High-temperature differential scanning calorimetry was used to understand the thermal properties of Si-rich metal–silicon alloys. Insoluble metals (A and B) were found to produce an alloy with discrete ASi2 and BSi2 dispersed phases. In contrast, metals that form a solid solution result in a dispersed phase that has a composition of AxB1−xSi2, where x varies continuously across each inclusion. This complex composition distribution is putatively caused by differences in the solidification temperatures of ASi2 versus BSi2. Though this behavior was observed for several different combinations of metals, we focus here specifically on the Cr/V/Si system. To better understand the range and most probable element concentrations in the dispersed silicide domains, a method was devised to generate histograms of their Cr and V concentrations from energy-dispersive X-ray spectroscopy hyperspectral images. Varying the Cr/V/Si ratio was found to change the shape of the element histograms, indicating that the distribution of silicide compositions that form is controlled by the input composition. Adding aluminum was found to result in dispersed phases that had a single composition rather than a range of Cr and V concentrations. This demonstrates that aluminum can be an effective additive for altering solidification kinetics in silicon alloys.

The solute equilibrium partition coefficients (ki) of C, Si, Mn, P, and S in high sulfur steel during the solidification process were investigated by the thermodynamic calculation. The effect of MnS precipitation on ki was explored. The results showed that the precipitation of MnS inclusion would influence the concentrations of solutes Mn and S, leading to the changing of ki. Due to the precipitation of MnS, the kC and kS decreased first and then increased with temperature decreasing, while kSi, kMn, and kP changed monotonously. The impacts of solidification temperature on kSi and kMn were greater than that on kC, kS, and kP. With the increase of S content, kC, kSi, and kP increased while kMn and kS decreased. Whereas, an opposite effect was found with the increase of Mn content. The order of influence extent by S and Mn contents was kSi > kS > kMn > kC > kP.

The solidification of undercooled Ni–3.3 wt% B alloy was studied by high-speed video analysis and microstructural analysis. For moderate initial undercooling (ΔTp = 75 K), the solidification interface for primary phase transformation manifests a shape of a planar dendrite, and possesses an constant growth velocity, for eutectic transformation whereas the interface presents multi-dendrite shape and spasmodic growth, so that a constant velocity cannot describe the interface exactly. These differences suggest that primary phase solidification is controlled by far-distance diffusion while eutectic solidification by short-distance diffusion. For large initial undercooling (ΔTp = 262 K), a kinds of large “white dendrites”, which is in fact composed of multiple phases, were found in the microstructure, from inside to outside of which, the eutectic phase changes from dot phases (anomalous structure) to irregular eutectic and then to regular eutectic, indicating that the center of “white dendrites” may be the nucleation zone of eutectic reaction.

Sn–Ag–Cu solder interconnects were made by solidifying the solder balls in a magnetic field and subsequently tested for their electromigration behavior. The orientation of the tin grains was analyzed by electron backscattered diffraction. It was found that the c-axis of Sn grain tended to rotate away from the direction of the magnetic field during solidification, resulting in an enhanced electromigration resistance for the solder joint when the current was applied along the direction of the magnetic field, as evidenced by a smaller electromigration-induced polarity effect in the growth of the interfacial intermetallic compound. Such a reduced polarity-effect of electromigration is shown to agree well with the anisotropy in the diffusivity of the active diffusion species, Cu, in the tetragonal Sn. The difference of free energy change caused by the anisotropy in the magnetic susceptibility of the tetragonal Sn during solidification is suggested to be the main factor for this phenomenon.

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Here we focus on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.

Low-cost La(FexSi1-x)13 alloys exhibiting the large magnetocaloric effect (MCE) are one of the most promising magnetic refrigerant candidates for room temperature magnetic refrigeration. The NaZn13-type phase (hereinafter 1:13 phase) is believed to play a key role in the MCE of these alloys. While the formation of the 1:13 phase directly from the melt upon cooling was challenging, in this paper we demonstrate that the 1:13 phase can be formed directly during solidification. We found that three kinds of solidification microstructure were formed because a competitive nucleation occurred between the 1:13 and α-(Fe,Si) phase during the solidification of LaFe11.5Si1.5 alloy. In case of a high cooling speed, a large amount of NaZn13–type phase with equiaxed grains and a small amount of α-(Fe,Si) phase were formed because of a dominant nucleation rate of 1:13 phase. When the cooling rate was small, a large number of α-(Fe,Si) phase with dendrites were formed because the nucleation rate of α-(Fe,Si) phase is larger than that of the 1:13 phase. These results revealed that nucleation rates of phases is very important to the composition formation and microstructure of LaFe11.5Si1.5 alloys.

