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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.

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.

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.

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.

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.

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 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.

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.

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.

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 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.

We explored the possibility of using xenon as a molecular probe to characterize graphitic non-uniform pores in activated carbon (AC), and studied its isotherms with a Grand Canonical Monte Carlo (GCMC) simulation. To model non-uniform pores, we used a wedge pore model, a better description of the pore space in AC, and studied the effects of the pore length, the wedge angle and the temperature on the behaviour of the adsorption and desorption isotherms. For temperatures below the triple point, the isotherm exhibits two distinct regions: in the region of low loadings it shows a step-wise behaviour as the adsorption progresses from the tip of the wedge, followed by the second region of gradual increase in the adsorbed density with pressure. A distinct feature is the possible existence of multiple hysteresis loop in the first region and the reversibility of the isotherm in the second region. The hysteresis is due to the commensurate packing of molecular layers across the pore to form domains along the axial direction of the pore and the number of layers is incremented by one as we move from one domain to the next. We have found that the hysteresis disappears when either the wedge angle is greater than a critical value or the temperature is greater than the so-called bifurcation temperature. The second region of reversibility is due to the formation of the condensate separated from the gas phase with a concave interface whose radius of curvature is found to satisfy the Kelvin equation.

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.

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.

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.

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.

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.

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.

The multidimensional structure of mildly unstable detonations are examined by numerical computations. These phenomenon have grown in interest since the development of propulsion devices such as pulsed and rotating detonation engines. Rectangular, diagonal and spinning modes are observed in a near-limit propagation detonation. High-order numerical integration of the reactive Euler equations have been performed to analyze the averaged structure, the shock dynamics of a single-cell detonation propagating in a square channel. Computations show a good agreement with the experimental cellular structure, showing the relevance of the slapping waves in the rectangular modes. The hydrodynamic thickness as well as the pdf shock dynamics are similar in the 2D and 3D cases, but the mean quantities vary on a quantitative basis. Moreover, the presence of strong forward jets is attested, which comes from simultaneous triple point line collisions with the walls.

Self-consistent field theory (SCFT), as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a fourth-order exponential time differencing Runge-Kutta algorithm (ETDRK4) to solve the modified diffusion equation (MDE) which is the most time-consuming part of a SCFT calculation. By making a careful comparison with currently most efficient and popular algorithms, we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE, resulting in a boost of the overall computation efficiency, while it shares the same spatial accuracy with other algorithms. In addition, to demonstrate the power of our ETDRK4 algorithm, we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O70 phase, the lamellar phase and the cylindrical phase.

A previous paper (Duerig and Bhattacharya in Shap Mem Superelasticity 1:153–161, 2015) introduced several engineering considerations surrounding the R-phase in Nitinol and highlighted a common, if not pervasive, misconception regarding the use of the term Af by the medical device industry. This paper brings additional data to bear on the issue and proposes more accurate terminology. Moreover, a variety of tools are used to establish the forward and reverse stress–temperature phase diagrams for a superelastic wire typical of that used in medical devices. Once established, the two most common methods of measuring transformation temperatures, Differential Scanning Calorimetry and Bend Free Recovery, are tested against the observed behavior. Light is also shed upon the origin of the Clausius–Clapeyron ratio (dσ/dT), the triple point, and why such large variations are reported in superelastic alloys.

Frequencies of acoustic and electromagnetic resonances were measured in a quasispherical acoustic resonator at the temperature of the triple point of water. The resonator was filled with helium 4He. Based on the analysis of experimental data, a value for the Boltzmann constant of kB = 1.380651·10–23 J·K–1 with uncertainty of 2.4 ppm was obtained.

Liquid viscosity is an important physical property utilized in engineering designs for transportation and processing of fluids. However, the measurement of liquid viscosity is not always easy when the materials have toxicity and instability. In this study, a modified scaled variable reduced coordinate (SVRC)-quantitative structure property relationship (QSPR) model is suggested and analyzed in terms of its performance of prediction for liquid viscosity compared to the conventional SVRC-QSPR model and the other methods. The modification was conducted by changing the initial point from triple point to ambient temperature (293 K), and assuming that the liquid viscosity at critical temperature is 0 cP. The results reveal that the prediction performance of the modified SVRC-QSPR model is comparable to the other methods as showing 7.90% of mean absolute percentage error (MAPE) and 0.9838 of R 2. In terms of both the number of components and the performance of prediction, the modified SVRC-QSPR model is superior to the conventional SVRC-QSPR model. Also, the applicability of the model is improved since the condition of the end points of the modified model is not so restrictive as the conventional SVRC-QSPR model.

