Hypercooling Limit Research Articles

Role of hypercooling limit in supercooling behavior and glass formation

Role of hypercooling limit in supercooling behavior and glass formation

Hypercooling limit and physical properties of liquid MoNbReTaW refractory high-entropy alloy

ABSTRACT The thermophysical properties of refractory MoNbReTaW high-entropy alloy in both supercooled liquid and high-temperature solid states were explored by an electrostatic levitation technique. The maximum supercooling attains 504 K, and the hypercooling limit is derived as 571 K. The liquid density at liquidus temperature is measured to be 13.3 g cm−3, which increases linearly with decreasing temperature at a slope of 6.83 × 10−4 g cm−3 K−1. The liquid alloy exhibits 5.3% relative volume shrinkage during crystallization. The thermal expansion coefficient of liquid and solid alloy at liquidus temperature are determined as 5.0 × 10−5 K−1 and 3.6 ×10−5 K−1, respectively. The liquid specific heat at liquidus temperature is found to be 38.2 J mol−1 K−1, and basically displays a linear decreasing tendency with temperature. According to the calculated enthalpy of fusion 24.7 kJ mol−1 and measured specific heats, the temperature-dependent entropy and Gibbs free energy difference between supercooled liquid and crystalline solid are obtained.

Unexpected behavior of the crystal growth velocity at the hypercooling limit

The crystal growth velocity is one thermodynamic parameter of solidification experiments of undercooled melts under non-equilibrium conditions, which is directly accessible to observation. We applied the electrostatic levitation technique in order to study the crystal growth velocity $v$ as a function of the undercooling $\Delta T$ for the intermetallic, congruently melting binary alloy NiTi and the glass forming alloy Cu--Zr, as well as for the Zr-based ternary alloys (Cu$_{\mathrm{x}}$Ni$_{\mathrm{1-x}}$)Zr ($x= 0.7, 0.6$) and the Ni-based ternary alloy Ni(Zr$_{\mathrm{x}}$Ti$_{\mathrm{1-x}}) (x= 0.5)$. All investigated systems within this work, except the eutectics $Cu_{56}Zr_{44}$ and $Cu_{46}Zr_{54}$, exceeded the hypercooling limit $\Delta T_{\mathrm{hyp}}$ and, remarkably, every $v(\Delta T)$ relation changed significantly at $\Delta T_{\mathrm{hyp}}$. Our results for glass forming CuZr indicate that the influence of the diffusion coefficient $D(T)$ on $v(\Delta T)$ at high undercoolings, as claimed in literature, cannot be the sole reason for the existence of a maximum in the $v(\Delta T)$ behaviour. These observations could make a valuable contribution concerning an extension of growth theories to undercooling temperatures $\Delta T > \Delta T_{\mathrm{hyp}}$. Nevertheless, our finding has direct consequences to various disciplines, as our earth and all living beings are examples for non-equilibrium systems. The scatter of our velocity data is at least two orders of magnitude smaller than measurements performed by former works due to our experimental setup, which allowed precise contactless triggering at a specific undercooling, and our analysis method, which considered the respective solidification morphologies.

Phase selection in hypercooled alloys

The effect of the hypercooling limit on the crystal growth velocity v as a function of the undercooling temperature ΔT for intermetallic binary and ternary alloys remains unexplained yet. In combination with the electrostatic levitation technique, we performed in-situ high energy synchrotron X-ray diffraction measurements at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, to investigate the phase formation of the binary alloy NiTi, the Zr-based ternary alloys (NixCu1−x)Zr (x=0.3,0.4) and the Ni-based ternary alloy Ni(Zr0.5Ti0.5) for solidification events at undercooling temperatures ΔT<ΔThyp and ΔT>ΔThyp, whereas ΔThyp are the corresponding hypercooling limits of the systems. Our results indicate that the cubic B2-type (CsCl-type, space group Pm3 m #221) phase is always the primary solidifying phase for all investigated alloys. This holds for all undercoolings obtained. Thus, the deceleration effect observed in the crystal growth velocity for all investigated alloys at their hypercooling limits seems to be caused by something different than the formation of different phases.

Hyper-cooling limit, heat of fusion, and temperature-dependent specific heat of Fe-Cr-Ni melts

Thermophysical properties of Fe-Cr-Ni melts are studied using electrostatic levitation and rapid solidification techniques. Six hypoeutectic Fe0.72CrwNi(0.28−w) alloys with a Cr/Ni ratio of around 0.8 were melted and solidified at different degrees of undercooling. From the observed relationship between the undercooling and thermal plateau time, the hyper-cooling limit and heat of fusion of Fe0.72CrwNi(0.28−w) melts are determined as a function of Cr mass fraction. A ratio of specific heat and total hemispherical emissivity of the Fe-Cr-Ni melts is calculated using the time-temperature profiles. A new method is presented to evaluate the temperature dependence of specific heat for undercooled melts and applied to this alloy family.

