Hart Equation Research Articles

Doublet doped titanate ferroelectric system for capacitors and NTC thermistor applications

A simple negative temperature coefficient (NTC) thermistor Ba0.85Sr0.15Ti0.85Zr0.15O3 system is elaborated using a conventional solid-state reaction route. The structural analysis confirms that the elaborated pseudo-cubic system, which is indexed in the P4mm space group, exhibits one single phase. The dielectric properties and the electrical resistivity data are investigated over a large temperature range from 413 K to 673 K. In this temperature interval, the Steinhart–Hart equations are employed to confirm that Ba0.85Sr0.15Ti0.85Zr0.15O3 is a promising system for sensor application. Accordingly, the thermistor constant (β=10154 K), the sensitivity factor (-5.5 %/K≤α≤-2 %/K), the activation energy (Ea=0.875 eV), and the stability factor (SF=2.27) parameters are calculated to approve that Ba0.85Sr0.15Ti0.85Zr0.15O3 exhibits an NTC-thermistor behavior. The temperature dependence of the electrical resistivity confirms that Ba0.85Sr0.15Ti0.85Zr0.15O3 reveals a semiconductor behavior. The dielectric investigation shows that Ba0.85Sr0.15Ti0.85Zr0.15O3 exhibits a motivating dielectric properties (elevated dielectric constant value (105<ε’<106) and low dielectric losses (mostly < 0.007) with almost frequency independence between 20 Hz to 500 kHz). The colossal dielectric response of Ba0.85Sr0.15Ti0.85Zr0.15O3 is attributed to the internal barrier layer capacitor (IBLC) and the surface barrier layer capacitor (SBLC) effects. Such response suggests the suitability of Ba0.85Sr0.15Ti0.85Zr0.15O3 ceramic for high temperature capacitor applications.

Algorithm Execution Time and Accuracy of NTC Thermistor-Based Temperature Measurements in Time-Critical Applications

This paper addresses the challenges of selecting a suitable method for negative temperature coefficient (NTC) thermistor-based temperature measurement in electronic devices. Although measurement accuracy is of great importance, the temperature calculation time represents an even greater challenge since it is inherently constrained by the control algorithm executed in the microcontroller (MCU). Firstly, a simple signal conditioning circuit with the NTC thermistor is introduced, resulting in a temperature-dependent voltage UT being connected to the MCU’s analog input. Next, a simulation-based approximation of the actual temperature vs. voltage curve is derived, resulting in four temperature notations: for a look-up table principle, polynomial approximation, B equation and Steinhart–Hart equation. Within the simulation results, the expected temperature error of individual methods is calculated, whereas in the experimental part, performed on a DC/DC converter prototype, required prework and available MCU resources are evaluated. In terms of expected accuracy, the look-up table and the Steinhart–Hart equation offer superior results over the polynomial approximation and B equation, especially in the nominal temperature range of the NTC thermistor. However, in terms of required prework, the look-up table is inferior compared to the Steinhart–Hart equation, despite the latter having far more complex mathematical functions, affecting the overall MCU algorithm execution time significantly.

Intra‐specific competition affects the density tolerance and grain yield of maize hybrids

AbstractIncreasing plant density usually increases the intra‐specific competition of maize plants. This study was conducted to determine whether maize (Zea mays L.) hybrid density tolerance is related to intra‐specific competition. Field experiments were conducted using a split‐plot design, the main plots contained four maize hybrids, and subplots were 12 plant densities varied from 1.5 to 18 × 104 plants ha−1. This study focused on dry matter accumulation, grain yield (GY), competition intensity (CI), and absolute severity of competition (ASC) based on the above treatments. Among all tested hybrids, GY exhibited a curvilinear response to plant density, which was well characterized by the Steinhart–Hart equation. Maize hybrids differed in optimum GY in descending order as follows: Zhongdan909 (ZD909) &gt; Xianyu335 (XY335) = Yedan13 (YD13) &gt; Zhongdan2 (ZD2). The CI and ASC of tested maize hybrids indicated that intra‐specific competition increased with increasing plant density. In most cases, the CI and ASC of older maize hybrids were higher than those of modern maize hybrids when plant density exceeded 9.0 × 104 plants ha−1. The results showed that the slope of the linear regression of ASC and plant density (i.e., the k‐value) could be used to compare the intra‐specific CI of maize hybrids, and there were significant negative correlations of k‐value with optimum plant density and GY. Intra‐specific competition is negatively correlated with the density tolerance of maize hybrids. This relationship may provide new insights for determining future maize breeding targets.

