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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.

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.

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 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 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.

With the development of computer technology and theoretical chemistry, the speed and accuracy of first-principles calculations have significantly improved. Using first-principles calculations to predict new topological materials is a hot research topic in theoretical and computational chemistry. In this work, we focus on a well-known material, sodium chloride (NaCl), and propose that the triple point (TP), quadratic contact triple point (QCTP), linear and quadratic nodal lines can be found in the phonon dispersion of NaCl with Fm3¯ m type structure. More importantly, we propose that the clear surface states connected to the projected TP and QCTP are visible on the (001) surface. It is hoped that further experimental investigation and verification for these properties as mentioned above.

We present a new wide-ranging correlation for the thermal conductivity of ethane-1,2-diol (ethylene glycol) based on critically evaluated experimental data. The correlation is designed to be used with an existing equation of state, and it is valid from the triple point to 475 K, at pressures up to 100 MPa. The estimated uncertainty is 2.2 % (at the 95 % confidence level), except in the dilute gas region which is estimated to be 20 %, as there are no measurements in this region for comparison.

The triple points of carbon dioxide (CO2 TP) and sulfur hexafluoride (SF6 TP) are candidate substitutes for the triple point of mercury from the set of defining points of the international temperature scale of 1990. For the replacement to be successful, the measurement performances of CO2 TP and SF6 TP need to be improved. Compounds of CO2 and SF6 contain different isotopes of carbon, oxygen and sulfur. They fractionate in the solid and liquid phase of the compounds and shift the phase transition temperatures. Thus, the isotopic effect is a probable cause for inconsistency of measurements of CO2 TP and SF6 TP, which has motivated us to investigate it. According to the reported fractionation factors and abundances of isotopes, we predict the temperature corrections to vary from − 0.023 mK to 0.051 mK for measurements of the CO2 TP. This narrow variation implies that the refining process causes only an insignificant change compared with the natural abundances of the minority isotopes 13C and 18O in the source gas. Consequently, the small change will probably cause a minor inconsistency for measurements of the CO2 TP. By contrast, for measurements of the SF6 TP the predicted temperature corrections range from − 0.022 mK to 1.223 mK. Our predictions suggest that further investigations of the isotopic effect on measurements of the TP of CO2 and the TP of SF6 are desirable, particularly for the latter molecule.

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.

The canonical problem of transonic dense gas flows past two-dimensional compression/expansion ramps has recently been investigated by Kluwick & Cox (J. Fluid Mech., vol. 848, 2018, pp. 756–787). Their results are for unconfined flows and have to be supplemented with solutions of another canonical problem dealing with the reflection of disturbances from an opposing wall to finally provide a realistic picture of flows in confined geometries of practical importance. Shock reflection in dense gases for transonic flows is the problem addressed in this paper. Analytical results are presented in terms of similarity parameters associated with the fundamental derivative of gas dynamics$(\unicode[STIX]{x1D6E4})$, its derivative with respect to the density at constant entropy$(\unicode[STIX]{x1D6EC})$and the Mach number$(M)$of the upstream flow. The richer complexity of flows scenarios possible beyond classical shock reflection is demonstrated. For example: incident shocks close to normal incidence on a reflecting boundary can lead to a compound shock–wave fan reflected flow or a pure wave fan flow as well as classical flow where a compressive reflected shock attached to the reflecting boundary is observed. With incident shock angles sufficiently away from normal incidence regular reflection becomes impossible and so-called irregular reflection occurs involving a detached reflection point where an incident shock, reflected shock and a Mach stem shock which remains connected to the boundary all intersect. This triple point intersection which also includes a wave fan is known as Guderley reflection. This classical result is demonstrated to carry over to the case of dense gases. It is then finally shown that the Mach stem formed may disintegrate into a compound shock–wave fan structure generating an additional secondary upstream shock. The aim of the present study is to provide insight into flows realised, for example, in wind tunnel experiments where evidence for non-classical gas dynamic effects such as rarefaction shocks is looked for. These have been predicted theoretically by the seminal work of Thompson (Phys. Fluids, vol. 14 (9), 1971, pp. 1843–1849) but have withstood experimental detection in shock tubes so far, due to, among others, difficulties to establish purely one-dimensional flows.

The present investigation reports the size-dependent melting behavior of bi-phasic Pb-17.5 at. pct Sb-free alloy nanoparticles, consisting of face-centered cubic (Pb) and rhombohedral (Sb) phases. These free nanoparticles (devoid of matrix) were synthesized via the solvothermal route, and subsequently different sizes were obtained by controlled heat treatment at 373 K under protective Ar atmosphere for the various durations. DSC and in situ TEM studies were used to probe the melting behavior. The experimental results reveal classical behavior, indicating the normalized eutectic temperature was inversely proportional to the nanoparticle radius. The in situ TEM investigation shows that melting initiates at the triple point among (Pb)/(Sb) and an outer surface and subsequently the melt front propagates into (Pb) phase first and then into (Sb) phase. Detailed thermodynamic modeling of the Pb-Sb system with size was carried out to decipher the size-dependent melting behavior of the biphasic nanoparticles. The experimental finding was corroborated with a theoretically predicted phase diagram as a function of size showing a reasonable match.

