Nonlinear Temperature Dependence Research Articles

Viscosity, Density, Surface Tension, and Crystallization Behavior of Commercial Mold Fluxes

This study investigates the viscosity, density, surface tension, and crystallization behavior of two commercial mold fluxes that are utilized to cast ultralow‐carbon, low‐carbon, and medium‐carbon steel grades, as well as electric steels (high‐B magnetic and grain‐oriented steels). Experiments are performed in the temperature range of 1073–1673 K using the rotating bob method, maximum bubble pressure method, buoyancy method, and single hot thermocouple technique. The phase structure is investigated via scanning electron microscopy and X‐ray powder diffraction. The results indicate that viscosity and density exhibit nonlinear temperature dependence. Increased basicity (CaO/SiO2) results in reduced viscosity and elevates the break temperature of the mold fluxes. Furthermore, the incubation time required for phase formation decreases with increasing basicity. Finally, time–temperature transformation and continuous cooling transformation diagrams are constructed.

Defect induced Raman shifts and bandgap engineering in layered SnSe2+δ bulks

In the context of the extensive application prospect of two-dimensional (2D) chalcogenides, we synthesized layered SnSe2+δ bulks with defects employing a hybrid chemical vapor transport-melt approach. Both the Eg and A1g Raman characteristic peaks in SnSe2+δ are dominated by cubic anharmonicity, coupled with nonlinear temperature dependencies below 140 K. Notably, the reduction in phonon energy observed in these vibrational modes can be ascribed to defect-mediated Raman scattering, irrespective of deficient or excess Se defects. However, the lower consistency in the Raman shifts of the in-plane Eg vibrations compared to the out-of-plane A1g modes suggests that the defects predominantly entail the absence of Se atoms and the substitutions of Sn by Se, delineating a continuum of Se-deficient and Se-enriched compositions. Furthermore, Se defects induce the contraction of the indirect bandgaps, facilitating a transition from medium to narrow bandgap semiconductors in SnSe2+δ, which underscores the tunable nature of the bandgaps through the incorporation of Se defects. These discoveries present an avenue for bandgap engineering and foster a deeper comprehension of the phonon and thermal properties of layered chalcogenides for further advanced technologies.

A two-phase nonlinear optimization method for routing and sizing district heating systems

This paper presents a method to find the optimal topology, pipe sizing, and operational parameters of a district heating system under consideration of one design point. The current high costs of district heating systems set limits regarding the minimum heat demand density required for economic network expansions. Optimized routing with ideal pipe sizing and optimal operating parameters offers a potential for cost reduction. Therefore, this paper introduces a new two-phase method for district heating network expansion planning. This method consists of consecutive optimizations, starting with a mixed-integer linear programming followed by a nonlinear optimization. During the mixed-integer linear programming, the district heating system is optimized with continuous diameters, and the nonlinear pressure and temperature dependencies must be linearized. The resulting topology and the continuous diameters are afterward handed over to a nonlinear sparse sequential quadratic programming. The continuous diameters are discretized using a numerical continuation strategy that gradually forces the continuous diameter variables into discrete diameter choices. As a proof of concept, the district heating system for a small town with 400 consumers is optimized and analyzed. The two-phase optimization is performed in 251.68sec, and in most cases, discrete or near discrete diameters are achieved in a nonlinear continuous optimization.

Influence of Lifshitz Transition on the Intrinsic Resistivity of Cu2N Monolayer.

The Lifshitz transition (LT), a topological structure transition of Fermi surfaces, can induce various intricate physical properties in metallic materials. In this study, through first-principles calculations, we explore the nontrivial effect of the LT on the intrinsic resistivity of the Cu2N monolayer arising from electron-phonon (el-ph) scattering. We find that when the LT is induced by electron doping, the multibranch Fermi surface simplifies into a single-band profile. Such an LT leads to a decoupling of low-frequency flexural phonons from el-ph scattering due to mirror symmetry. Consequently, the resistivity of the Cu2N monolayer at room temperature significantly decreases, approaching that of slightly doped graphene, and highlighting the Cu2N monolayer as a highly conductive two-dimensional metal. Moreover, this LT can bring about a nonlinear temperature dependence of the intrinsic resistivity at a high temperature.

Structural Coarse-Graining via Multiobjective Optimization with Differentiable Simulation.

