Undercooled Liquid Research Articles

Replacing eutectic growth by glass formation for liquid Ni59.5Nb40.5 alloy under containerless state

The eutectic growth kinetics and glass forming ability of undercooled liquid Ni59.5Nb40.5 alloy were investigated by containerless processing via electromagnetic levitation (EML) and drop tube (DT) techniques. The maximum liquid undercoolings attained 120K (0.08 TE) at levitated state and 564K (0.38 TE) under free fall condition respectively. As liquid undercooling increased, three distinctive undercooling regimes were determined experimentally. At low undercoolings, normal lamellar eutectic growth occurred, with a eutectic growth velocity of 27mms-1 at 120K undercooling under EML condition. In the intermediate undercooling range between 184 and 380K, Nb7Ni6 phase could nucleate primarily and independently, which resulted in a typical hypereutectic microstructure. Once undercooling exceeded 380K, both eutectic growth and Nb7Ni6 dendrite growth were suppressed, leading to the formation of amorphous phase. Molecular dynamics simulation revealed that alloy viscosity increased significantly with liquid undercooling, which contributed to the reduced nucleation rate and suppressed crystal growth.

Phase selection mechanism and eutectic growth kinetics of refractory Nb<sub>81.7</sub>Si<sub>17.3</sub>Hf alloy under electrostatic levitation condition

The phase selection mechanism and eutectic growth kinetics of Nb<sub>81.7</sub>Si<sub>17.3</sub>Hf alloy are investigated by electrostatic levitation technique. The maximum undercooling of this alloy reaches 404 K(0.19<i>T</i><sub>L</sub>). By analyzing the cooling curves, its hypercooling limit is obtained to be 527 K (0.24 <i>T</i><sub>L</sub>). A critical undercooling of 194 K is determined for the transition of solidification path. Below this undercooling threshold, (Nb) phase firstly nucleates and grows into primary dendrites, resulting in the enrichment of Si and Hf in the residual melt, which is conducive to the formation of the (Nb)+<i>α</i>Nb<sub>5</sub>Si<sub>3</sub> eutectics. Therefore, (Nb)+<i>α</i>Nb<sub>5</sub>Si<sub>3</sub> lamellar eutectics form in interdendritic space. With the increase of undercooling, the growth velocity of primary (Nb) dendritic follows a power function, while the eutectic growth velocity increases slowly. The maximum values of (Nb) dendritic reaches 89.4 mm/s. A modified LKT/BCT model is used to calculate the growth velocity of (Nb) dendrites. The results are in good agreement with the experimental values, indicating that after the LKT model is modified slightly, it can be used to describe the rapid dendrite growth behavior of the (Nb) phase in the Nb<sub>81.7</sub>Si<sub>17.3</sub>Hf alloy melt. Meanwhile, the lamellar spacing of (Nb)+<i>α</i>Nb<sub>5</sub>Si<sub>3</sub> eutectics notably decreases to 360 nm at 194 K undercooling. Above the critical threshold, the primary (Nb) dendrites disappear, whereas (Nb) phase and Nb<sub>3</sub>Si phase nucleate independently in the undercooled liquid and grow into anomalous eutectics. The growth velocity of anomalous eutectic exhibits a power function relationship with the increase of undercooling, with a maximum value of 115.9 mm/s. The interphase spacing of (Nb)+Nb<sub>3</sub>Si anomalous eutectics is larger than that of (Nb)+<i>α</i>Nb<sub>5</sub>Si<sub>3</sub> lamellar eutectics. Owing to the formation of nanosized eutectics and the increase of volume fraction of (Nb) phase, the alloy fracture toughness at 194 K reaches 21.9 MPa·m<sup>1/2</sup>, which is 3.4 times as large as that under small undercooling condition.