A system of equations is developed to calculate the properties of dissociated steam in the temperature and pressure ranges of 1250–3400 K and 0.01–10.00 MPa. These equations are based on detailed tables for dissociated steam compiled for a mixture of atoms of hydrogen and oxygen, hydroxyl OH, molecules of hydrogen and oxygen, and steam at a reference temperature of 0 K. Since the expansion of dissociated steam in a thermal engine results in its transformation into its common form, the equations for the parameters of dissociated or nondissociated steam uses the same reference temperature, i.e., the water triple point of 273.16 K. A system of equations for the calculation of dissociated-steam properties is derived with the generalized thermodynamic equation, which takes into account the change in the chemical potential and the composition of the mixture during steam dissociation, the Gibbs energy equation, differential thermodynamic equations, and equations for calculation the properties of nondissociated steam. To minimize the deviation of the steam properties calculated by the proposed equations from the table values, the considered temperature and pressure ranges have been divided into three regions. The deviation of the steam properties calculated by the proposed equations from the table values does not exceed 0.05–0.09%. The developed equations can be used in calculations of the processes of cooling of burners and combustion chambers during the combustion of hydrogen–oxygen mixtures, as well as cycles of heat engines that use high-temperature steam as a working fluid at temperatures over 1250 K.

Most research into the formation of the lamellar eutectics has focused on the growth patterns. However, those growth patterns can be attributed to the behavior of the triple junction, at which the solute distribution determines the long-range spatial periodicity of patterns. From both theoretical validation and phase-field simulations, we characterize the solute concentration at the triple point and demonstrate the existence of abnormal solute distribution. The solute concentration at the triple point equals the eutectic concentration only when the coexisting solid phases are evenly distributed, which is essential to balance the concentration gradient and maintain the interfacial thermodynamic equilibrium.

We studied the electric-field-induced tilt angle in SmA of MC881 and found the field-induced, first-order phase transition to SmC∗ in the SmA temperature region just above temperature-induced antif...

In this study, the flow, temperature and solute concentration fields in the melt during the CZ growth process are numerically investigated. The results show that the magnitude and distribution of the solute concentration in the melt is strongly affected by the convective flow and thermal distribution. The maximum solute concentration always occurs at the crucible sidewall where the maximum temperature in the melt is found and the solute concentration at the crystal-melt interface increases from the triple point to the centerline. Heat transport from the side crucible wall towards the crystal-melt interface is enhanced by the crucible rotation. The level of the solute concentration inside the melt is reduced due to the lowering of the maximum temperature at the crucible wall. As a consequence, the distribution of the solute concentration along the crystal-melt interface becomes smaller and more uniform as the crucible rotation rate increases. However, after the crucible rotation rate becomes large enough, the maximum solute concentration and the solute concentration along the crystal-melt interface start to increase. Heat transport inside the melt is also affected by the crystal rotation. The centrifugal force induced by the crystal rotation generates a vortex below the crystal-melt interface. This vortex gets larger and stronger as the crystal rotation rate increases. In the smaller crystal rotation rate regime, this vortex is very small, suppressing the solute concentration at the crystal-melt interface. Therefore, the solute concentration along the crystal-melt interface becomes less when the crystal rotation rate is higher, although there is an increase in the maximum solute concentration in the melt due to the higher maximum temperature. In the higher crystal rotation rate regime, there is a reduction in the convexity of the crystal-melt interface due to enhancement of heat transport from the bottom wall of the crucible by vortex motion under the crystal-melt interface. Therefore, there is a switch to an increase in the transport of solute impurities into the crystal-melt interface. Hence, the solute concentration along the crystal-melt interface increases as the crystal rotation rate increases. However, with a further increase in the crystal rotation rate, as the shape of the crystal-melt interface changes becoming concave towards the melt, the solute concentration along the crystal-melt interface decreases because the maximum temperature is significantly reduced. In this study, both counter- and iso-rotations are considered. The results of a comparison of the cases of iso- and counter- crystal rotation show that the lowest and most uniform solute distribution along the crystal-melt interface is achieved when there is no crystal rotation and the crucible rotation rate is fixed at 1 rpm. In other words, the lowest and most uniform solute concentration can be achieved with the only crucible rotation.

