Thermodynamics of Liquid–Liquid Criticality in Supercooled Water in a Mean-Field Approximation

In a recent publication, it has been shown how a non-analytic scaling theory of critical phenomena can describe the available experimental information for the thermodynamic properties of supercooled water, when it is assumed to exhibit a liquid–liquid critical point. In this article, we present a mean-field equation of state which also represents the experimental data for supercooled water. Compared to the scaling theory, the mean-field equation has the advantage of simplicity for practical calculations of the properties of supercooled water. The insensitivity to a particular form of a critical equation of state is due to a lack of experimental data asymptotically close to the liquid–liquid critical point. Hence, while the assumed existence of a liquid–liquid critical point in water can account for the observed thermodynamic behavior of supercooled water, the actual location of such a liquid–liquid critical point cannot be determined accurately from the available experimental thermodynamic property data.     

Physical Limit of Stability in Supercooled Liquids

The kinetic spinodal (KS) in supercooled liquids, similar to the KS in superheated and stretched liquids, has been introduced as a locus where the mean time of formation of a critical nucleus becomes shorter than a relaxation time to local equilibrium. If the surface tension of the solid–liquid interface is known, the kinetic spinodal is completely determined by the equation of state of the supercooled liquid. The theory was tested against experimental data for the surface tension and the homogeneous nucleation limit for supercooled water. Reasonably good agreement between theoretical predictions and experimental data was observed. A prediction of the high-temperature limit for glass transitions is also discussed.     

基于气动悬浮激光加热技术YAG熔体高温热物理性能评测

钇铝石榴石Y₃Al₅O₁₂(Yttrium Aluminum Garnet, 简记为YAG)材料具有优异的光、热和电学性能, 引起了广泛关注。但高熔点和冷却过程中复杂的相选择机制, 使YAG熔体特别是熔点以下过冷区内的热物理性能参数获得困难。利用自主搭建的气动悬浮无容器激光加热装置, 基于受迫振动和光学描影等原理, 在1750~2650 K宽达900 K的温区内, 评测了YAG熔体的黏度、表面张力和密度。研究表明, 与Al₂O₃熔体相比, YAG熔体密度具有更高的温度敏感性, 具有高约1倍的平均线膨胀系数; 不同于表面张力随温度变化不敏感的Al₂O₃熔体, YAG熔体的表面张力随温度升高产生略微降低; 与Al₂O₃熔体的黏温关系相比, 在熔点以下的过冷区内发现YAG熔体具有更陡峭的黏温变化趋势。     

Using numerical simulation methods for the analysis of heating and cooling thermograms characterizing the melting and crystallization of water

The differential heat conduction equation that characterizes the melting and crystallization processes has been analyzed by numerical simulation methods in application to water. The correlation between the calculated and measured thermograms has been established for experimental values of the temperature of breakage of the liquid-crystalline structure (276 K) and the temperature of explosive crystallization of supercooled water (268 K).     

Effect of bubble nuclei on freezing of supercooled water

In order to clarify effects of bubble nuclei on freezing of supercooled water, various kinds of experiments were carried out with invisible sizes of bubbles in supercooled water. Water samples were kept in a test tube and cooled down at a constant cooling rate until the water solidified. The degree of supercooling at freezing was then measured. Two kinds of water surfaces were applied. One was exposure to the atmosphere, and the other was covered with silicone oil. Three kinds of pressure conditions were applied. The first type was atmospheric pressure. The second type was compression up to 6.0 atm. The third type was evacuated down to 0.02 atm. Two holding time periods before starting the experiments were applied. One was 30 min and the other was 24 h. It was found that the degree of supercooling at freezing is high in the case of the free surface compared to the one with oil–water surface. The reason suggested was that the bubbles in the water can be released from the surface in the case of normal atmospheric exposure and trapped at the oil–water interface in the case of water covered with oil. Hence, it was clarified that the freezing of supercooled water is affected by the existence of bubble nuclei.     

Subcritical free-surface flow caused by a line source in a fluid of finite depth

An integral equation is derived and solved numerically to compute the flow and the free surface shape generated when water flows from a line source into a fluid of finite depth. At very low values of the Froude number, stagnation point solutions are found to exist over a continuous range in the parameter space. For each value of the source submergence depth to free stream depth ratio, an upper bound on the existence of stagnation point solutions is found. These results are compared with existing known solutions. A second integral equation formulation is discussed which investigates the hypothesis that these upper bounds correspond to the formation of waves on the free surface. No waves are found, however, and the results of the first method are confirmed.     