Peritectic solidification mechanism of substantially undercooled liquid Fe-Y-B ternary alloys

Liquid Fe84Y10B6 and Fe74Y16B10 peritectic type alloys were substantially undercooled up to 382 (0.25 TL) and 400K (0.26 TL) with drop tube technique. The molecular dynamics simulation results revealed that the former alloy was characterized by larger Fe, Y and B self-diffusion coefficients and activation energies. In low undercooling regime, γFe phase in Fe84Y10B6 alloy and Y2Fe17Bx phase in Fe74Y16B10 alloy formed preferentially, faceted τ1(Y2Fe14B) phase subsequently developed through peritectic transition. With the increase of undercooling, peritectic transition was promoted by the refined primary phases. Once liquid undercoolings reached certain critical values, a stronger nucleation driving force is provided for τ1 phase, resulting in its direct nucleation and growth by suppressing the formation of primary phases and the following peritectic transformations. If liquid undercooling rose further, there occurred the faceted to non-faceted growth mode transition of the main peritectic τ1 phase. This indicates that high undercooling and rapid solidification is an effective approach to modulate phase transition pathway and microstructural evolution of rare earth alloys.

Multiscale modeling of short pulse laser induced amorphization of silicon

Silicon surface amorphization by short pulse laser irradiation is a phenomenon of high importance for device manufacturing and surface functionalization. To provide insights into the processes responsible for laser-induced amorphization, a multiscale computational study combining atomistic molecular dynamics simulations of nonequilibrium phase transformations with continuum-level modeling of laser-induced melting and resolidification is performed. Atomistic modeling provides the temperature dependence of the melting/solidification front velocity, predicts the conditions for the transformation of the undercooled liquid to the amorphous state, and enables the parametrization of the continuum model. Continuum modeling, performed for laser pulse durations from 30 ps to 1.5 ns, beam diameters from 5 to 70 μm, and wavelengths of 532, 355, and 1064 nm, reveals the existence of two threshold fluences for the generation and disappearance of an amorphous surface region, with the kinetically stable amorphous phase generated at fluences between the lower and upper thresholds. The existence of the two threshold fluences defines the spatial distribution of the amorphous phase within the laser spot irradiated by a pulse with a Gaussian spatial profile. Depending on the irradiation conditions, the formation of a central amorphous spot, an amorphous ring pattern, and the complete recovery of the crystalline structure are predicted in the simulations. The decrease in the pulse duration or spot diameter leads to an accelerated cooling at the crystal–liquid interface and contributes to the broadening of the range of fluences that produce the amorphous region at the center of the laser spot. The dependence of the amorphization conditions on laser fluence, pulse duration, wavelength, and spot diameter, revealed in the simulations, provides guidance for the development of new applications based on controlled, spatially resolved amorphization of the silicon surface.

Dendrite growth kinetics and microstructure evolution mechanism of Ni2TiAl intermetallic compound within substantially undercooled liquid Ni64Al19Ti17 alloy

The dendrite growth kinetics and microstructure evolution mechanism of the Ni2TiAl intermetallic compound within substantially undercooled liquid Ni64Al19Ti17 alloy were investigated using electrostatic levitation (ESL) and drop tube (DT) techniques. The growth velocity of primary Ni2TiAl dendrites displayed a power-law relation with liquid undercooling, achieving a maximum of 80 mm/s at the undercooling of 254 K (0.16 TL). The solidification pathway transformed from primary Ni2TiAl growth plus subsequent (Ni3Ti+Ni2TiAl) eutectic growth into the successive growth of Ni2TiAl and Ni3Ti phases as the alloy undercooling increased sufficiently. The high cooling rates of freely falling alloy droplets effectively suppressed the martensitic transformation observed for primary Ni2TiAl intermetallic compound under typical ESL radiative cooling condition. Both nanoindentation and Vickers hardness performances of the Ni2TiAl phase formed under these two conditions exhibited conspicuous enhancement due to grain refinement effects. The microstructures with martensitic transformation under ESL condition showed higher hardness than those under DT condition despite their larger grain size.