Solidification of a liquid drop on a vertical wall is a typical phase change heat transfer problem that exists widely in natural and engineering situations. In this study, we present the fully resolved two-dimensional simulations of such a problem by a front-tracking/finite difference method. Because of gravity, the liquid drop assumed stick to the cold wall shifts to the bottom during solidification. Numerical results show that the conical tip at the solidified drop top is still available with the presence of volume expansion, but the tip location is shifted downward, resulting in an asymmetric drop after complete solidification. The tip shift, height and shape of the solidified drop are investigated under the influences of various parameters such as the Prandtl number Pr, the Stefan number St, the Bond number, the Ohnesorge number Oh, and the density ratio of the solid to liquid phases ρsl. We also consider the effects of the growth angle ϕgr (at the triple point) and the initial drop shape (in terms of the contact angle ϕ0) on the solidification process. The most influent parameter is Bo whose increase in the range of 0.1–3.16 makes the drop more deformed with the tip shift linearly increasing with Bo. The tip shift also increases with an increase in ϕ0. However, increasing Oh (from 0.001 to 0.316), St (from 0.01 to 1.0) or ρsl (from 0.8 to 1.2) leads to a decrease in the tip shift. Concerning time for completing solidification, an increase in Bo, ϕgr or ϕ0, or a decrease in St, or ρsl results in an increase in the solidification time. The effects of these parameters on the drop height are also investigated.

The objectives of this paper are to (1) validate the present numerical modeling framework for liquid hydrogen cavitating flow, (2) investigate the dynamic evolution of liquid hydrogen cavitating flows in a wide range of free-stream conditions and (3) propose a thermal parameter to evaluate and predict the transition process of two typical cavitation dynamics in thermo-fluids. The dynamic evolutions of liquid hydrogen cavitating flows in a wide range of free-stream conditions (T∞ = 14–33 K, U∞ = 63.9 m/s, 90 m/s, σ∞ = 0.38, 0.8, 1.2) are numerically investigated. General agreements are obtained between the numerical results and the experimental measurements, including the pressure distribution, temperature drop as well as the cavity structures. The results show that the cavitation behaviors near the triple point are similar to cavitating flows without thermodynamic effects. Two typical cavitation dynamics named the quasi-isothermal mode and the thermo-sensitive mode in liquid hydrogen are observed under the same cavitation number and flow velocity. When the free-stream T∞ is below 30 K (TN ≤ 0.85), as the temperature increases, the cavity area increases to the maximum around the thermal transition temperature and then decreases when the cavitation dynamics transits from the quasi-isothermal mode to the thermo-sensitive mode. Further analysis indicates that the thermal transition temperature for liquid hydrogen is approximately at T∞ = 17 K and the transition temperature slightly increases with the increasing free-stream velocity and cavitation number. When the free-stream T∞ is above 30 K (TN > 0.85), the thermodynamic effects significantly decrease due to the suddenly changed physical properties. And then, the cavitation dynamics turns from the thermo-sensitive mode to the quasi-isothermal mode with the increasing temperature. The modified C-factor including both the thermodynamic effects and the effects of turbulent pressure fluctuations proposed in this paper could quantitatively evaluate and predict dynamics transition from the quasi-isothermal mode to the thermo-sensitive mode in thermos-fluids cavitating flows. It could be utilized as a parameter to design the operating conditions for thermos-fluids apparatus or system to avoid the maximum cavitation aggressiveness around the thermal transition temperature.

We present a new wide-ranging correlation for the viscosity of ethane-1,2-diol (ethylene glycol) based on critically evaluated experimental data. The correlation is designed to be used with an existing equation of state, and it is valid from the triple point to 465 K, at pressures up to 100 MPa. The estimated uncertainty is 4.9 % (at the 95 % confidence level), except in the dilute-gas region which is estimated to be 15 %, as there are no measurements in this region for comparison. The correlation behaves in a physically reasonable manner when extrapolated to 750 K and 250 MPa, however care should be taken when using the correlations outside of the validated range.

The International Temperature Scale of 1990 (ITS-90) is commonly expressed in terms of the ratio of the resistance of a standard platinum resistance thermometer (SPRT) to the resistance at the triple point of water. Most high-precision thermometry relies on the alternating current (AC) method due to its manifold practical benefits. However, there are some negative consequences of using AC methods, and it is of particular interest to quantify the effect of the measuring current frequency on the realized temperature of the ITS-90 fixed points. In this work, the effect of the measuring current frequency was investigated by measuring the differences between the AC and direct current (DC) resistance ratios at various fixed-point temperatures. Two AC at 30 Hz and 90 Hz and one DC at a reversal frequency of 3 Hz were used to measure the resistance ratios at four ITS-90 metal fixed points, namely, mercury, water, zinc, and silver; seven SPRTs having different nominal resistances (e.g., 0.25 Ω, 0.6 Ω, 2.5 Ω, and 25 Ω) were employed to explore the effect of frequency on the measured resistance ratio. It was found that the frequency dependence was most noticeable at the freezing point of silver where the insulation leakage and its transient dielectric polarization were expected to manifest themselves the most significantly. For other fixed points, the frequency dependence was found to be insignificant, implying that under normal conditions the benefits of the AC measurements can be fully utilized without affecting the calibration uncertainties of the tested types of SPRTs.

