Growth In Multicomponent Alloys Research Articles

A new scheme for simulating diffusion-controlled growth in multi-component alloys

Simulation of diffusion-controlled phase growth has long been practiced by strictly following Fick-Onsager-Darken law for diffusion under the assumptions of local equilibrium and sharp interface. However, a major pain point is the difficulty of finding operating tie-lines at the interface for multi-component alloys. In the present work, a new scheme is presented to deal with this difficulty by extending from Larsson and Reed scheme (Larsson and Reed, Acta Mater. 56 (2008) 3754–3760). The flux balance equations are rewritten to enhance the accuracy and fulfilled from the very beginning of simulations. The simulation results of the Fe-Mn-Mo and Fe-C-Mn ternary systems, as well as high-order systems, demonstrate the applicability and robustness of the new scheme. The simulation of the Fe-C-Mn system reveals the details of the early stages of the bcc phase growth, showing a shrink of bcc before its growth with two growth modes smoothly switched.

Rapid solidification mechanism of liquid quinary Ni-Zr-Ti-Al-Cu alloy investigated by high-speed cinematography

<sec> The ability to undercool and solidification mechanism of liquid quinary Ni<sub>40</sub>Zr<sub>28.5</sub>Ti<sub>16.5</sub>Al<sub>10</sub>Cu<sub>5</sub> alloy are investigated by electromagnetic levitation (EML) and drop tube (DT) technique. Under the EML condition, the maximum undercooling of levitated alloy can reach up to 290 K (0.21<i>T</i><sub>L</sub>). Under the DT condition, the alloy achieves higher undercooling than EML, and solidifies finally into metallic glass. At lower undercooling, the solidification structure of the alloy is composed of primary Ni<sub>3</sub>Ti phase, secondary Ni<sub>10</sub>Zr<sub>7</sub> phase and eutectic (Ni<sub>10</sub>Zr<sub>7</sub>+Ni<sub>21</sub>Zr<sub>8</sub>) phase. With the rise of undercooling, the solidification structure displays the following evolution events: phase morphology refinement, primary phase inhibition, phase number reduction, and amorphous phase formation.</sec><sec> By using the high-speed cinematography technique, three nucleation modes are distinctly observed on the levitated alloy melt surface at the beginning of solidification, that is, single-point nucleation, multi-point nucleation and annular nucleation. The levitation state corresponding to single-point mode nucleation is relatively stable, and the alloy undercooling is also relatively low. The annular nucleation only occursin the case with high rotation speed, and the undercooling is greater than 208 K. The discrepancy between nucleation modes is due to the He gas flow for forced cooling. </sec><sec> The theoretical calculations indicate that the alloy droplets achieve high undercoolingand large cooling rate under the DT condition. The experimental results show that when the droplet diameter decreases to 498 μm, the amorphous phase begins to appear in the alloy particles. It is noteworthy that the amorphous phase is preferentially formed inside the droplet, but not on the outer surface. The morphology of solidification structure reveals that different regions of the droplet have various local undercoolings, which result in the distribution characteristics of amorphous phase. The volume fraction of amorphous phase increases linearly with the decrease of particle diameter. When the droplet diameter decreases to 275 μm, the alloy droplets are completely frozen into glassy particles.</sec><sec> The average eutecticspacing values are also measured at different alloy undercoolings. Compared with the classical binary eutectic growth model, the experimental eutectic growth law exhibits a large deviation in index. This indicates that the eutectic growth in multicomponent alloys displays more complex kinetic characteristics.</sec>

Dendrite tip selection during isothermal free growth in multi-component alloys: Marginal stability theories and insights from phase-field simulations

