Triple Point Research Articles

Abstract We revisit the structure of the phase diagram of the two-component mean-field Bose mixture at finite temperatures, considering both the cases of attractive and repulsive interspecies interactions. In particular, we analyze the evolution of the phase diagram upon driving the system towards collapse and point out its distinctive features in this limit. We provide analytical insights into the global structure of the phase diagram and the properties of the phase transitions between the normal phase and the phases involving Bose–Einstein condensates. Inter alia we analytically demonstrate that for sufficiently weak interspecies interactions a 12 the system generically exhibits a line of quadruple points but has no triple nor tricritical points in the phase diagram spanned by the chemical potentials µ 1, µ 2 and temperature T. In contrast, for sufficiently large, positive values of a 12, the system displays both triple and tricritical points but no quadruple points. As pointed out in recent studies, in addition to the phase transitions involving condensation, the mixture may be driven through a liquid–gas type transition, and we clarify the conditions for its occurrence. We finally discuss the impact of interaction- and mass-imbalance on the phase diagram of the mixture.

A remarkable discovery of two thermodynamic states has been made, where the loci of the minima of modified isothermal compressibility (κ* = ∂v/∂P) along the isotherms and isobars cross for the 19 fluids considered here—from helium to water, including the van der Waals fluid and air. These unique Universal Compressibility Points (UC1 and UC2), in terms of the reduced pressure (P/Pc) and temperature (T/Tc) of (1.001, 0.875) and (1.065, 0.802), exist in the subcritical vapor region. They do not involve any phase transitions like triple point, critical point, and dwij point. The existence of these states reinforces the need for an integrated analysis of the anomalous region from subcritical to supercritical states. Intricate, complex similarities and deviations in fluids' behavior are demonstrated when the thermodynamic/transport properties and the fluids' characteristics, such as the acentric factor, dipole moment, degree of freedom, and spherical symmetry, are considered together. Although the property behavior and the shape and size of the anomalous regions may remain similar for many polar, nonpolar, and special fluids, the anomalies in certain fluids, e.g., helium, ethanol, and methanol, may be far more complex. These findings raise new questions about the mechanisms that produce and strengthen/weaken the anomalies. Also presented are the correlations for the boundaries of the anomalous regions of 15 fluids that are extremely accurate against their real diagrams. The similarity among these fluids has led to one set of correlations, which can serve as the first estimate of the anomalous regions of regular fluids.

Abstract The National Research Council of Canada (NRC) recently piloted the second international key comparison of triple point of water cells, CCT-K7.2021, where participants submitted a transfer cell and a report of the temperature difference between their transfer cell and their respective national reference. By comparing the differences between each transfer cell, NRC could calculate the differences between each participant’s national reference. While there was good agreement among all the participants, there was a large variation among the submitted uncertainties. This was possibly due to the complexity of the uncertainty analysis, which typically has many correlated components between the transfer cell and the national reference that partially cancel when the difference is taken. The Measurement Standards Laboratory of New Zealand (MSL) carried out its analysis using a detailed measurement model that included all known correlations and applied an algorithmic approach fully compliant with the Guide to the Expression of Uncertainty in Measurement. As a consequence, MSL submitted an uncertainty value less than half the uncertainty values submitted by almost all of the other participants. This paper describes the measurement model implemented by MSL and demonstrates how accounting correctly for correlations leads to a significantly lower uncertainty. The paper also shows how applying the same method to the previously published NRC analysis results in a reduction in the NRC uncertainty by a factor of about 2.5, making it smaller than the MSL uncertainty.

The “triple point” paradigm of aluminosilicates revisited

The substances that make up the three-component reciprocal system of fluorides and chlorides of potassium and cadmium have various applications, both individually and in mixtures. The faceting elements of the ternary reciprocal system include in binary systems the formation of compounds KF∙CdF2, KCl∙CdCl2 of congruent and compound 4KCl∙CdCl2 of incongruent melting. The crystallization tree is constructed. Taking into account the compounds, a crystallization tree has been constructed that has a linear structure and includes five stable secondary triangles. The triangles are separated from each other by four stable secants, of which three secants have a quasi-binary character. The crystallization tree allows one to predict crystallizing phases in secondary phase triangles. In four secondary phase triangles, the formation of triple points of invariant four-phase equilibria is noted. The secondary phase triangle KCl–K4CdCl6–KCdF3 does not contain an invariant point. The system of fluorides and chlorides of potassium and cadmium belongs to the adiagonal triangulate type. Chemical interaction under standard conditions is described. Modeling of chemical interaction for figurative points of composition corresponding to intersections of stable and unstable secants has been carried out using thermodynamic data of the starting materials and binary compounds. The formation of three equivalence points is noted on two stable secants. On the other two stable secants, two equivalence points are noted. According to thermodynamic calculations, for two mixtures out of ten, reactions cannot be realized under standard conditions. The proposed technique for describing chemical interactions can be used for other types of ternary reciprocal systems with exchange reactions with both diagonal and diagonal types of partitioning. Mixtures corresponding to equivalence points on unstable secants with a heat effect of reactions greater than 50 kJ can be used as single-action exothermic mixtures.

