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In this study, the solid–liquid equilibria of five binary systems containing refrigerants with low global warming potential, namely carbon dioxide (R744) + 1,1-difluoroethene (R1132a), R1132a + 2,3,3,3-tetrafluoropropene (R1234yf), R1132a + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)), trifluoromethane (R23) + R1234yf, and R23 + R1234ze(E), was experimentally determined. Two experimental setups based on the cooling curve method were employed to measure the samples obtained from different sources. The results obtained using the two setups were in good agreement with the experimental uncertainty. In addition, the experimental data were compared with the values calculated using the Schröder equation, showing limited deviations. The accuracy of the experimental setups was tested by measuring the triple-point temperatures of the components of the studied binary systems, showing good agreement between the experimental data obtained for the pure refrigerants and the data available in the literature., International Journal of Refrigeration, 144, pp. 254-263; 2022

The triple point temperature of refrigerants is crucial because it serves as a reference for the lower limit of their use temperature in a refrigeration system. In this study, the triple point temperatures for recently proposed refrigerants with low global warming potential were experimentally determined. Ten hydro-fluoro-olefins, two hydro-chloro-fluoro-olefins, and trifluoroiodomethane were investigated. The triple point temperatures of the refrigerants were determined from the obtained cooling and heating curves. To improve measurement accuracy, measurements were conducted on samples obtained from different companies using two different measurement devices. The measured data were found to be in good agreement within the estimated measurement uncertainty., International Journal of Refrigeration, 133, pp.172-180; 2022

Recent studies on supercritical nitrogen revealed clear changes in structural markers and dynamical properties when the coordination number approaches its maximum value. The line in P and T space where these changes occur is referred to as the Frenkel line. Here, we qualitatively reproduce such changes in the supercritical regime using the popular “optimized potential for liquid simulation” (OPLS) classical force field for molecular dynamics. Unfortunately, at 160 K, OPLS nitrogen predicts sublimation rather than producing a liquid phase; therefore, we developed our own force field to achieve quantitative agreement with experimental data. We confirm the asymptotic behavior of the coordination number on crossing the Frenkel line and note an associated change in the diffusion constant, consistent with the non-rigid to rigid liquid-like character of the “transition”. The simulations allow us to track the Frenkel line to subcritical temperatures and demonstrate that it terminates at the triple point. This establishes the experimentally measurable changes, which could unequivocally determine the Frenkel line in other systems.

Ternary 0.552Pb(Ni1/3Nb2/3)O3-xPbZrO3-(0.448-x)PbTiO3 (PNN-PZ-PT) ceramics near the triple point compositions were fabricated by an improved two-step sintering method. The triple point composition 0.552PNN-0.135PZ-0.313PT ceramic has outstanding piezoelectric performance with piezoelectric coefficient d33 = 1200 pC/N. Its easy fabrication and low cost make this piezoelectric material an excellent candidate for high sensitivity sensors and ultrasonic transducers. The evolution of domain structures for ceramics with composition near the triple point provides deeper insight into the mechanism of ultrahigh piezoelectric properties of PNN-PZ-PT ceramics.

Some studies in recent years have shown the possibility of extending the application temperature of the natural refrigerant carbon dioxide (CO2) below its triple point. Thus, CO2 could be a potential alternative refrigerant for R-23 in ultralow-temperature (ULT) refrigeration systems. This paper introduces a special cascade system, whose lower stage can be switched between a CO2 sublimation cycle and a conventional R-23 cycle, so that both cycles can be compared directly under the same ambient conditions. The sublimation system features a unique sublimation heat exchanger, which allows the operation with an extra carrier fluid in order to improve the heat transfer and reduce the blockage by solid CO2. In this study, experiments were carried out using HFE-7500 as the carrier fluid (“wet sublimation”) as well as without the carrier fluid (“dry” sublimation). The system was able to be operated continuously in both operating mode. A refrigerating capacity of 600 W was achieved at a sublimation temperature of -79°C. The transient behavior and blocking issues of the system are discussed. The efficiency of the sublimation system during stable operations are compared with the result of the reference R-23 system. It shows that there is still large potential for improvement on the system performance of the CO2 sublimation system.

The flow field of the rotating detonation wave engine can be better understood by unwrapping the flow field in two dimensions, viz., axial and the azimuthal directions assuming that the properties do not vary in the radial direction. The flow features consist of detonation wave, trailing oblique shock wave, contact surface between fresh reactants and inert product gases and between detonation products and shocked inert product gases. The triple point is formed by the intersection of the detonation wave, oblique shock wave and Prandtl–Meyer expansion waves. Thermodynamic analysis is carried out to find out the different states of the flow field around the triple point. Shock polar and expansion flow computations are carried out to obtain the relationship between pressure ratio and flow deflection angle. The intersection of the shock polar and the expansion process indicates the existence of attached shock solution. Further, it leads to the evaluation of performance parameters of the rotating detonation wave engine. Case studies based on hydrazine–nitrogen tetroxide, hydrogen–oxygen, ethylene–oxygen and hydrogen–air systems indicate occurrence of attached oblique shocks under the realistic conditions of operation. The acoustic impedance is not the only parameter to explain the existence of attached oblique shock. It is only a derived quantity based on the upstream conditions of the detonation wave. These conditions uniquely fix the conditions ahead of the oblique shock wave and hence the velocity difference at the shear layer separating the fresh reactants and the detonation products of the previous cycle. These aspects are examined based on the case studies considered in this study. Under the realistic conditions of the case studies reported, based on this simple analysis the trailing oblique shock wave is always attached.

This work explores a nonlinear resistive field-grading material to shield the triple points prior to silicone encapsulation, thus, increasing the power module's partial discharge inception voltage. The material is aimed at coating the metal edges of a trench on a direct-bond-copper substrate for over 10 kV applications. To find the desired coating properties that would significantly reduce the field intensity at the triple point, an application-specific guideline is first prescribed for determining the baseline properties of the coating. Then, electric field simulations show that with only 10% coverage of coating at each triple-point edge, the field stress across the trench could be reduced by as much as 40%, i.e., over 67% improvement in the partial discharge inception voltage. A parametric study is done to evaluate the effect of each of the material properties, as well as the coating width, and shows that the improvement in field-stress reduction could be further increased. The material properties prescribed in this study can serve as targets for materials designers and engineers to develop insulation materials for packaging medium-voltage power modules.