A new wide-ranging correlation for the viscosity of xenon, based on the most recent theoretical calculations and critically evaluated experimental data, is presented. The correlation is designed to be used with an existing equation of state, and it is valid from the triple point to 750 K, at pressures up to 86 MPa. The estimated expanded uncertainty (at a coverage factor of k = 2) varies depending on the temperature and pressure, from 0.2 % to 3.6 %. A term accounting for the critical enhancement is also included. The correlation behaves in a physically reasonable manner when extrapolated to 200 MPa; however, care should be taken when using the correlations outside of the validated range.

Topologically non-trivial electronic structure is a feature of many rare-earth half-Heusler alloys, which host atoms with high spin-orbit coupling bringing in the non-triviality. In this article, using the first-principles simulations, rare-earth half-Heusler YPdBi, ScPdBi, LaPdBi, LuPdBi, YPtBi and LuPtBi alloys are studied under strain to reveal multiple band inversions associated with topological phase transitions. From our simulations we find that, as a result of first band-inversion, the Brillouin zone of the diamagnetic half-Heusler alloys hosts eight triple points whereas, the second band inversion causes the emergence of sixteen more triple points. These band-inversions are observed to be independent of the spin-orbit coupling and are the reason behind increasing occupation of bismuth 7s orbitals as volume of the unit cell increases. The surface electronic transport in different triple point semi-metallic phases is found to evolve under strain, as the number of Fermi arcs change due to multiple band inversions. Once the second band inversion occurs, further application of tensile strain does not increase the number of triple points and Fermi arcs. However, increasing tensile strain (or decreasing compressive strain) pushes the triple point crossing to higher momenta, making them more effective as source of highly mobile electrons. These observations make a pathway to tune the bulk as well as surface transport through these semi-metals by application of tensile or compressive strain depending on the unstrained relative band-inversion strength of the material.

Evolution of magnetism in single crystals of the van der Waals compound $\mathrm{V}{\mathrm{I}}_{3}$ in external pressure up to 7.3 GPa studied by measuring magnetization and ac magnetic susceptibility is reported. Four magnetic phase transitions, at ${T}_{1}=54.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}, {T}_{2}=53\phantom{\rule{0.16em}{0ex}}\mathrm{K}, {T}_{\mathrm{C}}=49.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, and ${T}_{\mathrm{FM}}=26\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively, have been observed at ambient pressure. The first two have been attributed to the onset of ferromagnetism in specific crystal-surface layers. The bulk ferromagnetism is characterized by the magnetic ordering transition at Curie temperature ${T}_{\mathrm{C}}$ and the transition between two different ferromagnetic phases ${T}_{\mathrm{FM}}$, accompanied by a structure transition from monoclinic to triclinic symmetry upon cooling. The pressure effects on magnetic parameters were studied with three independent techniques. ${T}_{\mathrm{C}}$ was found to be almost unaffected by pressures up to 0.6 GPa whereas ${T}_{\mathrm{FM}}$ increases rapidly with increasing pressure and reaches ${T}_{\mathrm{C}}$ at a triple point at \ensuremath{\approx} 0.85 GPa. At higher pressures, only one magnetic phase transition is observed moving to higher temperatures with increasing pressure to reach 99 K at 7.3 GPa. In contrast, the low-temperature bulk magnetization is significantly reduced by applying pressure (by more than 50% at 2.5 GPa) suggesting a possible pressure-induced reduction of vanadium magnetic moment. First-principles calculations of $\mathrm{V}{\mathrm{I}}_{3}$ under pressure allow us to ascribe the evolution of ${T}_{\mathrm{C}}$ with pressure to the reduction of interplanar distance, including the observed slope change at 0.6 GPa. These calculations also describe the associated band gap closing, showing that with a modest compression the material would become metallic. Overall, the large pressure range covered corresponds to a significant change of interplanar interactions. The obtained data thus allow us to shed light on how does the transition between the three-dimensional (3D) and quasi-2D system affect magnetic interactions in the system.

