Method For Measurement Of Diffusivity Research Articles

AMIDR: A Complete Pulse Method for Measuring Cathode Solid-State Diffusivity

Lithium transport within cathode material is driven by diffusion. While fast cathode diffusion is desired, solid-state diffusivity is one of the most difficult cell material properties to measure. However, it is an important property to understand as cathode capacity is often limited by poor diffusivity. GITT (Galvanostatic Intermittent Titration Technique) is a common diffusivity measurement method. This technique is accomplished by applying a series of constant current pulses to a cell and analyzing the voltage response. While easy to use, this method only measures near the surface of the active material by assuming that it takes the geometry of a semi-infinite plane. This approximation means that GITT is only accurate when measuring the very initial voltage response. However, the voltage response cannot be analyzed too early as this may amplify error produced by CDL (double layer capacitance) and RI (interface resistance) found at the cathode-electrolyte interface which GITT does not account for. EIS (Electrochemical Impedance Spectroscopy), an AC method, is better suited for distinguishing CDL/RI from diffusivity but also struggles to evaluate diffusivity beyond the surface of active material within a reasonable time frame1. In addition, instruments capable of quality EIS are often cost prohibitive compared to DC cell testers.The voltage responses after the first few moments of a pulse are relevant when evaluating cell behaviour in real-world applications and should be considered to produce comprehensive measurements of diffusivity and its performance impact. AMID (Atlung Method for Intercalant Diffusion) is a multi-rate pulse method produced by this lab which uses a series of pulses, both short/fast and long/slow, and an approximation-free analytical model (developed by Sven Atlung) for diffusion in a spherical particle, not a semi-infinite plane2. However, AMID cannot differentiate diffusion impedance from resistance and therefore requires that resistance be considered negligible. In addition, while AMID mathematics are free of approximations, the typical multi-rate pulse protocol does require that series of pulses be approximated as singular pulses3. Lastly, the multi-rate pulse protocol limits the state-of-charge resolution of diffusivity measurements.AMIDR (Atlung Method for Intercalant Diffusion and Resistance) incorporates a GITT-style single pulse protocol with AMID-style mathematics modified to account for resistance as shown in Figure 1b). AMIDR collects pulse data with a pseudo-logarithmic time distribution. This means that the same number of data points is collected in 0.1-1.0 seconds, 1.0-10 seconds, 10-100 seconds and so on. Unlike GITT which measures diffusivity at an early arbitrary point in a pulse, AMIDR considers the entire length of a pulse comprehensively. Fractional capacity is calculated for each datapoint by dividing the actual capacity with the ideal “impedance-free” capacity expected at that voltage as shown in Fig 1c). These fractional capacity values, normalized from 0-1, are fitted to the modified Atlung model. This modified Atlung model is nearly the same as the original Atlung model except an additional term is added for capacity limited by resistance. Unlike AMID, AMIDR measures both diffusivity and resistance simultaneously by using both as fitting parameters. Lastly, while CDL is usually small enough for RI to behave simply like ohmic resistance on relatively short time scales (>0.1 seconds), AMIDR has the option to account for CDL/RI when relevant such as near the bottom of a complete discharge.AMIDR is a new diffusivity measurement method tailored for cathode material in Li-ion batteries. By combining the advantages of various previous diffusivity methods, AMIDR eliminates many of their concerns and sources of error such as sampling of only the material surface, alternate confounding sources of impedance, and expensive equipment as seen in Figure 1a). When paired with proper cell design (i.e. ultra-low single layer cathode loading to remove pore impedance and reference electrodes to remove anode impedance), AMIDR can produce high resolution diffusivity measurements with improved accuracy and applicability to real-world cell performance.References C. Deng and W. Lu, Journal of Power Sources, 473, 228613 (2020).A. Liu et al., J. Electrochem. Soc., 168, 070503 (2021).M. Doyle, J. Newman, and J. Reimers, Journal of Power Sources, 52, 211–216 (1994). Figure 1. (a) Comparison of various Diffusivity measurements. (b) The modified Atlung model for diffusion in a spherical particle. (c) How pulse data is converted to the unitless Atlung model. Figure 1

Effect of the heat flow distribution and thermophysical properties of the pipe wall and fluid on the wall temperature response to a rising Taylor bubble

A novel non-intrusive thermal diffusion measurement (TDM) method has been proposed for measuring the phase flowrates of gas–liquid slug flows in our previous research. Since the structure of TDM was arbitrarily designed and needed to be optimized for accurate measurement, the effect of the heat flow distribution and the thermophysical properties of the pipe wall and fluid on the wall temperature response to a rising Taylor bubble (TB) is further investigated by using the CFD tool in this paper. The wall temperature and temperature rise are used to describe the wall temperature response, and their variation rules with heat flow distribution and the thermophysical properties of the pipe wall and fluid are presented and analyzed based on heat transfer. The simulation results indicate that the optimal heating length for a large wall temperature rise and small power consumption is 0.6D, and the optimal pipe material should be with small density and specific heat and a suitable thermal conductivity of about 15 W/(m·K). Moreover, the wall temperature response is obvious, especially for TBs moving in the liquid with large fluid thermal conductivity, density, and specific heat, and small viscosity. The paper can clarify the wall temperature response mechanism of the heated pipe wall and provide a theoretical basis for the development of the TDM method.