CO2 shipping is a viable transport alternative when pipelines are impractical. Lack of experience in large-scale CO2 shipping projects implies uncertainty in selecting optimal cargo conditions and operational safety procedures. The risk of uncontrolled release of CO2 arises in case of mechanical failure of storage or cargo vessels, and a thorough understanding of the discharge phenomena, including the propensity for solid formation, is necessary to develop safety protocols. A refrigerated experimental setup is established in this study to investigate the release phenomena of liquid CO2 under shipping conditions. The rig features a dome-ended cylindrical pressure vessel, a discharge pipe section and a liquid nitrogen refrigeration system that enables conditioning near the triple point – at ∼0.7 MPa, 223 K - and higher liquid pressures (∼2.6 MPa, 263 K). Pressure, temperature and mass monitoring were considered to enable an extensive observation of the leakage behaviour under typical operation scenarios. Three different sets of experiments were considered to inform the designer in the selection of optimal process conditions, with low-pressure (0.7 – 0.94 MPa, 223–228 K), medium-pressure (1.34–1.67 MPa, 234–245 K) and high-pressure tests (1.83–2.65 MPa, 249–259 K) demonstrating distinct behaviours relative to phase transitions, leakage duration and solidification of inventory.

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.

Compared with the conventionally gaseous or liquid working media, the specific internal energy of supercritical carbon dioxide (SCD) is higher at the same temperature and pressure, and the critical temperature of carbon dioxide is close to room temperature, making SCD a potential new working medium for pneumatic launch. To analyze the feasibility of this conception, an analytical model of a pneumatic catapult is established on basis of the conservations of mass and energy. The model consists of a high-pressure chamber and a low-pressure chamber connected by multiple valves, and there is a movable piston in the low-pressure chamber that can push an aircraft to accelerate. The effects of the launch readiness state of SCD in the high-pressure chamber, the initial volume of the low-pressure chamber and the valve control on the movement of the aircraft are analyzed. It is found that there is a restrictive relation between the temperature and pressure of the launch readiness state of SCD, i.e., there is a maximum allowable launch readiness pressure when the launch readiness temperature is fixed. If this restrictive relation is not satisfied, the working medium in the low-pressure chamber will drop to its triple point within a few milliseconds, leading to a launch failure. Owing to this restrictive relation, there is an optimal launch readiness state of SCD with the highest working capacity for any allowable launch readiness temperature. The pressure of the low-pressure chamber will decrease significantly as the initial volume increases, leading to a decreased acceleration of the aircraft. The acceleration can be controlled below a critical value by a designed sequential blasting technique of multiple valves. The calculated results show that a 500 kg aircraft can be accelerated from 0 to 58 m/s in 0.9 s with 36 kg of carbon dioxide. This research provides a new technique for the controllable cold launch of an aircraft.

Kelvin (K) is SI base unit of thermodynamic temperature. In its 26th meeting held on Nov 2018, General Conference on Weights and Measures (CGPM) has approved the redefinition of kelvin by fixing the value of the Boltzmann Constant (k) to be 1.380649 × 10−23 when expressed in the unit J K−1, which was measured at temperature of triple point of water (TPW, 273.16 K), to maintain the consistency with old definition. The redefined SI units are implemented worldwide from May 20, 2019. Still, TPW is very important and fundamental fixed point, for both, thermodynamic (T) and practical International Temperature Scale of 1990 (ITS-90, T90), where the thermodynamic and practical scale have the equal value. At CSIR-NPL, we are developing acoustic gas thermometry (AGT) for the realization of Boltzmann constant-based new kelvin and to disseminate the thermodynamic temperatures. For the relative AGT and for the calibration of capsule SPRTs at various ITS-90 sub-ranges, the measurement capability at TPW need to be of very low uncertainty. For this purpose, we have realized an ensemble of three TPW cells, of known isotopic composition and deviation with Vienna Standard Mean Ocean Water (VSMOW), using long-stem SPRTs and high-precision DC Resistance Thermometry Bridge (0.02 ppm) with temperature-stabilized resistance standards. Ice mantles in TPW cell were prepared using the multiple insertions of metal rods cooled in liquid nitrogen (LN2), and annealed for about 48 h before measurements. All the associated uncertainty parameters, such as repeatability, reproducibility, isotopic, and impurity, residual gas pressure, hydrostatic head, heat flux immersion, self-heating of SPRT, light piping, resistances and bridge measurements were carefully evaluated and expanded uncertainty was computed to be ± 57 µK, ± 60 µK and ± 58 µK, (k = 2) for cells C1, C2, and C3, respectively. The obtained TPW realization uncertainties are commensurate with the established international comparisons for TPW. This ensemble of TPW cells is designated as National Reference and successfully placed in temperature dissemination services at CSIR-NPL, National Metrology Institute (NMI) of India.

The reflection of a converging cylindrical shock over a double curved wedge was investigated experimentally and numerically. The double curved wedge was specially designed to ensure that the wedge angle only changes at the corner during the cylindrical shock reflection. Seven different reflection processes existing in the planar case were reproduced in the converging case. The sudden variation of the wedge angle alters the strength of the disturbance propagating along the converging shock. Depending upon the type of the flow-induced pressure waves, which dominate the type of the wave behind the reflection over the second wedge, the propagation of the disturbance is either promoted or restrained. Comparison of the lengths of the disturbed shock front between the single wedge reflection and the double wedge reflection indicates that the history of the reflection over the first wedge would affect the reflection over the second wedge. Provided that the Mach reflection over the second wedge is fully developed, it approaches the Mach reflection of an identical shock over a single wedge with the same wedge angle as the second wedge. Relative to the planar case, the convex curved surface in the converging case promotes the disturbance propagation and increases the trajectory angle of the triple point.

