Maximum Supercooling Research Articles

Volume Crystallization of a Nickel Droplet Containing Refractory Nanoparticles upon Its Impact onto a Substrate

A mathematical model is developed for nonequilibrium volume crystallization of a metallic droplet modified by mechanically activated refractory nanoparticles upon its impact onto a solid substrate. The model takes into account the kinetics of heterogeneous and homogeneous nucleation during melt cooling. Specific features of crystallization of a liquid metal (nickel) depending on the concentration and size of modifying particles are examined numerically. A typical feature of the process considered is the maximum supercooling of the melt, whose magnitude depends on the particle size and cooling intensity. Homogeneous nucleation is almost absent. The calculated radii of droplets solidified on the substrate are in good agreement with available experimental data.

Observation of ice nucleation in acoustically levitated water drops

The supercooling and nucleation of acoustically levitated water drops were investigated at two different sound pressure levels (SPL). These water drops were supercooled by 13to16K at the low SPL of 160.6dB, whereas their supercoolings varied from 5to11K at the high SPL of 164.4dB. The maximum supercooling obtained in the experiments is 32K. Statistical analyses based on the classical nucleation theory reveal that the occurrence of ice nucleation in water drops is mainly confined to the surface region under acoustic levitation conditions and the enlargement of drop surface area caused by the acoustic radiation pressure reduces water supercoolability remarkably. A comparison of the nucleation rates at the two SPLs indicates that the sound pressure can strengthen the surface-dominated nucleation of water drops. The acoustic stream around levitated water drops and the cavitation effect associated with ultrasonic field are the main factors that induce surface-dominated nucleation.

Frazil dynamics and precipitation in a water column with depth-dependent supercooling

When seawater becomes supercooled, collections of small ice crystals, known as frazil ice, form and grow. A model of frazil ice dynamics is presented that deals explicitly with the buoyant settling of frazil crystals onto an overlying surface. This yields further insight into transport associated with the ice pump mechanism, whereby ice is melted at depth and transferred to a shallower location as a result of the pressure variation of seawater’s freezing temperature. The model is applied to a vertical cross-section through an Ice Shelf Water plume beneath Filchner–Ronne Ice Shelf, Antarctica, and helps to elucidate the depth-variation in its properties for the first time, as well as predicting the precipitation rate of frazil crystals. The model predicts that frazil ice should be preferentially located in a narrow layer near the ice shelf base as a result of the maximum supercooling there and an influx of crystals rising under their own buoyancy. The deposition of these crystals onto the ice shelf is governed by the balance between crystal rising and turbulent transfer of frazil away from the shelf, which is investigated in some detail.

Deducing solid–liquid interfacial energy from superheating or supercooling: application to H2O at high pressures

We present a general method to determine the solid–liquid interfacial energy (γsl) from the maximum supercooling (or superheating), and apply it to the water–ice system. For solid–liquid phase transitions, the nucleation-theory-based systematics of maximum superheating and supercooling relate a dimensionless nucleation barrier to the superheating (supercooling) and heating (cooling) rates. Given superheating (or supercooling) values from either experiments or simulations, γsl can then be deduced from the dimensionless nucleation barrier, equilibrium melting temperature and enthalpy of fusion. We demonstrate the accuracy of this approach using molecular dynamics (MD) simulations of the Lennard–Jones system: our predictions of γsl at various pressures are in excellent agreement with independent, direct MD simulations. With this approach, we predict γsl for the water–ice (Ih and III) system using experimental supercooling values in the pressure range of 0–0.3 GPa. The predicted value (28 ± 0.8 mJ m−2) agrees with measurements on H2O–Ih at ambient pressure.

Solid–liquid interfacial tension in metals: correlation with the melting point

The corresponding-states approach, previously developed by the author to predict the surface tension properties of pure solid and liquid metals, has been extended to crystal–melt interface tension analysis. A simple expression, scaled linearly with the melting temperature Tm and with the atomic volume of the solid at the melting point as Ωsm−2/3, has been derived for the solid–liquid interface tension γsl of pure metals. It was shown that γsl and its temperature dependence are determined mainly by the balance of the interfacial entropy and the entropy of fusion. At the melting temperature, the suggested formula predicts values agreeing with experimental data obtained from maximum supercooling measurements and from nucleation kinetics experiments. The results are compared with empirical relationships and discussed in the light of recent molecular-dynamics simulations.

Nonequilibrium melting and crystallization of a model Lennard-Jones system.

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.

