[en] A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than previous formulations and permits one to eliminate nonequilibrium effects at the interface. Dendrite growth simulations with vanishing solid diffusivity show that both the interface evolution and the solute profile in the solid are accurately modeled by this approach

[en] We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large-scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance. (c) 2000 The American Physical Society

No abstract available

[en] During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than either solid phase. When the parent or both solid phases are morphologically unstable, i.e., for a small temperature gradient/growth rate ratio (G/v_p), one solid phase usually outgrows and covers the other phase, leading to a cellular-dendritic array structure closely analogous to the one formed during monophase solidification of a dilute binary alloy. In contrast, when G/v_p is large enough for both phases to be morphologically stable, the formation of the microstructure becomes controlled by a subtle interplay between the nucleation and growth of the two solid phases. The structures that have been observed in this regime (in small samples where convection effects are suppressed) include alternate layers (bands) of the parent and peritectic phases perpendicular to the growth direction, which are formed by alternate nucleation and lateral spreading of one phase onto the other as proposed in a recent model [R. Trivedi, Metall. Mater. Trans. A 26, 1 (1995)], as well as partially filled bands (islands), where the peritectic phase does not fully cover the parent phase which grows continuously. We develop a phase-field model of peritectic solidification that incorporates nucleation processes in order to explore the formation of these structures. Simulations of this model shed light on the morphology transition from islands to bands, the dynamics of spreading of the peritectic phase on the parent phase following nucleation, which turns out to be characterized by a remarkably constant acceleration, and the types of growth morphology that one might expect to observe in large samples under purely diffusive growth conditions

[en] We present a method to compute accurately the weak anisotropy of the solid-liquid interfacial free energy, a parameter which influences dendritic evolution in materials with atomically rough interfaces. The method is based on monitoring interfacial fluctuations during molecular dynamics simulation and extracting the interfacial stiffness which is an order of magnitude more anisotropic than the interfacial free energy. We present results for pure Ni with interatomic potentials derived from the embedded atom method

[en] We summarize recent advances in modeling of solidification microstructures using computational methods that bridge atomistic to continuum scales. We first discuss progress in atomistic modeling of equilibrium and non-equilibrium solid-liquid interface properties influencing microstructure formation, as well as interface coalescence phenomena influencing the late stages of solidification. The latter is relevant in the context of hot tearing reviewed in the article by M. Rappaz in this issue. We then discuss progress to model microstructures on a continuum scale using phase-field methods. We focus on selected examples in which modeling of 3D cellular and dendritic microstructures has been directly linked to experimental observations. Finally, we discuss a recently introduced coarse-grained dendritic needle network approach to simulate the formation of well-developed dendritic microstructures. The approach reliably bridges the well-separated scales traditionally simulated by phase-field and grain structure models, hence opening new avenues for quantitative modeling of complex intra- and inter-grain dynamical interactions on a grain scale

[en] We present a novel multi-scale Dendritic Needle Network (DNN) approach in order to model well-developed highly-ramified dendritic microstructures on the coarser scale of several crystal grains while retaining a faithful quantitative description of the transient dynamics of individual dendritic branches. This approach is intended to bridge the scale gap between phase-field and cellular automaton methods. The dynamics of each needle-like branch, characterized by its tip velocity V and radius ρ, is fixed by two conditions: (i) on the inner tip scale, a standard microscopic solvability condition relates ρ²V to the strength of surface tension anisotropy, and (ii) on the outer diffusion length scale, a flux balance condition relates the product ρV² to a flux intensity factor extracted from a contour integral analogous to the J-integral of fracture mechanics. The method is tested for low supersaturation and reproduces the analytical solutions for both early stage and steady state growth dynamics. The results are directly compared with a quantitative phase-field simulation for an experimentally relevant supersaturation. We present as well an illustrative simulation for highly branched polycrystalline growth. This model should permit to investigate the macroscale grain evolution through the dynamics of individual primary dendrites and higher-order branches, controlled by both the intragrain history-dependent selection and the intergrain dendrite interactions.

[en] Experiments have widely shown that a steady-state lamellar eutectic solidification front is destabilized on a scale much larger than the lamellar spacing by the rejection of a dilute ternary impurity and forms two-phase cells commonly referred to as ''eutectic colonies.'' We extend the stability analysis of Datye and Langer [V. Datye and J. S. Langer, Phys. Rev. B 24, 4155 (1981)] for a binary eutectic to include the effect of a ternary impurity. We find that the expressions for the critical onset velocity and morphological instability wavelength are analogous to those for the classic Mullins-Sekerka instability of a monophase planar interface, albeit with an effective surface tension that depends on the geometry of the lamellar interface and, nontrivially, on interlamellar diffusion. A qualitatively new aspect of this instability is the occurrence of oscillatory modes due to the interplay between the destabilizing effect of the ternary impurity and the dynamical feedback of the local change in lamellar spacing on the front motion. In a transient regime, these modes lead to the formation of large scale oscillatory microstructures for which there is recent experimental evidence in a transparent organic system. Moreover, it is shown that the eutectic front dynamics on a scale larger than the lamellar spacing can be formulated as an effective monophase interface free boundary problem with a modified Gibbs-Thomson condition that is coupled to a slow evolution equation for the lamellar spacing. This formulation provides additional physical insights into the nature of the instability and a simple means to calculate an approximate stability spectrum. Finally, we investigate the influence of the ternary impurity on a short wavelength oscillatory instability that is already present at off-eutectic compositions in binary eutectics. (c) 1999 The American Physical Society

[en] We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius ρ [which is crudely approximated by ρ≅(1-α)ρ_Iv where ρ_Iv is the Ivantsov tip radius of an isothermal paraboloid with the same tip velocity and α is the stiffness anisotropy]. The universal tip shape, which excludes this distortion, is well fitted by the form z=-r²/2+A₄r⁴ cos 4φ where |z| is the distance from the tip and all lengths are scaled by ρ_Iv. This fit yields A₄ in the range 0.004-0.005 in good quantitative agreement with the existing tip morphology measurements in succinonitrile [LaCombe et al., Phys. Rev. E 52, 2778 (1995)], which are reanalyzed here and found to be consistent with a single cos 4φ mode nonaxisymmetric deviation from a paraboloid. Moreover, the fin shape away from the tip is well fitted by the power law z=-a|x|^5/3 with a≅0.68. Finally, the characterization of the operating state of the dendrite tip is revisited in the light of these results. (c) 2000 The American Physical Society

[en] The columnar-to-equiaxed transition is a technologically important phenomenon that controls the grain structure in the casting of alloys. Analytical and coarse-grained models, used to investigate this transition, rely on several assumptions concerning dendrite growth kinetics and grain structures. In the first part of this two part paper, we test these assumptions using a two-dimensional (2D) dendritic needle network model that describes both the transient growth dynamics of primary, secondary and higher order branches of the dendritic network within each grain and the solutal interactions between grains that can grow with arbitrary shapes. Our results provide novel insights into the columnar-to-equiaxed transition, distinguishing between abrupt and progressive transitions with different grain structures. Furthermore, they highlight the limitations of commonly used assumptions in analytical and coarse-grained numerical models of this transition. These results are extended to 3D in part II of the paper.