Large Undercooling Research Articles

Far-from-equilibrium solid–liquid interfacial properties of aluminum

Simulating quantitatively far-from-equilibrium conditions, which is relevant to a host of rapid solidification processes, has remained a major challenge where theoretical models and physical mechanisms for far-from-equilibrium solid–liquid (SL) interface are essential. Herein, we investigate the effects of far-from-equilibrium state and external strain on SL interfacial properties by using capillary fluctuation method and models based on transition rate theory. Under an extreme temperature gradient (TG), both SL interfacial stiffness (S) and SL interface velocity (v) are found to increase with TG. The nonlinear relationship between v and temperature is revealed over a large undercooling range (640 K). It is found that an external strain (ϵ) of 1%–3% could decrease S by 10%–30%. v is found to increase with external strains at large undercooling. Tensile strains decrease the activation energy (Q) and viscosity, thus facilitating SL interface movement. A strain-dependent Gibbs–Thomson condition is proposed by incorporating linear S-ϵ and Q-ϵ relations. Our systematically theoretical discussion on the far-from-equilibrium SL interfacial properties could provide a predictive guideline on SL interface behavior in the additive or extreme manufacturing.

A DSC study of undercooling thermodynamics and crystallization kinetics for liquid Ag-Si alloys

The undercooling thermodynamics and crystallization kinetics of pure silver, hypoeutectic Ag-2%Si, and eutectic Ag-3.1%Si alloys were explored with differential scanning calorimetry. Liquid silver was highly undercooled by an extent of 200 K (0.16Tm) within molten B2O3 denucleating agent. The nucleating incubation time and crystallization kinetics were investigated under isothermal condition. It was found that the crystal incubation time of nucleation generally decreased with enhanced undercooling. The analyses based on classical nucleation theory showed that heterogeneous nucleation was still dominant even at substantial undercoolings. The transformed solid fraction was derived to elucidate the crystallization kinetics of liquid silver by Johnson-Mehl-Avrami equation. The Avrami exponent was revealed to vary with liquid undercooling and crystallization extent. High cooling rate and denucleating agent were two effective ways to achieve large undercoolings for liquid Ag-Si alloys. The primary (Ag) dendrites were refined with increased undercoolings in hypoeutectic Ag-2%Si alloy. Irregular (Ag)+(Si) eutectics were the typical solidification microstructures for eutectic Ag-3.1%Si alloy at small undercoolings, while primary (Ag) dendrites displayed a remarkable volume fraction at extended undercoolings.

Metastable phase separation and crystalline orientation feature of electromagnetic levitation processed CoCrCuFeNi high entropy alloy

The metastable liquid phase separation and rapid solidification kinetics of CoCrCuFeNi high entropy alloy (HEA) has been investigated by electromagnetic levitation (EML) technique. The maximum liquid undercooling attained 452 K (0.27TL), and the critical undercooling to initiate phase separation was determined as 172 K. By modulating the degree of alloy undercooling, the overall macrosegragation pattern achieved a transition from homogeneous dendrites into dispersed structures and finally into core-shell structures. Both microstructure and electron backscatter diffraction (EBSD) characterizations revealed that liquid undercooling played a crucial role in the modulation of dendritic anisotropy correlated with crystalline orientations. Coarse high entropy face-centered cubic (HEF) dendrites were produced with 〈100〉 preferred orientation at small undercoolings. Once undercooling exceeded the threshold of 172 K, the previously uniform liquid alloy was separated into Cu-depleted and Cu-rich zones. Numerous equiaxed HEF grains of relatively random orientation together with some twin crystals were displayed in Cu-depleted zone, whereas in Cu-rich zone HEF phase solidified into many slender dendrites. Theoretical analyses indicated that equiaxed grains were produced in the regime of thermal diffusion-controlled dendritic growth with actual solidifying velocity up to 42.7 m s−1. Furthermore, physical properties examinations demonstrated that large liquid undercoolings enhanced the alloy microhardness and low temperature saturated magnetization but reduced its electrical resistivities.