Wettability, Diffusion Behaviors, and Modeling of Ni Nanoparticles and Nanowires in Brazing Inconel 718

Ni nanoparticles (NPs) and nanowires (NWs) are compared as brazing filler metals for joining Inconel 718. NWs significantly enhance the strength of brazed joints compared to NP joints (270 MPa). Herein, joints formed with a pure NW pellet and a NW–NP mixed pellet yield average lap shear bonding strengths of 319.2 and 370 MPa, respectively. The experiment displays that the contact angle in brazing with NPs is higher than that with NWs. A modified Hart's equation is also proposed for predicting the effective interdiffusion coefficients of nanomaterials that account for surface diffusion in addition to lattice and grain boundary diffusion. The diffusion coefficients calculated by the modified Hart's equation are consistent with the values determined by Sauer–Friese analysis for NPs, but for NWs, the diffusion coefficients determined by Sauer–Friese are mainly controlled by grain boundary diffusion, significantly higher than those predicted by the modified Hart's equation due to size‐dependent transient liquid phase diffusion. This explains the enhanced brazing strength with NW fillers.

Negative Temperature Coefficient Resistance of CaTiO3 for Thermistor Application

Present research presents CaTiO3 as an important negative temperature coefficient resistance (NTCR) thermistor material. Two routes were adopted such as solid state reaction and high energy ball milling (HEBM) for comparative analysis. X-ray diffraction (XRD), and Steinhart–Hart equation used for characterization of material formation and thermistor property. XRD pattern shows single phase orthorhombic symmetry or both samples. Electrical resistance found by LCR meter shows about NTCR behaviour and Steinhart–Hart model provides information for its suitability towards thermistor industry. To know the faster response nature time domain analysis performed on both samples. To the best knowledge, there are not much data available on properties of CaTiO3 as thermistor based temperature sensor material, which lead this research work. Enhanced sensing behaviour observed in CaTiO3 processed through HEBM. Both the samples signifies their strong potential in thermistor industry with sensitivity in the range of 4000–6700 K with exponential electrical resistance change in the specified temperature range.

Development of a Stable High-Temperature Diamond Thermistor Using Enhanced Supporting Designs

Diamond is an excellent material for a high-temperature thermistor given its superior material properties. Despite its long history of the development, diamond thermistor is not widely used for commercial sensors because it is difficult to maintain optimum conditions for the diamond thermistor to operate at high temperature ranges in a compact size. In this paper, we demonstrate methods to improve the practicality and the feasibility of the diamond thermistor, focusing on the supporting components. The diamond thermistor design, where the diamond is sandwiched between contact pads, is tested up to 700 °C and being characterized by the Steinhart–Hart equations. For temperatures higher than 700 °C, the design of the thermistor is improved by encasing it in a metal sheath tube that protects and seals the diamond thermistor. Our supporting components provide oxygen free environment and a sturdy structure for the sensor components in a compact size. The encased diamond thermistor operates up to 880 °C and shows stable performance in a cycling test between 880 °C and the room temperature. An additional long-term stability test is performed at various temperatures for 10-hour durations. The tests show that the metal sheath tube design enables the diamond thermistor to be used as a practical temperature sensor at high-temperature ranges.