Nanoscale inhomogeneities in undercooled benzoic acid: A molecular dynamics study

The dynamics of undercooled organic liquids is very complex and still far from being fully understood. A major problem is the lack of general algorithms to recognize nanoscale inhomogeneities that exploit different inner structures with respect to the bulk liquid. We show that a geometry-independent energy criterion, coupled with the requirement that the cluster must survive for times longer than thermal fluctuations, can be consistently used to individuate persistent and recognizable (meta)stable inhomogeneities or, possibly, subcritical clusters in benzoic acid. The algorithm applies to all organic liquids, regardless of their ability to form hydrogen bonds. We show that undercooled benzoic acid becomes granular with respect to the thermodynamically stable liquid, hosting medium size inhomogeneities composed of up to 17 molecules for durations on the order of hundreds of picoseconds. These correlate with the predicted increase of density and viscosity upon undercooling. Most important, the inner structure of these inhomogeneities is intermediate between the liquid and the crystal. Stacking interactions, analogue to those present in the crystal, begin to develop in the largest persistent clusters. The pros and cons of the method are discussed in the context of non-classical nucleation theories.

Dendrite Growth in Single-Grain and Cyclic-Twinned Sn–3Ag–0.5Cu Solder Joints

The microstructure of electronic solder joints is generated by the solidification of a small volume of bulk undercooled liquid. Here, we study β-Sn dendrite growth in Sn–3Ag–0.5Cu in the specific geometry and nucleation conditions of ball grid array (BGA) solder joints by combining electron backscatter diffraction and imaging of microstructures. It is shown that, while ⟨110⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle 110\\rangle$$\\end{document} is the preferred dendrite growth direction, out-of-plane branching and growth with ⟨11W⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle 11W\\rangle$$\\end{document} directions are important for allowing dendrites to fan out into the spheroidal volume of BGA joints due to the low symmetry of β-Sn. We find that the crystallographic orientation of β-Sn at the nucleation point plays a strong role in subsequent dendrite growth. In single-grain joints, dendrites are often unfavorably oriented for growth, resulting in different types of zig-zag dendrite growth. In cyclic-twinned joints, it is shown how competitive out-of-plane trunk growth between three dendrite orientations produces {101} boundaries and the characteristic beachball microstructure.

Liquid state property and rapid peritectic solidification of refractory Mo-33.3 at.% Zr alloy under electrostatic levitation condition

The thermophysical properties and rapid solidification mechanism of liquid Mo-33.3 at.% Zr peritectic alloy were investigated by electrostatic levitation technique, which attained a maximum undercooling of 387 K (0.16 TL). At its liquidus temperature, the density, surface tension, viscosity and solute diffusion coefficient of this refractory alloy were determined as 8.14 g/cm3, 1.60 N/m, 11.32 mPa·s and 1.41 × 10−9 m2/s, respectively. The primary (Mo) dendrite growth started from multi-point nucleation, while its growth velocity agreed well with the prediction of LKT/BCT dendrite growth theory and reached an upper value of 43 mm/s. The subsequent peritectic transition was characterized by a power-law kinetics relation between the nominal growth velocity of peritectic Mo2Zr phase and peritectic undercooling, displaying a maximum velocity of 46 mm/s. The increase of liquid undercooling facilitated the completion of peritectic transition and refined the microstructure of residual primary (Mo) phase, thus enhancing the Vickers hardness of this alloy gradually up to 1190.9 HV at the maximum undercooling.

On Hillert-Style Non-equilibrium Thermodynamics

Hillert often used the combined first and second law of thermodynamics to discuss and derive the principles of equilibrium as well as non-equilibrium thermodynamics. His method will now be reviewed and applied to reactions in homogeneous systems as well as transport processes As an example of homogeneous systems undercooled liquids and glasses is discussed.

Ultrafast laser-induced topochemistry on metallic glass surfaces

Manufacturing multifunctional nanocomposite materials and engineered surface nanopatterns involves a strategic blend of topography, crystal structures, and chemistry. Here, we report the controllable formation of crystalline nanoparticles and intermetallic compounds on thin films of metallic glasses (Zr50Cu50, Ti50Cu50, and Zr67Ag33) irradiated by ultrafast laser beams. Mapping the structural modification of the photoexcited and subsequently heated alloys reveals previously neglected chemical reactions with air, offering a direct solution for incorporating nanoparticles into an amorphous oxide matrix and broadening the range of laser-induced surface self-organization features. Our findings are attributed to the occurrence and enrichment of oxygen surface contamination that reacts with selected elements of the metallic glasses. Additionally, the growth of the crystalline phase from undercooled liquid may originate from the dissolution of oxides. Finally, our results establish that the combination of crystalline nanoparticles on amorphous periodic patterns can be universally obtained in a wide range of binary systems of irradiated metallic glasses.