In the realm of multiscale molecular simulations, structure-based coarse-graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems, such as polymers. This involves optimizing CG interactions by matching static correlation functions of the corresponding degrees of freedom in all-atom (AA) models. Here, we present a versatile method, namely, differentiable coarse-graining (DiffCG), which combines multiobjective optimization and differentiable simulation. The DiffCG approach is capable of constructing robust CG models by iteratively optimizing the effective potentials to simultaneously match multiple target properties. We demonstrate our approach by concurrently optimizing bonded and nonbonded potentials of a CG model of polystyrene (PS) melts. The resulting CG-PS model effectively reproduces both the structural characteristics, such as the equilibrium probability distribution of microscopic degrees of freedom and the thermodynamic pressure of the AA counterpart. More importantly, leveraging the multiobjective optimization capability, we develop a precise and efficient CG model for PS melts that is transferable across a wide range of temperatures, i.e., from 400 to 600 K. It is achieved via optimizing a pairwise potential with nonlinear temperature dependence in the CG model to simultaneously match target data from AA-MD simulations at multiple thermodynamic states. The temperature transferable CG-PS model demonstrates its ability to accurately predict the radial distribution functions and density at different temperatures, including those that are not included in the target thermodynamic states. Our work opens up a promising route for developing accurate and transferable CG models of complex soft-matter systems through multiobjective optimization with differentiable simulation.

A Sub-1-V Nanopower MOS-Only Voltage Reference

A novel low-power MOS-only voltage reference is presented. The Enz–Krummenacher–Vittoz (EKV) model is adopted to provide a new perspective on the operating principle. The normalized charge density, introduced as a new variable, serves as an indicator when trimming the output temperature coefficient. The proposed voltage reference consists of a specific current generator and a 5-bit trimmable load. Thanks to the good match between the current source stage and the output stage, the nonlinear temperature dependence of carrier mobility is automatically canceled out. The circuit is designed using 55 nm COMS technology. The operating temperature ranges from −40 °C to 120 °C. The average temperature coefficient of the output voltage can be reduced to 21.7 ppm/°C by trimming. The power consumption is only 23.2 nW with a supply voltage of 0.8 V. The line sensitivity and the power supply rejection ratio at 100 Hz are 0.011 %/V and −89 dB, respectively.

Flow instability in high-Prandtl-number liquid bridges with fully temperature-dependent thermophysical properties

The axisymmetric steady two-phase flow of a differentially heated thermocapillary liquid bridge in air and its linear stability is investigated numerically, taking into account dynamic interfacial deformations in the basic flow. Since most experiments require a high temperature difference to drive the flow into the three-dimensional regime, the temperature dependence of the material properties must be taken into account. Three different models are investigated for a high-Prandtl-number thermocapillary liquid bridge with nominal Prandtl number ${\textit {Pr}}=28.8$ : the Oberbeck–Boussinesq (OB) approximation, a linear temperature dependence of all material properties and a full nonlinear temperature dependence of all material properties. For all models, critical Reynolds numbers are computed as functions of the volume of the liquid bridge, its aspect ratio, its dimensional size and as a function of the strength of a forced axial flow in the ambient air. Under most circumstances the OB approximation overpredicts and the linear model underpredicts the critical Reynolds number, compared with the model based on the full temperature dependence of the material properties. Among the main influence factors are the proper selection of the reference temperature and, at larger temperature differences, the temperature dependence of the viscosity of the liquid.

A new transient hot-wire thermal conductivity apparatus and measurements of helium at temperatures from 20 K to 300 K

In this study, an apparatus based on the transient hot-wire method (THW) was designed to measure the thermal conductivity of cryogenic fluid within the temperature range of 20–300 K and the pressure range of 0–20 MPa, with a relative expanded uncertainty Ur(λ) of 0.0284 (k = 2, 95 %). The experimental data of methane, ethane, and carbon dioxide showed good consistency with the ECS model, validating the reliability of the apparatus. In addition to the linear temperature dependence of hot-wire resistance above 70 K, the nonlinear temperature dependence below 70 K is calibrated, and the feasibility of the THW method for measurements in the temperature range of 20–70 K is validated. Subsequently, the thermal conductivity data for helium are presented from 20 to 300 K. The temperature rises of hot-wire during the measurement agreed well with the simulation calculation results. Furthermore, a thermal conductivity model for helium gas up to 600 K was developed. The presented data in this work, as well as previously published data, demonstrated good agreement with the model calculation results, with an average absolute relative deviation (AARD) of 1.46 %.