Freezing of a water droplet due to evaporation—heat transfer dominating the evaporation–freezing phenomena and the effect of boiling on freezing characteristics

One of the authors has proposed a novel transport/storage system for the waste cold from the gasification process of liquefied natural gas (LNG), which consists of an evaporator, a cold trap, and a pipeline. In order to estimate the performance of this system, one should know the pressure in the evaporator, in which evaporation–freezing of a PCM occurs, and in the cold trap, as well as the pressure drop of the pipeline due to the flow of low pressure vapor of the PCM. In this paper, the cooling/freezing phenomena of a water droplet due to evaporation in an evacuated chamber was experimentally examined, and the heat transfer dominating the evaporation-freezing phenomena was investigated in order to estimate the pressure in the evaporator. From the results, it was shown that the water droplet in the evacuated cell is effectively cooled by the evaporation of water itself, and is frozen within a few seconds through a remarkable supercooling state, and that the cooling rate of the water droplets were dominated by heat transfer within the droplet under the abrupt evacuation condition. The later result means that, in order to obtain an ice particle by evaporation–freezing, the surroundings of the water droplet should be evacuated at the pressure as low as the saturate pressure of water at the maximum supercooling temperature of the droplet.

The transition mode of dilute binary alloys during directional solidification near to the absolute stability limit

The morphological evolution near the absolute stability limit during directional solidification has been studied systematically on dilute Al–Mn alloys. It is found that the interfacial morphology of Al–0.52wt%Mn and Al–1.2wt%Mn alloys changes from coarse cellular structure to fine cells, and then again to be coarsened with the increase of velocity to near the absolute stability limit. This indicates that there exists a minimum cell spacing corresponding to the maximum effective constitutional supercooling. As the growth rate approximates to or exceeds the critical velocity of absolute stability by calculation according to M–S theory, the interfacial morphology of Al–0.52wt%Mn alloy may still retain a cellular structure. For Al–1.2wt%Mn alloy, when the growth velocity is near the absolute stability limit, the fine cells may change to a band or grain-like structure which in some cases takes an oscillating manner, which possibly implies the existence of a non-linear effect during high growth rate.

Freezing and ice crystals formed in a cylindrical food model: part II. Comparison between freezing at atmospheric pressure and pressure-shift freezing

Cylindrical gelatin gels were pressure-shift frozen at different pressure levels (100, 150 and 200 MPa). Temperature and pressure profiles were compared and the maximum supercooling obtained after pressure release was evaluated. A comparison between the freezing steps at atmospheric pressure and those of pressure-shift freezing was carried out to compare the time steps during the processes. The degree of supercooling increased with the level of pressure. For pressure-shift freezing, the size of ice crystals appeared to be more homogeneous in the whole sample and independent of the location. The mean representative ice crystal diameter decreased as the pressure level increased. This may be due to the degree of supercooling achieved during pressure-shift freezing. The ice crystal size for pressure-shift frozen sample was smaller than those obtained with classical freezing methods. A regression between the supercooling level and the mean ice crystal size was proposed.

Overwintering strategy in Pyrrhocoris apterus (Heteroptera): the relations between life-cycle, chill tolerance and physiological adjustments

Seasonal dynamics of ecophysiological parameters are described which are relevant to overwintering in field-collected adults of a Czech population of the red firebug, Pyrrhocoris apterus. Five life-cycle phases were distinguished using the duration of pre-oviposition period as a criterion: reproductive activity (spring–early summer), intensification of reproductive diapause (RD) (peak of summer), maintenance of RD (late summer–early autumn), termination of RD (late autumn–early winter), and low temperature quiescence (LTQ) (winter). The supercooling capacity and chill tolerance (c.t.) increased simultaneously with the termination of RD and all three processes were triggered/conditioned by autumnal decrease in ambient temperatures. Maximum supercooling capacity and c.t. ‘outlived’ the end of diapause and persisted throughout the LTQ state. The limits of c.t. were estimated as −15°C/1–2 weeks for 50% survival. Ribitol, sorbitol, arabinitol, and mannitol were accumulated in the winter-sampled insects. Relatively low concentrations of polyols (dominating ribitol reached ca. 1% FW) indicate that they do not function as colligative cryoprotectants. However, because their seasonal occurrence coincided with the highest c.t., their non-colligative cryoprotectant effects would merit further study. Although the overwintering microhabitat of P. apterus is buffered, the temperatures may fall to −13°C during exceptionally cold winters and thus, the parameters of c.t. seem to be just appropriately tuned to the local overwintering conditions.

