Rod Eutectics Research Articles

Numerical investigation of eutectic growth dynamics under convection by 3D phase-field method

Control of eutectic growth trajectory is a technologically important subject in metallurgy and applied physics. The interaction between solute transport and interface capillary determines eutectic growth under convection. By employing a multiphase-field lattice-Boltzmann method, together with a parallel-adaptive mesh refinement algorithm, the effect of convection on 3D eutectic growth is quantified including lamellar and rod eutectics. The flow-induced solute distribution changes eutectic growth dynamics by establishing a new solute transport equilibrium. The growth behaviors of different eutectic patterns are investigated, and the eutectic growth dynamics is largely dependent on the constitutional undercooling and the curvature undercooling ahead of the solidification front. The natural convection changes the width ratio of coexisting solid phases, while the forced convection causes a tilt band for both lamellar and rod eutectics. Rod-to-lamellar transition under larger convection intensity, which is first predicted by numerical techniques, is discussed and good agreement with previous works is achieved. The deep understanding of the convection effect can help guide how to regulate eutectic patterns through changing the solidification condition.

Rapid eutectic growth: from rod growth to diffusionless solidification.

Numerous experimental data on the rapid solidification of eutectic systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by the suppression of eutectic decomposition due to diffusionless (chemically partitionless) solidification beginning at a high but finite growth velocity of crystals. In the present work, a model is suggested for the diffusionless growth to analyse the atomic diffusion in the rod eutectic couples growing into supercooled liquid. A simplified calculating method for the equation related to the Bessel function in the solution of the growth of rod eutectics is obtained. This method can also be used in the calculation of other rod eutectic growth models. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Comments on “A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems”*

A mistake in the eutectic growth model published by Adrian V. Catalina et al. (Adrian V. Catalina, Subhayu Sen, and Doru M. Stefanescu: Metall. Mater. Trans. A, 2003, vol. 34A, pp. 383–94) was identified. First, we have re-derived the model following Catalina’s assumption. Furthermore, the two Fourier coefficients were directly obtained following the classical eutectic model (JH model). Finally, the validity of our derivation is closed-loop verified based on the combination of the above two derivations.

Authors’ Reply to Comments on “A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems”

Authors’ Reply to Comments on “A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems”

The Rod Eutectic Growth under Rapid Solidification Conditions

The Rod Eutectic Growth under Rapid Solidification Conditions

Phase equilibria in the CdAs2–Cd3As2–MnAs ternary system

We determined, using a set of physicochemical methods, including X-ray powder diffraction (XRD), differential thermal analysis, and microstructure studies, that the CdAs2–Cd3As2–MnAs ternary system is bounded by three eutectic-type quasi-binary sections: Cd3As2–MnAs, CdAs2–MnAs, and Cd3As2–CdAs2. For Cd3As2–MnAs and CdAs2–MnAs sections, the eutectic coordinates are, respectively, 75 mol % Cd3As2 + 25 mol % MnAs, T m.eut = 604°C; and 92 mol % CdAs2 + 8 mol % MnAs, T m.eut = 608°C. These are rod eutectics. Manganese solubilities in Cd3As2 and CdAs2 phases are insignificant and, according to XRD and SEM, they do not exceed 1 at %. The binary eutectics of the quasi-binary sections form ternary eutectic Cd3As2 + CdAs2 + MnAs, whose average composition as probed by SEM is 34.5 at % Cd, 63 at % Cd and 2.5 at % As and T m.eut = 600°C. Cadmium and manganese arsenide alloys are ferromagnets with the Curie point at ~320 K. The magnetic and electric properties are due to ferromagnetic MnAs microinclusions.

Uniformly valid asymptotic solutions of rod eutectic growth in directional solidification for contact angles being the normal order

We consider system of rod eutectic growth under directional solidification for the normal amplitude of the contact angles. The objective of this work is to obtain the uniformly valid asymptotic solutions for steady growth of rod eutectics using the asymptotic expansion method. For the contact angles being the normal order, system of rod eutectic growth will exist a boundary layer at the triple phase junction. According to different length scales, we divide the whole liquid region into three subregions. Solutions in every subregion are derived by asymptotic expansion method. Finally, all the asymptotic expansion solutions are matched in the intermediate regions and the composite solutions are obtained. Results show that the average undercooling in front of both phases are not equal. The dimensional average undercooling exhibits a minimum at the critical eutectic spacing. The critical spacing of SCN-DC is predicted and it is in agreement with the small-spacing stability limit.