Local instantaneous heat transfer characteristics around a rising single Taylor bubble and the temperature response of relatively thick pipe wall under local constant heat flux

A novel non-intrusive thermal diffusion measurement (TDM) method is proposed to measure the flow rate of gas–liquid two-phase flows under the slug flow state in our previous research. To improve the measurement accuracy of TDM by clarifying the real-time correspondence between wall temperature change and Taylor bubble (TB) location, the local instantaneous heat transfer characteristics around a rising single TB and the corresponding temperature response of the pipe wall are further investigated in detail by using the CFD tool in this paper. During the passage of TB, the local heat transfer between the pipe wall and fluid was analyzed based on the dynamic velocity field and temperature boundary layer, and the temperature on the fluid–solid interface presents the opposite trend with the heat transfer coefficient. For the zone upstream of the heat flux center, the lag time and increase of the wall temperature become large and weak along the radial direction, respectively, whereas the lag time is independent of the axial location, TB velocity, and TB length. Meanwhile, the increase in wall temperature shows an upward trend with the TB length for short TBs but is the same for long TBs.

Lock-in photothermal method for in-plane thermal diffusivity measurements using arrayed temperature sensors on suspended SiNx membranes.

A device consisting of a line- or spiral-shaped temperature sensor array on a two-dimensional (2D) silicon nitride (SiNx) membrane of thickness 50 or 150nm is developed for use in the lock-in photothermal method to determine the in-plane thermal diffusivity of SiNx membranes in air and in vacuum. The results of 2D heat diffusion are analyzed by the quadrupole method, and the system is approximated to the one-dimensional (1D) fin standing in a surrounding media (the fin approximation). The results show that 2D thermal diffusion on the membrane is affected not only by heat exchange with the surrounding environment but also by parallel thermal diffusion caused by heat conduction in the air along the membrane surface. The measurement using photothermal heating and contact detection of the temperature response enables the phenomenon to be detected consistently at a wide frequency range of temperature waves (50-1000Hz). The measured thermal diffusivity values of the SiNx membrane are much smaller than those of bulk material, which can be reasonably considered an effect of the confined state of the phonon in the nanoscale geometry of the membrane.

How to Measure Solid State Lithium-ion Diffusion using the Atlung Method for Intercalant Diffusion

A systematic investigation of the factors that affect lithium diffusion coefficient measurements in the Atlung Method for Intercalant Diffusion (AMID) is carried out. Single crystal LiNi0.6Mn0.2Co0.2O2 is used for method development. The factors include electrode mass loading, separator thickness, electrolyte solvent choice and salt molarity, voltage interval sizes, open circuit relaxation time, C-rate choice, and charge vs discharge direction. In an ideal diffusivity measurement method, none of these factors listed should impact the true material diffusivity since it should be a purely material property. However, as we demonstrate here, all these experimental parameters should be selected carefully to minimize cell and electrode resistance contributions so that one can measure true lithium diffusivity in a material that is independent of current direction. We propose a low electrode loading cell design that is applicable for all diffusion measurement methods consisting of an ultrathin electrode coating (0.2 mAh cm−2), thin separator and 1.5 M LiPF6 ethylene carbonate: dimethyl carbonate 1:1 electrolyte. Additionally, we show diffusivity is not dependent on charge or discharge direction in NMC622, and we compare AMID results to Galvanostatic Intermittent Titration. Specific to AMID 15 min OCV time with 0.1 V intervals are suitable for this measurement.

Fast Fourier transform Ångström method for fast thermal measurements of microfibers.

The Ångström method is a promising thermal diffusivity measurement method for microfibers. Based on the heat-loss Ångström method and micro-Ångström method, the FFT (Fast Fourier Transform) Ångström method can be used to shorten the testing time and enhance the testing robustness of thermal conductivity. The FFT Ångström uses multi-frequency superimposed input signals and then uses the FFT for frequency division analysis. Since different frequencies are input at the same time, the measuring time is greatly reduced. Moreover, because different frequencies are input in the same environment, the random and environmental perturbations of the frequencies are the same, enhancing the fitting robustness. In contrast, the single feeding strategy is relatively time-consuming, and its measurement homogeneity for different frequencies cannot be guaranteed. By comparing the measurement results from a multi-frequency input and separated single-frequency input, the FFT shows good feasibility and robustness. It may also have great potential in other types of thermal wave measurements.

