Thin-sample Directional Solidification Research Articles

Grain growth competition and formation of grain boundaries during solidification of hcp alloys

Grain growth competition during directional solidification of a polycrystal with hexagonal (hcp) symmetry (Mg-1wt%Gd alloy) is studied by phase-field modeling, exploring the effect of the temperature gradient G on the resulting grain boundary (GB) orientation selection. Results show that selection mechanisms and scaling laws derived for cubic (fcc, bcc) crystals also apply to hcp materials (within their basal plane), provided a re-estimation of fitting parameters and re-scaling to account for the sixfold symmetry. While grain growth competition remains stochastic with rare events of unexpected elimination or side-branching along the developing GBs, we also confirm an overall transition from a geometrical limit to a favorably oriented grain limit behavior with an increase of thermal gradient within the dendritic regime, and the progressive alignment of dendrites and GBs toward the temperature gradient direction with an increase of G during the dendritic-to-cellular morphological transition. Comparisons with original thin-sample directional solidification experiments show a qualitative agreement with PF results, yet with notable discrepancies, which nonetheless can be explained based on the stochastic variability of selected GB orientations, and the statistically limited experimental sample size. Overall, our results extend the understanding of GB formation and grain growth competition during solidification of hcp materials, and the effect of thermal conditions, nonetheless concluding on the challenges of extending the current studies to three dimensions, and the need for much broader (statistically significant) data sets of GB orientation selected under well-identified solidification conditions.

Formation of locked-lamellar grains in a slightly hypoeutectic Al-Al2Cu alloy during thin-sample directional solidification

We studied the formation and growth of locked-lamellar microstructures in a thin sample of a slightly hypoeutectic Al-Al2Cu alloy. The coupled-growth dynamics, including early stages and steady-state regimes, was observed optically in real time during directional solidification. The orientation of the α (Al) and θ (Al2Cu) crystals was measured ex situ in a series of eutectic grains by X-ray Laue microdiffraction. A nucleation event of a θ crystal on a pre-existing α crystal, and the subsequent growth of a eutectic grain with a type-C orientation relationship, that is, with a coincidence of {123}-α and {100}-θ planes, were observed in situ. In type-C eutectic grains, lamellar locking occurred parallel to the low-energy coincidence plane. A regular (floating) coupled-growth dynamics was observed in misoriented eutectic grains.

Decoupled versus coupled growth dynamics of an irregular eutectic alloy

We present an experimental study of irregular growth patterns observed in real time during thin-sample directional solidification of a faceted/nonfaceted eutectic alloy, namely, the transparent 2-amino-2-methyl-1,3-propanediol (AMPD)-succinonitrile (SCN) system. The body-centered cubic SCN crystals are nonfaceted, while monoclinic AMPD crystals grow as faceted needles. At low velocities (<0.3 µms−1), a decoupled growth regime is observed, during which the tip of the AMPD crystals grows ahead of the SCN-liquid interface. At intermediate velocities, an unsteady coupled-growth regime takes place, with intermittent pinning of triple SCN-AMPD-liquid junctions, and frequent noncrystallographic branching. At higher velocities (>1 µms−1), two-phase fingers form.

Influence of morphological instability on grain boundary trajectory during directional solidification

The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a transparent alloy, and by numerical simulations with the phase-field method in two dimensions. We find that low-angle grain boundaries (subboundaries) with an anisotropic interfacial free energy grow tilted at an angle θt with respect to the temperature gradient axis. θt remains essentially equal to its value imposed at equilibrium as long as the solidification velocity V remains low. When V increases and approaches the cellular instability threshold, θt decreases, and eventually vanishes when a steady-state cellular morphology forms. The absence of mobility of the subboundary in the solid is key to this transition. These findings are in good agreement with a recent linear-stability analysis of the problem.

Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Λ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ∼V−1/2, Λ is observed to increase with V (∂Λ/∂V>0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that ∂Λ/∂V<0. We show through simulations that this trend inversion for Λ(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. We explain the observed inversion of ∂Λ/∂V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.

Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study

We present the results of a comprehensive phase-field study of columnar grain growth competition in bi-crystalline samples in two dimensions (2D) and in three dimensions (3D) for small sample thicknesses allowing a single row of dendrites to form. We focus on the selection of grain boundary (GB) orientation during directional solidification in the steady-state dendritic regime, and study its dependence upon the orientation of two competing grains. In 2D, we map the entire orientation range for both grains, performing several simulations for each configuration to account for the stochasticity of GB orientation selection and to assess the average GB behavior. We find that GB orientation selection depends strongly on whether the primary dendrite growth directions have lateral components (i.e. components perpendicular to the axis of the temperature gradient) that point in the same or opposite directions in the two grains. We identify a range of grain orientations in which grain selection follows the classical description of Walton and Chalmers. We also identify conditions that favor unusual overgrowth of favorably-oriented dendrites at a converging GB. We propose a simple analytical description that reproduces the average GB orientation selection from 2D simulations within statistical fluctuations of a few degrees. In 3D, we find a similar GB orientation selection as in 2D when secondary branches grow in planes parallel and perpendicular to the sample walls. Remarkably, quasi-2D behavior is also observed even when those perpendicular sidebranching planes are rotated by a finite azimuthal angle about the primary dendrite growth axis as long as the absolute values of those azimuthal angles are equal in both grains. In contrast, when the absolute values of those azimuthal angles differ markedly, we find that unusual overgrowth events at a converging GB are promoted by a high azimuthal angle in the least-favorably-oriented grain. We also find that diverging GBs can be strongly affected by those azimuthal angles, while converging GBs exhibit a weak dependence on those angles. For diverging GBs, GB orientation is also strongly affected by the relative signs of the lateral components of the primary dendrite growth directions in both grains.

Quantitative determination of the solidus line in the dilute limit of succinonitrile–camphor alloys

Different phase diagram measurements for succinonitrile–camphor alloys to date have yielded different values of the solute partition coefficient and the freezing range of the alloy. These parameters are critical to model solidification microstructure evolution. New measurements are made to precisely characterize the dilute limit of the succinonitrile–camphor phase diagram using thin-sample directional solidification experiments where convection is negligible, so that solute transport in the melt is purely diffusive, and the temperature gradient is constant in time. These results are confirmed through complementary measurements by differential scanning calorimetry and isothermal annealing. Possible measurement uncertainties in previously measured solidus lines are discussed. Experimental results were further confirmed using a boundary layer model of transient planar interface dynamics.

Stability of three-phase ternary-eutectic growth patterns in thin sample

Near-eutectic ternary alloys subjected to thin-sample directional solidification can exhibit stationary periodic growth patterns with an ABAC repeat unit, where A, B, and C are the three solid phases in equilibrium with the liquid at the eutectic point. We present an in-situ experimental study of the dynamical features of such patterns in a near-eutectic In–In2Bi–Sn alloy. We demonstrate that ABAC patterns have a wide stability range of spacing λ at given growth rate. We study quantitatively the λ-diffusion process that is responsible for the spacing uniformity of steady-state patterns inside the stability interval. The instability processes that determine the limits of this interval are examined. Qualitatively, we show that ternary-eutectic ABAC patterns essentially have the same dynamical features as two-phase binary-eutectic patterns. However, lamella elimination (low-λ stability limit) occurs before any Eckhaus instability manifests itself. We also report observations of stationary patterns with an [AB]m[AC]n superstructure, where m and n are integers larger than unity.

Determination of the Jackson–Hunt constants of the In–In2Bi eutectic alloy based on in situ observation of its solidification dynamics

We present a real-time observation study of lamellar patterns in thin-sample directional solidification of a near-eutectic In–In2Bi metallic alloy. The spacing range of stability is shown to extend from about 0.9λJH to 2.2λJH, where λJH is the Jackson–Hunt minimum undercooling spacing, in agreement with what was observed earlier in transparent eutectics. We analyze the time evolution of non-uniform spacing distributions using a previously established semi-empirical “spacing-diffusion” law [Akamatsu et al., Metal. Mater. Trans. A 35 (2004) 1815]. We obtain a quantitative estimate of the Jackson–Hunt constants and other material parameters relevant to eutectic growth, among which λJH2V=48±7μm3s-1 and D=505±75μm2s−1, where V is the solidification speed, and D is the solute diffusion coefficient in the liquid.

Weakly faceted cellular patterns versus growth-induced plastic deformation in thin-sample directional solidification of monoclinic biphenyl

We present an experimental study of thin-sample directional solidification (T-DS) in impure biphenyl. The platelike growth shape of the monoclinic biphenyl crystals includes two low-mobility (001) facets and four high-mobility {110} facets. Upon T-DS, biphenyl plates oriented with (001) facets parallel to the sample plane can exhibit either a strong growth-induced plastic deformation (GID), or deformation-free weakly faceted (WF) growth patterns. We determine the respective conditions of appearance of these phenomena. GID is shown to be a long-range thermal-stress effect, which disappears when the growth front has a cellular structure. An early triggering of the cellular instability allowed us to avoid GID and study the dynamics of WF patterns as a function of the orientation of the crystal.