The features of the bulat steel melting technology are explained by metastable initial crystallization of Fe-C melts, which starts from volume-dispersed delta-phase. The variant of corresponding metastable phase diagram is suggested on the basis of previous research. The diagram includes liquid-liquid critical point and monotectic triple point.

We consider a method of transferring the temperature of the triple point of water with an acoustic resonator configuration for measuring the Boltzmann constant. It is shown that the transfer of the temperature of the triple point of water in a resonator using a highly sensitive differentiator does not require the use of absolute means of measurement and implemented with uncertainty limited only by thermal noise. The method enables reducing uncertainty in the temperature transfer when measuring the Boltzmann constant, whose accurate measurement is necessary for transition to a new definition of the unit of temperature.

The phase boundary between akimotoite and ringwoodite + stishovite in MgSiO3 was determined using a multi-anvil high-pressure apparatus and synchrotron X-ray radiation. The phase relation was determined by observing the recovered samples using an electron microprobe analyzer. Experimental pressures were monitored by the in situ powdered X-ray diffraction data of gold, which was put in the sample chamber. The reaction boundary between akimotoite and ringwoodite + stishovite was found to occur at P (GPa) = 22.0–0.0012 × T (K). The pressure dependence of the slope of the reaction boundary, dP/dT, determined in our study was smaller than that determined by Gasparik (J Geophys Res 95:15751–15769, 1990). The triple point of ringwoodite + stishovite–wadsleyite + stishovite–akimotoite estimated in our study was at ~20 GPa and ~1700 K.

Self-sustained detonation waves in flake aluminum dust/air mixtures have been studied in a tube of diameter 199 mm and length 32.4 m. A pressure sensor array of 32 sensors mounted around certain circumferences of the tube was used to measure the shape of the detonation front in the circumferential direction and pressure histories of the detonation wave. A two-head spin detonation wave front was observed for the aluminum dust/air mixtures, and the cellular structure resulting from the spinning movement of the triple point was analyzed. The variations in velocity and overpressure of the detonation wave with propagation distance in a cell were studied. The interactions of waves in triple-point configurations were analyzed and the flow-field parameters were calculated. Three types of triple-point configuration exist in the wave front of the detonation wave of an aluminum dust/air mixture. Both strong and weak transverse waves exist in the unstable self-sustained detonation wave., 25 pages, 13 figures, 1 table

This paper reports on precise measurements of the non-uniqueness (interpolation errors) associated with using Standard Platinum Resistance Thermometers (SPRTs) in the range from − 196 °C to 100 °C. Six long-stem SPRTs were compared with unprecedented (

We have developed an adiabatic calorimeter with a small glass Hg cell to calibrate capsule-type standard resistance thermometers (SPRTs) at the triple point of Hg (TPHg), which is one of the defining fixed point of the International Temperature Scale of 1990 (ITS-90). Using this system with high-purity Hg (99.999 99 %), we calibrated SPRTs at the TPHg and evaluated the uncertainty of the calibration. Compared with a calibration system at the National Metrology Institute of Japan (NMIJ/AIST), which uses a large stainless steel Hg cell, for a small cell in an adiabatic calorimeter the temperature distribution from hydrostatic pressure can be suppressed. In addition, the influence of heat flux can also suppressed by using the adiabatic calorimeter. Consequently, the standard combined uncertainty for the realization of TPHg was estimated to be 0.12 mK, much less than the uncertainty of the conventional system using the large stainless Hg cells. Furthermore, by measuring the cooling curve of Hg at different cooling rates, we confirmed that the degree of supercooling of high-purity Hg in the small glass cell reached approximately 18 K, which is much larger than that achievable in not only large Hg cells but also small cells. This large supercooling may be related to the high purity of the Hg employed, the small hydrostatic height of the Hg, and/or the surface contact between Hg and cell.