Method for dynamic measurement of thermal diffusivity during laser soldering of biological tissues

In this paper, we propose a method for dynamic measurement of the thermal diffusivity coefficient during laser soldering of biological tissues. The method is based on modelling the function of temperature dependence on time during cooling of biological tissue after exposure to laser radiation. The simulation is carried out by solving the heat equation for a homogeneous biological tissue and the absence of external heat sources. The desired value of the thermal diffusivity coefficient was determined by optimizing the residual functional of the temperature functions from time obtained experimentally and by solving the thermal diffusivity equation. Experiments were carried out to measure the thermal diffusivity coefficient by the proposed method for myocardial and skin tissues at maximum heating temperatures of 40, 50, 60 °C. The measured values of the thermal diffusivity coefficient for the myocardium are in the range from 2.3 to 2.7 m2/s*10-6, and for the skin from 1.5 to 1.7 m2/s*10-6.

Development for High Spatial Resolution Thermal Effusivity Measurement Method and High Functional Thermal Diffusivity Measurement Method

Development for High Spatial Resolution Thermal Effusivity Measurement Method and High Functional Thermal Diffusivity Measurement Method

Microscale heat-flux meter for low-dimensional thermal measurement and its application in heat-loss modified Angstrom method

A microscale heat-flux meter is designed based on micro-hotwire and infrared thermal microscopy. Its feasibility in low-dimensional thermal measurement is verified by its application in heat-loss modified Angstrom method for simultaneous measurement of thermal diffusivity, thermal conductivity and specific heat. The hotwire and the sample under test are placed in a vacuum chamber. Through an observation window, the infrared microscopy can capture the thermal image including the hotwire and the sample. When the hotwire is heated, the temperature distribution along the wire is acquired by the readings extracted from the thermal image, which enables the determination of nonlinear and local temperature gradient. This gradient, according to Fourier's Law, can be used to calculate the local heat flux. When a sample is attached to the middle of the hotwire, the attached point is appeared to be a singularity in the temperature distribution along the hotwire, which poses a rigorous challenge to calculate the heat flux flowing into the sample. Here we tried some approaching strategies and verified that the local heat flux at second derivative minima around the singularity is a good enough approximation. The mathematical and physical origins for this approximating strategy are also discussed. This microscale heat-flux meter is a general technique, which is promising for an extension to other thermal measurements.

Examination of Thermal Diffusivity Measurement Method of Sample in Contact with Transparent Plate by Flash Method Considering Thermal Radiation

Examination of Thermal Diffusivity Measurement Method of Sample in Contact with Transparent Plate by Flash Method Considering Thermal Radiation

Analytical Solution of a Generalized Two-Dimensional Model for Laser-Flash Thermal Diffusivity Measurements

This paper presents a two-dimensional model that generalizes the use of the laser flash method for thermal diffusivity measurements of homogeneous, opaque, and two-dimensional (2-D) anisotropic solid materials in the form of thin disk-shaped samples. The model employs partial central or annular pulse heating of the front sample side and a temperature detection over a generally decentralized circular surface on the rear or front sample side. A general analytical solution of related 2-D heat conduction problem with boundary and initial conditions that may exist in reality (such as radiation heat transfer between specimen surfaces and the environment, nonuniform pulse heating, finite pulse duration, and laser pulse penetration) is presented in a partial integral form. The solution for the transient temperature over the decentralized detection surface is transformed from a double integral to a single integral, which reduces the processing time in numerical computation. A simplified solution is given for the partial uniform pulse heating, rectangular pulse duration, and negligible laser pulse penetration depth. Following the simplified solution, four different applications of the presented model for the case of the rear-side temperature detection are described, together with an example of a related sensitivity analysis for the selected set of parametric values. The influence of the size and position of the detection surface on the transient temperature response is separately analyzed, and the results are presented in the last section of the paper.

Method and Validation for Measurement of Effective Thermal Diffusivity and Conductivity of Pebble Bed in High Temperature Gas-Cooled Reactors

The effective thermal diffusivity and conductivity of pebble bed in the high temperature gas-cooled reactor (HTGR) are two vital parameters to determine the operating temperature and power in varisized reactors with the restriction of inherent safety. A high-temperature heat transfer test facility and its inverse method for processing experimental data are presented in this work. The effective thermal diffusivity as well as conductivity of pebble bed will be measured at temperature up to 1600 °C in the under-construction facility with the full-scale in radius. The inverse method gives a global optimal relationship between thermal diffusivity and temperature through those thermocouple values in the pebble bed facility, and the conductivity is obtained by conversion from diffusivity. Furthermore, the robustness and uncertainty analyses are also set forth here to illustrate the validity of the algorithm and the corresponding experiment. A brief experimental result of preliminary low-temperature test is also presented in this work.