Detecting Variable Resistance by Fluorescence Intensity Ratio Technology.

We report a new method for detecting variable resistance during short time intervals by using an optical method. A novel variable-resistance sensor composed of up-conversion nanoparticles (NaYF4:Yb3+,Er3+) and reduced graphene oxide (RGO) is designed based on characteristics of a negative temperature coefficient (NTC) resistive element. The fluorescence intensity ratio (FIR) technology based on green and red emissions is used to detect variable resistance. Combining the Boltzmann distributing law with Steinhart–Hart equation, the FIR and relative sensitivity SR as a function of resistance can be defined. The maximum value of SR is 1.039 × 10−3/Ω. This work reports a new method for measuring variable resistance based on the experimental data from fluorescence spectrum.

Automated complex for thermistors calibration and measurement of their parameters

The article describes in details a principle and operating modes of automated measuring system based on the Arduino platform, designed to study the temperature dependence of thermistors electrical resistance and to determine their parameters: the temperature coefficient of resistance in the temperature range T = (265 – 355) K and the time constant characterizing thermal inertness of the thermistor. Some testing results of the developed complex were presented and, using the Levenberg – Marquardt algorithm, the thermistor was calibrated – coefficients entering Steinhart – Hart equation were calculated.

Advances in Sea Surface Layer Temperature Measurements with Fast Responding Thermistor Arrays on Drifting Buoys

A precise and accurate ocean temperature measurement system is essential for better understanding and knowledge of the spatial and temporal variability of thermal stratification of the upper-ocean layers is fundamental. The National Institute of Ocean Technology, Chennai has indigenously developed a novel negative temperature coefficient (NTC) thermistor based sensor array with RS232 digital output for drifting buoy (Pradyu) (DB) wherein, it is mainly used in ocean observation applications. The DB is built with Indian satellite (INSAT) for real time data telemetry. The NTC sensing element is used in developing the temperature sensor for the measurement of sea surface layer temperature. The Steinhart–Hart equation and coefficients are applied on each sampling to zero down the error components involved in temperature measurements which corresponds to the nonlinear functionality of the NTC element. In-house developed SST sensor and sensor array are calibrated and extensively tested in laboratory conditions. The results of the SST and sensor array laboratory calibrations and field validations are briefly presented here with significant data sets collected in the Bay of Bengal warm pool regions.

FPGA Implementation of Steinhart–Hart Equation for Accurate Thermistor Linearization

This paper presents fixed point operation-based Field Programmable Gate Arrays (FPGA) implementation of Steinhart–Hart Equation (SHHE) for thermistor linearization. FPGA implementation issues of SHHE are presented and their solutions are proposed and experimentally validated in a LabVIEWTM environment. Experimental temperature calibration, performed using a M/S Fluke drywell calibrator, revealed a lowest nonlinearity of 0.11% for an industrial grade thermistor in the input temperature range from −20 °C to 120 °C. Therefore, the main contribution of this work is to demonstrate the lowest nonlinearity for a wider temperature range. This work is expected to be very useful to instrumentation engineers as it employs a time-tested technique, for thermistor linearization in FPGA, leading to the lowest nonlinearity for a larger input temperature range.

