Undercooled Melt Research Articles

Multiphase Field Modeling of Dendritic Solidification of Low-Carbon Steel with Peritectic Phase Transition

In the present study, an improved multiphase field model with taking into consideration the S/L interface anisotropy is proposed to simulate the dendritic growth with peritectic transition of low-carbon steel, and a new random heterogeneous nucleation method is proposed to treat the γ phase nucleation during the peritectic solidification process. The γ phase growth around the dendrite (the single dendrite and polycrystalline ferrite) and the subsequent peritectic transformation during the peritectic solidification are simulated. The results show that when the temperature reaches the γ phase nucleation temperature, γ nuclei suddenly nucleate at the δ/L interface, and laterally grow with the movement of L/γ/δ triple point around the δ/L interface of δ dendrite. After the δ dendrite is fully wrapped by the continuous intervening γ phase, the γ phase continues to grow with direct phase transformation from both δ phase and liquid phase. With the increase of melt undercooling, more δ phase and liquid phase are consumed to form γ phase, and the intervening γ phase between the δ dendrite and liquid phase becomes more and more thick, but the δ dendrite arm becomes more and more thin. During the dendritic solidification process, the solute would be rejected from dendrite trunk with the dendritic growth and enriched at the dendrite boundary, especially at the dendrite root. The solute enrichment at the dendrite root would inhibit the γ phase growth at the dendrite root and thus the thickness of intervening γ phase at the dendrite root is thinnest around the dendrite. Moreover, the solute concentration in γ phase is among the δ phase and liquid phase, because the carbon solubility in γ phase is higher than that in δ phase, but lower than that in liquid phase.

A review on the theory of stable dendritic growth.

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented. The sharp interface model and stability criteria for various crystallization conditions and crystalline symmetries met in actual practice are formulated and discussed. The review is also focused on the determination of the main process parameters-the tip velocity and diameter of dendritic crystals as functions of the melt undercooling, which define the structural states and transitions in materials science (e.g. monocrystalline-polycrystalline structures). Selection criteria of stable dendritic growth mode for conductive and convective heat and mass fluxes at the crystal surface are stitched together into a single criterion valid for an arbitrary undercooling. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Dendritic growth of ice crystals: a test of theory with experiments

Motivated by an important application of dendritic crystals in the form of an elliptical paraboloid, which widely spread in nature (ice crystals), we develop here the selection theory of their stable growth mode. This theory enables us to separately define the tip velocity of dendrites and their tip diameter as functions of the melt undercooling. This, in turn, makes it possible to judge the microstructure of the material obtained as a result of the crystallization process. So, in the first instance, the steady-state analytical solution that describes the growth of such dendrites in undercooled one-component liquids is found. Then a system of equations consisting of the selection criterion and the undercooling balance that describes a stable growth mode of elliptical dendrites is formulated and analyzed. Three parametric solutions of this system are deduced in an explicit form. Our calculations based on these solutions demonstrate that the theoretical predictions are in good agreement with experimental data for ice dendrites growing at small undercoolings in pure water.

Nucleation-Controlled Phase Selection in Rapid Solidification from Undercooled Melt of DyMnO<sub>3</sub>

The equilibrium crystal structure of LnMnO3 (Ln: lanthanide) has been reported to be orthorhombic when La3+ to Dy3+ are used as Ln3+, and hexagonal when Ho3+ to Lu3+ are used. Whereas Kumar et al. reported a two-phase structure of orthorhombic and hexagonal phases is formed in DyMnO3 when it was solidified from the undercooled melt under containerless state. The reason for the formation of the two-phase structure was not thoroughly addressed and discussed. We investigated the formation mechanism for the two-phase structure from the undercooled melt of DyMnO3 in detail. As a result, the surface morphology, microstructure, and crystal structure of the samples, in which the nucleation was forced at a predetermined temperature with a Mo needle, indicated that the hexagonal and orthorhombic phases are dominant at high and low temperatures, respectively. When the sample was quenched from below 1670 K in a water bath, as-solidified sample consisted of h-DyMnO3 and o-DyMnO3. Whereas a single phase of h-DyMnO3 was obtained in the sample quenched from above 1670 K. This phenomenon can be quantified in terms of nucleation-rate determined phase selection. That is, the activation energy for forming a critical nucleus calculated based on the model of the crystal-melt interface proposed by Turnbull and Speapen suggests that the o-DyMnO3 phase can be heterogeneously nucleated on the interface of the initially formed h-DyMnO3 phase. This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 85 (2021) 155–161. The abstract and captions of Figs. 1–10 are modified.

