Undercooled Melt Research Articles

Unraveling conditions for W-shaped interface and undercooled melts in Cz-Si growth: A smart approach

In Cz-Si growth, concave and W-shaped solid–liquid interfaces and undercooled melts are primary contributors to the degradation of crystal quality, particularly structure loss, defect generation, non-uniform dopant distribution, and crystal twisting, making their avoidance crucial. We employed a classification tree machine learning approach to investigate the importance of 15 process and furnace design parameters and their critical ranges for the formation of various types of W-shaped interfaces and undercooled melts at different scales, both in dimensional and dimensionless forms, and across a wide range of process conditions. Moreover, symbolic regression was used to predict minimal melt temperature based on the aforementioned inputs. Training data were obtained by CFD modeling. The classification tree for combined output identified the Grashof, Reynolds for crystal, and Stefan numbers, along with the percentage of silicon solidified, as the most decisive inputs. Symbolic regression for the temperature of undercooled melt highlighted crucible diameter, pulling rate, and the power of the bottom heater as key parameters.

Morphology Control of Nanoporous Gold Through Selective Dissolution of Au–Ge Eutectic Microstructures

The synthesis of nanoporous gold (np‐Au) through the conventional method of dealloying a more reactive element from AuTherma alloys has been extensively studied and applied in various fields, particularly catalysis. Herein, a novel approach to creating droplet‐like np‐Au through the selective dissolution of Au–Ge eutectic microstructures is explored. This work reveals that adjusting the undercooling of the eutectic melt during solidification allows for the tuning of pore and ligament sizes. It is demonstrated that this undercooling can be modified, either directly or indirectly, by adjusting either the cooling rate or the heterogeneous nucleation site density of the eutectic melt. The findings, aligned with the model based on classical theory for eutectic solidification, elucidate the connection between the tuning of pore and ligament sizes in the eutectic microstructure and the undercooling of the eutectic melt. Importantly, it is established that this phenomenon is applicable across a variety of compositions, including hypereutectic, eutectic, and hypoeutectic. The ability to regulate pore and ligament size in single crystals of np‐Au droplets offers a novel approach to synthesizing catalytic np‐Au crystals with enhanced mechanical and thermal stability compared to conventional methods.

Optimizing the microstructure and enhancing the mechanical prsoperties of hypereutectic Al–Si alloys by Mg addition

The impact of Mg on the solidification structure of hypereutectic Al–Si alloys with different Si contents (15 wt% and 18 wt%) was investigated. 3%Mg was added to Al–15Si alloy to modify the phases in the solidification structure for the improvement of mechanical properties, and T6 heat treatment was used to optimize the microstructure and precipitate strengthening phase. The solidification structure was observed by OM and TEM respectively, and the precipitation behavior of each phase was detected through DSC. The results show that the addition of Mg decreased the undercooling of the alloy melt, thus suppressing the precipitation of primary Si phase. Nanoscale β” precipitates were precipitated in the matrix after T6 heat treatment. This resulted in an increase of 54% and 165% in the UTS and EL of the alloy, reaching 252 MP and 15.1%, respectively. Primary Si crystals were present in two forms in Al–18Si–8Mg alloy: spinel twin and non-twin, while Mg2Si always maintained the faceted crystals during the growing process, where only (100) and (111) crystal planes were observed. XRD, SEM and EBSD have been used to prove that Mg2Si crystals with different morphologies could become the heterogeneous nuclei of two types of primary Si crystals. The process of nucleation and growth of primary Si with Mg2Si as the heterogeneous nuclei was experimentally analyzed and theoretically predicted.

Study on the characteristics and high-temperature dissolution mechanism of eutectic carbides in medium-alloy steel

In this study, the high-temperature evolution of eutectic carbides in a medium-alloy steel was investigated as well as their precipitation mechanism. Results revealed that MC and M6C eutectic carbides in the steel appeared during the final solidification due to the segregation of Mo and V and the melt undercooling. These eutectic carbides consist of blocky shapes with varying orientations, and rod-like shapes with the same orientation. Further investigation was confirmed that the carbides (MC and M6C) exhibited an intergrowth behavior. The cooling rate had a direct influence on the secondary dendrite arm spacing (SDAS), which decreased from 180 to 130 μm as the rate ranged from 0.6 to 21.9 °C/min. After holding for 0, 25, 50, and 80 h, respectively, the volume percentage of eutectic carbides exhibited a significant decreasing trend from 2 to 0.2%. Additionaly, the carbides exhibited irregular morphology after holding for 0–50 h, respectively, and which was transformed into the rod-like shape with a small size distributed along the grain boundaries after holding for 80 h. This phenomenon was attributed to the mutual diffusion between Mo, V, and other alloying elements in the carbides and Fe element in the steel matrix.