Lamellar to Rod Eutectic Transition in the Hypereutectic Nickel-aluminum Alloy

Directional solidification experiments were carried out on the hypereutectic Ni-25 at.% Al alloy to examine the effect of growth velocity on the eutectic microstructure. The growth velocity was varied from 1 to 20μm/s at a constant temperature gradient of 10.0K/mm. The microstructural observations of unidirectionally solidified samples show that the lamellar eutectic growth was observed in the sample solidified at a constant velocity of 1μm/s and the rod eutectic growth at velocities higher than 10μm/s. A microstructural transition from lamellar to rod eutectics was achieved at the intermediate velocity. The lamellar to rod eutectic transition was shown to result from the compositional change due to the presence of strong convection in the melt. The undercooling-spacing curves showed that the average eutectic spacings for the lamellar and the rod structures were 1.6 times larger than that in the minimum undercooling for a given velocity.

Dynamics of rod eutectic growth patterns in confined geometry

The dynamics of rod-like eutectics are examined using a directional solidification setup, which allows real-time observation of the whole solidification front in specimens of transparent eutectic alloys -here, succinonitrile-(D)camphor. In steady-state, rod eutectic growth patterns consist of triangular arrays, more or less disturbed by topological defects. In the absence of strong convection and of crystallographic anisotropy, the long-time evolution of the pattern is dominated by "imperfections" of the system, such as misalignment of the temperature gradient, and finite-size. In this study, we present experimental results on the finite-size effects on rod eutectics and show that a rod to lamella transition takes place as a result of finite-size effect only, at a given alloy concentration.

Microstructure evolution and mechanical properties of Mg–Ge binary magnesium alloys

Microstructures and mechanical properties of Mg–Ge binary alloys (G1, 0·5 wt-%; G2, 1·0 wt-%; G3, 1·5 wt-%; G4, 2·0 wt-%; G5, 2·5 wt-% and G6, 3·5 wt-%) were investigated. The results show that the microstructures of Mg–Ge binary alloys consist of two components: α-Mg dendrites and rod eutectic of (α-Mg+Mg2Ge) in which the rod shaped precipitates are the intermetallic compound Mg2Ge phase with the orientation relationship [3 1 0]Mg2Ge//[0 0 0 1]α−Mg and (−1 3 −1)Mg2Ge/13·51°/(0 −1 1 0)α−Mg. The grain size of α-Mg dendrites is refined effectively in alloys. The solidification behaviour of Mg–Ge binary alloys is analysed. The tensile tests indicated that the ultimate tensile strengths of Mg–Ge binary alloys are enhanced while the elongations are reduced.

Properties of sintered high speed steel: L. Kosec et al (University of Ljubljana, Ljubljana, Slovenia)

Directional solidification experiments were carried out on the hypereutectic Ni-25 at.% Al alloy to examine the effect of growth velocity on the eutectic microstructure. The growth velocity was varied from 1 to 20 μm/s at a constant temperature gradient of 10.0 K/mm. The microstructural observations of unidirectionally solidified samples show that the lamellar eutectic growth was observed in the sample solidified at a constant velocity of 1 μm/s and the rod eutectic growth at velocities higher than 10 μm/s. A microstructural transition from lamellar to rod eutectics was achieved at the intermediate velocity. The lamellar to rod eutectic transition was shown to result from the compositional change due to the presence of strong convection in the melt. The undercooling-spacing curves showed that the average eutectic spacings for the lamellar and the rod structures were 1.6 times larger than that in the minimum undercooling for a given velocity.