The growth velocity during solidification of an undercooled melt of a Co-Cu alloyprocessed by electromagnetic levitation was measured using a high speed video camera.Applying a model of local non-equilibrium solidification, theoretical predictions ofdendrite growth velocity and dendritic growth radii are compared with high-accuracymeasurements of the growth kinetics. As the undercooling ΔT reaches a critical valueconsistent with the dendrite growth velocity being equal to the atomic diffusion speedVD in bulk liquid,ΔT =ΔT(VD),the velocity-undercooling relationship exhibits a break-point. A distinct change in thedendritic growth mechanism exists with the onset of complete solute trapping andchemically partitionless solidification of the core of the main stems of the dendritesoccurs. A complete transition to the thermally controlled growth of dendrites occurs atΔT =ΔT(VD)that leads to essential changes in the microstructure of dendritic patterns The phenomenonof dendritic fragmentation in Co-Cu melts, solidifying at ΔT <ΔT(VD),is discussed.

In this work the thermal and kinetic analysis of the cooling and solidification of a near eutectic Al-Cu alloy is performed using inverse thermal and solidification kinetics analysis. The Fourier thermal analysis is applied to experimental cooling curves to obtain data on solid fraction evolution and latent heat of solidification. Inverse thermal analysis is applied to calculate the global heat transfer coefficients that allow correct simulation of the cooling of experimental probes. The free growth method is used to obtain the eutectic growth coefficients. All the obtained parameters are feed into a heat transfer-solidification kinetics model to validate the methodology and results generated from this work. It is found a relatively good agreement between experimental and predicted cooling curves which suggest that this methodology could be used to generate useful information needed to simulate eutectic solidification.

Solidification of undercooled Ni–4.5 wt% B alloy melt was investigated by glass fluxing and cyclic superheating. A maximum melt undercooling up to ΔTp = 283 K has been achieved. If ∆Tp < 175 ± 10 K, the primary solidification is L → Ni3B; the structure consists of Ni3B dendrite + lamellar eutectic; the phase sizes and fractions depend on ∆Tp. If ∆Tp ≥ 175 ± 10 K, the primary solidification is L → Ni/Ni23B6; the structure consists of the dot-phase region + the anomalous eutectic/network boundary; the phase fractions mainly depend on ∆Tr; the dot phases are determined as rod eutectic and dot precipitates, while the network boundary is the divorced eutectic. The solidification pathways show that there is a common critical nucleation temperature, 1227 ± 10 K, for metastable eutectic reaction in hypoeutectic and hypereutectic Ni–Ni3B alloys.

Solidification of undercooled Ni–3.3 wt% B alloy melt was investigated by glass fluxing. If ΔTe < 140 ± 10 K, two recalescences appear, indicating that stable eutectic reaction occurs; if ΔTe ≥ 140 ± 10 K, three recalescences can be observed, indicating that metastable eutectic reaction occurs. Analysis indicates that the phase fractions of the as-solidified structure can be predicted by the recalescence delay times in the cooling curves. High-speed video images show that the solidification interface of primary solidification changes from single dendritic shape to spherical shape with increasing ΔTp; the interface of eutectic solidification changes from many small “dendrites” to a single large one with increasing ΔTe; the interface of residual liquid solidification changes from many small rings to a single large one with increasing ΔTr. The growth velocity of eutectic solidification suggests a coupled growth at small and moderate undercoolings and decoupled growth at large undercooling, whereas that of residual liquid solidification cannot be interpreted by the available models.

A Stefan problem is a free boundary problem where a phase boundary moves as a function of time. In this article, we consider one-dimensional and two-dimensional enthalpy-formulated Stefan problems. The enthalpy formulation has the advantage that the governing equations stay the same, regardless of the material state (liquid or solid). Numerical solutions are obtained by implementing the Godunov method. Our simulation of the temperature distribution and interface position for the one-dimensional Stefan problem is validated against the exact solution, and the method is then applied to the two-dimensional Stefan problem with reference to cryosurgery, where extremely cold temperatures are applied to destroy cancer cells. The temperature distribution and interface position obtained provide important information to control the cryosurgery procedure.