Rapid solidification of Al-Cu droplets of near eutectic composition

Near eutectic Al-Cu droplets were rapidly solidified by Impulse Atomization. A wide range of microstructural scales was obtained at different cooling rates and undercoolings. The micrographs of the investigated samples revealed two distinct zones of different structural morphologies: An undulated eutectic morphology developed during recalescence following the single grain nucleation and a regular lamellar eutectic morphology resulting from the solidification of the remaining liquid post recalescence. The volume fraction of each zone was measured as a function of the droplet diameter, and the nucleation undercooling was deduced using the hypercooling limit equation. Scanning Electronic Microscopy imaging and microhardness measurements were used to evaluate the microstructural scale, and mechanical properties.

Metastable phase selection from undercooled Zr77Rh23 liquid alloys

From measurements of X-ray and neutron scattering of electrostatically levitated Zr77Rh23 liquids, a variety of metastable crystallization behavior was observed. The metastable phase selection in deeply undercooled liquid droplets is characterized and their crystallization pathways discussed. A metastable phase previously identified as a primary devitrification product from the metallic glass formed when undercooling was maximized to near the hypercooling limit. The direct formation of α–Zr and the equilibrium C16 phase as well as a newly discovered Zr5Rh3 (Mg5Si3-type) phase are also reported.

Heterogeneous nucleation and dendritic growth within undercooled liquid niobium under electrostatic levitation condition

The physical mechanisms of crystal nucleation and dendritic growth within undercooled niobium were systematically studied by electrostatic levitation and molecular dynamics methods. The maximum undercooling was achieved as 454K (0.16Tm), while the hypercooling limit was determined as 706K (0.26Tm). The undercooling probability displayed Poisson distribution and indicated the occurrence of heterogeneous nucleation. The calculated critical nucleus size reduced rapidly with undercooling and the solid-liquid interface energy was deduced to be 0.367Jm−2. In addition, the dendritic growth velocity of pure niobium exhibited a power relation versus undercooling, and reached 41ms−1 at the maximum undercooling.

Nanosized Nucleus-Supercooled Liquid Interfacial Free Energy and Thermophysical Properties of Early and Late Transition Liquid Metals

Crystal–liquid interfacial free energy is important to understand in crystal study, for example, nucleation, crystal growth, and vitrification. Here, we report the nanosized nucleus-supercooled liquid interfacial free energy of early and late transition liquid metals using the electrostatic levitation (ESL) technique and classical homogeneous nucleation theory (CNT). For the estimation of the interfacial free energy, we obtained thermophysical parameters of the transition liquid metals (Ti, Fe, Ni, Zr, Nb, Rh, and Hf), such as hypercooling limit (ΔThyp), specific heat (Cp), total hemispherical emissivity (eT), and density (ρ). The estimated interfacial free energies of Ti, Ni, and Zr agreed well with a previous report having similar hypercooling limit and fusion enthalpy, while Fe, Nb, Rh, and Hf show different values from the report. This reflects the importance of accurate measurement of the two quantities. The obtained Turnbull’s coefficients (α) of the liquid metals is higher than 0.45. The interfacia...

Crystal–liquid interfacial free energy and thermophysical properties of pure liquid Ti using electrostatic levitation: Hypercooling limit, specific heat, total hemispherical emissivity, density, and interfacial free energy

Thermophysical properties of liquid Ti are measured by a newly developed electrostatic levitation. In this study, we measure a hypercooling limit (ΔThyp), specific heat (Cp), total hemispherical emissivity (εT), and density (ρ) of liquid Ti. The ΔThyp of the liquid Ti is 341K. The Cp of the liquid Ti shows very weak temperature dependence during supercooling. The εT and ρ of the liquid Ti are given by 0.329 and ρ(T) (g/cm3)=(4.16−2.36)·10−4 (T−Tm). Finally, the interfacial free energy is estimated with the measured thermophysical parameters. The interfacial free energy is 0.164J/m2, and Turnbull’s coefficient is 0.48.

