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The thermodynamic extremal principle was applied to model of rapid solidification of non-stoichiometric intermetallic compounds and the Co- x at.%Si alloys ( x  = 50, 53, 55) were undercooled to test the model. It is the model with but not the model without solute drag that can be derived self-consistently in thermodynamics. Unique dual sluggish and abrupt growth stages were found in undercooled Co-53 at.%Si and Co-55 at.%Si alloys. The first (second) sluggish stage is solute-controlled (thermal-controlled). The first (second) abrupt growth stage is ascribed to the sharp occurrence of solute trapping (inverted partitioning) and disorder trapping that initiates the transition from solute-controlled (thermal-controlled) to thermal-controlled (kinetic-controlled) growth. Since the predictions by the current (previous) model with (without) solute drag predicted well (deviate drastically from) the experimental results, solute drag was suggested be significant upon rapid solidification. The current work solved such an open problem, i.e. solute drag in solidification, and is helpful for not only understanding the non-equilibrium phenomena that is of theoretical importance but also controlling the non-equilibrium microstructures that is of technological importance. [ABSTRACT FROM AUTHOR]

The liquid–metal-cooling (LMC) directional-solidification process offers refinement of dendritic structure due to the increased cooling rate from enhanced heat extraction. However, under some conditions in the LMC process substantial lateral heat extraction occurs that leads to a change in dendrite morphology, resulting in grain nucleation or lateral growth – the formation of long secondary dendrite arms overgrowing favorably aligned primary dendrites. The conditions under which lateral growth occurs during solidification of alloys CMSX-486 and René-N4 have been studied experimentally and via solidification modeling. Solidification experiments have been conducted in a LMC furnace that utilizes liquid tin as the cooling medium and a floating ceramic baffle. A mold geometry was designed to evaluate a range of thermal conditions during solidification and assess the tendency for lateral growth. Correlations between dendritic structure, solidification-front curvature, solidification rate and thermal gradients have been analyzed. A criterion for predicting the onset of lateral growth based on the inclination of the solidification front at the casting surface is demonstrated. [ABSTRACT FROM AUTHOR]

In a previous paper (Castle et al., 2014) [17], we employed a melt fluxing technique to study the velocity-undercooling relationship and microstructural development of a Cu-8.9wt.% Ni alloy in order to investigate the fundamental mechanism behind the rapid solidification phenomenon of "spontaneous grain refinement". A number of growth transitions were identified with increasing undercooling, including an extended dendrite orientation transition through: fully 〈100〉-oriented→multiply twinned, mixed 〈100〉/〈111〉-oriented→fully 〈111〉-oriented. Here, we present the results of an identical study of a Cu-Ni alloy of lower Ni content and observe a similar set of growth transitions, with some notable differences. In particular, three distinct grain refinement mechanisms have been observed between the two alloys, including: recrystallization, dendrite fragmentation and dendritic seaweed fragmentation. It appears that the mechanism selected depends strongly upon the original growth structure present, which we suggest is dictated by the balance between the capillary and kinetic anisotropies; with the addition of Ni to Cu either increasing the strength of the kinetic anisotropy, decreasing the strength of the capillary anisotropy, or a combination of both. The unambiguous identification of three different spontaneous grain refinement mechanisms in two closely related alloys is significant as it may help to resolve some of the debate surrounding the "true" grain refinement mechanism. [ABSTRACT FROM AUTHOR]

Abstract: Directional solidification via the liquid metal cooling process results in refined microstructure and reduced defects, thus providing improved mechanical performance of single crystal (SX) materials. However, the enhanced heat extraction inherent to the process results in a curved solidification front that may lead to non-axial growth of dendrites near the casting walls. The mechanism by which the lateral growth occurs has been investigated by microstructure modeling via solute-adjusted, diffusional growth of dendrites. Local thermal profiles derived from continuum solidification models were used as inputs to a dendrite-growth model capable of simulations in both two and three dimensions. A finite difference calculation of the diffusion field and volume of fluid tracking for the growth of the dendrite front was coupled to predict the microstructure evolution during directional solidification. Model predictions were compared to experimentally observed dendritic structures. In addition, a parametric analysis was conducted to evaluate the sensitivity of the dendrite-growth mode to changes in thermal, structural (such as dendrite position and spacing) and model parameters. The inclination angle of the solidification front strongly influenced the evolution of dendritic structure. The degree of misorientation of the 〈001〉 SX orientation from the withdrawal axis significantly contributed to the onset of lateral dendritic growth. [Copyright &y& Elsevier]