The numerical modeling of a binary solidification with a mushy layer mechanism is considered in this manuscript. The nonlinear coupled system of equations describes the heat and mass diffusions of a one-dimensional spatial variable in the semi-infinite interval. Also formulated is a transformed system in a finite interval. We propose numerical methods for solving the nonlinear system using a threshold strategy based on fixed computation-domain approach. Our calculated results and those from the LeadEx field experiment are well-matched in their tendencies.

A new finite element level set method is developed to simulate the interface motion. The normal velocity of the moving interface can depend on both the local geometry, such as the curvature, and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation. The key idea of the method is to use an interface-fitted finite element mesh. Such an approximation of the interface allows an accurate calculation of the solution to the diffusion equation. The interface-fitted mesh is constructed from a base mesh, a uniform finite element mesh, at each time step to explicitly locate the interface and separate regions defined by the interface. Several new level set techniques are developed in the framework of finite element methods. These include a simple finite element method for approximating the curvature, a new method for the extension of normal velocity, and a finite element least-squares method for the reinitialization of level set functions. Application of the method to the classical solidification problem captures the dendrites. The method is also applied to the molecular solvation to determine optimal solute-solvent interfaces of solvation systems.

Phase change in ice-water systems in the geometry of horizontal cylindrical annulus with constant inner wall temperature and adiabatic outer wall is modeled with an enthalpy-based mixture model. Solidification and melting phenomena under different temperature conditions are analyzed through a sequence of numerical calculations. In the case of freezing of water, the importance of convection and conduction as well as the influence of cold pipe temperature on time for the complete solidification are examined. As for the case of melting of ice, the influence of the inner pipe wall temperature on the shape of the ice-water interface, the flow and temperature fields in the liquid, the heat transfer coefficients and the rate of melting are analyzed. The results of numerical calculations point to good qualitative agreement with the available experimental and other numerical results.

Les alliages biphasés α2/γ de base TiAl sont des candidatsprometteurs pour des applications à hautes températures dans les domaines del’aéronautiques. Leur développement reste limité du fait de la faible robustesse de laréponse aux traitements thermiques en particulier en présence de macroségrégation ou de laréactivité à haute température, limitant la surchauffe du métal liquide et donc lacoulabilité de ces alliages. Les procédés de coulée centrifuge permettent un remplissagedes moules à grande vitesse ce qui permet de pallier la faible coulabilité. Lacaractérisation de ce procédé passe par une meilleure compréhension de la formation desmacroségrégations en présence de force centrifuge. Dans cette étude nous présentons lesrésultats de modélisation de macroségrégation prenant en compte la force centrifuge et lemouvement des grains pour un alliage de base Ti-Al-Nb.

The effect of superheating and substrate morphology on heat exchange at the melt-solid interface was studied. An experimental device was set up to yield a unidirectional heat flow from the Sn-Pb bath to the lubricated steel substrate and the heat transfer resistance was evaluated from the thickness of the solidified material at a fixed time. A higher solidification efficiency was obtained with moderate superheating, and also with a proper choice of surface topography and lubricant.

The recognition that postcumulus processes significantly modify primary textures in layered mafic intrusions has thrown into question many early observations on which classical crystallization theories are based. Petrographic observations combined with quantitative textural analysis of samples from various stratigraphic levels of the Lilloise intrusion, East Greenland, demonstrate that postcumulus textural modification of cumulates, formed during the solidification of a closed system magma chamber, may be detected. Crystal size distribution (CSD) measurements of Lilloise cumulates and the resulting CSD profiles are compared to predicted theoretical closed system CSD profiles. Similarities between the measured CSD profiles and published predicted CSD profiles support Lilloise magma evolving in a closed system chamber and indicate that primary crystallization processes can be distinguished using quantitative textural techniques. Textural coarsening driven by syn-magmatic deformation is suggested to be the dominant postcumulus process affecting CSD plot morphology. CSD slope values and profiles (plot shapes) remain relatively constant for a given liquidus mineral (particularly olivine and clinopyroxene), so that the number of phases on the liquidus at any one time affects mineral modal abundances. As a result, CSDs generally exhibit overall smaller grainsizes and progressively lower nucleation densities at higher levels in the intrusion.