Design of the ROV Dedicated Seafloor Heat Flow Probe

As the exploration of the natural gas hydrate is developed towards the target drilling phase, the traditional EWING-type and LISTER-type heat flow probe is unable to meet the needs of fine detection of the seafloor heat flow in the target area of the nature gas hydrate. The ROV (Remotely Operated Vehicle) dedicated seafloor heat flow probe is designed based on the status and operating characteristics of ROV which has been already adopted in China, which is suitable for measuring the large-scale and high-density seafloor in-situ heat flow, analyzing and understanding the fine thermal structure and thermal state of the special geological structure, and focusing on solving seafloor heat flow measurements in local structure. In the ROV dedicated seafloor heat flow probe, a high-precision NTC thermistor is adopted as the sensor, and ADUC845 chip with an internal integration of 24-bit high-resolution A/D converter is selected as the main processor. Furthermore, the ROV (Remotely Operated Vehicle) dedicated seafloor heat flow probe can measure the resistance values of the thermistors in five channels through the measurement mode of DC unbalanced bridge in a way of time sharing, and use STEINHART &amp; HART equation to conduct R-T conversion, thus obtaining a more accurate geothermal gradient curve of the seafloor sediments after correction by the seven-point three-phase data conversion method, of which the measurement accuracy is 0.005℃ and the resolution ratio reaches 0.001℃. And it can also obtain the valuable raw data of the heat flow with the sea trial of the “SeaLion ROV” of Chinese scientific investigation vessel “Ocean VI” and the “Jiaolong HOV (Human-Occupied Vehicles)” of “Xiangyanghong XVI” vessel.

Effect of dynamic recrystallization at tool-chip interface on accelerating tool wear during high-speed cutting of AISI1045 steel

Acceleration of tool crater wear in high-speed cutting is usually attributed to the high tool–chip interface temperature increasing diffusion coefficient(DEff), where the role of microstructure is ignored. The main purpose of this paper is to study the influence of microstructure evolution at second shear zone on tool element diffusion ability and crater wear with increasing cutting speed, which establishes the base for the research of tool wear evolution forecast. Based on the Orthogonal turning experiment of AISI1045 steel, the effect of cutting speed(V) on crater wear and microstructure of second shear zone was notable: (1) the crater wear increased drastically at 361mmin−1<V< 560mmin−1, in which the change to lower or higher cutting speed was relatively flat; (2)the images obtained by field-emission scanning electron microscopy showed dramatically microstructure evolution occurred at second shear zone, and extremely refined dynamic recrystallization grain, with 80nm to 300nm grain size, was formed as cutting speed increased. The very fine dynamic recrystallization grain significantly increased the fraction of high-diffusion channel (grain boundary area), and thus the diffusion coefficient was enhanced. Based on this idea, the impact of dynamic recrystallization grain, coupled with tool–chip interface temperature calculated by Oxley model, on diffusion coefficient was explored by Hart equation. The analysis has shown that the influence of dynamic recrystallization grain on tool crater wear was significant by increasing DEff.

Calibration and self-validation of thermistors for high-precision temperature measurements

In this paper we discuss influencing variables affecting the uncertainty of high-precision temperature measurements (u<1mK) by means of NTC thermistors. These are proper instrument settings, a suitable choice (distribution) of calibration temperatures in due consideration of uncertainties, self heating and the number of parameters in the calibration equation. Within this work we used 4 wire measurements to eliminate the influence of lead resistances, switched dc current to reduce errors by thermoelectric effects and amplifier offsets, a reference resistor with a nominal value close to the thermometer resistance to maximize the resolution and a maximum current consistent with the input voltage range and self heating of the thermistor.We present results of high-precision calibrations of a so called super-stable thermistor and demonstrate the influence of changes of the calibration equation on the interpolation error. Our results confirm previous findings that the number of parameters in the interpolation equation can have a considerable influence on the interpolation error. It was confirmed that the Steinhart–Hart equation shows a poor performance and should be replaced by the more suitable models recommended in White et al. (2014). For the quantification of the long term stability of a calibration we recommend repeated single-point validations at the triple-point of water. If these are supplemented by measurements at the gallium fixed-point possible changes of the curvature of the characteristics can be detected.