A model of heterogeneous undercooled liquid and glass accounting for temperature-dependent nonexponentiality and enthalpy fluctuation.

Dynamic heterogeneity is a fundamental characteristic of glasses and undercooled liquids. The heterogeneous nature causes some of the key features of systems' dynamics such as the temperature dependence of nonexponentiality and spatial enthalpy fluctuations. Commonly used phenomenological models such as Tool-Narayanaswamy-Moynihan (TNM) and Kovacs-Aklonis-Hutchinson-Ramos fail to fully capture this phenomenon. Here we propose a model that can predict the temperature-dependent nonexponential behavior observed in glass-forming liquids and glasses by fitting standard differential scanning calorimetry curves. This model extends the TNM framework of structural relaxation by introducing a distribution of equilibrium fictive temperature (Tfe) that accounts for heterogeneity in the undercooled liquid. This distribution is then frozen at the glass transition to account for the heterogeneous nature of the glass dynamics. The nonexponentiality parameter βKWW is obtained as a function of temperature by fitting the Kohlrauch-Williams-Watts (KWW) equation to the calculated relaxation function for various organic and inorganic undercooled liquids and glasses. The calculated temperature dependent βKWW shows good agreement with the experimental ones. We successfully model the relaxation dynamics far from equilibrium for two silicate systems that the TNM model fails to describe, confirming that temperature dependent nonexponentiality is necessary to fully describe these dynamics. The model also simulates the fluctuation of fictive temperature δTf during isothermal annealing with good qualitative agreement with the evolution of enthalpy fluctuation reported in the literature. We find that the evolution of enthalpy fluctuation during isothermal annealing heavily depends on the cooling rate, a dependence that was not previously emphasized.

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.

Primary dendrite growth within binary Fe71Ge29 eutectic alloy under duplex levitation states

The primary β-Fe3Ge2 dendrite growth kinetics within liquid Fe71Ge29 eutectic alloy was studied by both acoustic levitation and electrostatic levitation techniques, with maximum experimental undercoolings of 130 and 143 K, respectively. At small undercoolings, (α1 + β-Fe3Ge2) eutectic growth proceeded and then transformed to lamellar (ε-Fe3Ge + β-Fe3Ge2) microstructure by peritectoid reaction. Once liquid undercooling reached 56 K, β primary phase started to nucleate preferentially and its maximum growth velocity attained 13.5 mm/s at 143 K undercooling. By acoustic levitation processing, β dendrites were distributed inside the alloy droplet. Under electrostatic levitation state, β dendrites were distributed both at the periphery and within the interior of alloy droplet, and their volume fraction was significantly higher than that under acoustic levitation. Numerical simulation results indicated that a duplex flow was induced by alloy droplet shape oscillation and acoustic streaming. The flow exhibited maximum intensity near the alloy surface, which inhibited the achievement of larger undercoolings during acoustic levitation.

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.

Spiral eutectic growth dynamics facilitated by space Marangoni convection and liquid surface wave

Eutectic alloys display excellent application performances since the essential function of coupled microstructures is quite different from that of single-phase and peritectic alloys. However, due to the strong natural convection within liquid alloys under normal gravity, the eutectic growth process on earth usually produces traditional rod-like or lamellar composite microstructures, which hinders the exploration of distinctive coupled growth patterns. Here, we carried out the rapid solidification of hypoeutectic Zr64V36 alloy to explore novel coupled growth dynamics aboard the China Space Station under a long-term stable microgravity condition. An extreme liquid undercooling of 253 K was achieved for this refractory alloy, displaying a strong metastability in outer space. We find that a radial coupled pattern grew out of the nucleation site, accompanying a ripple-like surface microstructure. This resulted from the rapid eutectic growth within a highly undercooled alloy in combination with a liquid surface wave excited by the electrostatic field under microgravity. Especially, a spiral coupled growth mode occurred during radial eutectic growth and surface wave spreading, which were controlled by the Marangoni convection effect on the fluid flow pattern and eutectic growth dynamics. Our findings contribute to the coupled growth investigation by modulating gravity levels to develop multi-pattern microstructures.