Quantitative phase-field simulations of globulitic solidification from the critical nucleus with the effects of interface curvature and attachment kinetics

A one-dimensional quantitative phase-field model (thin-interface approximation) considering the effects of interface curvature and attachment kinetics was implemented to simulate the solidification of a solid sphere (globulitic solidification) of a pure substance in an undercooled infinite melt, beginning from the critical nucleus. The classical sharp interface model for the same problem was also solved and the growth velocity and interface temperature were calculated and compared with the results of the phase-field model. Numerical conditions of the phase-field model, namely interface thickness, numerical mesh spacing, and critical nucleus model, that give close agreement with the sharp interface model (quantitative modeling) were determined. The possibility of a unique controlling step of the overall solidification kinetics by heat transfer or interface attachment kinetics or even of a mixed control was analyzed by defining relative undercoolings at the solid–liquid interface. For both metallic and non-metallic materials, growth is initially controlled by interface attachment kinetics, but, as the solid sphere grows and the melt heats up, it changes to the mixed control regime with heat transfer before spherical growth becomes unstable. The spherical radius for the change to mixed control increases when the kinetic coefficient or the magnitude of melt undercooling increases, because the heat transfer step is facilitated relative to that of attachment kinetics.

Retained Free Energy with Enhanced Nucleation during Electrostatic Levitation of Undercooled Fe-Co Alloys

Double recalescence in many ferrous alloy systems involves rapid solidification of metastable ferrite from the undercooled melt with subsequent transformation to stable austenite. Containerless processing is used to monitor the process using pyrometry and high-speed cinematography such that delay behavior can be predicted based on the application of the retained damage model (RDM). When comparing Fe-Cr-Ni alloys to Fe-Co alloys, the cluster attachment rate is enhanced while free energy retention is reduced. These trends are tied to specific alloy properties. A retained free energy criterion is proposed based on the ratio of thermophysical properties used to define the transformation driving force such that the thermodynamic limit for energy retention may be predicted. Surprisingly, at long delay times, healing occurs such that much of the retained free energy is not available to enhance the transition from metastable to stable phases. At delay times less than one second, no healing is observed and the RDM correctly predicts transformation delay behavior over a wide range of alloy compositions.

Molecular dynamics simulations of oxide ion migration in La2Ga3O7.5 with completely ordered interstitial oxide ions

Molecular dynamics simulations were performed on metastable La2Ga3O7.5 melilite ceramics, which were synthesized previously by direct crystallization of an under-cooled melt. La2Ga3O7.5 possesses the theoretically maximum content of interstitial oxide ions featuring complete ordering but ~3 orders of magnitude lower oxide ion conductivities compared with disordered La1·54Sr0.46Ga3O7.27 within 573–773 ​K. One dimensional diffusion paths of interstitial oxide ion was identified in La2Ga3O7.5 based on the molecular dynamics simulations, which shows that the interstitial oxide ions can migrate from the pentagonal ring containing GaO5 pyramid unit to its neighboring pentagonal ring free of interstitial oxide ion mainly along the a axis through a synergic mechanism involving continuous breaking and reformation of Ga2O8 units assisted by rotation and deformation of GaOn polyhedra and knock-on process between interstitial and framework oxygen atoms. Such constrained dimensionality on the diffusion paths arising from the confining effect for a large number of oxygen interstitials in the highly relaxed and ordered melilite superstructure accounts for the lower oxide ion conductivity in La2Ga3O7.5.

Multiphase and multiphysics modeling of dendrite growth and gas porosity evolution during solidification

Gas porosity is one of the most detrimental defects that can considerably deteriorate mechanical properties of casting parts. Simulating the interaction between gas porosity and solidifying microstructure is challenging due to multiphase and multiphysical characteristics. In this work, a solid-liquid-gas multiphase-field lattice-Boltzmann model is developed to describe the complex multiphase interaction during solidification. The model relaxes the assumption of pure metal system, simplified bubble shape and pure diffusion condition. It can consider solid growth, bubble motion, interface deformation, component transport, melt flow, and partition of both alloy solute and dissolved gas species. The model is validated in terms of mass conservation, mapping operation to the two-phase model, Laplace pressure condition, and bubble dynamics. The effectiveness of the model is further evaluated by comparing with other four models and experiments. The model is successfully used to describe the interaction between gas porosity and magnesium dendrite. The dependence of phase fractions on the characteristic parameters including melt undercooling, interface mobility coefficient and internal bubble pressure is quantified to explore the multiphase equilibrium. The proposed model can be regarded as complementary to the previous models and it is suitable for addressing the problems involving the solid-liquid-gas multiphase and multiphysical characteristics.

