Solid-phase Diffusion Research Articles

Numerical investigation on the polarization and thermal characteristics of LiFePO4-based batteries during charging process

• An electrochemical-thermal couple model is developed for pouch lithium-ion batteries. • Effects of charge rate on polarization and heat generation are numerically studied. • Sudden rises in total polarization are mainly linked to solid-phase diffusion polarization. • Over 85% of the heat in the cell core under 8C charging comes from irreversible heat. • Charge energy efficiency of the cell at different current levels is further analyzed. High-current charging exacerbates internal polarization and abnormal heat generation, stymieing the development of fast-charging technology for lithium-ion batteries. Based on battery disassembly and charge test experiments, an electrochemical-thermal coupling model was developed and validated in this paper. The variation patterns of various polarization and heat generation of pouch-type lithium iron phosphate (LFP) batteries at different charge rates and their influence mechanisms were investigated numerically. Results indicate that the changes in charge voltage profiles are strongly linked to total cell polarization, and excessive charge current aggravates internal polarization, with the average polarization voltage reaching 109.2 mV at 8C, which is 471.7% higher than at 1C. The polarization in the electrodes dominates the cell polarization, especially at the negative electrode. Activation polarization accounted for the largest share of electrode polarization, the change in polarization profiles in the initial and final stages depended mainly on the solid-phase diffusion polarization. Besides, the large cell temperature difference at high charge currents is attributed to the order of magnitude difference in heat generation rates between the positive tab and the cell core. The cell temperature rise is primarily due to heat production in the cell core, where the proportion of irreversible heat increases nonlinearly with the charge rate, exceeding 85% of the total heat generation at 8C. The charge energy efficiency reduces gradually with increasing charge rate and is only 0.948 at 8C. These findings will help to develop appropriate charging protection strategy for better battery operation and life.

Preparation of D-A-D conjugated polymers based on [1,2,5]thiadiazolo[3,4-c]pyridine and thiophene derivatives and their electrochemical properties as anode materials for lithium-ion batteries

Based on the fact that D-A-D CPs (donor-acceptor-donor conjugated polymers) can significantly improve the lithium-ion storage performance of anode materials, three D-A-D CPs (PMTP, PMOTP, and PDOTP) were prepared by simple chemical polymerization reactions with [1,2,5] thiadiazole [3,4-c] pyridine as the acceptor unit and methylthiophene (MTh), methoxythiophene (MOTh), and 3,4-ethylenedioxythiophene (EDOT) as the donor unit, respectively. Each polymer was compounded in situ with the carbon nanotubes (CNTs) to prepare the PMTP@CNT, PMOTP@CNT, and PDOTP@CNT, respectively, all of which were used as the anode materials for the lithium-ion batteries. The capacities of PMTP, PMOTP, and PDOTP were 762.6, 933.4, and 1351.4 mAh g−1 after 160 cycles at 0.1 A g−1, respectively. The order of magnitude of the specific capacity of the three polymers was PDOTP > PMOTP > PMTP, which was due to the fact that with the increasing electron-donating ability of the donor unit of the polymer, the LUMO energy level gradually decreased, the HOMO energy level gradually increased, and the Eg gradually decreased, resulting in an increase in its redox ability and conductivity. The Galvanostatic intermittent titration technique (GITT) showed that the lithium-ion diffusion coefficients of the three electrodes were comparable. XPS demonstrated that lithium ions were mainly stored on the CC and CN of the three polymers (PMTP, PMOTP, and PDOTP). The b-values showed that their electrochemical reactions were controlled by both the internal solid-phase diffusion process and capacitive process. The CV, GCD, cycling stability performance, and rate capability tests showed that all the three electrodes had good electrochemical performance, among which PDOTP@CNT had the best performance and was well suited as the anode material for the Li-ion battery. D-A-D CP provides a new pathway for the development of electrode materials for high-capacity lithium-ion batteries.

Correlating Electrochemical Kinetic Parameters of Single LiNi1/3 Mn1/3 Co1/3 O2 Particles with the Performance of Corresponding Porous Electrodes.

Characterizing microscale single particles directly is requested for dissecting the performance-limiting factors at the electrode scale. In this work, we build a single-particle electrochemical setup and develop a physics-based model for extracting the solid-phase diffusion coefficient (Ds ) and exchange current density (i0 ) from electrochemical impedance measurements. We find that the carbon coating on the LiNi1/3 Mn1/3 Co1/3 O2 surface enhances i0 . In addition, Ds and i0 decay irreversibly by ≈25 % and ≈10 %, respectively, when the cutoff charge voltage increases from 4.3 V to 4.4 V. Moreover, we correlate intrinsic parameters of single particles with the performance of porous electrodes. Porous electrodes assembled with active particles with higher i0 values deliver a greater capacity and faster capacity fade. The methods developed in this combined experimental and theoretical work can be useful in correlating the single-particle scale and porous-electrode scale for other similar systems.