Grain refinement in solidification of undercooled Fe2B intermetallic compound alloy

Spontaneous grain refinement widely occurs in solidification of highly undercooled solid solution alloys, but the case in stoichiometric intermetallic compound alloys is seldom concerned. In this paper, Fe2B alloy was undercooled up to 336 K to investigate the solidification structure’s evolution with undercooling. It is shown that the equilibrium peritectic reaction L + FeB → Fe2B is completely suppressed and there is only an Fe2B phase to solidify at various undercoolings. As the undercooling increases, Fe2B crystals change from a faceted into non-faceted morphology, and grain refinement takes place from 48 K undercooling until a fully refined solidification structure is obtained above 92 K undercooling. When the sample solidified at a large undercooling is immediately annealed at high temperature, the grains are coarsened quickly. In combination with the electron backscattered diffraction and transmission electron microscopy analysis results, it is suggested that the solidification stress-induced recrystallization triggers the grain refinement in Fe2B alloy.

Microstructure evolution in undercooled Ag-50at. %Cu hypereutectic alloy

Ag–Cu alloys, as one type of typical eutectic solders, have been widely used in microelectronic packaging. The welding performance of Ag–Cu solders is closely associated with their microstructures. However, the microstructure evolution of Ag–Cu alloys during solidification is still poorly understood. In this work, a new melt fluxing technique was proposed to investigate the microstructure evolution of undercooled Ag-50at.%Cu hypereutectic alloy. The maximum undercooling of Ag-50at.%Cu alloy can reach up to 135 K. The obtained results show that the microstructures consist of primary dendrite and lamellar eutectic at low undercooling (ΔT – 10 K). With the increase of undercooling, dendrites undergo refining (ΔT < 65 K) and then disappear completely (ΔT = 78 K) and appear again (ΔT = 119 K). It is also discovered that cellular lamellar eutectics formed with ΔT within range of 65 K–78 K. Unexpectedly, irregular microstructures are observed when ΔT > 135 K. Theoretical calculation results indicate that the formation of irregular eutectic is associated with the dendritic fragmentation and eutectic coarsening under larger undercooling (ΔT = 135 K). These results not only elucidate the relationship between the solidification microstructure and undercooling of Ag-50at. %Cu hypereutectic alloys but also has positive significance for other hyper-eutectic systems.

Investigation on nonequilibrium crystallization of highly undercooled Cu–Ni–Co alloys

Deep undercooling rapid solidification experiments of Cu–Ni–Co alloys were carried out using the molten glass purification cycle superheat method. 130 K, 177 K and 277 K undercooling degrees were obtained and analysed for Cu55Ni43Co2 alloy. The crystallographic information obtained by EBSD and the dynamics of the solidification front taken by high speed photography were analysed and it was concluded that both the formation of relatively rounded equiaxed grains during the first refinement and the subsequent formation of finer subcrystals were due to the release of a large amount of solidification energy during the solidification process. The re-glow stage releases a large amount of latent heat of solidification resulting in the remelting of the dendrites. TEM tests were carried out on Cu55Ni43Co2 alloy with a maximum undercooling of 277 K. It was found that part of the substructure showed a high density dislocation network. By analysing the effect of increasing undercooling on the microstructure evolution, combined with the EBSD and TEM characterisation data, it was found that the stress-induced recrystallization mechanism was the dominant factor in the grain refinement mechanism at large undercooling.

A genome dependence of metastable phase selection on atomic structure for undercooled liquid Nb90Si10 hypoeutectic alloy

The phase selection mechanism within undercooled liquid Nb90Si10 hypoeutectic alloy was investigated by electrostatic levitation technique combined with deep neural network molecular dynamics. A stepwise-solidification procedure was conducted, where the primary phase and eutectic microstructure successively solidified from undercooled liquid alloy and undercooled residual liquid, respectively. The intermetallic phase of the eutectic structure transfers from Nb3Si to βNb5Si3 and finally into αNb5Si3 compound with the increase in liquid undercooling. The deep neural network molecular dynamic simulations have shown that the phase selection between Nb3Si and Nb5Si3 is mainly controlled by the short-range order of residual liquid, considering that the predominant short-range configuration transforms from Nb3Si-like to Nb5Si3-like structures. The αNb5Si3-like medium-range order, which is characterized by vertex-connected ⟨0,2,8,4⟩ clusters, is shown to significantly influence the competitive nucleation of the αNb5Si3 and βNb5Si3 phases. The residual liquid favors the αNb5Si3-like medium-range order rather than βNb5Si3 at large undercoolings, which explains the transformation from βNb5Si3 to αNb5Si3.