Efficient Calibration Tool for Thermistor Temperature Measurements

We propose a tool to calibrate the coefficient variables of the Steinhart–Hart equation, which are used in temperature measurement with a negative temperature coefficient thermistor. The previous method modifies the coefficient variables manually, but the proposed tool takes a measured temperature and automatically modifies the coefficient variable. The proposed calibration tool provides a graphical user interface program for the convenience of users. It is applied to the 4-point temperature measurement of polymerase chain reaction and has a degree of precision of ±0.1 °C in the temperature measurement evaluation

Analytical and numerical prediction of harmonic sound power in the inlet of aero-engines with emphasis on transonic rotation speeds

Tone noise radiated through the inlet of a turbofan is mainly due to rotor-stator interactions at subsonic regimes (approach flight), and to the shock waves attached to each blade at supersonic helical tip speeds (takeoff). The axial compressor of a helicopter turboshaft engine is transonic as well and can be studied like turbofans at takeoff. The objective of the paper is to predict the sound power at the inlet radiating into the free field, with a focus on transonic conditions because sound levels are much higher. Direct numerical computation of tone acoustic power is based on a RANS (Reynolds averaged Navier–Stokes) solver followed by an integration of acoustic intensity over specified inlet cross-sections, derived from Cantrell and Hart equations (valid in irrotational flows). In transonic regimes, sound power decreases along the intake because of nonlinear propagation, which must be discriminated from numerical dissipation. This is one of the reasons why an analytical approach is also suggested. It is based on three steps: (i) appraisal of the initial pressure jump of the shock waves; (ii) 2D nonlinear propagation model of Morfey and Fisher; (iii) calculation of the sound power of the 3D ducted acoustic field. In this model, all the blades are assumed to be identical such that only the blade passing frequency and its harmonics are predicted (like in the present numerical simulations). However, transfer from blade passing frequency to multiple pure tones can be evaluated in a fourth step through a statistical analysis of irregularities between blades. Interest of the analytical method is to provide a good estimate of nonlinear acoustic propagation in the upstream duct while being easy and fast to compute. The various methods are applied to two turbofan models, respectively in approach (subsonic) and takeoff (transonic) conditions, and to a Turbomeca turboshaft engine (transonic case). The analytical method in transonic appears to be quite reliable by comparison with the numerical solution and with available experimental data.

Temperature sensing behavior of poly(3,4-ethylenedioxythiophene) thin film

Temperature sensing behavior of poly(3,4-ethylenedioxythiophene) (PEDOT) thin film was investigated at the temperature range of −20°C to 60°C. PEDOT thin films were fabricated by in situ polymerization, where 3,4-ethylenedioxythiophene (EDOT) and ferric p-toluene sulfonate (FTS) were used as a monomer and an oxidant, respectively. The monomer and the oxidant solutions in 1-butanol were prepared separately and mixed just before in situ polymerization. The mixed solution was cast on a substrate and polymerization was carried out at 70°C for 30min, followed by washing with methanol and drying under vacuum.Resistance change of PEDOT film with temperature was monitored using two probe method. It was observed that resistance of PEDOT film monotonically decreased with increasing temperature, confirming a typical temperature dependence of the electrical resistance of semiconductors with negative temperature coefficient (NTC). However, resistance of PEDOT thin film was not stable with repeated heating and cooling. Resistance at the same temperature increased with repeated heating and cooling cycles. We found that stability of PEDOT thin film could be significantly improved by heat treatment of PEDOT film at 150°C for 1h and sealing the PEDOT thin film. Temperature-dependent resistance of the stabilized PEDOT thin film could be fitted to the Steinhart–Hart equation from −20°C to 60°C range even after repeated cycles, suggesting its potential application as a flexible thin film thermistor.

Atomistic understanding of diffusion kinetics in nanocrystals from molecular dynamics simulations

Understanding the grain size effect on diffusion in nanocrystals has been hampered by the difficulty of measuring diffusion directly in experiments. Here large-scale atomistic modeling is applied to understand the diffusion kinetics in nanocrystals. Enhanced short-circuit diffusivity is revealed to be controlled by the rule of mixtures for grain-boundary diffusion and lattice diffusion, which can be accurately described by the Maxwell-Garnett equation instead of the commonly thought Hart equation, and the thermodynamics of pure grain-boundary self-diffusion is not remarkably affected by varying grain size. Experimentally comparable Arrhenius parameters with atomic detail validate our results. We also propose a free-volume diffusion mechanism considering negative activation entropy and small activation volume. These help provide a fundamental understanding of how the activation parameters depend on size and the structure-property relationship of nanostructured materials from a physical viewpoint.