Remarkable undercooling capability and metastable thermophysical properties of liquid Nb84.1Si15.9 alloy revealed by electrostatic levitation in outer space.

The stable manipulation, high undercooling, and thermophysical property measurement of the liquid Nb84.1Si15.9 refractory alloy were successfully achieved by the electrostatic levitation technique on board the China Space Station. By controlling the superheating temperature, a maximum liquid undercooling up to 421K (0.18 TL) was obtained in the space environment, and two distinct solidification paths with different recalescence features were realized at metastable undercooled states. The liquid density and the ratio of specific heat to emissivity were measured in a wide temperature range from 1841 to 2346K, which displayed linear and quadratic relations vs temperature, respectively. The liquid emissivity was further deduced from the specific heat of the liquid alloy calculated by molecular dynamics simulation. In addition, both the density and structural characteristics of the undercooled liquid alloy were also analyzed by MD calculations.

Crystalline Microstructure, Microsegregations, and Mechanical Properties of Inconel 718 Alloy Samples Processed in Electromagnetic Levitation Facility

The solidification of Inconel 718 alloy (IN718) from undercooled liquid is studied. The solidification kinetics is evaluated in melted and undercooled droplets processed using the electromagnetic levitation (EML) technique by the temperature–time profiles and solid/liquid (S/L) interface movement during recalescence. The kinetics is monitored in real time by special pyrometrical measurements and high-speed digital camera. It is shown that the growth velocity of γ-phase (the primary phase in IN718), the final crystalline microstructure (dendritic and grained), and the mechanical properties (microhardness) are strongly dependent on the initial undercooling ΔT at which the samples started to solidify with the originating γ-phase. Particularly, with the increase in undercooling, the secondary dendrite arm spacing decreases from 28 μm to 5 μm. At small and intermediate ranges of undercooling, the solidified droplets have a dendritic crystalline microstructure. At higher undercooling values reached in the experiment, ΔT>160 K (namely, for samples solidified with ΔT=170 K and ΔT=263 K), fine crystalline grains are observed instead of the dendritic structure of solidified drops. Such change in the crystalline morphology is qualitatively consistent with the behavior of crystal growth kinetics which exhibits the change from the power law to linear law at ΔT≈160 K in the velocity–undercooling relationship (measured by the advancement of the recalescence front in solidifying droplets). Study of the local mechanical properties shows that the microhardness increases with the increase in the γ″-phase within interdendritic spacing. The obtained data are the basis for testing the theoretical and computational of multicomponent alloy samples.

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.

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.

Atomistic insights into sluggish crystal growth in CoNi-containing multi-principal element alloys

Understanding the sluggish kinetics is of great significance for improving the properties of multi-principal element alloys (MPEAs). In this paper, the crystal growth in undercooled CoNi, CoNiFe and CoNiPd alloys was studied by molecular dynamics (MD) to show atomistic insights into sluggish crystal growth kinetics. The added Fe and Pd lead to a decrease in the crystal growth velocity and more significant sluggish crystal growth kinetics was observed in CoNiPd. After minimizing the instantaneous potential energy of atoms adjacent to the Solid/Liquid (S/L) interface, it was found that the decreased crystal growth velocity as the number of principal elements could be accounted by the accompanying change of inherent structure. The exploration of bulk undercooled liquid showed that the diffusion kinetic in liquid does not play a critical role on the sluggish crystal growth kinetics. Besides, the investigation of atomic structure in front of the smooth S/L interface revealed that the sluggish crystal growth kinetics induced by properties of element was associated with the atomic spontaneous ordering degree.