Creep deformation and rupture behavior of nitrogen-alloyed (0.14 wt.%) nuclear grade 316LN austenitic stainless steel were investigated for the varying stress levels at 873 K and 923 K. The power-law dependency of creep properties such as steady-state creep rate and rupture life on applied stress was observed. For a given applied stress condition, a systematic increase in strain to failure was noticed with increasing temperature from 873 K to 923 K. Irrespective of test temperatures, creep rupture elongation of the steel increased with the increase in rupture lifetime ( $t_{r}$ ) for $t_{r} > 1000$ h. Analysis indicated that the interdependency between creep properties could be well described by the modified Monkman-Grant relationship. The predominance of inter-granular fracture arising from the triple point cracks and/or coalescence of cavities was observed at all the tested conditions for the steel. The enhanced tendency for wedge cracking was noticed for high stress levels at 873 K and 923 K. The evaluated damage tolerance factor $(\lambda ) < 5$ and the calculated ratio between time to reach the Monkman-Grant strain and creep rupture lifetime in the range of 0.69 to 0.80 indicated the accumulation of Monkman-Grant strain for the major fraction of lifetime during creep deformation of 316LN steel.

The reflection of a moving shock wave over a wedge immersed in a still gas and the reflection of a wedge induced steady shock wave over symmetrical and asymmetrical reflecting surfaces have received intensive considerations since more than 70 years ago. Here we consider a different shock reflection problem—reflection of a moving shock wave over an initially steady oblique shock wave induced by a wedge immersed in supersonic flow. For the flow condition we considered, five moving triple points, with each connecting an incident shock wave, a reflected shock wave and a Mach stem, are identified. By using the reference frame co-moving with each triple point, the type of each shock wave of this triple point is clarified. The present study is significant in that it treats a new shock reflection problem leading to a new shock reflection configuration and showing potential applications in supersonic flow with unsteady shock interaction.

Hypothesis: As a fluid approaches three phase coexistence, adsorption may take place by the successive formation of two intervening wetting films. The equilibrium thickness of these wetting layers is the result of a delicate balance of intermolecular forces, as dictated by an underlying interface potential. The van der Waals forces for the two variable adsorption layers may be formulated exactly from Dzyaloshinskii-Lifshitz-Pitaevskii theory, and analytical approximations may be derived that extent well beyond the validity of conventional Hamaker theory. Calculations: We consider the adsorption equilibrium of water vapor on Silver Iodide where both ice and a water layers can form simultaneously and compete for the vapor as the triple point is approached. We perform numerical calculations of Lifshitz theory for this complex system and work out analytical approximations which provide quantitative agreement with the numerical results. Findings: At the three phase contact line between AgI/water/air, surface forces promote growth of ice both on the AgI/air and the water/vapor interfaces, lending support to a contact nucleation mode of AgI in the atmosphere. Our approach provides a framework for the description of adsorption at three phase coexistence, and allows for the study of ice nucleation efficiency on atmospheric aerosols., Accepted Manuscript

Thermal metrology laboratory at the National Institute of Standards (NIS-Egypt) has been working to realize the International Temperature Scale-1990 (Preston-Thomas in Metrologia 27:3–10, 1990). High-precision thermal control is required especially with low-temperature fixed points that were realized within adiabatic calorimeters. In this study, a new algorithm module has been developed to control precisely the accurate temperature based on equal partitioning the temperature domain to be equivalent to the sensitivity of controlling thermometer (0.00391 K−1). The algorithm technique is required to maintain and stabilize the temperature of an adiabatic evacuated copper can that is located inside a thermally isolated calorimeter; the modified fractional proportional-integration function and sensitivity partial temperature function (SPTF) for temperature control have been designed and developed. The improved discrete SPTF has showed a thermal stability better than 28 ± 1.8 mK at temperature extremely close to the triple point of water cell (Tcell = 273.16 K) with reliable response time within 18 ± 1 min of performance. The thermal parameters of the new adiabatic calorimeter have been calculated such as the heat capacity of the load and the thermal resistance between the regulated shield and the measuring sample. The estimated uncertainty related to the measurements has been improved to ± 0.28 mK.

This study presents the criteria for shape control in the micro-pulling-down (μ-PD) method for low-wettability systems (dewetting μ-PD method), which enables us to achieve highly shape-controllable crystal growth. In the dewetting μ-PD method, the presence of the die wall inhibits the direct observation of the meniscus during the process. Therefore, in this study, the meniscus shape was calculated using the Young–Laplace equation to predict the optimal crystal growth conditions. The free-end and fixed-end boundary conditions to be satisfied for the differential equations were defined at the triple point, with the melt on the die wall. The relationship between the crystal diameter and pressure in the fixed-end condition, wherein the wetting angle (α) at the triple point of the crystal was 90°, indicated the suppression of the melt infiltration by the presence of crystals. The gap between the die and crystal was minimized for the contact angle (θ) and growth angle (αgr) in the fixed-end and free-end conditions, at which |αgr + θ – π| was minimum at a given pressure under the assumption of single-valued solutions. The results of this study will facilitate the formation of noble-metal alloys with a net shape and expand the scope for the development of new materials.

In this paper, we investigate the improvement of varistor devices with a ZnO-based material. In this goal, pure and 1% Bi-doped ZnO nano-powders have been synthesized at different sintering temperatures by a soft chemistry method: the sol–gel route. The used temperatures were carefully chosen to obtain the desired phases: (α-Bi2O3, β-Bi2O3, and δ-Bi2O3). Characterizations were made by XRD and TEM to determine the structural properties and particle sizes of Bi phases. XRD spectra confirmed the wurtzite structure and the presence of many transition phases for each sintering temperatures with an average grain size varying from 42 nm to 76 nm. TEM and SEM images of the samples allowed us to study the location of different phases, their morphologies, and the size of particles, and they show a mixture of nano-objects of different sizes and shapes. The electrical characteristics J(E) were measured to correlate these results with the varistor effect which indicate a good nonohmic behavior for all samples; the threshold voltage VB ranges between 242 and 701 V/cm and the coefficient of nonlinearity between 10.26 and 14.5. The total absence of phase transitions between the grains of the triple point in the ZnO–Bi2O3-based varistor is presented. Moreover, we show that the majority of phase transitions are located at the boundary of grains and forms a Shottky barrier which is suitable to improve the protective effect of surge arresters for hugely suppressing over-voltages in power and network systems.