Synthesis, Crystallization, and Electrochemical Characterization of Room Temperature Ionic Liquid Bromidostannates(II/IV).

Ionic liquids (IL) are valuable in a variety of applications due to their high electrochemical stability and physical properties. Using the cation 1-methyl-3-octylimidazolium, [OMIM]+, the bromidostannate RTIL [OMIM][Sn+IIBr3], "undercooled melt" [OMIM][Sn+IVBr5], and IL [OMIM]2[Sn+IVBr6] were synthesized. The uncommon solid state structure of [SnBr5]- was elucidated in the form of its RTIL salt. Additionally, the IL based on tribromine-monoanion [OMIM][Br3] was used to dissolve metallic Sn, selectively resulting in the formation of [SnBr3]- as confirmed by Raman spectroscopy. Subsequent cyclic voltammograms (CV) of [SnBr3]- confirmed the deposition potential of metallic Sn and renewal of the polybromide [Br3]-. The RTIL bromidostannates were stable compounds, making a selective electrochemical investigation of the deposition of metallic Sn(0) to Sn(+II)/Sn(+IV) redox process possible, via conductance and CV measurements. The CVs of the RTILs and of solutions in propylene carbonate had the redox couples of Sn(0)/[Sn+IIBr3]-/[Sn+IVBr5]-.

In situ studies of liquid-liquid phase separation, solidification sequence and dendrite growth kinetics in electrostatically levitated Ti–Y alloys

Melts of hypomontectic Ti75Y25, near-monotectic Ti70Y30 and hypermonotectic Ti60Y40 composition were undercooled and solidified using an electrostatic levitation facility. Liquid-liquid phase separation, solidification sequence and dendritic growth velocities in undercooled melts were investigated in situ using high-energy X-ray diffraction (HEXRD) and optical imaging with a high-speed video camera. HEXRD observations confirm that undercooled melts of the three Ti−Y compositions are separated into a Ti-rich liquid and a Y-rich liquid prior to solidification. The solidification sequence of the separated liquids depends on nucleation of α-Y with hcp structure from the Y-rich liquid and on nucleation of β-Ti with bcc structure from the Ti-rich liquid. Optical imaging observations suggest that the dendrite growth velocities of α-Y and β-Ti during recalescence are often time dependent and that they do not show any consistent trends with increasing nucleation undercooling. These unusual growth kinetics can be attributed to dynamic interactions between growing dendrites and droplets of a separated liquid. Scanning electron microscopy studies show that the phase-separated samples solidify into a core-shell structure or an island-and-sea-like structure. These microstructures can be understood in terms of the liquid-liquid phase separation and the droplet-dendrite interactions during solidification.

The effect of superheat on the nucleation undercooling of metallic melts

The influences of the superheating temperature (Ts) on the nucleation undercooling (ΔT) of metallic melts were investigated by using molecular dynamics simulations based on the embedded atom model (EAM) potential function. The results agree with the intuitive expectation that extremely high heating rates followed by short equilibration time lead to a superheating and partial melting of the solid phase. The fraction of the remained crystalline clusters in the superheated phase depends on the superheating temperature Ts and the equilibration time, as long as Ts is below the maximal superheating. A subsequent fast cooling facilitates a substantial undercooling of the molten phase. The achieved undercooling ∆T below the steady‐state melting temperature Tm depends on the size and the concentration of the crystalline clusters remained in the liquid phase, and thus on the initial superheating temperature Ts. Based on the simulated results, a model was proposed for describing the relationship of ΔT and Ts, with which simulated data are well fitted and the maximal undercooling for metals can be predicted.