Dendritic Si growth morphologies in highly undercooled Al–Si alloys

The morphology of primarily crystallizing Si in hypereutectic Al-(20, 40, 55) wt%Si alloys during conventional casting (nucleation undercooling ΔT<1 K) and solidification at high undercoolings (ΔT up to 335 K) has been investigated. As expected, at higher undercoolings a higher nucleation frequency and fast growth of primary Si is observed, leading to the formation of multiple microstructural zones. Instead of the well-known plate-like Si in the as-cast microstructure, various morphologies of primary Si such as faceted and non-faceted blocky morphologies as well as dendrites with aligned side branches showing constant spacing features are observed after solidification at high undercoolings. The special Si dendrites only grow in a limited range of melt concentrations and undercoolings. The transition from faceted to non-faceted growth appears to occur in several steps, as Si dendrites with similar features of the secondary arms as in non-faceted metal alloys are also observed.

Microstructure regulation and performance of titanium alloy coating with Ni interlayer on the surface of mild steel by laser cladding

The preparation of Ti-alloy coating on the steel surface via laser cladding is very easy to form Fe-Ti phase and large tensile residual stress, which is not conducive to the performance of Ti-alloy coating. Here, Ti-6Al-4V coating (TC4-coating) was prepared on the mild steel substrate using laser cladding technology with Ni-alloy as the interlayer, and the Fe-Ti phase inside was completely suppressed. Increasing the powder feeding rate and scanning speed can change the undercooling of the alloy melt and the preferred growth orientation of the grains, while limiting the abnormal grain growth and grain boundary segregation, which is beneficial for grain refinement and equiaxed crystal formation. Reducing the scanning speed and powder feeding rate can increase the molten pool lifetime, thereby increasing the dilution rate of the coating and facilitating the formation of Ti2Ni phase. The abundant Ti2Ni inside the coating gives the TC4-coating greater microhardness (>500 HV0.1) and better corrosion resistance (Icorr of 7.00 × 10−8 A·cm−2). Grain refinement of the coating texture caused by the increase of powder feeding rate and scanning speed, as well as the high content of β-Ti phase and martensite structure, can improve the adhesion and shear strength of TC4-coating (386 ± 31 MPa).

Impact of sulfur addition on the structure and dynamics of Ni–Nb alloy melts

We investigated the change in the structure and dynamics of a Ni–Nb bulk metallic glass upon sulfur addition on both microscopic and macroscopic scales. With the sulfur concentration of 3 at. %, where the composition Ni58Nb39S3 exhibits the best glass forming ability in the investigated sulfur concentration range, both the equilibrium and undercooled melt dynamics remain almost unchanged. Only in the glassy state does sulfur seem to result in mass transport less decoupled to the viscosity of the undercooled liquid, where the measured Ag tracer diffusion coefficient is slower in the ternary alloy. With the structural disorder introduced by the alloying sulfur, the improved glass forming ability is attributed to geometrical frustration, where crystal nucleation requires a depletion of sulfur and hence long range diffusion, as long as no primary sulfur-containing crystalline phase is involved.

Fast crystal growth in deeply undercooled ZrTi melts.

We investigate the growth of crystals in Zr50Ti50 melts by classical molecular-dynamics simulations with an embedded atom method and a Stillinger-Weber potential model. Both models display fast solidification rates that can be captured by the transition state theory or the Ginzburg-Landau theory at small undercoolings. Fast crystal-growth rates are found to be affected by the pre-existing ordering in liquids, such as the body-centered cubic-like and icosahedral-like structures. The interface-induced ordering unveiled by the crystal-freezing method can explain the rate difference between these two models. However, these orderings fail to rationalize the temperature evolution of the growth rate at deep undercoolings. We correlate the growth kinetics with the detailed dynamical processes in liquids, finding the decoupling of hierarchic relaxation processes when collective motion emerges in supercooled liquids. We find that the growth kinetics is nondiffusive, but with a lower activation barrier corresponding to the structural relaxation or the cage-relative motion in ZrTi melts. These results explore a new relaxation mechanism for the fast growth rate in deeply undercooled liquids.