Thermal Diffusivity Measurement Method of Transparent Material sandwiched between opaque plates by Flash Method

Thermal Diffusivity Measurement Method of Transparent Material sandwiched between opaque plates by Flash Method

Proposal of novel measurement method for thermal diffusivity from infrared thermal movie

A brand new thermal diffusivity measurement method was developed. In this new noncontact and absolute measurement method, thermal diffusivity was measured from infrared movie data. The model of one-dimensional thermal conduction was constructed by taking into account the thermal flow other than one-dimensional thermal conduction in the sample. On the basis of this thermal conduction model, the analytical equation for calculating thermal diffusivity was derived. A single-crystal sapphire plate was used as a test specimen for the new method. The test specimen was arranged to cause one-dimensional heat conduction. Infrared movies were taken by using an infrared camera at room temperature. Then, thermal diffusivity was numerically calculated from the acquired movie data using the analytical equation. It was experimentally demonstrated that thermal diffusivity was measured with an accuracy of around 10% error, from an infrared movie of a single-crystal sapphire sample.

The measuring technique developed to evaluate the thermal diffusivity of the multi-layered thin film specimens

In the present study, the thermal diffusivities of the Al, Si and ITO films deposited on the SUS304 steel substrate are evaluated via the present technique. Before applying this technique, the temperature for the thin film of the multi-layered specimen is developed theoretically for the one- dimensional steady heat conduction in response to amplitude and frequency of the periodically oscillating temperature imposed by a peltier placed beneath the specimen's substrate. By the thermal-electrical data processing system excluding the lock-in amplifier, the temperature frequency a 3 has been proved first to be independent of the electrical voltage applied to the peltier and the contact position of the thermocouples. The experimental data of phase difference for three kinds of specimen are regressed well by a straight line with a slope. Then, the thermal diffusivity of the thin film is thus determined if the slope value and the film- thickness are available. In the present arrangements for the thermocouples, two thermal diffusivity values are quite close each other and valid for every kind of specimen. This technique can provide an efficient, low-cost method for the thermal diffusivity measurements of thin films.

A new gas/supercritical fluid (SCF) diffusivity measurement method for CO2 saturated polymer systems using a dielectric property

A new gas/supercritical fluid (SCF) diffusivity measurement method for CO2 saturated polymer systems using a dielectric property

Theory and verification of a method for parameter-free laser-flash diffusivity measurement of a single-side object

A new single-side flash method for thermal diffusivity determination is presented. The method is based on a laser-flash pulse excitation and infrared thermography non-contact temperature measurement of a thermal response of a studied object. Using this method, the both excitation and measurement at one side (front side) of the studied object are provided. An exact knowledge of the thickness, absorbed energy, emissivity or other material parameters of the object as well as temperature measurement on the opposite side (back side) of the object are not required. Thus, the method can be described as an object parameter-free single-side thermal diffusivity measurement method. The thermal diffusivity measurement procedure and data processing using an approximation algorithm are described in the paper. Simulation and experimental verification of the method is presented for several materials.

Direct measurement of nanoscale lithium diffusion in solid battery materials using radioactive tracer of 8Li

We have developed an in situ and nanoscale Li diffusion measurement method in Li battery materials using an α-emitting radioactive 8Li tracer. In this method, while implanting a low-energy (8keV) 8Li beam, the α particles emitted at a small angle (10°) relative to the sample surface were detected as a function of time. Measurement for Li diffusion coefficients in a spinel phase LiMn2O4 (LMO) thin film has been started, which is used as an electrode in a Li ion secondary battery. An obvious Li diffusion effect in LMO was observed at the sample temperature of 623K, and the further measurement is underway.

Method for measurement of diffusivity: Calorimetric studies of Fe/Ni multilayer thin films

A calorimetric method for the measurement of diffusivity in thin film multilayers is introduced and applied to the Fe–Ni system. Using this method, the diffusivity in [Fe (25 nm)/Ni (25 nm)]20 multilayer thin films is measured as 4 × 10−3 exp (−1.6 ± 0.1 eV/kBT) cm2/s, respectively. The diffusion mechanism in the multilayers and its relevance to laboratory synthesis of L10 ordered FeNi are discussed.

Nanoscale diffusion tracing by radioactive 8Li tracer

We have developed a nanoscale diffusion measurement method using an α-emitting radioactive 8Li tracer. In this method, while implanting a pulsed 8 keV 8Li beam, the α particles emitted at a small angle (10°) relative to the sample surface were detected as a function of time. The method has been successfully applied to measuring lithium diffusion coefficients for an amorphous Li4SiO4–Li3VO4 (LVSO) thin film with a thickness of several hundred nanometers, demonstrating that the present method is sensitive to diffusion coefficients down on the order of 10−12 cm2/s, which is more sensitive by about two orders of magnitude than that previously achieved.