Abstract: Most theoretical work on dendrite growth has focused on dilute binary alloys, while most industrial alloys are concentrated multi-component systems. By incorporating the local non-equilibrium effects both at the interface and in the bulk liquid, the thermodynamic database and diffusional interaction, a model was developed for dendrite growth in undercooled concentrated multi-component alloys. An experimental study of dendrite growth in undercooled Ni–18at.% Cu–18at.% Co melts was carried out and the measured interface velocities (V) were well predicted by the present model over the whole undercooling range (ΔT =30–313K). During dendrite growth the partition coefficients change non-monotonically due to interaction between the species and changes in the dendrite tip radius. Interaction between the species also leads to a lower interface velocity and larger ΔT and V as the ΔT–V relation plateaus. The previous definition of constitutional undercooling, i.e. the sum of the contributions of each solute, is not applicable to concentrated multi-component alloys. The controlling mechanisms during dendrite growth are discussed with respect to the results of the calculations. [Copyright &y& Elsevier]

Abstract: A three-dimensional (3-D) cellular automaton model for dendritic growth in multi-component alloys is developed. The velocity of advance of the solid/liquid (S/L) interface is calculated using the solute conservation relationship at the S/L interface. The effect of interactions between the alloying elements on the diffusion coefficient of solutes in the solid and liquid phases are considered. The model is first validated by comparing with the theoretical predictions for binary and ternary alloys, and then applied to simulate the solidification process of Al–Cu–Mg alloys by a coupling of thermodynamic and kinetic calculations. The numerical results obtained show both the free dendrite growth process as well as the directional solidification process. The calculated secondary dendrite arm spacing in the directionally solidified Al–Cu–Mg alloy is in good agreement with the experimental results. The effect of interactions between the various alloying elements on dendritic growth is discussed. [Copyright &y& Elsevier]

Abstract: A new modeling approach combining the lattice Boltzmann method (LB) and the cellular automaton technique (CA) was developed to simulate solidification at the microscale. The LB method was used for the coupled calculation of temperature, solute content and velocity field, while the CA method was used to compute the liquid/solid phase change. To validate the accuracy of the LB–CA model and its efficiency for the simulation of dendrite growth under convection, comparisons of the tip characteristics and dendrite morphologies under various simulation conditions were made with those obtained by analytical means and by a finite element model coupled with the cellular automaton technique (FE–CA model). The results show that the LB–CA model is computationally much more efficient than the FE–CA model for simulations of dendritic microstructures under convection. The tip splitting phenomenon was captured for high cooling rates and with comparatively coarse grids due to mesh-induced anisotropy and thermal instabilities. The simulated dendrite morphologies obtained with various anisotropy and Gibbs–Thomson coefficients were discussed. The results show that the dendrite growth direction does not always follow the crystallographic direction and high branching phenomena can occur with small anisotropy and/or Gibbs–Thomson coefficients. [Copyright &y& Elsevier]

Abstract: A two-dimensional model combining the finite element method and the cellular automaton technique was developed to simulate dendritic growth occurring in the molten pool during the laser-engineered net shaping (LENS) process. Based on the simulation results and previously published experimental data, empirical expressions describing the relationship between the cooling rate and the dendrite arm spacing (DAS) were proposed. In addition, the influence of LENS process parameters, such as the moving speed of the laser beam, the layer thickness and the substrate size, on the DAS was also discussed. Finally, different dendrite morphologies calculated at different locations were explained based on local solidification conditions. The simulation results showed good agreement with previously published experiments. This work contributes to the understanding of microstructure formation and the resulting mechanical properties of LENS-built parts as well as providing a fundamental basis for optimization of the LENS process. [Copyright &y& Elsevier]