Properties and microstructural evolution of a ternary Cu–Co–Fe immiscible alloy solidified under high magnetic fields

In this study, ternary Cu52Co24Fe24 immiscible alloys are prepared with varying undercoolings and under a high magnetic field. The microstructure evolution and properties of the alloys are investigated. The temperature range of the immiscible gap is determined using CALPHAD. According to the excess Gibbs free energy of liquid, the addition of Fe promotes the demixing tendency of the Cu–Co–Fe ternary system during solidification. With the application of a magnetic field, the (Fe, Co)-rich phases transform from a globular shape to an elongated form along the direction of the magnetic field during solidification, which is due to the existence of the counteracting behavior of the interparticle magnetic dipole-dipole force at the critical droplet size. Under a high magnetic field, the obtained samples had a more dispersed minority phase, higher microhardness and better conductivity. However, the saturation magnetization of the samples with large undercooling decreases with increasing magnetic field due to the suppression of the phase separation behavior under a high magnetic field. This study proposes a novel technology for preparing immiscible alloys with excellent properties by applying a superimposed magnetic field during solidification.

Hypo-eutectic microstructure formation and nanomechanical response in Sn-3.0Ag-0.5Cu solder balls: Effects of undercooling

The microstructure control and refinement in length scale are pursued in the development of next generations of Pb-free solder alloys with high reliability in harsh environments. In the present work, the influences of nucleation undercooling, as brought by solder ball size, over the microstructure evolution and nanomechanical behavior in Sn-3.0Ag-0.5Cu (wt%) Pb-free solder alloys, have been quantitively investigated using Differential Scanning Calorimeter (DSC), Scanning Electron Microscopy (SEM) and nanoindentation. The results reveal that undercooling increases with the decrease of solder ball size. The frequency of interlaced grain microstructure was significantly increased in 200 μm balls, with a further increase of undercooling by ~10 K. The volume fraction of primary β-Sn increased with larger undercooling, leading to microstructure refinement with a finer spacing of both β-Sn dendrite and eutectic Ag3Sn. The length scale of refinement is on the order of ~2, as the solder ball size reduced from 650 μm to 200 μm. Nano-hardness and creep resistance increase with smaller ball size and larger undercooling. Nano-hardness values are relatively higher as more eutectic regions being measured due to the strengthening effect of finer and denser eutectic Ag3Sn, and also the refinement of interlaced β-Sn grains. The creep exponent is insensitive to the loading force or solder ball size. The variation of nanomechanical deformation behavior was reduced in the 200 μm balls, due to the substantial microstructure refinement, while the dominant creep mechanism stays as the dislocation climb for various solder ball sizes.

Effect of undercooling on microstructure evolution of Cu based alloys

Based on the deep undercooling rapid solidification method, the Cu based alloy has reached different undercooling degrees. The microstructure and evolution of non-equilibrium solidification of two alloys were systematically studied. It is found that grain refinement occurs in both the large undercooling range and the small undercooling range of the two alloys. EBSD technology was used to analyze the grain refinement structure, and the results showed that the grain refinement structure with large undercooling and that with small undercooling had completely different grain orientations. The grain refinement of low undercooling alloy is caused by dendrite remelting and fragmentation, while that of high undercooling alloy is completed by stress induced recrystallization. The evolution law of undercooling and microstructure hardness was systematically studied by using a microhardness tester. It was found that a sudden drop in grain size occurred near the critical undercooling, which is the direct evidence of grain refinement of non-equilibrium solidification structure of high undercooling alloy due to recrystallization.