A new wide-ranging correlation for the thermal conductivity of xenon, based on the most recent theoretical calculations and critically evaluated experimental data, is presented. The correlation is designed to be used with a high-accuracy Helmholtz equation of state, and it is valid from the triple-point temperature to 606 K and pressures up to 400 MPa. The estimated expanded uncertainty (at a coverage factor of k = 2) in the range of validity of the correlation varies depending on the temperature and pressure, from 0.2 % to 4 %. In the near-critical region, the uncertainty is expected to be larger and may exceed 4 %. The correlation behaves in a physically reasonable manner when extrapolated up to 750 K; however, care should be taken when using the correlation outside of the validated range.

The superfluidity phenomenon of helium, which was discovered in the 1930s by Kapitza (Nature 141:74, 1938) [1], is about 100 years old. The superfluidity, which a macroscopic quantum phenomenon, is related to the formation (“condensation”) of a finite number of particles in one quantum state. This condensate of particles features some properties of the dissipation-free motion, which are responsible for the superfluidity phenomenon (Schmitt in Introduction to superfluidity: field-theoretical approach and applications. Springer, 2004) [2]. Below we shall be concerned only with superfluidity of Helium-4, which is the most common of the two isotopes of helium in nature. The superfluidity of the second isotope (Helium-3), which is a much more involved insufficiently known problem (Audi et al. in Nucl Phys A 729:3–128, 2003) [3], is beyond the scope of this book. So, below by “helium” we shall mean Helium-4. Helium is an extremely unusual system. This inert gas condenses only at a few degrees Kelvin and only helium remains a fluid down to absolute zero \( T = 0 \). Solidification of helium requires pressure about 30 atm. Because of this, the phase diagram for helium does not contain the triple point, which is standard for all other substances. At normal pressure helium boils at 4.2 K, the thermodynamic critical point corresponds to 5.19 K at pressure 2.24 atm. The “reluctance” of helium to form crystals can be explained by quantum effects—because of small mass of atoms and weakness of their interactions, their deflections from the equilibrium position in helium crystal are comparable with the interatomic distance, which leads to the “delocalization” of atoms in the crystal. To a certain extent, the smallness of the amplitude of the zero-point vibrations of atoms in the crystal lattice is analogous to the behavior of electrons in an ordinary metal. A remarkable property of quantum crystals of helium is their ability to generate crystallization waves, which can be looked upon as a dissipationless recrystallization of the surface.

Electromigration (EM) has aroused substantial attention with the shrinkage of modern devices. EM is an interaction between electron carriers and atoms, meaning that it arises from atomic behaviour. Both the number of twin boundaries (TBs) and the direction of electron flow are crucial factors affecting EM behaviour. In this study, EM phenomena with perpendicular and parallel electron flow were investigated by high resolution transmission electron microscopy (HRTEM). Twin planes could limit the growth direction of voids in the parallel case. The evolution of smooth surfaces into step-like surfaces resulting from the triple point retarding EM has been demonstrated. With the measurement of the resistance, it could be concluded that the specimen with electron flow perpendicular to the TBs had better EM restriction. Columnar grains can confine the position of the voids. This study demonstrates the dynamic evolution of the surface structure, providing insight into the fabrication of interconnections in the integrated circuits industry.

We present an isothermal chamber designed and realized at the Italian Metrological Institute (INRiM) to stabilize the temperature of a quartz cell for Doppler-broadened precision spectroscopy of mercury atoms in the UV region for the practical realization of the new definition of kelvin. The challenge of this apparatus is the capability to control, with great accuracy, the temperature of a non-cylindrical quartz cavity containing the mercury vapors. The temperature was actively controlled and maintained stable within 0.05 mK at the triple point of water for 15 h, but longer periods are possible. The spatial uniformity was also characterized. The traceability of temperature measurements and the complete uncertainty budget are discussed.

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this letter, we carry out the first investigation of dynamical phase behaviour at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we find that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behaviour in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions., Comment: 6 pages and 6 figures

We report results from a series of diamond-anvil-cell synchrotron x-ray diffraction and large-volume-press experiments, and calculations, to investigate the phase diagram of commercial polycrystalline high-strength Ti-6Al-4V alloy in pressure–temperature space. Up to ∼30 GPa and 886 K, Ti-6Al-4V is found to be stable in the hexagonal-close-packed, or α phase. The effect of temperature on the volume expansion and compressibility of α–Ti-6Al-4V is modest. The martensitic α → ω (hexagonal) transition occurs at ∼30 GPa, with both phases coexisting until at ∼38–40 GPa the transition to the ω phase is completed. Between 300 K and 844 K the α → ω transition appears to be independent of temperature. ω–Ti-6Al-4V is stable to ∼91 GPa and 844 K, the highest combined pressure and temperature reached in these experiments. Pressure–volume–temperature equations-of-state for the α and ω phases of Ti-6Al-4V are generated and found to be similar to pure Ti. A pronounced hysteresis is observed in the ω–Ti-6Al-4V on decompression, with the hexagonal structure reverting back to the α phase at pressures below ∼9 GPa at room temperature, and at a higher pressure at elevated temperatures. Based on our data, we estimate the Ti-6Al-4V α–β–ω triple point to occur at ∼900 K and 30 GPa, in good agreement with our calculations.