Abstract: A steady-state dendrite growth model in a bulk undercooled melt was developed for a binary alloy assuming nonlinear liquidus and solidus. As an extension of Galenko and Danilov’s model [Galenko PK, Danilov DA. Phys Lett A 1997;235:271], the present model considered the non-equilibrium interface kinetics, the relaxation effect, i.e. non-equilibrium liquid diffusion and the curved phase boundary. In the current analysis of marginal stability, the kinetic effect played an important role. The model’s validity was reinforced in terms of thermodynamic calculations of the phase diagram, as fewer fitting parameters were used in the model predictions. Adopting three characteristic velocities, i.e. the critical velocity of the absolute solute stability , the velocity of the maximal tip radius and the velocity of bulk liquid diffusion V D, a quantitative agreement was obtained between the model predictions and the experimental results of an undercooled Ni–0.7at.% B alloy. A plateau observed in the velocity versus undercooling stage, i.e. , for intermediate undercoolings implied a transition from a mainly solute-controlled to a mainly thermal-controlled process. If the dendrite growth velocity equaled V D, an abrupt change of growth mode from the power law to linear growth proceeded, which could be ascribed to a transition from mainly thermal-controlled growth to purely thermal-controlled growth. [Copyright &y& Elsevier]

Abstract: The various types of facet Si dendrites observed on splat-quenched surfaces were analyzed in order to understand why the growth direction and morphology of the facet Si dendrites change with increasing undercooling. The growth directions of typical facet dendrites were determined to be 〈211〉, 〈110〉 and 〈100〉 using an electron backscatter pattern apparatus. It was found that both the 〈211〉 and 〈110〉 dendrites with twins were bounded by atomically smooth {111} planes. Therefore, their growth is governed by the incorporation of atoms at re-entrant corners formed by twins. The 〈100〉 dendrites with fourfold symmetry have no twins and are commonly observed at high undercoolings. Moreover, two kinds of 〈100〉 dendrites with different secondary arm directions 〈100〉 and 〈110〉 were clarified for the first time. The dendrite tip shape and facet planes, as determined using an atomic force microscope, suggest that the 〈100〉 dendrites are bounded by atomically rough {110} and {100} planes. That is, facet Si dendrites vary in their growth direction and morphology with increasing undercooling because the dendrites select atomically rough interfaces in order to promote the incorporation of atoms at high undercoolings. [Copyright &y& Elsevier]

This article addresses the formation of low angle grain boundaries which give rise to mosaicity, a phenomenon that has only recently received attention in the single crystal Ni-base superalloy field. In this work, post-mortem advanced microscopy characterisation techniques are employed to deduce the dendrite tip growth kinetics from transverse sections of a single crystal turbine blade. As a result, it has been possible to highlight the role of isotherm curvature in inducing lateral macro-segregation parallel to a growing solidification front. Using crystallographic data from time-of-flight energy-resolved neutron imaging and novel Bragg-dip post processing, it is established that lateral macro-segregation induces small angle grain boundaries which gives rise to mosaicity within single crystal Ni-base superalloys. Mosaicity demonstrates good correlation with the local primary spacing, where faster growing dendrites demonstrate greater deviation of 〈001〉 from the casting direction, as compared with those growing at a slower rate. In light of these findings, the origin of mosaicity and its implication to secondary grain formation is discussed. [Display omitted] [ABSTRACT FROM AUTHOR]

Gas porosity is one of the most detrimental defects that can considerably deteriorate mechanical properties of casting parts. Simulating the interaction between gas porosity and solidifying microstructure is challenging due to multiphase and multiphysical characteristics. In this work, a solid-liquid-gas multiphase-field lattice-Boltzmann model is developed to describe the complex multiphase interaction during solidification. The model relaxes the assumption of pure metal system, simplified bubble shape and pure diffusion condition. It can consider solid growth, bubble motion, interface deformation, component transport, melt flow, and partition of both alloy solute and dissolved gas species. The model is validated in terms of mass conservation, mapping operation to the two-phase model, Laplace pressure condition, and bubble dynamics. The effectiveness of the model is further evaluated by comparing with other four models and experiments. The model is successfully used to describe the interaction between gas porosity and magnesium dendrite. The dependence of phase fractions on the characteristic parameters including melt undercooling, interface mobility coefficient and internal bubble pressure is quantified to explore the multiphase equilibrium. The proposed model can be regarded as complementary to the previous models and it is suitable for addressing the problems involving the solid-liquid-gas multiphase and multiphysical characteristics. [Display omitted] [ABSTRACT FROM AUTHOR]