Crystal–Liquid Interfacial Free Energy of Supercooled Liquid Fe Using a Containerless Technique

We report a crystal–liquid interfacial free energy of a supercooled liquid Fe, which is estimated from the classical homogeneous nucleation theory, using a containerless technique, electrostatic levitation (ESL). Thermophysical properties on the supercooled and the stable Fe liquids that are prerequisite for the estimation of interfacial free energy are measured by the ESL, for the first time. A hypercooling limit, which is one of the important parameters to determine the interfacial free energy, is obtained with 357 °C. Specific heat (Cp) and total hemispherical emissivity (εT) are 45.1 ± 3 J/mol·K and 0.314 at melting temperature, respectively. The Cp of the supercooled liquid Fe shows weak temperature dependence, confirmed by a calculated cooling curve. Densities of the stable, the supercooled liquid, and the crystal phases of Fe are successfully measured in a wide temperature range from 650 to 1600 °C. Finally, the crystal–liquid interfacial free energy of Fe is estimated with the measured thermophysical parameters. The value is about 0.22 ± 0.01 J/m2, which is consistent with a molecular dynamic simulation result.

Evolution of solidification microstructure in undercooled Co80Pd20 alloys

Applying fluxing method, Co80Pd20 alloy melts were undercooled up to 340 K. Evolution of the solidification microstructure of the undercooled alloys was investigated. Within the range of the achieved undercooling (ΔT), two grain refinement events were observed. The first event happens in the range of 50 K<ΔT<265 K, while the second event takes place at ΔT>280 K. Based on experimental investigations and theoretical calculations, the mechanisms of grain refinements were illuminated. The first grain refinement event is induced by the remelting effects involved in the post-recalescence period, resulting in the formation of a spherical grained microstructure. In the narrow transition range of 265 K<ΔT<280 K, the microstructure is occupied by a mixture of coarse dendrites with equiaxed grains. When ΔT is higher than 280 K, which is rather above the hypercooling limit, recrystallisation of the rapidly solidified solid happens and leads to the formation of an equiaxed grained microstructure.

Modeling the overall solidification kinetics for undercooled single-phase solid-solution alloys. II. Model application

An overall solidification kinetic model was applied to undercooled Ni–15 at.% Cu alloy. A good agreement between the model predictions and the measured cooling curves was obtained by adopting a “phenomenological” heat boundary condition. Applying numerical calculations, it was demonstrated that solute is uniformly distributed at the purely thermal-controlled growth stage; a transition from non-equilibrium to near-equilibrium solidification occurs at the mainly thermal-controlled growth stage only if sufficiently high initial undercooling is available; and a transition from recalescence to post-recalescence occurs at the solutal-controlled growth stage wherein the current model reduces to Scheil’s equation. The volume fraction solidified during recalescence is the same as the ratio of the initial undercooling to the hypercooling limit, and solidification should end generally at a temperature between the prediction of Scheil’s equation and that of the Lever rule if back diffusion is considered.

Grain refinement in the solidification of undercooled Ni–Pd alloys

Two bulk Ni–Pd alloys Ni 75Pd 25 and Ni 54.8Pd 45.2 have been undercooled beyond their hypercooling limits. As undercooling increases, two grain refinements, occurring at low and high undercooling, respectively, were observed in the solidification of both alloys, even though the equilibrium crystallization temperature range of the latter is only 5 K. Reaching of the hypercooling limit did not change the microstructural morphology abruptly, and dendritic substructure could still be found in the refined grains. Such experimental results cannot be interpreted satisfactorily by the theory that the break-up of dendrites during solidification is dominated by capillary force. It is proposed that the grain refinement at low undercooling results from the remelting associated with chemical superheating, but that at high undercooling is due to the post-solidification recrystallization.

Solidification structure of undercooled Ni 54.6Pd 45.4 alloy

Ni 54.6Pd 45.4, a solid solution alloy without crystallization temperature range, has been undercooled by glass flux method up to the hypercooling limit. It was found that it solidified as pure metals. As undercooling increases, the secondary dendrite arm spacing decreases monotonously until a undercooling of 135 K, above which the secondary branches considerably degenerate. The solidification with undercoolings higher than 160 K leads to grain-refined structures. In this case, their average grain sizes continuously decrease with increasing undercooling even if the alloy has been hypercooled. The fact that grain refinement still takes place in the solidification of the hypercooled alloy indicates that the solidification time after recalescence is not a factor to dominate the grain refinement at large undercooling. Recrystallization of the solid in the post-solidification period should be responsible for the grain refinement.