The impact of the differing phase change characteristics on the electrocaloric effect (ECE) and thermophysical properties of Ba(ZrxTi1-x)O3 (BZT) were investigated. It is demonstrated that the ECE reduces strongly with increasing Zr concentration, from 1.25 K to 0.10 K. The strong reduction of ECE is associated with the vanishing of the latent heat as the nature of paraelectric to ferroelectric phase transition changes. Despite the second order nature of the phase transition, an enhanced electrocaloric responsivity, 0.225 × 10−6 Km V-1, occurs at the triple point composition ( x = 0.13), where the stability fields of ferroelectric phases converge. The decreasing ECE and thermophysical properties with increasing Zr concentration result in a more than one order of magnitude reduction in a caloric figure of merit, from ∼3500 J m−1s−1/2 to ∼200 J m−1s−1/2. The caloric figure of merit was used to compare the performance of other representative electrocaloric, magnetocaloric and mechanocaloric materials.

We carried out a comprehensive molecular simulation to investigate the evolution of the excess isotherms and the isosteric heat with respect to temperature for argon adsorption on strong and weak substrates. The temperature ranges from well below the bulk triple point temperature to above the bulk critical temperature to show the first- (second-) order transitions and the state of the system at the bulk coexistence pressure P0, whether it is non-wetting, partial wetting or complete wetting (preceded by pre-wetting). It is found that the key parameter that affects the dependence of the transitions on temperature and the state of the system at P0 is the relative difference between the isosteric heat and the heat of sublimation (or condensation). For strong substrates, the state of the system changes from partial wetting to complete wetting when the temperature crosses the bulk triple point temperature, and for temperatures well below the bulk triple point the 2D-condensation occurs in the first and second (and possible higher) layers. For weak substrates, the state of the system changes from non-wetting to complete wetting when the temperature crosses the wetting temperature TW, which is specific to the substrate. For temperatures greater than TW, complete wetting in weak substrates only occurs at pressures close to the bulk coexistence pressure P0 via the initial stage of clustering (unfavourable adsorption), followed by a pre-wetting (known as thin-to-thick transition), and this is reflected in the increase of the isosteric heat from a value less than the heat of condensation λ and approaching λ as the pressure tends to P0.

Experimental isotherms for argon and nitrogen adsorption on two non-graphitized carbon substrates, Carbopack B and Cabot BP280, do not obey Henry's Law in the range of pressures accessible to the most sensitive MKS pressure transducers. At high pressures, close to the bulk coexistence pressure (P0), the isotherms at temperatures below the bulk triple point temperature cross the P0 axis at a finite loading, a behaviour which is interpreted as incomplete wetting. It was found that the adsorbed density at P0 for Cabot BP280 is lower than that for Carbopack B which is, in turn, only slightly lower than that for the highly graphitized Carbopack F, suggesting that there is a long-range effect of the surface structure in non-graphitized carbon blacks, in the accumulation of higher layers, especially for Cabot BP280. We have carried out extensive Monte Carlo simulations to compare experimental observations with a molecular model for substrate surfaces decorated with crevices of molecular dimensions. From the analysis of the experimental data, it was found that the typical width of crevices is of the order of 0.65-0.9 nm. In the high pressure region, the crossing of the P0 axis by isotherms at temperatures below the bulk triple point temperature can be explained by an adsorbate structure which is less dense and more disordered than the fcc structure of the bulk crystal, with a consequent raising of the coexistence pressure between the adsorbate and the gas phase above P0. Adsorbate loading at the point where the isotherm crosses the P0 axis for Cabot BP280 is lower than for Carbopack B which can be attributed to a higher concentration of crevices leading to a lower adsorbate density and an irregular arrangement of atoms at the interface separating the adsorbed phase and the gas phase. This results in weaker gas-adsorbate interactions which supresses the build-up of higher layers. We suggest that the use of the adsorbed density at the bulk coexistence pressure, at temperatures below the bulk triple point temperature, can be a useful tool for assessing the presence and concentration of surface crevices on non-graphitized carbon black.

In the design of MV AC and DC spacers, the predominant factors are surface and interface conditions. Design is generally carried out on specifications and standards which are based on long-term experience and lab testing. However, the diffusion of power electronics with a trend to increase electric field, switching frequency, and rise time to achieve higher power density calls for an innovative, global approach to optimized insulation system design. A new methodology, based on field simulation, discharge modeling, and partial discharge inception measurements, called the three-leg approach, can form the basis to optimize insulation design for any type of supply voltage waveform. This paper focuses on the influence of the type of electrode on the inception and phenomenology of surface discharges and, as a consequence, on the interpretation of the results used for application of the three-leg approach. It is demonstrated that a typical electrode system used for insulating material testing can generate both gas and surface discharges at the triple point, when the electrodes have a smooth profile that is used to avoid corona or flashover. Hence, testing partial discharge may not provide a straightforward indication of the surface discharge inception and, thus, be partially misleading for insulation design. Another takeover is that such analysis must benefit from PD testing tools endowed with analytics able to provide automatic identification of the type of defect generating PD, i.e., internal, surface, and corona, since design and remedy actions can be taken, and adequate insulating materials developed, only knowing the type of source generating PD. Hence, testing partial discharge may not provide a straightforward indication of surface discharge inception and, thus, be partially misleading for insulation design. In addition to the importance of the three-leg approach to favor reliable and optimized design of insulation systems, there is a clear need to have a PD testing tool endowed with analytics. It should preferably be able to provide automatic identification of the type of defect generating PD, i.e., internal, surface, and corona.

The relationship of free surface area with temperature, power, and oxygen concentration in a silicon ingot grown by Czochralski method for solar cells was investigated by simulating the growing process of 4-, 6-, and 8-inch diameter ingots with a 24-inch quartz crucible. It was confirmed that the temperature at auto-temperature-control (ATC) sensor of 4-inch diameter ingot was higher than 6- and 8-inch diameter ingot due to the longer distance between triple point and ATC sensor, i.e., larger area of the free surface. In addition, it was observed that the power consumption for growing 4-inch diameter ingot was greater than 6-and 8-inch diameter ingot because of its smaller heat capacity resulted from smaller charge size. In particular, it was confirmed that the oxygen concentration of 4-inch diameter ingot was lower than those of 6- and 8-inch diameter ingots since the larger free surface area and weaker melt convection led to the lower oxygen concentration in 4-inch ingot. This understanding of the relationship of free surface area with oxygen concentration in a silicon ingot can be applicable directly to control oxygen concentration in growing different diameter of silicon ingots.