A nonlinear kinetic rate model for unifying fatigue crack growth rates of nickel-based superalloys at room and elevated temperatures

This study presents a nonlinear kinetic rate model to describe the temperature-dependence of fatigue crack growth rate (FCGR) of nickel-based superalloys across a wide range (20 to 650 °C). FCGR testing was performed using compact tension specimens of GH4742 superalloy. Metallography analysis on crack growth paths of two tested specimens suggests there is a local resistance to pure model I cracking at 20 °C, which can greatly be weakened at 650 °C. Compared to the classical Arrhenius equation, the proposed model captures the nonlinear temperature-dependence, and yields more accurate results by reducing the scatter factor from 5 to 3.

Non-linear temperature dependences of pseudoelastic stress and stress hysteresis of a nanocrystalline Ni47Ti50Fe3 alloy

This paper reports a study on non-linear temperature dependences of the critical pseudoelastic stress and stress hysteresis for stress-induced martensitic transformation deformation of a nanocrystallined Ni47Ti50Fe3 alloy. Such non-linear temperature dependences were found over a wide low temperature range from -196 °C to 20 °C and they defy the predictions of the Clausius-Clapeyron law for the transformation. The pseudoelastic behaviour exhibited two unusual characteristics, including a progressively decreasing dσ/dT slope and a rapidly widening stress hysteresis with decreasing the temperature. In-situ X-ray diffraction analysis indicated that the starting microstructure of the alloy for pseudoelastic deformation was a mixture of the B2 and a crystallographically suppressed R phase (denoted R*) within -8 °C to -196 °C. The volume fraction, the rhombohedral lattice distortion and the internal atomic shuffle of the suppressed R phase increased upon cooling. These continued evolutions of the crystal structure of the R* phase and the microstructure of the alloy upon cooling are ascribed to be responsible for the abnormal non-linear temperature dependences of the pseudoelastic stresses and the widening of the stress hysteresis.

Low-temperature electrical transport in the normal-state of overdoped cuprate superconductors

The low-temperature electrical transport in the normal-state of overdoped cuprate superconductors is investigated based on the t-J model. The momentum relaxation due to the umklapp scattering between electrons by the exchange of the effective spin propagator is employed to evaluate the electrical resistivity within the framework of the Boltzmann transport theory. It is shown that the quadratic temperature dependence of the resistivity develops in the far-lower-temperature region, and is followed by a nonlinear temperature dependence of the resistivity in an extremely-narrow-crossover region and a linear temperature dependence of the resistivity in the low-temperature region. The obtained results also show that the same spin excitation governs both superconductivity and the electron umklapp scattering responsible for the low-temperature linear in temperature resistivity in the overdoped regime.

A thermodynamic analysis of CLC transporter dimerization in lipid bilayers

The CLC-ec1 chloride/proton antiporter is a membrane-embedded homodimer with subunits that can dissociate and associate, but the thermodynamic driving forces favor the assembled dimer at biological densities. Yet, the physical reasons for this stability are confounding as dimerization occurs via the burial of hydrophobic interfaces away from the lipid solvent. For binding of nonpolar surfaces in aqueous solution, the driving force is often attributed to the hydrophobic effect, but this should not apply in the membrane since there is very little water. To investigate this further, we quantified the thermodynamic changes associated with CLC dimerization in membranes by carrying out a van 't Hoff analysis of the temperature dependency of the free energy of dimerization, ΔG°. To ensure that the reaction reached equilibrium at different temperatures, we utilized a Förster resonance energy transfer assay to report on relaxation kinetics of subunit exchange as a function of temperature. Equilibration times were then applied to measure CLC-ec1 dimerization isotherms at different temperatures using the single-molecule subunit-capture photobleaching analysis approach. The results demonstrate that the dimerization free energy of CLC in Escherichia coli-like membranes exhibits a nonlinear temperature dependency corresponding to a large, negative change in heat capacity, a signature of solvent ordering effects such as the hydrophobic effect. Consolidating this with our previous molecular analyses suggests that the nonbilayer defect required to solvate the monomeric state is one source of the observed change in heat capacity and indicates the existence of a generalizable driving force for protein association in membranes.

Theory of localization-hindered thermalization in nonlinear multimode photonics

Our society’s appetite for ultra-high bandwidth communication networks and high-power optical sources, together with recent breakthroughs in mode multiplexing/demultiplexing schemes, forced the photonics community to reconsider the deployment of nonlinear multimode systems. These developments pose fundamental challenges stemming from the complexity of nonlinear mode-mode mixing by which they exchange energy in the process towards an equilibrium Rayleigh-Jeans (RJ) distribution. Here we develop a universal one-parameter scaling theory for the relaxation rates of out-of-equilibrium excitations towards their RJ thermal state. The theory predicts an exponential suppression of the rates with increasing disorder due to the formation of stable localization clusters resisting the nonlinear mode-mode interactions that tend to separate them. For low optical temperatures, the rates experience a crossover from linear to nonlinear temperature dependence which reflects a disorder-induced reorganization of the low frequency eigenmodes. Our theory will guide the design of nonlinear multimode photonic networks with tailored relaxation-scales.