Thermographic investigation of the discrete fusion and crystallization supercooling of lead

The kinetics of lead melting and solidification were studied by the method of ballistic thermal analysis (BTA). It was established for the first time that the melting process involves three stages of fusion at TL1, TL2, and TL3, with the temperature differences TL2-TL1=0.3±0.05 K and TL3-TL2=0.6±0.1 K. The corresponding specific enthalpies of fusion are H1=H2=(0.4±0.05)H and H3=(0.15±0.05)H, where H=H1+H2+H3. Crystallization always proceeds at a temperature equal to that of the first stage of fusion (Ts-TL1). Accordingly, the crystallization supercooling of the melt exhibits discrete variation: ΔT1−=0, ΔT2−=0.06±0.02 K, and ΔT3−=3±0.5 K after the first, second, and third stage, respectively. Overheating of the melt to ΔT+=22±2 K is accompanied by the maximum supercooling ΔT4−=4±0.2 K.

Supercritical supersaturations and ultrafast cooling of the growth solution in liquid-phase epitaxy of semiconductors

A method for accomplishing ultrafast cooling is proposed which makes possible supercritical supersaturations of the growth solution in liquid-phase epitaxy. Growth boat designs providing cooling rates as high as are considered. The temperatures of contact, , of a GaAs substrate with a Ga-based solution and of a Si substrate with a Sn-based growth solution, calculated for various substrate and solution temperatures , are in good agreement with experimental values. The maximum attainable supercooling is markedly increased to as high as for the Ga - As system, when the growth solution is subjected to ultrafast cooling. The prospects of using the method for fabricating heterostructures with a large lattice mismatch are discussed.

Batch crystallization under continuous cooling: analytical solution for diffusion limited crystal growth

The kinetic equations of nucleation and crystal growth in a multicomponent system undergoing continuous cooling are solved for asymptotically slow cooling rates meaning that the maximum supercooling ΔTm is much smaller than the exponent A in the nucleation rate I exp(−AT−2). The growth rate is controlled by chemical diffusion so that it depends not only on the supercooling but also on the crystal size. The periods of metastable cooling, nucleation and relaxation are related as 1:p−1:p−1/3 where p = AΔT−2m 30–80 is a parameter characterizing the maximum supercooling Tm. It is a weak (logarithmical) function of all the parameters including the cooling rate Ṫ. The crystal sizes are determined by the density of nuclei produced during the nucleation period and depend on the cooling rate approximately as Ṫ−0.5. The theoretical predictions are found in a good agreement with experimental data for AlCu, AlSi, SnPb, and CaMgSi2O6CaAl2Si2O8NaAlSi3O8.

Measurement of density, sound velocity, surface tension, and viscosity of freely suspended supercooled liquids

Noncontact methods have been implemented in conjunction with levitation techniques to carry out the measurement of the macroscopic properties of liquids significantly cooled below their nominal melting point. Free suspension of the sample and remote methods allow the deep excursion into the metastable liquid state and the determination of its thermophysical properties. We used this approach to investigate common substances such as water,v-terphenyl. succinonitrile, as well as higher temperature melts such as molten indium, aluminum, and other metals. Although these techniques have thus far involved ultrasonic, eletromagnetic, and more recently electrostatic levitation, we restrict our attention to ultrasonic methods in this paper. The resulting magnitude of maximum thermal supercooling achieved has ranged between 10% and 15% of the absolute temperature of the melting point for the materials mentioned above. The methods for measuring the physical properties have been mostly novel approaches, and the typical accuracy achieved has not yet matched the standard equivalent techniques involving contained samples and invasive probing. They are currently being refined, however, as the levitation techniques become more widespread and as we gain a better understanding of the physics of levitated liquid samples.

Second, third and correlation moments from nonequilibrium and equilibrium fluctuation theory, N, P, T ensemble, compared between supercooled and superheated liquid water

A local nonequilibrium fluctuation (NEF) theory has been developed which applies to modest deviations from equilibrium when gradients, time dependences, etc., are absent, and, provided that long-range spatial correlations of the fluctuations are suppressed, for example, by droplet sizes down to 3 μm required to obtain thermodynamic data at the extremes of supercooling. The predictions from NEF theory are constrasted against those from equilibrium fluctuation (EF) theory using the extensive data available for metastable liquid water. NEF and EF second and third T and P moments were calculated and compared between the maximum supercooling and superheating spinodals, ≈227 K and ≈596 K, at 1 atm pressure. The EF second and third T and P moments are either small or zero near 227 K, but 〈(δ T) 2〉 and 〈(δ P) 2〉 approach +∞ near 227 K, and 〈(δ T) 3〉 and 〈(δ P) 3〉 approach -∞ and +∞, respectively, when calculated by NEF theory. Moreover, all NEF second moments, G, A, H, E, P, V, T and S, approach +∞ for supercooled water near 227 K, and correlation moments, e.g., entropy-pressure, also diverge. The positive infinities in 〈(δ P) 3〉 and 〈(δ P) 3〉 require some pressure fluctuations to reach the negative-pressure stability limit of supercooled water at 227 K, thus causing mechanical instability, but mechanical instability at 227 K is not obtained from EF theory. An even more important result is that the NEF second S moment diverges much faster near 227 K then the EF second S moment. This occurs because the NEF second S moment contains two diverging terms; the first is the same as the EF second S moment, but the second, more-rapidly diverging term, is related to the nonequilibrium entropy production. The NEF second E moment also is somewhat larger than the EF second E moment near 227 K, whereas other second moments, of A, H and V, are identical in EF and NEF theory. Several NEF second moment divergences do not result just from the infinities in the individual susceptibilities, but rather from the product of C P, β, or K T , with 1/( C VK T+βV ), which also approaches large values near 227 K. Differences between NEF and EF results also occur up to 596 K for superheated water.