Heat: a measure of the total kinetic energy of a body. Measured in joules (J). It depends on the mass of the body and the specific heat capacity of the body. Temperature: a measure of the average kinetic energy within a body. It describes the potential for heat energy to move from one body to another down a gradient from an area of high temperature to an area of lower temperature. It is measured using a temperature scale which is defined against fixed physical events such as absolute zero or the triple point of water. Heat capacity: the amount of heat energy necessary to be added to an entire body to increase the temperature by one degree Kelvin (J/K). Specific heat capacity: the amount of heat energy necessary to be added to one kilogram of a body to increase the temperature by one degree Kelvin (J/K/kg). Absolute zero: a hypothetical temperature at which all molecular movement stops (zero kinetic energy). This is not possible in reality. The ice point: this is the temperature at standard pressure (101.3 kPa) at which water exists in both a solid (ice) and a liquid form. Designated as 0 oC or 32 oF. The steam point (boiling point): the temperature at standard pressure (101.3 kPa) at which water exists in botha liquid and a vapour form. Designated as 100 oC or 212 oF. Triple point of water: the temperature at a pressure of 611 Pa (0.006 atm) at which water exists in a solid (ice), liquid and a vapour form. Designated as 0.01 oC.

The phase behavior and the properties of carbon dioxide confined in an ordered mesoporous carbon (CMK-3) during freezing near the bulk triple point have been investigated by in situ total neutron scattering. The CO2 condensed in the mesopores of CMK-3 is found to be in a much densified state comparable with the bulk dry ice. So far, CO2 densification effects have been observed only in microporous carbon materials.

The molecular structure and phase behavior of carbon dioxide confined in an ordered mesoporous carbon (CMK-3) are investigated by total neutron scattering with in situ adsorption and cooling/heating cycles. The neutron signal from CO2 sorbed in the micropores of CMK-3 shows clearly liquid-like properties. Close to the bulk CO2 triple point (T3), the mesopore-confined CO2 is found in a liquid yet strongly densified state with a density similar to that of solid dry ice. Upon cooling the CO2 loaded carbon sample below T3, it was observed that depletion of the confined phase occurs and CO2 molecules escape from the pores to solidify externally. It was concluded that depletion occurs only in “secondary” pores having larger sizes (>50 A) than the well-defined uniform mesopores (47 A) of CMK-3. These pores exist due to imperfect ordering of the hexagonal network of the carbon rods. Surprisingly, this phenomenon does not happen in the main mesopores (47 A), implying thus that 50 A is a critical size for depletion below T3. This in turn suggests that in larger pores a pore triple point cannot be attained. The depletion process is reversible with a temperature hysteresis; when heating the sample CO2 molecules re-fill the pores.

Key experimental studies (mainly pulse heating) aimed at obtaining the physical properties of the most refractory substance — graphite — in the temperature range of 2000–8000 K are discussed. The properties considered are enthalpy, input (Joule) energy, thermal expansion, specific heat, and electrical resistance, as well as their dependence on the level of applied pressure. The results obtained by pulsed current heating and laser pulse heating are compared. An abnormally high specific heat just before the melting point is recorded under fast (during microseconds) heating of graphite. These effects are presumably associated with the appearance of nonequilibrium defects. A connection between these anomalies and the explosive electron emission is noted.

In this paper, we investigate dynamic wetting in the curtain coating configuration. The two-phase Navier–Stokes equations are solved by a Volume-of-Fluid method on an adaptive Cartesian mesh. We introduce the Navier boundary condition to regularize the solution at the triple point and remove the implicit numerical slip induced by the cell-centered interface advection. We use a constant contact angle to describe the dynamic contact line. The resolution of the governing equations allows us to predict the substrate velocity at which wetting failure occurs. The model predictions are compared with prior computations of Liu et al. [C.Y. Liu, E. Vandre, M. Carvalho, S. Kumar, J. Fluid Mech. 808, 290 (2016); C.Y. Liu, M. Carvalho, S. Kumar, Chem. Eng. Sci. 195, 74 (2019)] and experimental observations of Blake et al. [T. Blake, M. Bracke, Y. Shikhmurzaev, Phys. Fluids 11, 1995 (1999)] and Marston et al. [J. Marston, V. Hawkins, S. Decent, M. Simmons, Exp. Fluids 46, 549 (2009)].

This paper develops a new empirical formula for the prediction of the triple point path in irregular shock reflection cases. Numerical simulations using a two-dimensional axisymmetric multi-material arbitrary Lagrangian–Eulerian formulation are employed to obtain the data of fluid density. Using the data of fluid density and nodal coordinates, the gradients of fluid density are determined and then used to generate numerical schlieren images. Based on these images, the triple point paths are derived and compared with the models of the Unified Facilities Criteria (UFC) and Natural Resources Defense Council (NRDC) as well as two models from the open literature. It is found that the numerically derived triple point paths are in good agreement with those predicted by a recently published model in the open literature for the typical ground range of shock wave propagation of up to 6 m. Considering the whole distance range, it is found that the agreement of different models of the triple point path with the numerical ones depends on the considered blast scenario, i.e., the scaled charge height. For small-scaled charge heights, the model of the UFC and the recently published model in the open literature are in better agreement with the numerical results than the other two models, whereas the NRDC model has the best agreement with the numerical results for large-scaled charge heights. Based on the numerical results, a new empirical formula is proposed for the prediction of the triple point path, which is valid for a wide range of the scaled charge heights from 0.5 to 3.5 m/kg1/3 and scaled ground distances up to 15 m/kg1/3.