Thermal diffusion behavior of Fe/Cu/Ni multilayer coatings: a molecular dynamics study

In this paper, the thermal diffusion behavior of Fe/Cu/Ni multilayer coatings was investigated by molecular dynamics. The results show that the Fe, Cu, and Ni elements can diffuse each other at 1250 K. Meanwhile, the intrinsic diffusion coefficients and interdiffusion coefficients of the Fe, Cu, and Ni were calculated. Besides, the diffusion mechanism for high melting-point elements of Fe and Ni at 1250 K was analyzed in the paper. According to the simulation result, the Fe and Ni lattices were disturbed by the active Cu particles. Fe and Ni particles at higher energies may move out of their original positions and migrate into the Cu lattice randomly. Thus, the Fe and Ni elements were involved in the thermal diffusion. This can be confirmed by the decrease of the peak and the disappearance of the secondary peak in the radial distribution function curves. However, the position of the curve peaks did not change. Thus, the lattice structure was still maintained during the whole diffusion process. The thermal diffusion of the three elements was carried out by particle substitution at the lattice positions. It was a solid phase diffusion process. Furthermore, there was a clear particle diffusion asymmetry at the original interface of the element. It was consistent with the diffusion asymmetry of diffusion-couple experiments. The primary reason for this diffusion asymmetry was the difference in the interaction potential of the three elements. This asymmetry was ultimately reflected in the intrinsic diffusion coefficient and the interdiffusion coefficient of each element. For the Fe–Cu–Ni ternary system, the largest diffusion coefficient was copper and the smallest was iron at 1250 K.

Preparation of cement-based Al2O3-MgO-SiO2 sagger and its corrosion mechanism by cathode material during calcination

Al2O3-MgO-SiO2 thin wall sagger bonded by CAS2 was prepared and then the corrosion test by cathode material was carried out. The results showed that Li2CO3 diffused to the surface or interior of sagger in terms of liquid or gas phase and involved in the reaction, and the resultants were mainly LiAlO2, LiAlSiO4, CaO and MgO, Li2O-Al2O3-SiO2 materials migrated to the original layer by driving force of dissolution-precipitation, while free CaO and MgO migrated to the precursor in terms of solid phase diffusion, therefore a loose working layer and a dense transition layer formed and led to large scale spalling.

Growth of self-aligned nonlayered TaC nanosheets on liquid copper by a solid phase diffusion strategy

Compared with layered 2D materials, nonlayered 2D materials combine atomic thickness and high-activity surface, leading to many unique properties. Herein, a solid phase diffusion strategy is raised to obtain self-aligned nonlayered TaC single crystals on liquid copper. Because of the immiscibility of Cu and Ta, a β-Ta nanolayer with a thickness of ∼7 nm would form on the surface of liquid copper by a long-time solid phase diffusion process. After introducing CH4, the β-Ta nanolayer could be converted into 10 μm TaC single crystals with a thickness of 10 nm. With the extension of the reaction time, TaC single crystals would form an ordered self-aligned state spontaneously under the action of lateral capillary force. Finally, the self-aligned TaC nanosheets are assembled into large-size TaC films with a thickness of 10 nm. This strategy paves a new way to grow large-size nonlayered 2D transition metal carbides.

Data-driven identification of lithium-ion batteries: A nonlinear equivalent circuit model with diffusion dynamics

An accurate battery model is essential for battery management system (BMS) applications. However, existing models either do not describe battery physics or are too computationally intensive for practical applications. This paper presents a non-linear equivalent circuit model with diffusion dynamics (NLECM-diff) which phenomenologically describes the main electrochemical behaviours, such as ohmic, charge-transfer kinetics, and solid-phase diffusion. A multisine approach is applied to identify the elements for high frequency dynamics, as well as a distributed SoC dependent diffusion model block is optimized to account for long time dynamics. The model identification procedure is conducted on a three-electrode experimental cell, such that NLECM-diff models are developed for each electrode to then obtain the full cell voltage. Results imply that the NLECM-diff reduces the voltage root mean square error (RMSE) by 49.6% compared to a conventional ECM in the long duration discharge and has comparable accuracy to a parameterized SPMe in the NEDC driving cycle. Additionally, the variation of diffusion-related characteristics of the negative electrode under different currents is determined as the primary reason of the battery models’ large low-SoC-range error. Furthermore, the diffusion process is determined as the dominant voltage loss contributor in the long duration discharge and the ohmic voltage loss is identified as the dominant dynamic under NEDC driving profile.

The Effects of Temperature and Cell Parameters on Lithium-Ion Battery Fast Charging Protocols: A Model-Driven Investigation

The risk of lithium plating is a key barrier to lithium-ion battery fast charging. Among other strategies, many alternative charging protocols have been proposed to reduce the plating propensity compared to the conventional constant current-constant voltage (CC-CV) protocol. However, conflicting results have been reported on their impacts on battery lifetime. This work investigates the performance of CC-CV and a boost charging protocol using an electrochemical-thermal model which accounts for nonlinear diffusion and reversible lithium plating. The relative performance of the protocols is found to ultimately depend on the solid phase and ion diffusion timescales. Boost charging is beneficial when both these timescales are short, i.e. in power cells in general or in energy cells at sufficiently high temperatures. The high concentration gradients that develop during the boost stage can sufficiently relax in the subsequent lower current stage to reduce the plating propensity in these cases. When the diffusion timescales are long, boost charging leads to increased plating heterogeneity (driven by the ion diffusion limitations) and slightly increased plating propensity (driven by the solid phase diffusion limitations). Our findings highlight the need to study alternative charging protocols at a wide range of conditions and on different cells before practical deployment.