The triple-point numbers and the triple-point spectrum of a closed 3-manifold are topological invariants that give a measure of the complexity of the 3-manifold using the number of triple points of minimal filling Dehn surfaces. Basic properties of these invariants are presented, and the triple-point spectra of $$\mathbb {S}^2\times \mathbb {S}^1$$ and $$\mathbb {S}^3$$ are computed.

A new method for deriving accurate thermodynamic properties of gases and vapors (the compression factor and heat capacities) from the speed of sound is recommended. A set of PDEs connecting speed of sound with other thermodynamic properties is solved as a nonlinear least squares problem, using a modified Levenberg–Marquardt algorithm. In supercritical domain, boundary values of compression factor are imposed along two isotherms (one slightly above Tc and another several times Tc) and two isochores (one at zero density and another slightly above ρc). In subcritical domain, the upper isochore is replaced by the saturation line, the lower isotherm is slightly above the triple point, and the upper isotherm is slightly below the critical point. Initial values of compression factor inside the domains are obtained from the boundary values by a cubic spline interpolation with respect to density. All the partial derivation with respect to density and temperature, as well as speed of sound interpolation with respect to pressure, is also conducted by a cubic spline. The method is tested with Ar, CH4 and CO2. The average absolute deviation of compression factor and heat capacities is better than 0.002 % and 0.1 %, respectively.

Some experimental studies have reported that physical properties of solid methane exhibit a number of anomalies in the temperature interval between $$0.5 T _\mathrm{tr}$$ and $$T _\mathrm{tr}$$ ( $$T _\mathrm{tr}$$ is triple point of methane). This paper contains an attempt of systematization and theoretical interpretation of the observed anomalies.

The triple point is a well-known feature on pressure–temperature phase diagrams. A multiferroic triple point is now reported for La-doped BiFeO3; La concentration and temperature are the phase variables and the phases display different spin (dis)order.

The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.

There are multiple ways to increase the accuracy of temperature measurement by reducing uncertainties of temperature scale realization by means of standard platinum resistance thermometers (SPRT) calibrated at the defining fixed points (DFPs). This paper demonstrates the possibility of reducing uncertainty of temperature scale realization by taking into account correlations between the SPRT resistances at the DFPs in calibration and temperature measurements. The BIPM document Uncertainties in the Realisation of the SPRT Subranges of the ITS-90 issued in 2009 provides an overview of the different approaches. In most cases, SPRT resistances at DFPs were considered as uncorrelated. Only correlations caused by using the same SPRT resistance at the triple point of water (TPW) in calibration and temperature measurement were taken into account. Furthermore SPRT resistances at the DFPs can be correlated with respect to some of the same conditions in the laboratory for SPRT resistances measured at the DFPs. This paper demonstrates that the uncertainty of temperature scale ITS-90 realization is unaffected by errors originating form SPRT calibration and temperature measurements when all the measured resistances are measured with the same error. Furthermore, it is shown that the use of correlation can reduce the uncertainty of temperature scale realization, and dealing with this problem will bring improvement in the field of uncertainty evaluation. Formulas for the calculation of uncertainties of temperature scale realization are presented, together with the correlation between SPRT resistances and simulations that show the impact of correlation on the uncertainty of the temperature scale realization.

We review the discovery of new phases of carbon (Q-carbon) and BN (Q-BN) and address critical issues related to direct conversion of carbon into diamond and hBN into cBN at ambient temperatures and pressures in air without any need for catalyst and the presence of hydrogen. The Q-carbon and Q-BN are formed as a result of quenching from super undercooled state by using high-power nanosecond laser pulses. We discuss the equilibrium phase diagram (P vs T) of carbon, and show that by rapid quenching, kinetics can shift thermodynamic graphite/diamond/liquid carbon triple point from 5000 K/12 GPa to super undercooled carbon at atmospheric pressure in air. Similarly, the hBN-cBN-Liquid triple point is shifted from 3500 K/9.5 GPa to as low as 2800 K and atmospheric pressure. It is shown that nanosecond laser heating of amorphous carbon and nanocrystalline BN on sapphire, glass, and polymer substrates can be confined to melt in a super undercooled state. By quenching this super undercooled state, we have created a new state of carbon (Q-carbon) and BN (Q-BN) from which nanocrystals, microcrystals, nanoneedles, microneedles, and thin films are formed depending upon the nucleation and growth times allowed and the presence of growth template. The large-area epitaxial diamond and cBN films are formed, when appropriate planar matching or lattice matching template is provided for growth from super undercooled liquid. The Q-phases have unique atomic structure and bonding characteristics as determined by high-resolution SEM and backscatter diffraction, HRTEM, STEM-Z, EELS, and Raman spectroscopy, and exhibit new and improved mechanical hardness, electrical conductivity, and chemical and physical properties, including room-temperature ferromagnetism and enhanced field emission. The Q-carbon exhibits robust bulk ferromagnetism with estimated Curie temperature of about 500 K and saturation magnetization value of 20 emu g−1. We have also deposited diamond on cBN by using a novel pulsed laser evaporation of carbon and obtained cBN/diamond composites, where cBN acts as template for diamond growth. Both diamond and cBN grown from super undercooled liquid can be alloyed with both p- and n-type dopants. This process allows carbon to diamond and hBN to cBN conversions and formation of useful nanostructures and microstructures at ambient temperatures in air at atmospheric pressure on practical and heat-sensitive substrates in a controlled way without need for any catalysts and hydrogen to stabilize sp3 bonding for diamond and cBN phases.