The principal length scales associated with dendritic solidification, which being the dendritic tip-radius (Rtip) and the primary dendritic arm spacing, are functions of the relative solutal interdiffusivities of the different components in a multi-component alloy. In this paper, we firstly derive marginal stability based theories to predict Rtip during isothermal free growth in any generic multi-component alloy for any generic diffusivity matrix. Here, we extend the Ivanstov solution of the diffusion problem in the liquid with a parabolic solid-liquid interface and propose the closure conditions between the Rtip and the selected dendrite tip velocity (V) based on modification of the classical marginal stability criteria for multi-component situations. Additionally, we derive the constant Rtip2V from phase-field simulations and using the Ivantsov parabola as the approximate interface shape compute the Rtip and the V, which we term as “Approximate microsolvability prediction (AMP)”. Thereafter, we compare our predictions of Rtip,V as well as phase compositions with independent phase-field simulation results for different choices of the diffusivity matrix, where we show that the analytical theories based upon the marginal stability theory are unable to accurately predict variations of the dendrite tip velocity V and the Rtip. We thereby utilize the phase-field simulation results to investigate the tip selection in multi-component alloys and derive an appropriate solvability constant σ∗. We find that the σ∗ in a multi-component alloy is a function of the diffusivity ratios of the components for the case of a diagonal diffusivity matrix.

Two-Phase Eutectic Growth in Al-Cu and Al-Cu-Ag

The microstructure developed by two-phase lamellar eutectics $$(\alpha )$$ – $$(\theta {\text {-Al}}_{2}{\text {Cu}})$$ in Al-Cu and Al-Cu-Ag alloys is analyzed. A model of two-phase eutectic growth in multicomponent alloys is used to determine the scaling law of the eutectic microstructure using the alloy thermophysical properties. The application of the model to these alloys shows that the addition of Ag to Al-Cu alloys does not significantly change the length scale of the microstructure, which is in agreement with previous experimental studies. This is explained by the combined phenomena of the decrease in interface energies with the addition of Ag and the superheating of the $$(\alpha )$$ phase interface induced by the Ag composition profile.

Theoretical and Numerical Study of Growth in Multi-Component Alloys

In multi-component systems, during diffusion-controlled growth of a precipitate from a supersaturated matrix, differential diffusivities lead to a selection of tie-line compositions different from the thermodynamic tie-line containing the alloy composition. In this paper, we address the multi-component version of the growth problem by extending Zener’s theory, and derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar, cylindrical, and spherical precipitates for independent as well as coupled diffusion of solutes in the scaling regime. We confirm our calculations by sharp interface and phase-field simulations in a ternary setting, in which we also extend the tie-line and growth constant predictions for two well-known limiting cases, namely partition and negligible partition under local equilibrium (PLE and NPLE).

The Role of Si and Cu Alloying Elements on the Dendritic Growth and Microhardness in Horizontally Solidified Binary and Multicomponent Aluminum-Based Alloys

Horizontal directional solidification (HDS) experiments were carried out with Al-3wtpctCu, Al-3wtpctSi, and Al- 3wtpctCu-5.5wtpctSi alloys in order to analyze the interrelation between the secondary dendrite arm spacing (λ 2) and microhardness (HV). A water-cooled horizontal directional solidification device was applied. Microstructural characterization has been carried out using traditional techniques of metallography, optical, and SEM microscopy. The ThermoCalc software was used to generate the phase equilibrium diagrams as a function of Cu and Si for the analyzed alloys. The effects of Si and Cu elements on the λ 2 and HV evolution of the hypoeutectic binary Al-Cu and Al-Si alloys have been analyzed as well as the addition of Si in the formation of ternary Al-Cu-Si alloy. The secondary dendrite arm spacing was correlated with local solidification thermal parameters such as growth rate (V L), cooling rate (T R), and local solidification time (t SL). This has allowed to observe that power experimental functions given by λ 2 = Constant (V L)−2/3, λ 2 = Constant (T R)−1/3 and λ 2 = Constant (t SL)1/3 may represent growth laws of λ 2 with corresponding thermal parameters for investigated alloys. Hall–Petch equations have also been used to characterize the dependence of HV with λ 2. A comparative analysis is performed between λ 2 experimental values obtained in this study for Al-3wtpctCu-5.5wtpctSi alloy and the only theoretical model from the literature that has been proposed to predict the λ 2 growth in multicomponent alloys. Comparisons with literature results for upward directional solidification were also performed.