Control of eutectic solidification microstructures through laser spot perturbations

We report on a new experimental technique for controlling lamellar (nonfaceted) eutectic microstructures and testing their stability in thin-sample directional solidification (TDS) of a model transparent alloy ( CBr 4 – C 2 Cl 6 ) . We observe the solidification front in real time by optical microscopy. We use micromanipulation with a holographic laser spot array for perturbing the solidification front on a scale ranging from one to ten times the average lamellar spacing value (typically 10– 100 μ m ). These perturbations arise from local heating due to the absorption of the laser light by the liquid slightly ahead of the front. We show that the laser spot perturbation technique can be efficiently used as a tool for mapping out the large range of accessible lamellar spacings and for creation of desired patterns such as smooth spacing gradients or tilt domains.

Overstability of lamellar eutectic growth below the minimum-undercooling spacing

We investigate the stability of lamellar eutectic growth by thin-sample directional solidification experiments and two-dimensional phase-field simulations. We find that lamellar patterns can be morphologically stable for spacings smaller than the minimum undercooling spacing λ m . Key to this finding is the direct experimental measurement of the relationship between the front undercooling and spacing, which identifies λ m independently of the Jackson and Hunt (JH) theory and of uncertainties of alloy parameters. This finding conflicts with the common belief that patterns with λ<λ m should be unstable, which is based on the Jackson-Hunt-Cahn assumption that lamellae grow normal to the envelope of the front. Our simulation results reveal that lamellae also move parallel to this envelope to reduce spacing gradients, thereby weakly violating this assumption but strongly overstabilizing patterns for a range of spacing below λ m that increases with G/V (temperature gradient to growth rate ratio). This range is much larger than predicted by previous stability analyses and can be significant for standard experimental conditions. An analytical expression is obtained phenomenologically, which predicts well the variation of the smallest stable spacing with G/V. We also present results that shed light on the history-dependent selection and long-time evolution of the experimentally observed range of spacings.

Dynamical polygonization below the cellular-bifurcation threshold in thin-sample directional solidification

We show that a polygonization of the crystal (formation of grain subboundaries) takes place during the growth in thin-sample directional solidification of a transparent nonfaceted alloy at solidification rates lower than the cellular-bifurcation threshold. We give experimental evidence that this phenomenon is due to a dynamical coupling between the lattice defects intersecting the growth front and the diffusive modes of instability of the front. We present a theoretical model of this process in two-dimensional systems.

Dynamics of a faceted nematic-smectic-B front in thin-sample directional solidification.

We present an experimental study of the directional-solidification patterns of a nematic-smectic-B front. The chosen system is C4H9-(C6H10)2CN (in short, CCH4) in 12 microm-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic-smectic-B interface presents a facet in one direction-the direction parallel to the smectic layers--and is otherwise rough and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V and the angle straight theta(0) between the facet and the isotherms. We focus on the phenomena occurring immediately above the instability threshold when straight theta(0) is neither very small nor close to 90 degrees. Under these conditions, we observe drifting shallow cells and a type of solitary wave, called "faceton," which consists essentially of an isolated macroscopic facet traveling laterally at such a velocity that its growth rate with respect to the liquid is small. Facetons may propagate either in a stationary or an oscillatory way. The detailed study of their dynamics casts light on the microscopic growth mechanisms of the facets in this system.

Traveling waves, two-phase fingers, and eutectic colonies in thin-sample directional solidification of a ternary eutectic alloy

We present an experimental investigation of the morphological transition of lamellar eutectic growth fronts called "formation of eutectic colonies" by the method of thin-sample directional solidification of a transparent model alloy, CBr4-C2Cl6. This morphological transition is due to the presence in the melt of traces of chemical components other than those of the base binary alloy (impurities). In this study, we use naphthalene as an impurity. The formation of eutectic colonies has generally been viewed as an impurity-driven Mullins-Sekerka instability of the envelope of the lamellar front. This traditional view neglects the strong interaction existing between the Mullins-Sekerka process and the dynamics of the lamellar pattern. This investigation brings to light several original features of the formation of eutectic colonies, in particular, the emission of long-wavelength traveling waves, and the appearance of dendritelike structures called two-phase fingers, which are connected with this interaction. We study the part played by these phenomena in the transition to eutectic colonies as a function of the impurity concentration. Recent theoretical results on the linear stability of ternary lamellar eutectic fronts [Plapp and Karma, Phys. Rev. E 60, 6865 (1999)] shed light on some aspects of the observed phenomena.