Growth kinetics of highly undercooled Al2O3 melts

An aeroacoustic levitator was employed to solidify the Al2O3 melt in a containerless condition at different melt undercoolings when a laser beam heating system was utilized. The sample was simulated to crystallize at well-defined temperatures and the recalescence front was imaged using a high-speed video. Both the observation of solidified microstructures and the theoretical calculation of the hypercooling limit of the undercooled melt indicated that the final microstructure should consist of the primary dendrite formed during rapid recalescence and the subsequent product yielded after recalescence near the melting temperature. Microstructure analysis showed that the advancement rate of the recalescence front should be viewed as the growth velocity of the undercooled melt. The accurate relationship of growth velocity versus melt undercooling was acquired, which was essential in characterizing the growth kinetics of the undercooled melts. Further analysis indicated that the linear kinetic coefficient for the free growth of Al2O3 was about 0.05 m/sK, which was much higher than that of some other compounds with complicated crystalline structures. The growth kinetics of the undercooled melt can be well clarified when considering the complexity level of the crystalline phase and the structure of coordination in the undercooled melt in comparison with some other oxides.

Microstructure of Y3Al5O12 garnet solidified from the melt undercooled beyond the hypercooling limit

The microstructural evolution of Y3Al5O12 garnet (YAG) in a wide undercooling range beyond the hypercooling limit (ΔT hyp) was investigated by containerless solidification processing. The dendrite to cellular-dendrite transition at high-growth velocity was observed at the undercooling beyond ΔT hyp. This transition may be explained by the hypothesis that it is difficult to form the well-developed secondary-dendritic arms from the hypercooled melt because of no remaining melt in the interdendritic regions. With a further increase in undercooling beyond ΔT hyp, a cellular microstructure disappeared, and copious amounts of small particles appeared at an undercooling of approximately 1000 K, which is near the glass-transition temperature where the viscosity is approximately 1012 Pas. It is suggested that multiple nucleation occurred in the highly viscous undercooled melt because of the high nucleation rate. The grain size of YAG, which was analyzed as a function of undercooling, gradually decreased with increasing undercooling even beyond ΔT hyp, and no fragmentation of dendrites was observed.

Rapid solidification of Y 3Al 5O 12 garnet from hypercooled melt

Containerless solidification of Y 3Al 5O 12 garnet (YAG) was carried out using an aero-acoustic levitator to elucidate the solidification process beyond the hypercooling limit (Δ T hyp). A YAG melt was seeded at different undercoolings by a SiO 2 trigger needle. The apparent plateau after recalescence disappeared at around Δ T=500 K and the post-recalescence temperature ( T post) decreased from the melting point with further increase in undercooling. Δ T hyp of YAG was estimated to be 769 K using the specific heat of liquid that was evaluated by a heat-transfer calculation from the obtained cooling curves. T post decreased before reaching the estimated Δ T hyp. Although this behavior was ascribed to heat extraction by the levitation gas, which suggests that the YAG melt did not solidify adiabatically due to the low thermal conductivity, the maximum undercooling of 1060 K indicates that the YAG melt solidified beyond Δ T hyp. Moreover, the cellular morphology of YAG was observed even beyond Δ T hyp. It can be seen that the cellular morphology is retained since the thermal supersaturation does not reach unity at Δ T hyp due to the large kinetic effect.

Solute Trapping in Highly Undercooled Succinonitrile-Acetone Alloys

Pure succinonitrile and three dilute succinonitrile-acetone alloys were undercooled in long and fine capillary tubes up to the hypercooling limit. Solidification was externally triggered and growth into the undercooled melt optically monitored. The undercooling dependence of the growth velocity was measured systematically for the pure material and the three alloys. It was found that above ΔT = 10 K all V-ΔT curves were parallel. Motivated by this observation it is shown that with freely growing alloy dendrites the only mechanism for parallel V-ΔT curves is complete solute trapping. From the parallel shift of the curves the T 0 -temperature can be estimated. Although in the presented experiments thin surface dendrites grow along the tube wall, and therefore the results for free growing dendrites cannot be adapted directly, the agreement between the theoretically estimated T 0 -temperatures and the temperatures estimated from the measurements is remarkable. From this observation and three additional assumptions it is proposed that in the succinonitrile-acetone system complete solute trapping occurs above a growth velocity of V = 0.4 m/s.

Nonequilibrium solidification of hypercooled Co–Pd melts

Co–Pd alloy melts are characterized by a low heat of fusion and, as a consequence, by a comparably small critical undercooling for the hypercooling limit ΔThyp of the order of 300 K. It is shown that containerless processing of bulk melts by electromagnetic levitation offers undercooling levels of ΔT≈350 K thus exceeding the hypercooling limit considerably. Solidification of undercooled melts from the hypercooling regime leads to rapid crystallization of the entire sample under nonequilibrium conditions. The electromagnetic levitation technique in combination with time-resolved recalescence detection was used to measure the growth velocity of Co–Pd alloy melts as a function of undercooling prior to solidification. The growth velocities of undercooled metallic melts were measured in an undercooling range exceeding the hypercooling limit. The experimental results are discussed within current theory of dendritic growth.