We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nano-droplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two dimensional systems arising from thermally induced interfacial wandering.

Ferroelectric GeTe is unveiled to exhibit an intriguing multiple non-trivial topology of the electronic band structure due to the existence of triple-point and type-II Weyl fermions, which goes well beyond the giant Rashba spin splitting controlled by external fields as previously reported. Using spin- and angle-resolved photoemission spectroscopy combined with ab initio density functional theory, the unique spin texture around the triple point caused by the crossing of one spin degenerate and two spin-split bands along the ferroelectric crystal axis is derived. This consistently reveals spin winding numbers that are coupled with time reversal symmetry and Lorentz invariance, which are found to be equal for both triple-point pairs in the Brillouin zone. The rich manifold of effects opens up promising perspectives for studying non-trivial phenomena and multi-component fermions in condensed matter systems., 5 pages, 5 figures

Tricritical phenomenon appearing in multiple phases is a fundamental and attractive issue in condensed-matter physics. Monopnictide DySb, a candidate for potential magnetic topological semimetal with an antiferromagnetic ground state, has been found to possess complex and intriguing field-induced magnetic phase transitions. In this work, critical behaviors of single-crystal DySb are investigated systematically, which generate a series of critical exponents including $\ensuremath{\beta}=0.244(2)$, $\ensuremath{\gamma}=0.827(2)$, and $\ensuremath{\delta}=4.425(1)$ for $H\ensuremath{\parallel}[001]$. The deduced critical exponents verified by Widom law and scaling equations are close to a tricritical mean-field model, suggesting a field-induced tricritical phenomenon in DySb. Based on the universality principle, a detailed $H\text{\ensuremath{-}}T$ phase diagram around the phase transition is constructed for $H\ensuremath{\parallel}[001]$, in which a tricritical point is revealed at temperature and field of (7.5 K, 51.4 kOe) on intersected boundaries of antiferromagnetic, forced ferromagnetic, and paramagnetic phases. Moreover, a triple point is found at the intersection (9.2 K, 19.7 kOe) of paramagnetic and two kinds of antiferromagnetic states. Such a fascinating phase diagram is indicative of delicate competition and balance between multiple magnetic interactions in this system, and lays a solid foundation for future research in topological transition and criticality.

The phase diagram of a face-centred cubic (FCC) antiferromagnet is calculated from the effective field theory (EFT) of Honmura and Kaneyoshi taking into account not only the effect of interaction with nearest neighbours, J 1, but also the effect of second neighbours, J 2. The phase diagram for the nearest neighbour case away from the triple point, which in our calculations is predicted to be at H = 4 and T = 0, is close to cluster variation method (CVM) and Monte Carlo (MC) results. Similar to MC and CVM predictions, we observe that the increasing second neighbours interaction pushes the triple point towards zero field. Our calculations also show that for α = −J 2/J 1 = 0.3, the triple point merges with the transition point of the L10 phase, one of the ground states, at H = 0 and changes the nature of phase transition from first- to second-order, in full agreement with Monte Carlo predictions. The phase diagram with the effect of second neighbours calculated for several values of α are in good agreement with available MC and CVM predictions.

We develop a phenomenological mean-field theory describing the hidden-order phase in $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ as a nematic of the ${B}_{1g}$ representation staggered along the $c$ axis. Several experimental features are reproduced by this theory: the topology of the temperature-pressure phase diagram, the response of the elastic modulus $({C}_{11}\ensuremath{-}{C}_{12})/2$ above the transition at ambient pressure, and orthorhombic symmetry breaking in the high-pressure antiferromagnetic phase. In this scenario, hidden order is characterized by broken rotational symmetry that is modulated along the $c$ axis, the primary order of the high-pressure phase is an unmodulated nematic, and the triple point joining those two phases with the high-temperature paramagnetic phase is a Lifshitz point.

The search for new topological materials that are realistic to synthesize has attracted increasing attention. In this study, we systematically investigated the electronic, mechanical, and topological semimetallic properties, as well as the interesting surface states, of the tetragonal monoxide of platinum, which is realistic to synthesize, via a first-principles approach. Our calculated results indicate that PtO is a novel topological semimetal with double nodal lines in the kz = 0 plane and a pair of triple topological nodal points along the A'-M-A directions. Obvious surface states, including Fermi arc and drum-head-like surfaces, could be found around nodal points and nodal lines. The dynamic and mechanical stabilities of P42/mmc-type PtO were examined in detail via calculation of the phonon dispersion and determination of elastic constants, respectively. Some other mechanical properties, including the bulk modulus, Young's modulus, shear modulus, Poisson's ratio, and Pugh's index, were considered in this study. P42/mmc-type PtO provides a good research platform for investigation of novel behaviors that combine mechanical properties and rich topological elements.