A model for eutectic growth in multicomponent alloys

A model for eutectic growth of multicomponent alloys is proposed. Among several other modifications brought to the classic theory of eutectic growth, the model introduces the phase fraction change as the main mechanism for maintaining an isothermal solid/liquid interface during solidification of eutectic alloys. A comparison between the theoretical results and experimental measurements for the Fe-C based alloys showed a good agreement for alloys of composition not too far removed from the eutectic point. The analysis also showed that an earlier proposed criterion for spacing selection of binary irregular eutectics, based on volume fraction of the faceted phase, can be applied to multicomponent alloys as well. The investigation performed on the effect of Si on the growth kinetics of Fe-C-Si eutectic alloys showed that the growth coefficient μ decreases with the increase of Si content.

A three-dimensional cellular automaton model for dendritic growth in multi-component alloys

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.

Modeling of equiaxed growth in multicomponent alloys accounting for convection and for the globular/dendritic morphological transition

A lagrangian model has been developed to predict the evolution of a single equiaxed crystal moving into an infinite medium, and intended to be coupled with a macroscopic code devoted to the solidification of large cast products. A particular attention is paid to the transition from globular to dendritic crystals because both morphologies can be observed in cast products. First, the model has been compared with experiments of settling NH 4Cl crystals in NH 4Cl-H 2O melts. Good agreements have been achieved provided that a suitable value is chosen for the stability constant of the dendrite tip growth model. The model is then applied to a multicomponent steel so as to outline the link between the morphology and the sign of the chemical segregation. Finally, the trends drawn from the model concerning the change in morphology are discussed so as to explain the concomitancy of the structural and chemical patterns observed in the equiaxed zone of heavy steel ingots.

Prediction of Solid-Liquid Interface Stability and Dendritic Growth in Multi-Component Alloys with Calphad Method

A method to predict the solid-liquid interface stability and the constrained dendrite growth of multi-component alloys was developed based on the Calphad method. The method was applied to several industrial Al-Si-Mg alloys, and the predicted results were compared with some former experimental data. The good agreement between the calculation results and the experimental data demonstrates the superiority of the present method to the classical one based on constant parameter assumptions.

Theory of plane front and dendritic growth in multicomponent alloys

Analytical solutions for the solute diffusion fields during plane front and dendritic growth in multicomponent alloys have been developed, taking into account the diffusive interaction between the species. It is found that the composition field for each of the n solutes is given by a sum of n expressions, each corresponding to the binary solution, but where the diffusion coefficients are replaced by the eigenvalues of the diffusion matrix. An extended constitutional undercooling criterion is deducted from the solution for plane front growth. A linear stability analysis of plane front growth is also presented. For dendritic growth, the diffusion field ahead of a growing paraboloid is calculated. Using the two latter solutions, growth of a dendrite at marginal stability is modelled. As an example, these models are applied to an hypothetical ternary system. From these results, some effects of diffusional interaction are shown and discussed.

On the formation of a centreline grain boundary during fusion welding

The formation of a centreline grain boundary during fusion welding constitutes a potential weldability issue and its presence may affect the life of a welded structure. In practice, it is therefore often appropriate to avoid it through the choice of suitable welding conditions. A numerical model for the formation of a centreline grain boundary is proposed. It involves the coupling of a semi-analytical heat transfer model and a treatment of dendritic growth in multicomponent alloys. It has been applied to the tungsten–inert gas (TIG) welding of IN718 superalloy. The thermal model and the predicted weld pool shape are validated against experimental observations. A weldability diagram is predicted, on which the conditions for centreline grain boundary formation are identified. The formation of a centreline grain boundary is found to be strongly dependent on welding power, and relatively independent of welding velocity. A weldability window arises if the formation of a centreline grain boundary is to be avoided.