Rapid dendritic solidification and structure hardening mechanism of substantially undercooled quaternary nickel alloys

The high undercooling and rapid solidification of liquid quaternary Ni-5%Cu-5%Sn-5%Si and Ni-5%Cu-5%Sn-5%Ge alloys were achieved by glass-fluxing technique to explore their dendritic growth kinetics, microstructural evolution and hardening mechanisms. The dendrite growth velocity of α-Ni phase was found to increase with the rise of bulk undercooling, which could be described by power law functions for both alloys. With the increase of liquid alloy undercooling, the morphology of α-Ni phase transformed from developed dendrites into equiaxed grains. Both the fine grain hardening and solute hardening effects resulted in the elevated Vickers hardness for these two alloys. Nano-sized Ni3Si precipitations were detected within the first alloy, which distributed homogeneously in the α-Ni phase matrix and transformed from faceted to nonfaceted morphology at sufficiently large undercoolings. The precipitate hardening effect dominated the Vickers hardness enhancement for this Si containing alloy. Rapid solidification could modulate the formation of ordered precipitate phase and thus improve the hardening effect by changing dislocation motion conditions.

Effects of undercooling on atomic crystallization behaviors and growth mechanisms of pure metals

The atomic crystallization behaviors at the crystal–melt interfaces in a broad range of undercoolings are investigated by molecular dynamics simulations for two representative pure metals, FCC Cu and BCC Ta. Results show that the atomic transformation displacements against temperature for both metals have the same trend, i.e., increasing significantly as temperature goes up at small undercooling and keeping invariant at large undercooling. By classifying the interfacial atomic attachment behaviors into ballistic and diffusive motions based on the displacement analysis, it is found that the crystal growth of both metals involves many ballistic attachments, and a small increment of diffusive attachments at the Ta interface leads to a significant energy barrier for crystallization comparing to that of Cu. The temperature effects on the interfacial structures and atomic dynamics to attach onto the crystal are also studied in detail, and their correlations with the different growth mechanisms at low and deep undercoolings are disclosed. Finally, the crystallization rate is proved to be dominated by the atomic transformation displacement and interfacial atomic movement rate for either metal, rather than the atomic thermal velocity or liquid diffusion coefficient.

Investigation of the preferred orientation relationships between the in-situ synthesized TiC and titanium matrix

The coplanar reciprocal lattice points (CRLPs) method was used to predict the preferred orientation relationships between α-Ti and TiC. The calculation result shows that two orientation relationships satisfy the criterion, i.e. (0001)α-Ti // (111)TiC, [12¯10]α-Ti // [11¯0]TiC and (101¯0)α-Ti // (111¯)TiC, [0001]α-Ti // [101]TiC. The predicted orientation relationships agree with the published experimental results and present a small lattice misfit on the interface plane. The calculated interface energies indicate that the Ti-terminated rather than C-terminated interface configuration will be formed. The negative interface energies explain the diffusion of the C atom on the interface region. The preferential orientation relationship of (0001)α-Ti//(111)TiC and [12¯10]α-Ti//[11¯0]TiC possesses the lowest interface energy and might be formed in a relatively slow cooling rate process. However, in some rapid cooling processes, the larger undercooling might lead to the formation of (101¯0)α-Ti//(111¯)TiC and [0001]α-Ti//[101]TiC, even if its interface energy is large than the former one. The calculation results indicate that the CRLPs method can provide an effective means to select the potential orientation relationships, on which the first principles calculation can be carried out in a reasonable and acceptable range.