We discuss a two-dimensional model that leads to a phase diagram which reproduces at least qualitatively that of a pure substance. It is known that a spring between two atoms is due to a bond created by the interaction between the electrons of both atoms. Consequently a variation of the quantum state of the electrons involved in the bond can modify the elastic force constant of the spring. That is a kind of atom-phonon coupling. We consider a square lattice of N identical atoms linked by springs between atoms first and second nearest neighbors. We assume that the elastic force constants of all the springs can vary. The system is studied by using a variational method. First order phase transitions are obtained. The phase diagram of the system displays the features observed in the phase diagram of a pure substance: three thermodynamic phases, three coexistence curves, one triple point and one critical point. Applied pressure can be introduced in the model.

A new acoustic gas thermometry (AGT) system, which introduces a 1-L quasi-spherical resonator (QSR) made of oxygen-free copper, was built at the National Metrology Institute of Japan (NMIJ/AIST). The inner surface of the new QSR was machined using a diamond-turn tool. Improvement in the pressure measurement was introduced to allow direct measurement of the gas pressure in the resonator. The new AGT system was evaluated based on the measurement of the speed of sound in argon at the triple point of water and the melting point of gallium under the pressure range from 700 kPa down to 50 kPa. Based on these speed of sound measurements, the thermodynamic temperatures at the melting point of gallium were determined. The speed of sound measurements at isotherms of 283.15 K and 293.15 K were also conducted, and the related thermodynamic temperatures were determined. Based on the measured thermodynamic temperature T, the values of difference between T and the temperature T90 based on the International Temperature Scale of 1990 (ITS-90), (T − T90), along with the associated uncertainties, were calculated. The (T − T90) obtained in the present work were 1.3 ± 0.7 mK, 2.7 ± 0.8 mK, and 4.1 ± 0.8 mK for T90 of 283.15 K, 293.15 K, and 302.9146 K, respectively. These values were found to be in agreement within the estimated uncertainty with the currently reported values that exist in temperature range overlapping with the present work.

High-temperature standard platinum resistance thermometers (HTSPRTs) are used to establish the International Temperature Scale of 1990 (ITS-90) for temperatures up to 960 °C. Currently available thermometers, which may differ in the design of the platinum winding of the sensor, the shape and finish of the sensor frame, the frame material, the protective sheaths, and sealing materials, need some treatments to exhibit the stabilities expected of them and some of the causes of the instability are not well understood. This paper demonstrates a novel model of commercial HTSPRT that reportedly employs a novel sensor winding construction designed to eliminate instability arising from strain on the sensor winding due to differential thermal expansion between the sensor and the sensor frame. The stability of eight different HTSPRTs, including the novel model, are compared at the triple point of water (TPW), the melting point of gallium, and the freezing points of tin, zinc, aluminum and silver. Heat treatments included annealing at 500 °C, a preheating temperature for use at the freezing points of aluminum and silver, and at 800 °C, which was selected for checking the stability of the HTSPRTs in the middle of the temperature range between the freezing points of aluminum and silver. The consistency of the resistance values at the different fixed points was also confirmed by calculating the S parameter. We found three HTSPRTs stable during the described thermal conditions within ± 0.5 mK at the TPW. The novel model of commercial HTSPRT was the best one with a stability in the resistance at the TPW of within ± 0.3 mK over the entire temperature range. These indicate that the stable three HTSPRTs are promising instruments to provide accurate temperature scale at temperatures from the freezing point of aluminum up to the freezing point of silver based on the ITS-90.

We present a theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$. Based on a strong-coupling Ginzburg-Landau functional that accounts for the relative stability of the bulk A and B phases of $^{3}\mathrm{He}$ at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\phantom{\rule{0.16em}{0ex}}\text{G}$ parallel to the rotation axis, $\mathbf{H}\ensuremath{\parallel}\mathbit{\ensuremath{\Omega}}$, are reported, as well as the supercooling transition line, ${T}_{\text{V}}^{*}(p,H)$. In zero field the vortex phases of $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ are separated by a first-order phase transition line ${T}_{\text{V}}(p)$ that terminates on the bulk critical line ${T}_{c}(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\ensuremath{\beta}$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, ${T}_{\text{V}}^{*}(p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\ensuremath{\gtrsim}60\phantom{\rule{0.16em}{0ex}}\text{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$.