The EU F-Gas Regulation grants exceptions from the GWP-related placing on the market prohibition for stationary refrigeration equipment for applications below -50 °C. Nonetheless, non-flammable refrigerants, which can be used for that temperature range, become increasingly expensive and rare inside the EU due to the phase down of HFCs under the regulation. Flammable alternatives based on methane, ethane and ethylene are available, but are not viable for all applications due to their flammability. Carbon dioxide cannot be used for applications below -50 °C due to CO2's triple point at -56 °C. Nitrous oxide with a triple point at -92 °C seems to be an alternative. However, possible exothermal decomposition of N2O calls for additional measures in order to be able to operate such systems safely. Two low-temperature systems have been developed, built and successfully operated at evaporation temperatures down to -80 °C with mixtures of N2O and CO2 and different lubricants at ILK and Karlsruhe University of Applied Sciences. The units achieved similar energy efficiency as the standard HFC-equipment used for freeze drying. Possible decomposition of N2O could successfully be supressed by various measures. CAUTION: Pure N2O as well as mixtures of N2O and CO2 with lubricants based on hydrocarbons can cause violent explosive decomposition reactions abruptly increasing the pressure inside a refrigeration system approximately tenfold.

A non-cubic equation of state is used to predict the solid-liquid, solid-vapor and liquid-vapor coexistences of pure substances. The equation of state is obtained using as input data the critical point, the boiling temperature, the triple point temperature and the acentric factor of the substance. In this work, some examples of phase diagrams predicted with the equation of state are reported in order to show its capabilities. Finally, a database with the parameters for different pure substances is presented.

The fusibility of salt mixtures in the anhydrous quadruple AlF3-KF-NaF-ZrF4 system was studied. The direction of lowering the melting point of substances in the tetrahedron of the composition of the quadruple system, the influence of complexation on lowering the melting point of salt mixtures, were clarified. The fusibility of salts in the ternary AlF3-NaF-ZrF4 system was investigated experimentally by methods of thermal phase analysis. The diagram of fusibility to the isotherm of 900 °C is constructed. Primary crystallization fields are represented by the phases of the initial salts (AlF3, KF, ZrF4) of the compounds that were formed in binary subsystems (2KF∙ZrF4, 7NaF∙6ZrF4, 3NaF∙4ZrF4, 5NaF∙3AlF3) and Na3AlF6-Na3ZrF7 solid solutions. The minimum melting point was 466 ° C in a triple eutectic. The fusibility of salt mixtures was experimentally studied in the subsystem K2ZrF6-Na2ZrF6-KAlF4-NaAlF4, which was a section of the tetrahedron of the composition of the quadruple system AlF3-KF-NaF-ZrF4. The fusibility diagram of this subsystem was constructed. A triple point with a melting point of 450 °C was found. Primary crystallization fields are represented by compounds K2ZrF6, Na2ZrF6 and solid solutions KAlF4-NaAlF4. The low-melting region of the compositions in the tetrahedron of the composition of the quadruple system was shifted to the faces NaF-KF-ZrF4 and AlF3-KF-ZrF4. The intense chemical interaction of the starting materials of the quadruple system with the formation of complex compounds and the extensive formation of solid solutions complicated the determination of crystallizing solid phases and the establishment of monovariant equilibria in quadruple mixtures. Quadruple eutectic in the four component system was formed by the merger of four monovariant lines. To calculate the composition of the quadruple eutectic by the melting temperature and the composition of the eutectic of the triple subsystems, the coordinates of the four triple points are necessary. The characteristic of two triple points was obtained as a result of an experimental study of the fusibility diagrams of auxiliary sections of a tetrahedron of the composition: K2ZrF4-Na2ZrF6-KAlF4-NaAlF4 and KZrF6-NaAlF4-(0,5NaF+0,5ZrF4)-KAlF4, which were located near the quadruple eutectic.

The dry ice sublimation process of CO2 is a unique technique in which temperature ranges below the triple point of −56 °C can be achieved in a CO2 refrigeration system. However, during the evaporation process of the actual refrigeration system, the dry-ice blockage maybe happens in the evaporator, which causes a risk of system failure in the suction of the compressor. In order to overcome this problem, in this study, an ultra-low temperature CO2 cascade refrigeration system with a novel tapered evaporator/sublimator was designed and constructed. The novel evaporator/sublimator included a swirl promoter, which induces the swirling flow of solid-gas two-phase flow. Experiments were conducted for the investigation of solid-gas two-phase flow heat transfer characteristics in the evaporator/sublimator. According to the experimental results, it is verified that the CO2 refrigeration system can operate consistently and steadily without dry ice blockage in the evaporator/sublimator. In addition, the dry ice particles are uniformly distributed along the inner wall of the evaporator/sublimator by the installation of the swirl promoter, and the heat transfer coefficient is considerably improved. © 2020, © 2020 Taylor & Francis Group, LLC

The solid-state phase transformation in the coarse-grained heat-affected zone of P91 steel under simulated welding thermal cycle has been investigated in situ by confocal scanning laser microscope. It is found that γ-austenite initiates from the triple point of δ-ferrite grain boundaries (GBs), then at ordinary δ-GBs, and eventually from grain interiors. Upon further cooling, martensite laths are observed to nucleate and growth instantaneously, with the growth rate being estimated ranging from 175 to 454 μm/s.

Crystal structures and piezoelectric properties of PbZrO3-PbTiO3-Pb(Ni1/3Nb2/3)O3 ceramics near the triple point composition, particularly characteristics of the pseudocubic phase, were investigated. The pseudocubic phase, which formed near the triple point composition, disappeared with increase in the PbZrO3 content. The pseudocubic phase had the Pm3m cubic structure. The tetragonal-pseudocubic morphotropic phase boundary (MPB) structure was developed during the tetragonal-to-cubic phase transformation. However, the rhombohedral phase directly transformed to the cubic phase because the structure of pseudocubic phase was similar to the rhombohedral structure. The specimens with pseudocubic phase and the specimens near pseudocubic phase exhibited nano-sized domains and small coercive electric fields, revealing their low domain wall energies. These specimens exhibited second-order ferroelectric-to-paraelectric phase transition and low Curie temperatures, confirming their low domain wall energies. The enhanced dielectric and piezoelectric properties of these specimens could be attributed to their low domain wall energies.