Highly ductile hypereutectic Al-Si alloys fabricated by selective laser melting

In the endeavor to maximize the refinement effect of primary Si and alleviate the inherent brittleness of hypereutectic Al-Si alloy, the approach of coating P as a modifier on powder was adopted. The ultimate aim was to create more heterogeneous fine AlP nucleus and enhance the nucleation efficiency of primary Si on AlP to refine the coarse primary Si to nano-scale during 3D printing. In the combination of large undercooling and high density of nucleation sites, the size of primary Si was successfully refined to 200–300 nm and the divorced eutectic was also induced to modify the microstructure of matrix. In the presence of nano-scale primary Si, the melting pool boundary (MPB) feature disappeared and the fracture mechanism also changed from load transfer to interfacial fracture. Compared with the pristine alloy, the ductility was increased four times without significantly changing the ultimate tensile strength (UTS) and wear resistance. The improvement of ductility is attributed to the refinement of primary Si, the disappearance of MPB features and the formation of divorced eutectic. The optimal tensile properties were: UTS-482 MPa, yield strength-320 MPa and ductility of 8.1% at 0.05 wt.% P. These are comparable to those for high-strength Al alloys.

Thermal diffusion coupled quantitative phase-field simulations with large undercooling

The numerical solution of phase-field model depends on the input interface-width particularly when the undercooling is high. In order to make the computation feasible, the interface is required to be thick, but such choice of interface-width renders the numerical solution inaccurate. In the present work, we investigate the effect of interface-width on phase-field computation with thermal diffusion under high undercooling. We show that the accuracy of phase-field computation is actually related to the interfacial-energy. A numerical strategy based on mobility-correction is formulated and applied to the transformation of γ→α-iron under various conditions. We also numerically solve the moving-boundary model based on the sharp interface and compare it with the phase-field computations to assess its accuracy. It has been observed that convergence of the phase-field computations to sharp-interface based predictions is remarkably good with the proposed computational strategy over a wide ranges of input interface widths and undercoolings.

Improved multi-order parameter and multi-component model of polycrystalline solidification

• The grain boundary energy can be predicted even at larger undercoolings by tuning the coefficient of the new introduced interpolation function. • The kinetic coefficient can be adjusted to match the grain boundary migration situation encountered during solid state transition. • A self-consistent nucleation method was successfully incorporated into the model through introduction of noise effects. Accurate nucleation driving force is used and temperature dependent noise amplitude expression is given. • Through employing the parabolic free energy fitting technique, the developed model can be effectively used to study the entire solidification process for a variety of alloys. Temperature dependent phase field parameters selection strategy is proposed and proved. • Two solid phases nucleation of Al-Cu alloy is realized through self-consistent noise term. This approach is suitable to study multiple solid phase solidification phenomena. In this paper, we present an improved multi-order parameter model for multi-component model of polycrystalline solidification. We introduce an interpolation function in the phase field dynamical equation to obtain controllable grain boundary energy at large undercooling. The same interpolation function is also employed in the kinetics coefficient to allow for better control of grain boundary migration. Temperature dependent phase field parameters and noise terms are consistently coupled into the dynamics of a binary system in a manner that allows for quantitative simulations in the thin interface limit. The model is applied to multi-phase solidification in Al-Cu alloy, where a parabolic fitting method is employed to model the free energy of Al-Cu phases and two-phase nucleation is demonstrated in directional solidification.

Effect of Co/Ni atomic ratio on the metastable phase formation in Co-Ni-B alloys

(Co1−xNix)79.3B20.7 (x = 0, 0.25, 0.5, 0.75, 1) alloys were solidified at different undercoolings, aimed at the effect of Co/Ni atomic ratio on the metastable phase formation and stability. Substitution of Co by Ni reduces the possibility for metastable M2B (M = Co or/and Ni) phase to form as primary solid at medium undercoolings. As a result, M2B phase completely disappears from the solidification of the alloys with x = 0.5, 0.75 and 1. All the Co-Ni-B alloys investigated solidify into single metastable M23B6 phase at large undercooling. The stability of metastable M23B6 phase however becomes worse as the Ni content increases, due to which it is decomposed into α-M and M3B phases in the post-solidification cooling process when x ≥ 0.75. A vertical section of the Co-Ni-B phase diagram with a content of 20.7 at% B was drawn, including the liquidus temperatures of M3B, M2B and M23B6 phases and the eutectic temperatures of L → α-M + M3B and L → α-M + M2B.