We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed and globally condensed states all coexist are possible depending on the value of the aspect ratio $a=L/H$ where $H$ is the stripe width and $L$ the wall separation. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value $8/\pi$. These predictions are tested using a fully microscopic classical Density Functional Theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted., Comment: 5 pages

The triple point of water (TPW, temperature 273,16 K) plays a vital and critical role in thermometry, because of its triple functions. The first one, it defines the temperature unit, the Kelvin, it is the reference point in Standard Platinum Resistance Thermometer (SPRT) calibrations, according to the International Temperature Scale of 1990 (ITS-90) [1]. On the other side, TPW metallic-sealed cell is the link to determine Boltzmann constant through the acoustic resonance techniques. TPW is the connection point between the current definition of the Kelvin and the future one, based on the Boltzmann constant [2]. The uncertainty related to the realization of TPW will propagate in all fixed point defined by ITS-90 text. The thermal metrology laboratory, at the National Institute for Standards (NIS-Egypt), has been working during the last 5 years with the cooperation with LNE-France on the development of metallic-sealed cells for the realization of the TPW [1–4]. Two techniques to solidify the water sample inside the cell were tested, the usual one; quenching (fast freezing) and a new modified smoothing (slow freezing starts at 90% of melted ice). The calculated value of impurities concentration was carried out; it is about of 1.29 × 10−6 mol. mole−1 which causes a deviation of about 142 μK. The uncertainty related to the realization of TPW has been improved up to ± 30 mK.

A two-dimensional Lattice Boltzmann model was established to study the dynamic physical process of frost growth on a cold flat surface. It is verified that the theoretical results are in good agreement with the experiment data with better accuracy. The frost morphology is explored by showing two-dimension density distribution with different cold surface temperatures. The results also include dynamic characteristics of frost properties such as thickness, deposition weight, volume fraction, density, temperature. According to the results, it is found that the nearer it is from the cold flat plate, the larger of frost crystal volume fraction and density are. The frost surface temperature increases rapidly at the early period of frosting and then increases gradually towards the triple point temperature of the water. The frost internal temperatures rise in a linear tendency with the frost thickness and decrease at the same frost layer location with frost growth. Super-saturation degree of moist air has non-negligible effect on frost growth parameters such as frost thickness, frost crystal deposition mass, frost deposition rate and frost crystal volume fraction.

As part of a larger project regarding the determination of argon content in oxygen based on measurements of the α–β solid–solid transition temperature of oxygen at 23.8 K, also the effect of argon on the β–γ solid–solid transition temperature at 43.8 K was measured. This transition being the main item of interest of these studies (correction of the O2 triple point temperature for argon content), the results obtained on the β–γ transition for two argon-in-oxygen mixtures (1002.29·10−6 and 351.14·10−6 mol·Ar·per·mol·O2) are presented here. A preliminary result from the first mixture, already included in a former publication, is combined with the present results for both mixtures to obtain an accurate value for the sensitivity of the temperature of the β–γ transition to argon content, along with a discussion regarding the effect of argon on the shape of the O2 transitions.

Molecular hydrogen is a fascinating candidate for quantum fluid showing bosonic and fermionic superfluidity. We have studied diffusion dynamics of thin films of H$_2$, HD and D$_2$ adsorbed on a glass substrate by measurements of elasticity. The elasticity shows multiple anomalies well below bulk triple point. They are attributed to three different diffusion mechanisms of admolecules and their "freezing" into localized state: classical thermal diffusion of vacancies, quantum tunneling of vacancies, and diffusion of molecules in the uppermost surface. The surface diffusion is active down to 1 K, below which the molecules become localized. This suggests that the surface layer of hydrogen films is on the verge of quantum phase transition to superfluid state., 5 pages, 3 figures

By using the generalized inverse-pole-figure model, the numbers of crystalline particles involved in different domain-switching near the triple tetragonal–rhombohedral–orthorhombic (T–R–O) points of three-phase polycrystalline ferroelectrics have been analytically calculated and domain-switching which can bring out phase transformations has been considered. Through polarization by an electric field, different numbers of crystalline particles can be involved in different phase transformations. According to the phase equilibrium conditions, the phase equilibrium compositions of the three phases coexisting near the T–R–O triple point have been evaluated from the results of the numbers of crystalline particles involved in different phase transformations.

A brief critical analysis of the theoretical P(T) liquid–vapor phase equilibrium curves is given. Based on the Clapeyron–Clausius equation and data on the heat capacity of water, a two-parameter expression of the P(T) curve is obtained for water in the temperature range from the triple point to 389 K. The parameters of the P(T) curve are determined from data on the pressure and heat of evaporation of water at the triple point. The accuracy of the P(T) function is comparable to the actual accuracy of standard thermodynamic tables for water and water vapor.