Young’s Modulus-Independent Determination of Fibre Parameters for Rayleigh-Based Optical Frequency Domain Reflectometry from Cryogenic Temperatures up to 353 K

The magnetic spectrometer AMS-100, which includes a superconducting coil, is designed to measure cosmic rays and detect cosmic antimatter in space. This extreme environment requires a suitable sensing solution to monitor critical changes in the structure such as the beginning of a quench in the superconducting coil. Rayleigh-scattering-based distributed optical fibre sensors (DOFS) fulfil the high requirements for these extreme conditions but require precise calibration of the temperature and strain coefficients of the optical fibre. Therefore, the fibre-dependent strain and temperature coefficients KT and Kϵ for the temperature range from 77 K to 353 K were investigated in this study. The fibre was integrated into an aluminium tensile test sample with well-calibrated strain gauges to determine the fibre’s Kϵ independently of its Young’s modulus. Simulations were used to validate that the strain caused by changes in temperature or mechanical conditions was the same in the optical fibre as in the aluminium test sample. The results indicated a linear temperature dependence of Kϵ and a non-linear temperature dependence of KT. With the parameters presented in this work, it was possible to accurately determine the strain or temperature of an aluminium structure over the entire temperature range from 77 K to 353 K using the DOFS.

Strong evidence of inter-layer optical phonons and low-temperature acoustic-phonon bunching in WS2/WSe2 hetero-structure

The nature of inter-layer optical phonons observed in the hetero-structure is being reported in this work. Additionally, phonon bunching between modes of both and can be ascertained in the acoustic region. The second-order bunching factor, , is seen to improve sharply upon reduction of temperature, below a critical temperature. Moreover, the integral intensity of the peaks increases almost exponentially with the applied power of the laser source. To a good approximation, the phonon frequency corresponding to most of the Raman active modes varies linearly with altered temperature (78–300 K). However, the mixed mode located at exhibits a non-linear temperature dependence over the working range of temperature. Prevailing phonon bunching aspects of the phonon replica discussed in terms of bunching factor, frequency correlation parameter, etc., are highlighted based on acquired low-temperature Raman data and theoretical analogy.

The effect of boron concentration on the electrical, morphological and optical properties of boron-doped nanocrystalline diamond sheets: Tuning the diamond-on-graphene vertical junction

In this paper, the effect of boron doping on the electrical, morphological and structural properties of free-standing nanocrystalline diamond sheets (thickness ~ 1 μm) was investigated. For this purpose, we used diamond films delaminated from a mirror-polished tantalum substrate following a microwave plasma-assisted chemical vapor deposition process, each grown with a different [B]/[C] ratio (up to 20,000 ppm) in the gas phase. The developed boron-doped diamond (BDD) films are a promising semiconducting material for sensing and high-power electronic devices due to band gap engineering and thermal management feasibility. The increased boron concentration in the gas phase induces a decrease in the average grain size, consequently resulting in lower surface roughness. The BDD sheets grown with [B]/[C] of 20,000 ppm reveal the metallic conductivity while the lower doped samples show p-type semiconductor character. The charge transport at room temperature is dominated by the thermally activated nearest-neighbor hopping between boron acceptors through impurity band conduction. At low temperatures (<300 K), the Arrhenius plot shows a non-linear temperature dependence of the logarithmic conductance pointing towards a crossover towards variable range hopping. The activation energy at high temperatures obtained for lowly-doped sheets is smaller than for nanocrystalline diamond bonded to silicon, while for highly-doped material it is similar. Developed sheets were utilized to fabricate two types of diamond-on-graphene heterojunctions, where boron doping is the key factor for tuning the shape of the current-voltage characteristics. The graphene heterojunction with the low boron concentration diamond sheet resembles a Schottky junction behavior, while an almost Ohmic contact response is recorded with the highly doped BDD sheet of metallic conductivity. The free-standing diamond sheets allow for integration with temperature-sensitive interfaces (i.e. 2D materials or polymers) and pave the way towards flexible electronics devices.