In situ study of non-equilibrium solidification of CoCrFeNi high-entropy alloy and CrFeNi and CoCrNi ternary suballoys

The solidification behavior of the CoCrFeNi high-entropy alloy and the ternary CrFeNi and CoCrNi medium-entropy suballoys has been studied in situ using high-speed video and synchrotron X-ray diffraction on electromagnetically levitated samples. In all alloys, the formation of a primary metastable bcc phase was observed if the melt was sufficiently undercooled. The delay time for the onset of the nucleation of the stable fcc phase, occurring within bcc crystals, is inversely proportional to the melt undercooling. The experimental findings are corroborated by thermodynamic calculations of stable and metastable phase diagrams for the (CoCrNi)-Fe section. Crystal-growth velocities for the CrFeNi, CoCrNi, and CoCrFeNi medium- and high-entropy alloys extracted from the high-speed video sequences in the present study are comparable to the literature data for Fe-rich Fe-Ni and Fe-Cr-Ni alloys, evidencing the same crystallization kinetics. The effect of melt undercooling on the microstructure of solidified samples is analyzed and discussed.

Nucleation-Controlled Phase Selection in Rapid Solidification from Undercooled Melt of DyMnO<sub>3</sub>

Nucleation-Controlled Phase Selection in Rapid Solidification from Undercooled Melt of DyMnO<sub>3</sub>

Diffusion, relaxation, and aging of liquid and amorphous selenium

Relaxation and aging rates of amorphous selenium and its undercooled melt are calculated by molecular dynamics based on an interaction model derived from density functional calculations. After a fast initial relaxation immediately following the quench, the decrease of diffusivity and the simultaneous increase of dynamic heterogeneity follow an exponential law given by defect annihilation. As observed previously in a Lennard-Jones glass, the non-Arrhenius aging of atomic volume and energy is determined by the time dependence of the diffusivity. The aging time is determined for long times by the diffusivity and diverges exponentially with decreasing temperature. Amorphous selenium differs from metallic glasses in that the breaking of covalent bonds is important for the long time decay of the intermediate self-scattering function (ISSF). Surprisingly for the temperatures investigated, aging of the relaxation times of the ISSF and the bond decay follow the aging of the diffusivity.

Anomalous structure transition in undercooled melt regulates polymorphic selection in barium titanate crystallization

The crystallization processes of titanates are central to the fabrication of optical and electrical crystals and glasses, but their rich polymorphism is not fully understood. Here, we show when and how polymorphic selection occurs during the crystallization of barium titanate (BaTiO3, BT) using in situ high energy synchrotron X-ray diffraction and ab initio molecular dynamic simulation. An anomalous structure transition is found in molten BT during cooling across the cubic-hexagonal transition temperature, which enables nucleation selection of BT by manipulating the undercooling: a cubic phase is preferred if nucleation is triggered at large undercooling, whereas a hexagonal phase is promoted at small undercooling. We further reveal that the nucleation selection between the cubic and the hexagonal phase is regulated by the intrinsic structure property of the melt, in particular, the degree of polymerization between Ti-O polyhedra. These findings provide an innovative perspective to link the polymorphic crystallization to the non-isomorphic structure transition of the melt beyond the conventional cognition of structural heredity.

Metastable–solid phase diagrams derived from polymorphic solidification kinetics

Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied to a model face-centered cubic (fcc) metal that undergoes phase transitions to the body-centered cubic (bcc) as well as the hexagonal close-packed phases at high temperatures and pressures. Large-scale molecular dynamics simulations of ultrarapid freezing show that bcc nucleates and grows well outside of the region of its thermodynamic stability. An extensive study of crystal-liquid equilibria confirms that at any given pressure, there is a multitude of metastable solid phases that can coexist with the liquid phase. We define for every crystal phase, a solid cluster in liquid (SCL) basin, which contains all solid clusters of that phase coexisting with the liquid. A rigorous methodology is developed that allows for practical calculations of nucleation rates into arbitrary SCL basins from the undercooled melt. It is demonstrated that at large undercoolings, phase selections made during the nucleation stage can be undone by kinetic instabilities amid the growth stage. On these bases, a solidification-kinetic phase diagram is drawn for the model fcc system that delimits the conditions for macroscopic grains of metastable bcc phase to grow from the melt. We conclude with a study of unconventional interfacial kinetics at special interfaces, which can bring about heterogeneous multiphase crystal growth. A first-order interfacial phase transformation accompanied by a growth-mode transition is examined.