From the bulk to clusters: Solid-liquid phase transitions and precursor effects

Abstract A review is given of the experiments done in order to understand the initial stages of melting and solidification of a material. We emphasize on new results obtained for ultrafine metal particles by using high sensitivity reflectance and electron microscopy measurements. These experiments show that melting certainly begins through a continuous and reversible transition and proceeds through the usual first-order transition. For ultrafine particles, these two processes have a relative importance which depend on the size, the first process having the major importance for the smallest particles. Undercooled state and subsequent solidification depend also on the size of the particle. For the smallest particles, the maximum supercooling temperature is found to coincide with the final temperature of the continuous transition leading to disappearance of the hysteretic behaviour usually found in solid-liquid transitions for ultrafine particles.

Nucleation behaviour of tripalmitin from a triolein solution

AbstractNucleation of tripalmitin (PPP) crystals from melt and from its binary triolein (OOO) solutions was studied by differential scanning calorimetry (DSC) and optical microscopy. Cooling DSC thermograms for either pure PPP or OOO exhibits a single exotherm. For the solutions, two widely separated peaks due to PPP and OOO were observed. The PPP peak is broadened and shifts down to a lower temperature as the OOO content in the solution increases. A modified Turnbull and Fisher equation was used for nucleation data analysis. The temperature for maximum supercooling of the solution is reduced by OOO but the degree of maximum supercooling remains unchanged at 22oK. An interfacial free energy of 9.45 erg/cm2 for β‐PPP/ melt was deduced. This value drops rapidly to a slightly lower value of 8.95 erg/cm2, in triolein solution. The effect of a reduced interfacial free energy on nucleation is critically discussed in the light of a simultaneous reduction in the melting point of β‐PPP in the solution.

On maximum supercooling in liquids

A realistic approximation has been utilized within the framework of homogeneous nucleation theory, to calculate the change in volume free energy Δ G v on solidification, and the maximum supercooling temperature T 0 for a few metallic and semiconducting systems. The approximation includes the maximization of the nucleation rate and the hyperbolic form for the specific heat change i.e. ΔC p = C/ T. It yields unique values of T 0/ T m which are found to be consistent with those between 1 3 and 1 2 as often quoted in the literature.

Adiabatic nucleation and glasses

A recently developed Adiabatic Nucleation Theory (ANT), which has been shown to be in good agreement with the largest experimental supercoolings of pure liquid elements (mostly metals), is applied to organic, inorganic and metallic glasses. It is demonstrated that, in order to obtain a glass by cooling from the melt, the (normal, slow cooling) glass transition temperature ( T g) has to be systematically: (i) higher or (ii) only slightly lower than the maximum supercooling temperature ( T −), predicted by ANT. In the former case, rapid quenching is sometimes necessary in order to avoid (or reduce) crystallization initiated by heterogeneous nucleation and in the second case, rapid quenching is always necessary in order to also avoid homogeneous nucleation. The latter case can be explained by the fact that T g can be “raised” above T − by fast quenching. Only polymers containing co-polymers may show T g's which are considerably lower than T −, because these co-polymers may stabilize (eventually small) amorphous domains of the principal polymer below T −. Other materials with low T g's ( T g ⪡ T −) just do not form glasses by quenching from the liquid, but can eventually be obtained in the amorphous, glassy form by condensation from the vapour phase on a cold substrate. In this latter case, the glass is really “composed” well below T − and T g. In conclusion it can be stated that the glass forming ability is well characterized by T g/ T −.

Maximum supercooling of silicon encapsulated in SiO2

An SiO2-encapsulated silicon-on-silica structure has been used to examine quantitatively the supercooling of Si. Fully melted, isolated Si islands generally exhibit a maximum supercooling of 235 °C, i.e., their freezing occurs at a temperature around 1175 °C. The implications of this behavior for the growth of thin Si films on amorphous substrates via zone melting are presented and briefly discussed.