Design of A series of high-performance topology catalyst APt3 (A = Dy, Nd, Sc, Sm, Y, Pr) materials

The A Vuong Formation, located within the southern Truong Son Belt in central Vietnam, comprises low- to high-grade metamorphic rocks that record crucial insights into the region’s tectonic evolution. Our field investigations reveal that it mainly consists of the psammitic and pelitic schists, intercalated with some mafic or siliceous layers, and locally cut by leucocratic veins. The indicative mineral assemblages in the pelitic to psammitic schists define two metamorphic zones: a greenschist-facies biotite-chlorite zone and an amphibolite-facies staurolite zone. Based on conventional geothermobarometry, the peak metamorphic condition in the staurolite zone was estimated at ca. 5.5–8.7 kbar and 590–640℃, followed by a retrograde stage at 4.4–7.4 kbar and 530–570℃. Notably, a porphyroblastic andalusite observed in a pelitic schist from this zone is rimmed by kyanite with a preferred orientation. In addition, it includes kyanite, sillimanite, and an intergrowth of staurolite + quartz as inclusions. These features suggest their equilibrium during the prograde stage, reflecting a pressure-temperature transition from andalusite to kyanite stability. The prograde metamorphic condition is thus constrained at the triple point of andalusite-kyanite-sillimanite. The petrological evidence and estimated metamorphic conditions for the current pelitic schists support a unique anti-clockwise pressure-temperature trajectory, rather than a clockwise one. Its thermobaric feature is well aligned with the amphibolite-facies metamorphism of the neighboring Dai Loc Complex, and contrasts with that of the Kham Duc Complex (Kontum Massif).

Purpose This study aims to investigate the critical yet unregulated parameter of measurement current in thermistor thermometry. Focusing on quantifying the self-heating effect’s influence on measurement accuracy, it establishes operational guidelines for current selection in precision temperature measurements at metrological reference points. Design/methodology/approach Through systematic experimental research, three distinct thermistor thermometers were evaluated at two International Temperature Scale fixed points: water triple point (0.01 °C) and gallium melting point (29.7646 °C). The experimental design incorporated parametric analysis of measurement current variations, with particular emphasis on characterising the relationship between electrical power dissipation and resultant temperature measurement deviations. Findings The experimental results revealed a linear correlation between power dissipation and measurement deviations, demonstrating that maintaining dissipation power below 5 µW limits measurement errors to within 1 mK. However, this study also identified a practical trade-off: while lower currents reduce self-heating effects, they simultaneously increase measurement system complexity and implementation challenges. Originality/value This research provides systematic quantification of measurement current impacts across different thermistor types at primary temperature standards. The established 5 µW power dissipation threshold offers concrete operational guidance for metrological applications. Furthermore, the proposed methodology for balancing measurement accuracy against technical feasibility presents novel insights for precision temperature measurement system design.

We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.

Archaeological research carried out in the old town centre in 2009 and 2016 yielded important information regarding Ljubljana’s development. The earliest archaeological traces of the medieval settlement in the Town Square area near the present-day Triple Bridge point to a pre-urban core of the subsequent town, which began to develop before the mid-twelfth century, which at least roughly coincided with the time when the Spanheim family arrived in central Carniola. Then followed urban planning. The streets were laid out before the plots were marked out and build on. Such an ambitious project was usually not part of the town’s natural evolution but a result of organizationally and financially complex reconstruction of the existing settlement, which can be understood as the founding of the town. According to archaeological data and mentions in written sources, Ljubljana may have been founded during the period of Herman of Spanheim (1161–1181), Duke of Carinthia. However, it is not excluded that this already happened during the time of his brothers Henry (1144–1161) or Ulrich. The latter was the first to name himself after Ljubljana in 1144.