Evaluation of resistance–temperature calibration equations for NTC thermistors

The characteristics of thermistors for temperature measurement are the high sensitivity to yield a high resolution and the high accuracy in the narrow temperature range. This performance of this sensing element is affected by its calibration equation. Seven calibration equations were selected to evaluate the fitting agreement of the resistance–temperature data of four types of thermistors in this study. The parameters of these calibration equations are estimated using least squares method. The performance of these equations was compared with several statistics. The results of this study indicated that the basic equation and Steinhart and Hart equations were not the adequate calibration equation for four table data of thermistor. The Hoge-3 equation, 1 / T = A 0 + A 1 ℓ nR T + A 2 ( ℓ nR T ) 2 + A 3 ( ℓ nR T ) 3 + A 4 ( ℓ nR T ) 4 , was the best equation for seven calibration equations. The form of this equation was a 4 th -degree polynomial equation. It was easy to be incorporated into IC circuit to serve as a calculation equation to transform the measured resistance into the temperature value. The nonlinear least squares method and the criteria for comparison also could be applied to evaluate the fitting ability of calibration equations for other thermistors.

Temperature measurements by means of NTC resistors and a two-parameter approximation curve

Table data for resistance-versus-temperature ( R– T) dependence of negative temperature coefficient resistors (NTCRs), which have resistance R N = 10,000 Ω at a temperature of 25 °C and limits of error ±0.2 °C in the range from 0 °C to 70 °C [Fenwal Electronics Catalog: Thermistoren UNI Kurve; Typ: UUA41J1, UUA41J8 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C); BetaTHERM Sensors, http://www.betatherm.com; BetaCURVE Thermistor Series III 10K3A1W2 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C), http://www.betatherm.com/datasheets/datasheet.php?p_id=69#; Advanced Thermal Products, http://www.atpsensor.com/; coated chip thermistor A1004-C3 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C), http://www.atpsensor.com/ntc/ntc_rvt_pdfs/rvt_pdf.html; Epcos, http://www.epcos.com; uni-curve NTC thermistor S 863/10k/F40 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C), http://www.epcos.com/inf/50/db/ntc_02/00920093.pdf], are analysed. Determination of two approximation curves is described: a three-parameter one (abbreviated AC1) and a two-parameter one (AC2). These curves are compared with the three-parameter Steinhart–Hart equation (S&H) by using the table data of resistance for different NTCRs and calculating the following for all of them: unknown parameters by the least-squares method, approximated temperature using determined parameters, and the difference from the table data of temperature. The obtained results are presented, showing a very good agreement of curves, with their mutual differences within a few millikelvins, and the differences from the table data mostly within ±10 mK for the range from 0 °C to 70 °C (differences are larger only at a few points). Therefore, the presented two-parameter approximation curve AC2 can be very conveniently used with some NTCRs for the calculation of unknown temperature from the measured resistance.

Expressions for the effective diffusivity in materials with interphase boundaries

AbstractWe address the problem of calculating the long-time-limit effective diffusivity in stable two- phase polycrystalline material. A phenomenological model is used where the high diffusivity interphase boundaries are treated as connected “coatings” of the individual grains. Derivation of expressions for the effective diffusivity with segregation is made along Maxwell lines. Monte Carlo simulation using lattice-based random walks is used to test the validity of the expressions. It is shown that for the case analysed the derived expressions for the effective diffusivity are in very good agreement with simulation results. The equivalent of the Hart equation is also derived. It is shown to be in poor agreement with simulation results.