Electrical and thermal transport properties of liquid Fe under high pressure have important implications for the dynamics and thermal evolution of planetary cores and the geodynamo. However, electrical resistivity (ρ) and thermal conductivity (k) of liquid Fe at high pressure still remain contentious properties. To date, only two experimental investigations of ρ of liquid Fe in the pressure region below 7 GPa are reported in literature. Here we report the results of measurements of ρ for solid and liquid Fe (inversely proportional to k through the Wiedemann-Franz law) at pressures from 3 to 12 GPa, using a large multi-anvil press. We show that ρ of liquid Fe decreases as a function of pressure up to the δ-γ-liquid triple point at ~5.2 GPa, and subsequently remains invariant from 6 to 12 GPa, which is consistent with an earlier study on liquid Ni. Our results demonstrate an important effect of solid phase on the structure and properties of liquid Fe. Our values of ρ for solid and liquid Fe are used to calculate k in Mercury’s solid inner core and along the adiabat in the liquid outer cores of Moon, Ganymede, Mercury and Mars. Our robust values of thermal conductivity place the focus on uncertainties in thermal expansion as the cause of variation in values of core conducted heat. Except for Mercury, our adiabatic heat flux values in these terrestrial cores validate the use of similar values used in several previous studies. Our high values of core adiabatic heat flux in Mercury would provide a stabilizing effect on, and lead to an increase in thickness of, the thermally stratified layer at the top of the core.

Recent international comparisons showed that there is still room for improvement in triple point of water (TPW) realization uncertainty. Large groups of cells manufactured, maintained and measured in similar conditions still show a spread in the realized TPW temperature that is larger than the best measurement uncertainties (25 µK). One cause is the time-dependent concentration of dissolved impurities in water. The origin of such impurities is the glass/quartz envelope dissolution during a cell lifetime. The effect is a difference in the triple point temperature proportional to the impurities concentration. In order to measure this temperature difference and to investigate the effect of different types of impurities, we manufactured doped cells with different concentrations of silicon (Si), boron (B), sodium (Na) and potassium (K), the glass main chemical components. To identify any influence of the filling process, two completely independent manufacturing procedures were followed in two different laboratories, both national metrology institutes (VSL, Netherlands and UME, Turkey). Cells glass and filling water were also different while the doping materials were identical. Measuring the temperature difference as a function of the liquid fraction is a method to obtain information about impurities concentrations in TPW. Only cells doped with 1 µmol·mol−1 B, Na and K proved to be suitable for measurements at different liquid fractions. We present here the results with related uncertainties and discuss the critical points in this experimental approach.

The dynamics of the processes proceeding upon explosion of condensed explosives in the air has been investigated. The paper discusses the physical model, the computing method, and the results of modeling a two-dimensional hydrodynamic fl ow initiated by the explosion of a spherical charge at some height above the ground surface. Explosions of charges at a height comparable to the size of the region occupied by the explosion products are considered. The results of calculations have made it possible to obtain a detailed space–time pattern of the initiated fl ow and investigate the incipient formation, propagation, interaction, and subsequent attenuation of shock waves. It has been shown that the distance to the surface can strongly influence the fl ow dynamics and parameters of shock waves.