Modulation of characteristic zones in NiTi alloys fabricated via wire arc additive manufacturing

The application of additive manufacturing (AM) is gradually extending to different industrial sectors. Most additively manufactured metallic components typically exhibit an inherent columnar grain structure, the control of which has been a challenging issue. In this study, the microstructures of the characteristic zones (heat-affected zone and transition zone) were controlled by adjusting the deposition strategy and arc mode during wire arc additive manufacturing (WAAM) of NiTi alloy. Compared to the sample fabricated by cold metal transfer (CMT) mode, the oscillating (O) sample shows a higher tensile strength of 793.6 MPa, while the pulsed (P) sample shows a better elongation of 5.8%. The high strength of the O samples is mainly due to the significantly lower aspect ratio of its columnar grains, while fine equiaxed grain structure in the transition zone of the P samples is responsible for the better plasticity. Different microstructures in the characteristic zones can be tailored by combining the forced melt flow, pulse frequency and undercooling, which provides vast freedom for the associated mechanical properties control. Our work provides a new strategy to regulate the microstructure and thus mechanical properties of additively manufactured NiTi alloys.

The Solid–Liquid Phase Interface Dynamics in an Undercooled Melt with a Solid Wall

A new boundary integral equation for the interface function of a curved solid/liquid phase interface propagating into an undercooled one-component melt is derived in the presence of a solid wall in liquid. Green’s function technique is used to transform a purely thermal boundary value problem to a single integro-differential equation for the interface function in two- and three-dimensional cases. It is shown that a solid wall represents an additional source of heat and melt undercooling can be negative in the vicinity of the wall. The new boundary integral equation has a limiting transition to previously developed theory in the absence of a solid wall.

Thermophysical properties and rapid solidification mechanism of liquid Zr&lt;sub&gt;60&lt;/sub&gt;Ni&lt;sub&gt;25&lt;/sub&gt;Al&lt;sub&gt;15&lt;/sub&gt; alloy under electrostatic levitation condition

In this study, the thermophysical properties and rapid solidification mechanism of highly undercooled liquid Zr&lt;sub&gt;60&lt;/sub&gt;Ni&lt;sub&gt;25&lt;/sub&gt;Al&lt;sub&gt;15&lt;/sub&gt; alloy are investigated through the electrostatic levitation technique. The maximum undercooling of this alloy reaches 316 K (0.25&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;L&lt;/sub&gt;). Both density and surface tension display a linear relationship with temperature, while viscosity is related to temperature exponentially. When alloy undercooling is less than 259 K, two significant recalescence events are observed during solidification, corresponding to the formation of pseudobinary (Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni + Zr&lt;sub&gt;5&lt;/sub&gt;Ni&lt;sub&gt;4&lt;/sub&gt;Al) eutectic and ternary (Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni + Zr&lt;sub&gt;5&lt;/sub&gt;Ni&lt;sub&gt;4&lt;/sub&gt;Al + Zr&lt;sub&gt;2&lt;/sub&gt;Ni) eutectic. The growth velocity of the binary eutectic phase gradually increases with further undercooling and reaches a maximum undercooling value of 259 K. In contrast, once undercooling exceeds 259 K, a single recalescence event occurs, leading to the independent nucleation of all three compound phases from alloy melt and the rapid growth of a ternary anomalous eutectic structure. Notably, the growth velocity of the ternary eutectic phase exhibits a gradual decline with further undercooling. This diminishing trend of the growth velocity suggests that further undercooling might entirely suppress crystal growth dynamically at a threshold of 385 K. With classical nucleation theory and the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, the onsets of crystallization for the three phases are calculated, thereby constructing a time–temperature-transformation (TTT) diagram. This diagram elucidates the competitive nucleation among the three phases in the undercooled melt. Both theoretical and experimental evidence reveal that Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni phase is primarily nucleated at lower undercooling levels, whereas under higher cooling condition, it is possible for all three phases to nucleate simultaneously.

Study on structure refinement mechanism in rapid solidification of a deeply undercooled Cu60Ni38Co2 alloy

Employing molten glass purification and cyclic overheating technologies, a Cu60Ni40 alloy was modified by introducing trace amounts of Co element. Through this process, we aimed to understand how the addition of Co element influences the microstructure morphology of the alloy. By combining the BCT model and metallographic analysis, the intrinsic factors of microstructure transformation in the alloy were studied. In the case of small undercooling, solute diffusion dominates dendritic growth, but the undercooled melt is limited to a narrow range of growth, resulting in the formation of coarse dendritic morphology in Cu–Ni alloy. As the undercooling increases, the growth of dendrites is gradually controlled by both solute diffusion and thermal diffusion, and the remelting effect of dendrites is also gradually enhanced. During rapid solidification with lower undercooling, the dendrites formed by the undercooled melt can be remelted to form numerous crystal seeds. Within a moderate undercooling range, dendrites grow directionally due to thermal diffusion and exhibit specific characteristics. At high undercooling, the dendrites' directional growth, primarily driven by thermal diffusion, undergoes stress fragmentation.