In-situ observation of S/L interface migration and mechanical property increase of Inconel 600 alloy prepared by electromagnetic levitation

The Inconel 600 alloy was highly undercooled and its S/L interface migration during recalescence was observed in real time by using the electromagnetic levitation (EML) system. The characteristic of S/L interface migration and the dendritic growth velocity are strongly dependent on undercooling. At a small undercooling, the γ phase nucleates and grows to the undercooled melt with a sharp interface, and the corresponding microstructure appears as dendrite with strong texture. Nevertheless, once the undercooling exceeds the critical undercooling the sharp S/L interface transforms to a planar shape, which is attributed to the formation of equiaxed grain with a diffused orientation distribution. The 60°<111> annealing twins are generated only when the undercooling is larger than 130 K, due to the obvious recrystallization and sufficient driving force. Besides, the compressive tests were performed on the bulk Inconel 600 alloy samples. The results demonstrate that the elastic modulus is affected little by the undercooling, however, the yield strength obviously increases with the enhancement of undercooling. The strengthening mechanism is mainly ascribed to the formation of sub grain boundaries and annealing twins.

Simulation of dendrite collision behavior based on cellular automata-lattice Boltzmann model

In the alloy solidification process, the movement behavior of free dendrites in the melt is one of the key issues in studying the formation process of the alloy solidification structure. The cellular automata-lattice Boltzmann coupling model has become a main numerical model for numerical simulation of solidification microstructure in recent years. In this paper, cellular automata and lattice Boltzmann model for simulating dendrite growth are improved to simulate the movement of equiaxed grains in undercooled melt. In the improved model, the Galilean invariant momentum exchange method is used to calculate the fluid force, the motion equation of the center of mass is solved to calculate the motion displacement of the dendrite, the motion of the dendrite is realized through the dynamic mesh technology, and the rigid sphere model is used to deal with the collision of the dendrite. The settlement of a single dendrite in the undercooled melt of Al-4.7% Cu alloy, the settlement of two round particles in the Newtonian fluid, and the elastic collision of two dendrites are all simulated by this model. The simulation results show that this model can maintain the morphology of dendrites well in the process of calculating dendrite growth motion, and this model can calculate the collision process of irregular dendrites. The movement of dendrite disturbs the melt around it, resulting in a significant change in the concentration of melt around it, which affects the growth of dendrite and aggravates the asymmetry of dendrite growth.

Experiments to understand crystallization of levitated high temperature silicate melt droplets under low vacuum conditions

We report experiments on crystallization of highly undercooled forsterite melt droplets under atmospheric and sub-atmospheric pressure conditions. Experiments have been conducted under non-contact conditions using the principles of aero-dynamic levitation. Real time dynamics of solidification, along with the transient evolution of surface textures, have been recorded using high speed camera for three cooling rates. These images have been matched with the time-tagged temperature data to understand the effect of pressure conditions and cooling rates on the crystallization dynamics. Compared to normal pressure, relatively higher levels of undercooling could be achieved under sub-atmospheric conditions. Results showed a strong dependence of surface textures on pressure conditions. For any externally employed cooling rate, relatively small length scale morphological textures were observed under sub-atmospheric conditions, in comparison to those achieved under ambient conditions. The observed trends have been explained on the basis of influence of pressure conditions on recalescence phenomenon and the rate at which latent heat of crystallization gets dissipated from the volume of the molten droplet. Sub-atmospheric experiments have also been performed to reproduce one of the classical chondrule textures, namely the rim + dendrite double structure. Possible formation conditions of this double structure have been discussed vis-à-vis those reported in the limited literature. To the best of our knowledge, the reported study is one of the first attempts to reproduce chondrules-like textures from highly undercooled forsterite melt droplets under sub-atmospheric non-contact conditions.

Statistical learning for evaluation of crystal growth in low-melting alloy droplets with application to quasicrystal-forming Ti–Zr–Ni alloys

The evaluation of the crystal growth in undercooled alloy melts is essential for investigations of their solidification behavior. Low-melting alloy systems usually exhibit little self-illumination and cinematography is not often feasible. A time-temperature data based statistical learning approach is presented to evaluate the crystal growth in an undercooled droplet, where a spatial geometry-informed, errors-in-variables probabilistic model is developed based on the prediction of the dendrite growth paths. The preferable growth mechanism and growth velocities can be evaluated from statistical model selection and parameter estimation. Based only on the pyrometry data of two Ti–Zr–Ni alloys, a bulk growth mechanism is justified and the growth velocities in both the stable C14 phase and metastable icosahedral phase are able to be measured and statistically interpreted.