The surface tensions of graphene oxide nanofluids of five mass concentrations were measured by the oscillation droplet method in an acoustic levitator. The oscillation information of the suspension droplets was obtained by combining acoustic levitation with image recognition technology, and a shape correction coefficient a was introduced to modify the Rayleigh equation. Over the temperature ranging from − 7 to 10 °C, the surface tension of the graphene oxide nanofluids increases with increasing mass concentration and decreases with increasing temperature. Compared with the surface tension changes caused by an increase in the mass concentrations of nanofluids from 0.08 to 0.12% at − 7 °C, the surface tension slowly increases from 79.144 to 80.664 mN m−1 when the mass concentration increases from 0.02 to 0.08%. The change rate of the surface tension with temperature is linear in both supercooled and non-supercooled states. For nanofluids with a mass concentration of 0.02%, the values are − 0.185 and − 0.186, respectively, which are basically the same. However, with an increase in mass concentration, the surface tension increases abnormally in supercooled state. For nanofluids with mass concentrations of 0.05% and 0.08%, the curve of the surface tension has an inflection point at − 1.0 °C, while for mass concentrations of 0.10% and 0.12%, the inflection point is at 1.0 °C. All inflection points are distributed around the triple point temperature of water.

It has been established that nonmonotonic magnetization relaxation in Pt/Co/Ir/Co/Pt synthetic ferrimagnets (SF) with perpendicular magnetic anisotropy is caused by the coincidence of two or three switching fields between stable states of the SF magnetization (double or triple point). The fields of switching between the stable states of SFs are determined by the ratio of the Zeeman energy, interlayer exchange energy, and the energies of magnetization reversal barriers of each layer, depending on the thickness of the layers and temperature. It has been shown that the selection of thickness and/or temperature enables reaching double and triple points at which the transition fields between the states coincide, which causes a nonmonotonic magnetic relaxation of SFs.

The paper presents a theoretical study for a supersonic boundary layer over a flat plate in a stream of air at Mach number M = 2 under the conditions of surface sublimation. The sublimation-prone material is naphthalene (C10H8). Calculations demonstrated that at a higher surface temperature the mass flowrate of naphthalene evaporation is increasing. This reduces the wall temperature in comparison with a similar flow without sublimation. The high molecular mass of naphthalene (vs. air) and reduction of wall temperature due to the wall material evaporation creates a higher density of the binary gas mixture (air and naphthalene vapor) near the wall. This modification of the boundary layer profiles induces a significant reduction of instability growth rate. This fact was confirmed by calculations based on the linear stability theory. It was found that boundary layer stabilization occurs for growing sublimation surface temperature; it becomes a maximum near the triple point temperature of the coating material. The eN method gives the estimates of the Reynolds number for laminar-turbulent transition. This shows a theoretical possibility of extension of the laminar boundary layer above a model with sublimation coating.

The paper presents the results of experimental studies of the arc discharge between the graphite electrodes in an argon atmosphere at a pressure of 0.1–100 kPa. The discharge was ignited after the destruction of a graphite bar heated by a fixed electric current and maintained for ~103 s at a temperature of ~3 kK. Evidence of the formation of liquid phase on the surface of the graphite electrodes at a temperature of ~3.2 kK is presented. Data on the saturated carbon vapor pressure are discussed. The pressure in the carbon triple point does not exceed ~0.1 kPa.

In this work, we studied detonation in condensed-phase explosives of PETN and the oblique shock waves in the surrounding fluid. The surrounding fluid was modeled as an ideal gas equation of state using the specific heat ratio as a parameter. Depending on the specific heat ratio, four types of flow structures were observed behind the oblique shock wave in the ideal gas. We measured the detonation/shock angles and the contact angle between the detonation products and the ideal gas. When the specific heat ratio was greater than the critical value, the oblique shock wave was detached from the detonation front at the PETN/ideal gas interface. When attached, three types of waves are observed, depending on the specific heat ratio: a strong oblique shock wave, strong and weak oblique shock waves which meet at the triple point as well as a weak oblique shock wave. To understand the properties of the flow near the detonation and the oblique shock waves, they were modeled as planar Chapman–Jouguet (CJ) detonation in PETN and as oblique shock waves in ideal gas. They were theoretically estimated as (1) Prandtl–Meyer expansion of the detonation products from the CJ state, and (2) oblique shock waves around a wedge using oblique shock theory or around a cone using the Taylor–Maccoll equation. From the flow models, we obtained a solution for the pressure equilibrium and parallel flows between the detonation products and ideal gas under the assumption that the wedge and cone angles correspond to the contact angle between them. For the attached cases, the solution was consistent with the simulated observations at the PETN/ideal gas interface. From the flow models, the maximum deflection angles for the detonation products and the ideal gas were obtained, and their magnitude correlations used to classify the four types of flow.

Evaporation is a typical heat and mass transfer process, which is important in both nature and industry. Here, the evaporation of five fluid samples (pure Ar, pure Kr and Ar/Kr mixtures with molar ratio Ar : Kr = 1 : 3, Ar : Kr = 1 : 1 and Ar : Kr = 3 : 1) on Pt surface was investigated using molecular dynamics simulations. Colligative properties of the mixtures led to the melting of the Ar/Kr mixtures (Ar : Kr = 1 : 1, Ar : Kr = 3 : 1) at 70 K below the triple point of Ar. Furthermore, under the same condition, the other systems were frozen as the solid state. The Pt surface at 90 K, over the boiling point of Ar, triggered the evaporation of Ar atoms in all the systems while the Kr atoms remained in the condensed state. Kr atoms were reported to be evaporated to a large extent when the Pt surface was heated to 120 K near the boiling point of Kr. The presence of Kr could reduce the evaporation of the Ar atoms, especially when the mole ratio of Ar : Kr in the mixture was 1 : 1 because the Ar : Kr = 1 : 1 system can effectively reduce the temperature of the gas-liquid interface. The temperature of the fluid samples then decreased with increase in distance between Pt and fluid atoms because the evaporated atoms could take the thermal energy away from the condensed films. Moreover, both Ar and Kr atoms, which were close to the Pt surface, hardly changed during evaporation because of the strong attractive force from the Pt substrate.