Magnetic field induced instability pattern evolution in an immiscible alloy

The magnetic field induced instability patterns have been observed in an undercooled immiscible Co–Cu alloy by an in situ magnetization measurement of the supercooled alloy melt. With the increase in magnetic field intensity and gradient, the undercooled immiscible melt experienced a transition from a core-shell structure to a layered structure at a lower field intensity and then a typical normal field instability pattern with the applied higher magnetic field gradient. Due to the different magnetic response ability of the separated phases in the presence of a magnetic field gradient, the transition of the morphology was complex, and its detailed investigations can provide important insight for better understanding of the ferrofluid and the creation of functional material. Furthermore, under an appropriate field gradient condition, it can achieve the subtle transitions between the diverse morphologies in an immiscible alloy.

An experimental study of the effect of water and chlorine on plagioclase nucleation and growth in mafic magmas: application to mafic pegmatites

Abstract. In this study, the effects of H2O and Cl on the grain size and nucleation delay of plagioclase in basaltic magma were investigated using dynamic and equilibrium experiments at 1150 ∘C, 300 MPa, and oxygen fugacity between FMQ − 1.65 and FMQ + 0.05 (fayalite–magnetite–quartz). Each experiment consisted of five samples of basaltic composition (from the Hamn intrusion in Northern Norway) containing varying amounts of H2O (up to 2 wt %) and Cl (up to 1 wt %). The equilibrium experiments were used as a reference frame for the phase assemblage, geochemical composition, and liquidus temperatures and were compared to thermodynamic models using MELTS software. Experimental phase abundances and plagioclase compositions are in good agreement with the predictions of MELTS. The dynamic experiments were initially heated above the liquidus temperature to destroy crystal nuclei and then kept at 1150 ∘C for 100, 250, or 1800 min. These experiments show that as the concentration of H2O in the melt increases, plagioclase nucleation is delayed, plagioclase abundance decreases, but its size increases. Therefore, the addition of H2O seems to favor plagioclase growth at the expense of nucleation. Thermodynamic and kinetic calculations corroborate an increase in the nucleation delay of plagioclase with increasing H2O content dissolved in the melt, suggesting that H2O decreases the undercooling of the silicate melt. The addition of Cl also seems to delay plagioclase nucleation, although this is not supported by kinetic calculations. Increasing the Cl content decreases plagioclase abundance but does not significantly affect its size. The homogeneous pegmatitic pockets of the mafic–ultramafic Hamn intrusion exhibit several petrological and geochemical features, suggesting that H2O and Cl enrichment in the silicate melt was the origin of the pegmatitic texture. The experimental results presented here indicate that H2O, rather than Cl, may have played an important role in the formation of the pegmatitic texture.

Effect of annealing at Tg on the crystallization behaviors of Au49Ag5.5Pd2.3Cu26.9Si16.3 metallic glass revealed by nanocalorimetry

Crystallization of metallic glass is not only affected by undercooling but also influenced by microstructure. However, the role of structure in the crystallization is still ambiguous. In this study, nanocalorimetry with a rapid quenching rate was used to obtain the critical cooling rates suppressing nucleation and crystal growth, realizing the in-situ preparation of the amorphous phase. Based on the nuclei-free metallic glass, annealing at Tg was performed to tune the microstructure. With a reheating analysis, the consecutive occurrence of relaxation, nucleation, and crystal growth during annealing was distinguished based on the evolution of crystallization heat. Moreover, the effect of annealing and the resulting microstructure evolution on the reheating crystallization was demonstrated. With the formation of nuclei, the stability of the undercooled melt deteriorated, causing the reduction of activation energy (Ea). When crystals formed during annealing, the confined residual amorphous phase was dominant for crystallization, and a higher Ea was observed.

Spherulites of supramolecular polymers formed from undercooled melts, and their adhesive properties

Abstract The solid-state properties of crystalline supramolecular polymers have generally remained unexplored. Herein, we investigated the isothermal crystallization of a supramolecular polymer and showed that, depending on the temperature, it formed distinct structures at a higher hierarchical level. Interestingly, the resulting crystalline forms showed distinct adhesive properties and mechanical-failure modes (adhesive or cohesive).