When humid air passing over the evaporator fins of air-source heat-pump systems makes contact with a surface with a temperature less than, but near, the triple point of water, condensation frosting occurs in three distinct stages: droplet growth and freezing, crystal growth and full growth. This paper presents a new model for droplet growth and freezing as part of a three-stage frosting model for condensation frosting conditions. During this study, the droplet growth and freezing model was validated individually and as part of the overall model using data gathered under conditions typical of heat-pump operation. The model results indicated that both the cold surface temperature and the relative humidity affected the droplet growth stage, though the cold surface temperature had the greater impact. The difference between the lengths of droplet growth stages across a 6°C surface temperature range was greater than 20 min, while it was approximately 5 min across a relative humidity range of 30%. The droplet growth stage significantly affected the remaining stages of frost growth by determining the thicknesses, densities and times at which the subsequent stage transitions occurred. Thus, this initial droplet growth and freezing stage should not be ignored in comprehensive condensation frosting models.This article is part of the theme issue 'Heat and mass transfer in frost and ice'.

A geotechnical site investigation has been conducted in the southern breakwater basin of the Port of Barcelona, for which hundreds of in-situ and lab tests have been performed. Among these tests, this study focuses on the evaluation of triple points. That is, at the prospected locations, there are results from seismic dilatometer Marchetti test (SDMT), cone penetration tests (CPTu), and laboratory tests based on soil samples. By using this information, the probabilistic distribution of the dynamic and geometrical properties of the soil profiles can be properly characterized. In this way, eleven closely spaced boreholes have been used to characterise the statistical properties of the input variables. Then, it has been performed a probabilistic generation of one-thousand soil profiles, which are statistically compatible with the data provided by the eleven aforementioned boreholes. Then, it has been analysed how the elastic properties of the generated soil profiles evolve once seismic waves have passed through them. To do so, a large set of ground motion recorded in hard soils have been employed. The main objective has been to obtain mathematical arrangements exhibiting highefficiency to predict parameters that can be used to characterize the nonlinear dynamic response of the soil. This has been achieved by employing bivariate and multivariate analyses in the log-log space. Results show that the soil response can be properly parametrized if considering intensity measures extracted from the ground motions acting at the bedrock level and specific soil parameters. Finally, fragility curves and surfaces have been derived for risk assessment purposes.

ABSTRACT The image of a finitely determined holomorphic germ $\Phi$ from $\mathbb {C}^2$ to $\mathbb {C}^3$ defines a hypersurface singularity $(X,0)$, which is in general non-isolated. We show that the diffeomorphism type of the boundary of the Milnor fibre $\partial F$ of X is a topological invariant of the germ $\Phi$. We establish a correspondence between the gluing coefficients (so-called vertical indices) used in the construction of $\partial F$ and a linking invariant L of the associated sphere immersion introduced by T. Ekholm and A. Szűcs. For this we provide a direct proof of the equivalence of the different definitions of L. Since L can be expressed in terms of the cross cap number $C(\Phi )$ and the triple point number $T(\Phi )$ of a stable deformation of $\Phi$, we obtain a relation between these invariants and the vertical indices. This is illustrated on several examples.

The temperature and grain size dependences of the ferroelectric phase transitions and dielectric properties of BaTiO3 nanoceramics are described by higher-order Landau–Ginzburg–Devonshire theory. A structurally stable 8th-order Landau–Ginzburg–Devonshire potential with the 2nd- and 4th-order coefficients varying with temperature and grain size is proposed for a phenomenology of BaTiO3 nanoceramics. The temperature–grain size phase diagram constructed on the basis of this potential model describes well the experimentally observed cubic–tetragonal–orthorhombic and cubic–orthorhombic–rhombohedral triple points and ferroelectric to paraelectric to ferroelectric reentrance phenomenon. The spontaneous polarization and dielectric constant of BaTiO3 nanoceramics are calculated. It is shown that dielectric anomalies appear at the phase transitions and dielectric peaks are depressed, and diffused with decreasing grain size.

Experimental challenges in determining the phase diagram of carbon at temperatures and pressures near the graphite-diamond-liquid triple point are often related to the persistence of metastable crystalline or glassy phases, superheated crystals, or supercooled liquids. A deeper understanding of the crystallisation kinetics of diamond and graphite is crucial for effectively interpreting the outcomes of these experiments. Here, we reveal the microscopic mechanisms of diamond and graphite nucleation from liquid carbon through molecular simulations with first-principles machine learning potentials. Our simulations accurately reproduce the experimental phase diagram of carbon near the triple point and show that liquid carbon crystallises spontaneously upon cooling. Metastable graphite crystallises in the domain of diamond thermodynamic stability at pressures above the triple point. Furthermore, whereas diamond crystallises through a classical nucleation pathway, graphite follows a two-step process in which low-density fluctuations forego ordering. Calculations of the nucleation rates of the two competing phases confirm this result and reveal a manifestation of Ostwald’s step rule, where the strong metastability of graphite hinders the transformation to the stable diamond phase. Our results provide a key to interpreting melting and recrystallisation experiments and shed light on nucleation kinetics in polymorphic materials with deep metastable states.

