-zone model is considered. Enthalpy formulation of the energy equation is solved using the lattice Boltzmann method. To compare the results, the same equation is also solved using the fully implicit finite volume method. Discrete ordinate method is used to compute the radiative information in both the approaches. Effects of radiative properties such as the extinction coefficient, the scattering albedo and refractive index on the solid fraction and temperature are analyzed. Results are validated with those available in the literature. Lattice Boltzmann method and the discrete ordinate method were found to work satisfactorily.     

Supercritical–subcritical crossover in solidification

We present formulas for the amplitude of the deflection of an unstable interface during the solidification of a pure substance. We then forecast the conditions for the appearance of either a supercritical or a subcritical pitchfork in terms of the input variables, emphasizing the importance of the depths of the two phases.     

Semi-implicit method for thermodynamically linked equations in phase change problems (SIMTLE)

Thermodynamic coupling of temperature and composition fields in phase-change problems has been a challenge for decades. A compromise has been always desired between numerical efficiency and detailed physical consideration, toward a general scheme. In the present work, a macro–micro numerical method is proposed to link the conservation equations of energy and species with the thermodynamics of the solidification problems. Firstly, the basic structure of the method, simplified with a local equilibrium assumption, is presented. The method is then extended to a multi-phase model, demonstrating a three-phase approach to the solidification of a eutectic binary alloy. Relaxing the limitations imposed by the equilibrium assumption, non-equilibrium and microscale considerations was also included subsequently by a suggested modification to the macroscopic mathematical model. Advantages gained through the general algorithm proposed are concerned with two features of the method; (a) consistency with the energy and species equations. (b) No need of a predefined solidification path; that allows for the usage of raw phase diagram curves and offers simplicity and generality for extension through complex problems (i.e. microscopic, multi-phase or non-equilibrium). A benchmark problem was employed to test the performance of the proposed method in two cases of local equilibrium and Scheil-like solidification. The obtained results were validated in comparison with available semi-analytical solution.     

Selection criterion for the growing dendritic tip in a non-isothermal binary system under forced convective flow

A free dendrite growth during solidification into external forced flow is analyzed using a sharp interface model. A criterion for selection of the stable growth mode is derived for the axisymmetric dendrite growing into non-isothermal binary system under convective flow. The criterion obtained rallies analytic results for dendrite growth under forced convection in a pure system [Ph. Bouissou, P. Pelce, Phys. Rev. A 40 (1989) 6673] and dendrite growth in a stagnant binary system [M. Ben Amar, P. Pelce, Phys. Rev. A 39 (1989) 4263].     

液态Ca7Mg3合金快速凝固过程中团簇结构的形成特性

采用分子动力学方法对液态Ca7Mg3合金凝固过程中团簇结构的形成特性进行了模拟研究. 采用双体分布函数、Honeycutt-Andersen(HA)键型指数法、原子团类型指数法(CTIM)以及遗传跟踪等方法对凝固过程中团簇结构的形成演变特性进行了分析. 结果表明: 在以冷速为1×1012 K·s-1 的快速凝固条件下, 系统形成以1551、1541、1431键型为主的非晶态结构; 二十面体基本原子团(12 0 12 0)在快速凝固过程中对非晶态结构的形成起决定性作用; 在合金凝固过程中, 团簇的稳定性不仅与构成团簇的基本原子团类型有关, 还与中心原子类型以及中心原子之间的连接方式有关. 由于(12 0 12 0)基本原子团能量较低并且在低温具有较好的遗传特性, 基本原子团之间很容易连接在一起组成更大的团簇. 所形成的团簇结构显著不同于那些由气相沉积、离子溅射等方法所获得的团簇结构.     

Analysis of a two-phase field model for the solidification of an alloy

In this paper we present some theoretical results for a system of nonlinear partial differential equations that provide a phase field model for the solidification/melting of a metallic alloy. It is assumed that two different kinds of crystallization are possible. Consequently, the unknowns are the temperature τ and the phase field functions u and v. The time derivatives ut and vt appear in the equation for τ (the heat equation). On the other hand, the equations for u and v contain nonlinear terms where we find τ.     