Development and Numerical Testing of a Model of Equiaxed Alloy Solidification Using a Phase Field Formulation

A computational framework is developed to understand the transient behavior of isothermal and non-isothermal transformation between liquid and solid phases in a binary alloy using a phase-field method. The non-isothermal condition was achieved by applying a thermal gradient along the computational domain. The bulk solid and liquid phases were treated as regular solutions, along with introducing an order parameter (phase field) as a function of space and time to describe the interfacial region between the two phases. An antitrapping flux term was integrated into the present phase-field model to mitigate the amount of solute trapping, which is characterized by the non-equilibrium partitioning of the solute. The governing equations for the phase field and the solute composition were solved by the cell-centered finite volume method using the open-source computational tool OpenFOAM. Simulations were carried out for the evolution of equiaxed dendrites inside an undercooled melt of a binary alloy, considering the effect of various computational parameters such as interface thickness, strength of crystal anisotropy, stochastic noise amplitude, and initial orientation. The simulated results show that the solidification morphology is sensitive to the magnitude of anisotropy as well as the amplitude of noise. A strong influence of interface thickness on the growth morphology and solute redistribution during solidification was observed. Incorporating antitrapping flux resulted in the solute partitioning close to the equilibrium value. Simulations show that the grain shape is unaffected by changes to crystallographic orientation with respect to the Cartesian computational grid. Thermal gradients exerted discernible effects on the solute distribution and the dendritic growth pattern. Starting with multiple nucleation events the model predicted realistic polycrystalline solidification and as-solidified microstructure.

The Boundary Integral Equation for Kinetically Limited Dendrite Growth

The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a constant crystallization velocity, which is the sum of the steady-state and translational velocities. The dendrite tips in the form of a parabola, paraboloid, and elliptic paraboloid are considered. Taking this solution into account, we obtain the modified boundary integral equation describing the evolution of the patterns and dendrites in undercooled binary melts. Our analysis shows that dendritic tips always evolve in a steady-state manner when considering a kinetically controlled crystallization scenario. The steady-state growth velocity as a factor that is dependent on the melt undercooling, solute concentration, atomic kinetics, and other system parameters is derived. This expression can be used for determining the selection constant of the stable dendrite growth mode in the case of kinetically controlled crystallization.

Viscosity and heat capacity of As2Se3 connected via Adam–Gibbs model

AbstractThe viscosity data measured by penetration and parallel‐plate methods for As2Se3 glass and undercooled melt were compared with literature data. The MYEGA equation (log η0 = −4.67 ± 0.12, m = 43.2 ± 0.4, and T12 = 441.7 ± 0.3 K) was used for the description of the selected viscosity data, including melt region (15 orders of magnitude). The heat capacity data for As2Se3 glass, undercooled melt, and melt, as well as for crystalline As2Se3 were determined for low and medium‐range temperature intervals. These data were compared with previously reported data. Equations that describe the heat capacity of As2Se3 in a broad temperature interval were formulated. The values of the standard molar enthalpy, Δ0THm0, and entropy, Δ0TSm0, at T = 298.15 K are 26.202 kJ·mol−1 and 193.8 J·mol−1·K−1, respectively. The heat capacity data determined from very low temperatures were used for the calculation of crystal, glass, and melt entropies. These heat capacity temperature dependencies were used both for the estimation of the Kauzmann temperature (TK = 292.5 K) and the glass entropy at 0 K (S0 = 25.96 J·mol−1·K−1), and for the determination of the excess entropy. The proportionality between the viscosity of the As2Se3 melt and the excess entropy clearly indicates the applicability of the Adam–Gibbs (AG) model.

Subgrain-assisted spontaneous grain refinement in rapid solidification of undercooled melts

The grain refinement mechanism for rapid solidification of undercooled melts is still an open problem even after 60 years of on-going studies. In this work, rapid solidification of undercooled Ni and equi-atomic FeCoNiPd melts was studied and spontaneous grain refinement was found at both low and high undercooling. After a detailed electron backscattered diffraction analysis, subgrain-induced grain orientation scattering and splitting were found to occur along with the transition from coarse dendrites to fine equiaxed grains at low and high undercooling, respectively, indicating that subgrains play an important role during the formation of fine equiaxed grains. On this basis, a compromise mechanism of subgrain-assisted spontaneous grain refinement was proposed. Because the dendrite re-melting induced thermo-mechanical process and fluid flow induced dendrite deformation occur simultaneously during the post-recalescence stage, stress accumulation would be maximum at both low and high undercooling, thus inducing dynamic recrystallization, during which the formation and rotation of subgrains make the grain orientations scattering and even splitting. Furthermore, the grain/subgrain size of undercooled FeCoNiPd ascribing to its unique co-segregation behavior keeps almost invariable from low to high undercooling, indicating that the co-segregation strategy would be effective to inhibit grain growth after rapid solidification and would be useful in practice.