Study on Surface Tension of Fluid Helium Three

As a standard property of helium-3, the surface tension is not only an important aspect to study the normal characteristics of this special cryogenic fluid, but also helpful to understand the Fermi quantum effects at low temperatures. After completion of studies on the thermodynamic and two typical transport properties (thermal conductivity and viscosity) of helium-3, all of the published experimental data of the surface tension of ³He have been collected. Different measurement techniques are compared and analyzed. The peculiar behavior of ³He surface tension, perhaps dominated by Fermi-Dirac quantum statistics, is analyzed and discussed at temperatures starting from zero to its critical point (3.3157 K). Based on a regular theoretical model for surface tension, a semi-empirical correlation is proposed for ³He covering the whole temperature range. The surface tension extrapolated to zero temperature by this equation is 1.5579×10⁻⁴ N · m⁻¹. In the vicinity of the critical point, the equation could be smoothly switched to the known scaling law, which takes the critical index 1.289. Comparison for the surface-tension behavior is performed between ³He and its isotope ⁴He, which obeys Bose-Einstein statistics.     

Thermodynamic Properties of 1,1,1,2,3,3,3-Heptafluoropropane

A vapor pressure equation has been developed for 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) based on previous measurements from 202 to 375K, from which the boiling point of HFC-227ea was determined. Based on the previous pressure–volume–temperature (PVT) measurements in the gaseous phase for HFC-227ea, virial coefficients, saturated vapor densities, and the enthalpy of vaporization for HFC-227ea were also determined. The vapor pressure equation and the virial equation of state for HFC-227ea were compared with the available data. Based on the previous measurements of speed of sound in the gaseous phase for HFC-227ea, the ideal-gas heat capacity at constant pressure and the second acoustic virial coefficient of HFC-227ea were calculated. A correlation of the second virial coefficient for HFC-227ea was obtained by a semiempirical method using the square-well potential for the intermolecular force and was compared with results based on PVT measurements. A van der Waals-type surface tension correlation for HFC-227ea was proposed, based on our previous experimental data by the differential capillary rise method from 243 to 340K.     

An SANS Study of Decomposition Kinetics in Amorphous Cu_(12.5)Ni_(10)Zr_(41)Ti_(14)Be_(22.5)

Phase decomposition in amorphous Cu12.5Ni10Zr411Ti14Be22.5 alloy as annealed in the super-cooled liquid range was studied by applying small angle neutron scattering (SANS). As annealed between 600 K and 700 K, the alloy was observed to decompose into two new amorphous phases,with the second phase precipitates embedded in the matrix of the first. Long time annealing of the alloy results in crystallization in addition to evolution of the decomposed microstructure.The kinetic diagram of the decomposition and crystallization for this alloy is given. The second phase precipitates have several nanometers in size and occupy a quite low volume fraction. The decomposition of the supercooled liquid in overall temperature range exhibits the features of spinodal reaction.     

Surface tension of liquid3He down to 0.3 K

The surface tension of liquid³He was measured by determining the surface wave velocity in the temperature range from 0.32 to 3.02 K. The decrease of the surface tension from the value at 0 K can be described as 22.3T ² mdyn/cm up to about 0.9 K and is quite different from that of⁴He. The extrapolated value to 0 K is 155.7±0.5 mdyn/cm. The data below 1.6 K were compared with Saam's model, where the surface tension is assumed to be given by the bulk free energy times the surface width and the quasi-two-dimensional free energy. Agreement between the data and the results calculated from the model is much improved if ripplons are taken into account. Data near the gas-liquid critical point, contrary to earlier results, show that the surface tension vanishes with a critical exponent of 1.24±0.05. This is in agreement with Widom's theory.     

Influence of Oxygen Adsorption on Surface Tension of Molten Nickel Measured Under Reducing Gas Atmosphere

The surface tension of molten nickel was measured under a reducing gas atmosphere of Ar–He–5 vol% H \(_{2}\) by an oscillating droplet method using electromagnetic levitation. The influence of the temperature dependence of the oxygen partial pressure of the gas on the surface tension was investigated. The surface tension of molten nickel was successfully measured over the very wide temperature range of 750 K, which included undercooling conditions. The temperature dependence of the surface tension did not exhibit a linear relationship but had a peculiar kink at around 1600 K, due to competition between the temperature dependence of the oxygen partial pressure and that of the oxygen adsorption equilibrium constant.     

Surface tension of pure liquid bismuth and its temperature dependence: Theoretical calculations

A theoretical method for calculating the surface tension of liquid metals as a function of temperature is proposed. A mathematical equation, based on statistical thermodynamics, is applied to calculate the surface tension of pure liquid bismuth, in the temperature range 545-620 K. The calculated surface tension of liquid bismuth was found to be 388 mJ/m², which is in excellent agreement with the reported experimental values (374-417 mJ/m²). The surface tension of bismuth decreases linearly with temperature, confirming a negative slope.     

Thermophysical Properties of Ag and Ag–Cu Liquid Alloys at 1098K to 1573K

The surface tension and density of liquid Ag and Ag–Cu alloys were measured with the sessile drop method. The sessile drop tests were carried out at temperatures from 1098K to 1573 K, on cooling (temperature decreasing stepwise) under a protective atmosphere of high purity Ar (6N). The density of liquid Ag and Ag–Cu alloys decreases linearly with increasing temperature, and an increase in concentration of copper results in a lower density. The surface tension dependence on temperature can be described by linear equations, and the surface tension increases with increasing Cu content. The results of the measurements show good agreement with existing literature data and with thermodynamic calculations made using the Butler equation.     