Two-dimensional (2D) magnetic materials have attracted considerable interest owing to their potential applications in spintronics and fundamental investigations into low-dimensional magnetism. Cr2Te3, a quasi-2D non-van der Waals magnet, exhibits a complex magnetic phase diagram due to competing magnetic interactions within and between layers. However, the precise nature and evolution of these magnetic phases remain unclear. Here, we utilize an ultrahigh-sensitive composite magnetoelectric technique, which probes the ac magnetostrictive coefficient, to systematically explore the temperature–magnetic field phase diagram of Cr2Te3 single crystals. Our results reveal the coexistence of multiple magnetic phases, including canted ferromagnetic, antiferromagnetic, and paramagnetic states. An additional canted ferromagnetic phase and a possible triple point are also proposed. The updated phase diagram provides deeper insights into the specific spin configurations associated with each phase. These findings further highlight the decoupled magnetic ordering between the Cr1/Cr3 layers and the Cr2 layer near the magnetic ordering temperatures.

The cause of Mars’s loss of surface habitability is unclear, with isotopic data suggesting a ‘missing sink’ of carbonate1. Past climates with surface and shallow-subsurface liquid water are recorded by Mars’s sedimentary rocks, including strata in the approximately 4-km-thick record at Gale Crater2. Those waters were intermittent, spatially patchy and discontinuous, and continued remarkably late in Mars’s history3—attributes that can be understood if, as on Earth, sedimentary-rock formation sequestered carbon dioxide as abundant carbonate (recently confirmed in situ at Gale4). Here we show that a negative feedback among solar luminosity, liquid water and carbonate formation can explain the existence of intermittent Martian oases. In our model, increasing solar luminosity promoted the stability of liquid water, which in turn formed carbonate, reduced the partial pressure of atmospheric carbon dioxide and limited liquid water5. Chaotic orbital forcing modulated wet–dry cycles. The negative feedback restricted liquid water to oases and Mars self-regulated as a desert planet. We model snowmelt as the water source, but the feedback can also work with groundwater as the water source. Model output suggests that Gale faithfully records the expected primary episodes of liquid water stability in the surface and near-surface environment. Eventually, atmospheric thickness approaches water’s triple point, curtailing the sustained stability of liquid water and thus habitability in the surface environment. We assume that the carbonate content found at Gale is representative, and as a result we present a testable idea rather than definitive evidence.

Laser direct-drive offers significant advantages in terms of target simplicity, improved energy coupling, and large fuel masses over indirect drive. However, performance degradations from hydrodynamic and laser-plasma instabilities seeded and driven by the direct illumination pose limitations on the parameter space available for achieving ignition. In this paper, new design improvements are identified to forge a path forward for a hydro-equivalent ignition demonstration. The first is related to a new formulation of the statistical model (SM) used to accurately predict target performance directly from input parameters such as laser pulse shape and target specifications. This new SM formulation provides direct guidance on target dimensions and laser beam-to-target radius to achieve the highest fusion yield on the OMEGA laser. The second improvement comes from cooling the deuterium–tritium (DT) ice layer below the triple point right before shot time leading to lower DT vapor densities and higher convergence. Guided by these design improvements, a Bayesian optimization algorithm was used to design an implosion that is predicted to closely approach a Lawson triple product that hydrodynamically scales to ignition if equivalent laser–target coupling is achieved at laser energies typical of the National Ignition Facility.

Abstract We analyze multitrace random matrix models with the help of the saddle point approximation and we introduce a multitrace term of type − c 1 c 3 to the action. We obtain the numerical phase diagram of the model, with a stable asymmetric phase and the triple point. Furthermore, we examine response functions in this model.

Fermi arcs are nontrivial surface states that exist in topological semimetals, which exhibit a variety of interesting effects, such as anomalous transport properties and chiral anomaly induced phenomena. Recently, the emerged Two-dimensional transition-metal dichalcogenide (TMDC) shows distinctive optical and electrical properties, makes it a promising platform for efficient modulation of Fermi arcs. By covering TMDC sheets on a photonic Dirac metamaterial (PDS), the quadrupole Dirac point splits into two triple degeneracy points (TDPs), each TDP share one Fermi arc. Through tuning the characteristics of TMDC layers, Fermi arcs and transmissions of PDS can be effectively modulated in multi-degrees of freedom. Unconventionally, we find the Fermi arcs may do not terminate at the degeneracy points but between the two type III TDPs. Fermi arcs with nonlocal effect are also investigated. Furthermore, topological transition from open (hyperbolic-like) to closed (elliptical-like) equi-frequency contours at TDP is also observed. Our findings may provide potential applications in flexible modulation of Fermi arcs with multiple functions.