Effects of size and cooling rate on solidification behavior of freestanding Sn-3.0Ag-0.5Cu solder balls

The diversity of electronic product types needs variable solder joint sizes and processing conditions, which can lead to the complexity and diversity of solidified microstructure in Sn-based solder joints. Due to the significant anisotropy of β-Sn in physical and mechanical properties, the solidified microstructure of the Sn-based solders after soldering should be carefully controlled. In this paper, Sn-3.0Ag-0.5Cu freestanding solder balls were used to understand the effects of size and cooling rate on the solidification behavior and microstructure. Larger undercooling, ∆T , was detected for smaller solder balls or under larger cooling rate. With the solder ball size increased from small level of 100 and 200 μm to medium level of 400 μm and then to large level of 700 μm and 1200 μm, the dominant solidified microstructure transformed from interlaced grain & beach ball to randomness and then to single grain. Correspondingly, three nucleation & growth models, i.e., single grain ( ∆T ≤ 20 K), cyclic twin (20 K ≤ ∆T ≤ 25 K) and interlaced grain & beach ball (25 K ≤ ∆T ), were proposed to explain the solidification behavior of β-Sn. A mapping of the most likely formed β-Sn microstructure regarding solder ball size and cooling rate was established to not only predict the major microstructure of solder balls but also optimize the process parameters for solder ball fabrication. • Effects of size and cooling rate on undercooling, secondary dendrite arms and grain features of β-Sn were studied systematically. • A mapping of the most likely formed β-Sn microstructure regarding different process parameters was established. • Three nucleation & growth models were proposed to explain the solidification behavior and microstructure of freestanding SAC solder balls.

Multiscale simulation of rapid solidification of an aluminium–silicon alloy under additive manufacturing conditions

At present, most multiscale simulation approaches to model the temperature evolution of the molten pool, and the resulting microstructure evolution for selective laser melting, assume an equilibrium freezing range and steady state solidification conditions. This is despite the solidification conditions being observed to be highly unsteady and non-equilibrium. These two assumptions lead to inaccurate predictions of the temperature evolution of the molten pool and thus microstructure predictions. To demonstrate this, an approach to scale-bridging computational models of the laser additive manufacturing process is presented, in which the temperature history is passed from a macroscale molten pool simulation to a microscale phase-field simulation. This linkage is achieved by volume mapping of the temperature field from the grid of the molten pool simulation to the grid of the microstructure simulation. To describe the system evolution at the scale of the molten pool, a computational fluid dynamics (CFD) method that captures the laser–metal interaction, vapour production, gas recoil pressure, fluid flow, surface tension, Marangoni flow, and heat conduction, convection, and radiation is applied. To capture the chemical kinetics of the phase-transition, a non-equilibrium CALPHAD-integrated phase-field (PF) model is applied. The discrepancy between the predictions of the solid front isotherm is quantified as ⩾ 100 K for an Al-10Si alloy under the large observed cooling rate. This leads to a spatial discrepancy in the solidification front between the CFD model, which assumes equilibrium freezing behaviour, and the PF model, which does not, of approximately 10 µm over 50 µs in the present case. Under these conditions, present formulations of multiphase CFD cannot accurately predict the solidification behaviour because of the assumption of equilibrium at the solid–liquid interface. Strategies for reconciling this discrepancy for materials that exhibit rapid solidification under large thermal undercooling will need to be developed for multiscale simulation of additive manufacturing to advance.

Phase-field modeling of dendritic growth of magnesium alloys with a parallel-adaptive mesh refinement algorithm

A two-dimensional phase field (PF) model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure. By applying a parallel-adaptive mesh refinement (Para-AMR) algorithm, the computational efficiency of the numerical model was greatly improved. Based on the PF model, a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy. The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient. A significant finding is acquired that with a large undercooling, the maximum solute concentration is located on both sides of the dendrite tip in the liquid, whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid. The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient, while the variation trend of the dendrite tip radius is the opposite. Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics, and the simulated results are consistent with the theoretical models proposed in the previously published works.