Theoretical investigation of the supersonic flat-plate boundary-layer properties under conditions of the surface material sublimation has been performed for Mach number M = 2. Naphthalene (C10H8) was chosen as the substance for the sublimation coating. Performed computations show that with increasing surface temperature due to stagnation temperature increase, the mass flow rate of naphthalene evaporation increases. Calculations performed on the basis of linear stability theory show that such an increase of evaporation leads to a noticeable decrease of the local growth rates of unstable perturbations in the boundary layer. It is found that stabilization of the boundary layer by the surface coating sublimation occurs with increasing temperature of the sublimation coating, reaching a maximum near the triple point temperature of the sublimation material. The carried out experiments confirmed the stabilizing effect of surface sublimation.

In the present study, both in situ experiment and multiphase field modeling are adopted to investigate the peritectic solidification of a low-carbon steel. The results show that the peritectic reaction occurs at the temperature of 3.4 K lower than the equilibrium peritectic temperature, the γ-austenite first nucleates at the δ/L boundary, and then rapidly propagates along the δ/L boundary by the advance of the L/γ/δ triple point till the δ-ferrite is encircled by the γ austenite. The whole peritectic reaction process is very fast, and the measured and predicted average propagation velocity of L/γ/δ triple point along the δ/L boundary are, respectively, 1.36 and 1.09 mm/s. This small difference between the measurement and prediction means that the developed multiphase field model is capable of predicting the peritectic reaction and peritectic transformation during the peritectic solidification process of Fe-C alloy, and the peritectic reaction can be regarded as a solute diffusion-controlled process. With the increase of cooling rate and undercooling, the advancing velocities of L/γ/δ triple point, L/γ interface and γ/δ interface increase, and thus the γ-austenite between the liquid phase and δ phase becomes longer and thicker for the same elapsed time.

In this paper, the solid – liquid equilibrium of the binary system containing difluoromethane (R32) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) was experimentally evaluated. An experimental setup was used to measure 20 different compositions of the binary system in the temperature range from 168.2 K to 132.00 K. The studied binary system showed an eutectic point which was estimated at the temperature of 132.00 K. The results for the solid – liquid equilibrium of the studied system showed a general agreement with the prediction provided by the Schroder equation, showing deviations generally within 2 – 3 K. In addition, in order to test the validity of the experimental setup, the triple point temperatures of the components of the binary system and four well described refrigerants (namely R125, R152a, R143a, and R41) were measured. The experimental results for the pure refrigerants agreed with reliable values available in the literature.

In this research, full density, single phase microstructure (in the XRD and SEM detection limits), and fine-grained SnO2 varistors with an average grain size of 0.65 μm was acquired at low temperature by the two-step sintering technique. The sintering temperature was successfully decreased from 1300 °C in the normal sintering to 1150 °C and 1100 °C of respectively the first and the second stage in the two-step sintering. The mechanism of grain growth suppression of the two-step sintered samples was discussed and it was suggested that in addition to triple point junction, solute drag and/or nano-secondary phases contribute to cease the grain growth. These SnO2 varistors exhibited ultra-high breakdown electric field of 26 kV/cm with a nonlinear coefficient of about 120 in the 1–10 mA/cm2 standard. The exact evaluation showed that this high value of the nonlinear coefficient is artificial and was the result of joule-self heating phenomenon. The true value of the nonlinear coefficient (28) is measured within the 0.1–1 mA/cm2 standard. Due to the joule self-heating phenomenon, the thermal runaway was observed for ultra-high voltage SnO2 varistors in DC-accelerated aging test conditions (0.85 E1mA/cm2 and room temperature). By changing DC-accelerated aging electric field to 0.85 E0.1 mA/cm2, TSS3-20h presented excellent stability after 10 h from room temperature to 75 ᵒC.

We evaluated the non-uniqueness of the temperature scale of the standard platinum resistance thermometer (SPRT) calibrated at the tripe point of sulfur hexafluoride (TPSF6), which is one of the candidates for the substitute of the triple point of mercury (TPHg). Three SPRTs calibrated at the TPSF6 were compared with a reference thermometer from 14 K to 250 K by using a precise comparison system for capsule type of thermometers. The uncertainty of the temperature scales from propagation of the uncertainties for calibrating SPRT was also evaluated. The result shows that the non-uniqueness of the temperature scale of the SPRT calibrated at the TPSF6 was almost equivalent to that of the ITS-90. This means that the triple point of TPSF6 possessed a capability for realization of the temperature scale which was equivalent to the ITS-90.

Acoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu–Goldstone theorem. Here, we show that this triple point can carry a topological charge \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{q}}$$\end{document}q that is a property of three-band systems with space-time-inversion symmetry. The charge \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{q}}$$\end{document}q can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes. We call triple points with nontrivial \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{q}}$$\end{document}q the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when Oh or Th groups protect it. The charge \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{q}}$$\end{document}q constrains the nodal structure and wavefunction texture around TATP, and can induce anomalous thermal transport of phonons and orbital Hall effect of electrons. Gapless points protected by the Nambu–Goldstone theorem form a new platform to study the topology of band degeneracies., The topological characteristics of acoustic phonons with triple degeneracy remain largely unexplored. Here, the authors propose a topological acoustic triple point characterized by a topological charge in a three-band system with PT symmetry.

The high-temperature and high-pressure response of magnesium has been investigated through shock-release experiments performed up to shock melting. The longitudinal and bulk sound speeds of Mg are reported along the Hugoniot from 25 to 56 GPa and used to determine the elastic properties and Gr\"uneisen parameter. The hexagonal close-packed (hcp)--body-centered cubic (bcc) phase transition is marked by a reduction in the determined shear wave speed. Thermal softening is observed to begin between 40 and 44 GPa, with incipient melt at 55.5 GPa, in close agreement with previous diffraction measurements under laser shock loading. Examination of the release profiles showed that two different responses were observed, depending on the peak stress. When plotted in a stress-energy phase diagram, the two responses are observed to form separate lines that intersect the static hcp-bcc phase transition and incipient melt. The results indicate that the hcp-bcc transition occurs on the Hugoniot at 28.4 GPa and place the hcp-bcc-liquid triple point \ensuremath{\sim}20 GPa. A multiphase equation of state is developed which places the melt boundary below the previously reported static measurements.