A front-tracking model to predict solidification macrostructures and columnar to equiaxed transitions in alloy castings

The solidified grain structure (macrostructure) of castings is predicted by process simulation using a newly extended front-tracking technique which models the growth of solid dendritic fronts through undercooled liquid during metallic alloy solidification. Such fronts are either constrained, as is the case with directed columnar growth from mould walls, or unconstrained, as is the case for multiple equiaxed growth from individual nucleating particles distributed throughout the liquid. Non-linear latent heat evolution is treated by incorporating the Scheil equation. Thermal conductivity changes with the solid fraction. A log-normal distribution of activation undercooling to initiate free growth from equiaxed nuclei is used, and the routines to deal with such growth followed by impingement of dendritic grains upon one another are verified by comparison with the results of analytical studies of simplified systems. The extensions to the model enable the predictions of equiaxed grain structure and, importantly, the columnar to equiaxed transition in inoculated alloy castings. The model is validated via comparison with experimental results. The front-tracking method is proposed as a suitable formulation for modelling alloy castings that solidify with a dendritic structure, either columnar, equiaxed, or both.     

Dispersion‐solidification liquid–liquid microextraction for volatile aromatic hydrocarbons determination: Comparison with liquid phase microextraction based on the solidification of a floating drop

Two microextraction techniques – liquid phase microextraction based on solidification of a floating organic drop (LPME‐SFO) and dispersive liquid–liquid microextraction combined with a solidification of a floating organic drop (DLLME‐SFO) – are explored for benzene, toluene, ethylbenzene and o‐xylene sampling and preconcentration. The investigation covers the effects of extraction solvent type, extraction and disperser solvents' volume, and the extraction time. For both techniques 1‐undecanol containing n‐heptane as internal standard was used as an extracting solvent. For DLLME‐SFO acetone was used as a disperser solvent. The calibration curves for both techniques and for all the analytes were linear up to 10 μg/mL, correlation coefficients were in the range 0.997–0.998, enrichment factors were from 87 for benzene to 290 for o‐xylene, detection limits were from 0.31 and 0.35 μg/L for benzene to 0.15 and 0.10 μg/L for o‐xylene for LPME‐SFO and DLLME‐SFO, respectively. Repeatabilities of the results were acceptable with RSDs up to 12%. Being comparable with LPME‐SFO in the analytical characteristics, DLLME‐SFO is superior to LPME‐SFO in the extraction time. A possibility to apply the proposed techniques for volatile aromatic hydrocarbons determination in tap water and snow was demonstrated.     

A Schur complement formulation for solving free-boundary,Stefan problems of phase change

A Schur complement formulation that utilizes a linear iterative solver is derived to solve a free-boundary, Stefan problem describing steady-state phase change via the Isotherm–Newton approach, which employs Newton’s method to simultaneously and efficiently solve for both interface and field equations. This formulation is tested alongside more traditional solution strategies that employ direct or iterative linear solvers on the entire Jacobian matrix for a two-dimensional sample problem that discretizes the field equations using a Galerkin finite-element method and employs a deforming-grid approach to represent the melt–solid interface. All methods demonstrate quadratic convergence for sufficiently accurate Newton solves, but the two approaches utilizing linear iterative solvers show better scaling of computational effort with problem size. Of these two approaches, the Schur formulation proves to be more robust, converging with significantly smaller Krylov subspaces than those required to solve the global system of equations. Further improvement of performance are made through approximations and preconditioning of the Schur complement problem. Hence, the new Schur formulation shows promise as an affordable, robust, and scalable method to solve free-boundary, Stefan problems. Such models are employed to study a wide array of applications, including casting, welding, glass forming, planetary mantle and glacier dynamics, thermal energy storage, food processing, cryosurgery, metallurgical solidification, and crystal growth.