Freezing phenomena of supercooled water under impacts of ultrasonic waves

In order to clarify effects of ultrasonic waves on supercoold water, ultrasonic waves were applied to supercooled water. Frequency of the ultrasonic waves applied was 45 kHz, and the intensities of the waves were 0.13 and 0.28 W cm⁻², respectively. Four cases of experimental conditions were selected; a case of a free surface, a case of an oil-water surface, a case of a free surface with a dipped metal bar and a case of an oil–water surface with a dipped metal bar. For each experimental condition, water was cooled at a constant cooling rate and the ultrasonic wave was applied from underneath until the water in a test tube solidified. It was found that in the case of 0.28 W cm⁻², the ultrasonic wave had distinct effects on freezing of supercooled water for all experimental conditions. On the other hand, in the case of 0.13 W cm⁻², the ultrasonic wave had an effect on freezing of supercooled water only under existence of a free surface and a metal bar.     

Experimental proof of the existence of a Widom line based on peculiarities of the behavior of hydrogen in nanoporous silicate at −45°C and atmospheric pressure

We have experimentally studied the thermal and microwave properties of a nanoporous medium (silica gel) with hydrogen-filled pores. On cooling down to about ?45°C at atmospheric pressure, the system exhibited chemical transformations, a first-order phase transition with heat evolution, and a sharp change in the power of microwave radiation at 34 GHz transmitted through a sample. It is concluded that this point on the phase diagram corresponds to a point on the Widom line featuring sharp increase in fluctuations of the entropy and density of supercooled water formed during hydrogen interaction with the surface of pores in silica gel. These results confirm the existence of a second critical point of water, from which the Widom line originates.     

A generalized equation for surface tension from the triple point to the critical point

A three-parameter generalized equation is proposed for surface tension from the triple point to the critical point. This equation not only fits the data well but also is good for interpolation between the normal boiling point and the critical point. This equation is also good for extrapolation to the triple point. This equation has been tested using the surface tension of water from the triple point to the critical point. The constants of this equation obtained using orthobaric surface tensions are given for a number of compounds. The isobaric surface tensions determined at a pressure of 1 atm do not differ significantly from the orthobaric surface tensions. Such data also have been used in obtaining equations from the triple to the critical point.Nomenclature T _c Critical temperature, K - T _t Triple point, K - T _m Melting point, K - T _r Reduced temperature, K - X (T _c-T)/T _c - Surface tension, dyne · cm^–1;10^–3N · m^–1 - _m Surface tension at the melting point - _f Surface tension at T _r=0.9 - _t Surface tension at the triple point - Relative deviation 100[ _obsd– _calcd]/ _obsd - Standard deviation [( _obsd– _calcd)²/(No. points—No. parameters)]^0.5     

An Analytical Equation of State for Alkaline Earth Metals

In this work, an analytical equation of state based on statistical mechanical perturbation theory, which was initially developed for normal fluids and can be applied to predict the P–V–T data for saturated liquid alkaline earth metals, is presented. The equation of state is that of Ihm, Song, and Mason, and the temperature-dependent parameters of the equation of state are calculated from a corresponding-states correlation as functions of the reduced temperature. Two scaling constants are sufficient for this purpose, the surface tension and the liquid density at the melting point. The equation of state is used to predict the saturated liquid density of molten alkaline earth metals from the melting point up to 2000 K, for which experimental data exist, within an accuracy of 5%.     

Characteristics of Standard Capsule-Type PtCo Resistance Thermometers Between 0.65 K and 25 K

Standard capsule-type platinum–cobalt (PtCo) resistance thermometers represent one of the few types of resistance thermometers that have been developed for precise thermometry in the cryogenic temperature range. These thermometers remain sensitive even at 0.65 K, which is the lower limit of the ITS-90. Standard capsule-type rhodium–iron (RhFe) resistance thermometers are another type of resistance thermometer intended for use in this temperature range and have been well characterized and are the de facto standard worldwide. Existing data show RhFe resistance thermometers are more reproducible than the corresponding PtCo resistance thermometer. However, it has become difficult to obtain brand-new standard capsule-type RhFe resistance thermometers since their production was discontinued in the early 2000s. Unfortunately, information regarding the characteristics of standard capsule-type PtCo resistance thermometers is limited compared to that available for RhFe resistance thermometers. In this study, the characteristics of two standard capsule-type PtCo resistance thermometers between 0.65 K and 25 K were investigated. Because the resistance versus temperature curves for these thermometers over this temperature range exhibit two inflection points, setting break points near each of the inflection points was found to be beneficial during polynomial curve fitting to obtain mK-level precision. Special attention was paid to the reproducibility of these thermometers, and it was observed that the reproducibility of one of the thermometers within the cryogenic temperature range was ±0.5 mK over 6 years, while the second thermometer showed a larger variation. Similar trends in the resistance characteristics of the two thermometers were observed at the triple point of water.