Effects of creep and strain on the thermal stability of rod eutectics

The thermal stability of a rod eutectic structure is investigated by including strain and creep effects. The rod eutectic is modeled as an elastic rod embedded in an elastic matrix and power law creep material. Previous investigators performed the analysis of an elastic rod in an elastic matrix. Through our analysis, the influence factor of the creeping matrix, Ω 1 , is found as Ω 1 = {3K B ϵ/√3(K + 4G 3 )δ 2} m ( ρ 0 3K Bϵ m) {1−( (r 2 2 r 0 2 ) m} 3m , where K B is the bulk modulus of the rod, ϵ is the misfitting parameter, K and G are the bulk and shear modulus of the elastic matrix respectively, ρ =ρ 0ϵ m is the constitutive equation of the creep material, t is the elapsed time, δ is the ratio of the rod radius to that of the elastic matrix, and r 2 r 0 is the ratio of the elastic matrix radius to the half distance of the rod spacing. If Ω 1 is small, the contribution of creep is neglected, and structural stability is approximated by the solution obtained with the elastic rod and matrix. In that case the stability criteria is identical with that obtained by previous investigators. However if mΩ 1 is increased, the contribution of creep to the stability solution is significant and the creeping material destabilizes the structure. The amplitude of the growth rate A λ approaches that obtained by the elastic rod and matrix model with increasing elapsed time. The time to reach the A λ of the elastic rod and matrix model is strongly dependent on the strain rate hardening exponent ( m). There exists a value of m to maximize instability. The stability of the rod obtained by the present analysis is compared with that obtained by using the elastic rod and matrix [A. M. Mayes and M. O. de la Cruz, Acta metall. 37, 615 (1989)].

On the linear instability of the rayleigh spheroidization process

The problem of diffusional stability of infinitely long cylinders with respect to spheroidization has been analyzed. It is well known that long solid cylinders will break down into individual particles of spherical geometry under the action of an appropriate shape perturbation. The driving force for this process is considered to be the chemical potential gradients associated with variations in curvature which develop on the surface, or interface, in response to the perturbation. The resulting diffusional flow of material can lead to a breakdown of the rod morphology. From a practical point of view, the cylindrical geometry is one which occurs in fiber reinforced composites and rod shaped precipitates in eutectic/eutectoid structures. The shape stability of such rods is an important aspect of high temperature mechanical behavior. The general method of study for this problem involves analyzing the time dependent behavior of a perturbation; which is an imposed, mass conserving and periodic surface wave of small amplitude. These surface undulations will be referred to here as Rayleigh surface waves. In most cases, attention is focused on the surface wavelength which gives the maximum growth rate of the perturbation. This choice has not been justified by experimental results on rod eutectics whichmore » show significant scatter in the instability wavelength, and little or no physical basis, such as a stability argument, has been presented for the operation of the maximum growth rate hypothesis in the growth of periodic Rayleigh surface waves. Despite the many detailed studies on the behavior of Rayleigh surface waves, the possibility that the surface waves themselves might actually be unstable has not been considered in the literature.« less

The effect of growth rate and morphological transitions on interphase spacings of Bi-Ag, Pb-Ag and Bi-MnBi eutectics

Samples of broken lamellar Bi-Ag, Pb-Ag and Bi-MnBi eutectics were grown unidirectionally between 10−5 and 10−2 cm sec−1. In all three situations, the temperature gradient was approximately 45°C cm−1. In this investigation, the eutectics exhibited a relationship λnR = constant resulting with n > 2. The high nvalues (compared to the normal rod eutectics in which n = 2) are believed to be a characteristic of such eutectics which display morphological variations dependent on growth rate (e.g. broken lamellar to rod transition at high growth rates). In the case of Bi-MnBi eutectic, the situation may be complicated further during slow growth as a result of a morphological instability of the MnBi phase. Two different interphase spacings can therefore be determined in the lower growth rate regime.

Fault migration vs. two-dimensional ostwald ripening as a mechanism for coarsening of rod eutectics

Fault migration vs. two-dimensional ostwald ripening as a mechanism for coarsening of rod eutectics

Coarsening of rod eutectics by fault migration

Coarsening of rod eutectics by fault migration

Elevated temperature stability of the Al−Al3Ni eutectic composite

The elevated temperature stability of the Al−Al3Ni rod eutectic is reexamined at 600°C. The original coarsening process is found to be two-dimensional Ostwald ripening. The morphology produced by this process is intrinsically stable but is subject to subsequent breakdown which is most likely due to the presence of longitudinal growth defects. Coarsening resumes after breakdown of the stable structure and is characterized by two-dimensional anisotropic Ostwald ripening. Extensive fiber shortening also takes place in this latter stage of coarsening.