Size- and temperature-dependent Young’s modulus of individual ZnS nanobelts

The Young’s modulus of individual ZnS nanobelts with thicknesses ranging from 30 to 110 nm is measured by a mechanical resonance method over a temperature range of 300–650 K. Nanobelts with thicknesses above ∼80 nm exhibit a Young’s modulus very close to their corresponding bulk value of 88 GPa, whilst thinner nanobelts with thicknesses down to 30 nm exhibit a Young’s modulus of ∼70 GPa. Incrementally heating a nanobelt of 110 nm thickness over a temperature range of 300–650 K presents a linearly decreasing Young’s modulus. The nanobelt is thus found to possess a temperature coefficient of Young’s modulus of −125.4 ± 2.8 ppm K−1, which is comparable to their bulk value of −147 ppm K−1. The temperature coefficient of Young’s modulus for nanobelts with thicknesses below 100 nm demonstrates a strong size effect, and is found to dramatically decrease to as low as −201.4 ± 10.2 ppm K−1 for the thickness of 30 nm. A nonlinear temperature dependence of Young’s modulus is experimentally identified for nanobelt with diameters below 100 nm, and the linear-nonlinear transition temperature decreases with the decrease of nanobelt thickness.

High-precision calibration for strain and temperature sensitivities of Rayleigh-scattering-based DOFS at cryogenic temperatures

Under extreme conditions such as cryogenic temperatures, the application of optical fiber sensors inevitably encounters significant challenges, which include the calibrations associated with the thermal problems of sensor placement and heat sinking and the nonlinear dependence of cryogenic temperatures. Thus, fundamental investigations involving high-precision calibrations of the strain and temperature at cryogenic temperatures are essential. To this end, in this study, the thermo-optic coefficient, temperature and strain sensitivity coefficients for a Rayleigh-scattering-based distributed optical fiber sensor (DOFS) were calibrated. This experiment was implemented using a self-built low-temperature test device, and the calibration study was conducted over a large cryogenic temperature range, from 77 K to room temperature. The results indicated that the strain sensitivity coefficient of the Rayleigh-scattering-based DOFS is temperature-independent, whereas the temperature sensitivity coefficient has a significantly nonlinear temperature dependence and is associated with the coating polymer layers of the fiber. The coefficients and fitting functions were obtained over a large range of cryogenic temperatures, which indicated the invaluable properties of optical fibers in practice. Furthermore, the strain and temperature of an aluminum beam under thermal and bending loads were measured. The results indicated good agreement between the optical fibers and strain gauges, which verified the availability and reliability of Rayleigh-scattering-based distributed optical fibers in cryogenic environments.

Fast Analytical Approaches for the Transient Axial Temperature Distribution in Single Wire Cables

In various technical areas, the requirements and the complexity of electrically conductive structures (cables and printed circuit board traces) and their insulating materials are increasing, which leads to higher demands on reliability. Therefore, better diagnosis and control functions are needed. Intelligent fusing strategies with electronic fuses, where the current flow can be switched by semiconductors, can play an important role. One approach is to monitor the insulation temperature in order to detect thermal overloads and switch off a current branch before the insulation is damaged. As especially in cables, a direct temperature measurement is troublesome, most approaches are based on current measurements. From a measured current, the cable insulation temperature can be derived using an electrothermal model. Those models can be very complex, especially when the transient and axial heat flow in a cable should be considered. The computational efforts for the commonly used numerical solution methods are high. Analytical approaches potentially reduce these efforts significantly. In this article, a new analytical approach for the calculation of the transient axial temperature distribution along an insulated single wire cable, considering the nonlinear temperature dependence of the cable parameters, is presented. It enables a precise and fast calculation of cable temperatures, e.g., for automotive cable harnesses. There it can be beneficial for the control of electronic fuses where computing resources are low. The cable insulation can be operated closer to the limits and the overload protection can still be guaranteed.

Boundary-scattering induced Seebeck coefficient enhancement in thin films within relaxation time approximation

We investigate the Seebeck coefficient based on the Boltzmann transport equation of electrons within the relaxation time approximation. Using boundary conditions along the film thickness of a thermoelectric material, we observe the enhancement of Seebeck coefficient due to electrons elastically scattering on the boundaries when the film thickness is reduced, which agrees with experimental observations and theoretical predictions. Using this simple approximation, the Seebeck coefficient of thin films increases up to 16% in comparison to the bulk value. The main factor that affects the increase of the Seebeck coefficient comes from the chemical potential which controls carrier concentrations. We also analyze the linear and non-linear temperature dependence of the Seebeck coefficient at various chemical potentials based on an explicit expression for the Seebeck coefficient in the bulk limit.