Pore formation mechanism and oxidation resistance of porous CoAl3 intermetallic prepared by rapid thermal explosion

Porous CoAl3 is a candidate material in the field of catalytic due to its high porosity, good thermostability and quasicrystal structure. However, its rapid preparation are still a challenge, and the oxidation resistance need to be further investigated. In this work, we have rapidly prepared porous CoAl3 by thermal explosion (TE) reaction and studied its oxidation process. The results show that two exothermic peaks at 616 °C and 646 °C, corresponding to the solid-phase diffusion and TE reaction, respectively. The heat released from the two reactions led to the expansion of the compact, which reached a maximum of 104% at 800 °C, and the corresponding open porosity reached at 53%. The pore sources include the original pores during the green compact pressing process, the Kirkendall pores generated by the solid-phase diffusion process and the in-situ pores generated by the Al consumption after the TE occurs. The cyclic oxidation of porous CoAl3 at 700 °C for 130 h only increased the weight by 1.52%, forming a continuous protective oxide film on the surface of the skeleton. It has been found that porous CoAl3 can combine the oxidation resistance of Co–Al monoliths alloys and the high porosity of porous materials, which have potential applications in the field of catalysis such as methanation at 600–700 °C.

Laser properties of active media based on ZnSe doped with Fe and In from spray pyrolysis deposited films

A technique was presented for obtaining laser media based on polycrystalline zinc selenide doped with iron from spray pyrolysis deposited films in the solid-phase diffusion process. The effect of the ligature film composition and the high-temperature treatment conditions on the lasing characteristics of Fe:(In):ZnSe active elements was investigated. Lasing with an energy of 100 mJ at a differential absorbed energy efficiency of 42% was obtained on 20 mm disk Fe:ZnSe element pumped by a pulsed electric-discharge HF laser.

Tuning the distribution of Tb in Nd-Fe-B sintered magnet to overcome the magnetic properties trade-off

A trade-off between the coercivity and other magnetic properties (remanence and maximum energy product) is a dilemma in current grain boundary diffusion (GBD) Nd-Fe-B sintered magnets. Here we report a new solid-liquid phase separation diffusion method for Nd-Fe-B magnets, which substantially and comprehensively enhances permanent magnetic performance, especially demagnetization curve squareness. The results show Tb diffused preferentially into the inside of magnets through the molten Nd-rich grain boundary phase during the liquid phase diffusion process. Then, uniform core-shell structures were formed during the subsequent solid phase diffusion process. This new GBD strategy increases the diffusion depth and avoids the evident Tb gradient that cause the deterioration of the magnetic performance of current GBD magnets. The microstructure and magnetic domain evolution in the Nd-Fe-B magnets diffused with both current and newly-developed techniques were also compared and investigated.

Enhanced Lithium-ion battery model considering critical surface charge behavior

Battery model is the basis of battery efficient and safe management. The widely used equivalent circuit model (ECM) generally shows poor behavior in predicting battery terminal voltage at low sate of charge (SOC), increasing the risk in the urgent use of a battery at low voltage greatly. To model strong nonlinearity of battery open circuit voltage (OCV), a solid-phase diffusion equation based surface SOC is proposed to characterize OCV behavior and establish the new structure of the enhanced ECM to describe low SOC behavior more precisely. Finally, a battery test platform was built to conduct battery tests for model validation. The results show that the root mean square error (RMSE) of the battery terminal voltage obtained from the proposed model at low SOC has been reduced to 8 mV compared with the RMSE of 17 mV from the traditional ECM model. It is expected that the proposed model can be employed in battery management systems to effectively improve the reliability and safety of emergency use of a battery at low SOC.

Low-Temperature Synthesis of Lithium Lanthanum Titanate/Carbon Nanowires for Fast-Charging Li-Ion Batteries.

Due to the lower working voltage and higher capacity, the Li-rich lithium lanthanum titanate perovskite (LLTO) anode is becoming a potential candidate for the commercial Li4Ti5O12 (LTO) Li-ion battery anode [Zhang, L. Lithium Lanthanum Titanate Perovskite as an Anode for Lithium Ion Batteries. Nat. Commun. 2020, 11, 3490]. However, a high temperature of 1250 °C is required to fabricate pure LLTO particles by the conventional solid-phase calcination method, limiting their further practical applications. Here, an in situ carbon nanospace confined method is developed to synthesize the pure LLTO with sub-nanometer grain size at an extremely low temperature of 800 °C. The LLTO precursor is confined in the in situ formed carbon nanowire matrix during heating, resulting in a shorter solid-phase diffusion distance and subsequently lower energy required for the formation of the pure LLTO phase. The low-temperature-synthesized pure LLTO/carbon composite nanowires (P-LLTO/C NWs) exhibit improved lithium storage performances than the traditionally prepared LLTO due to the fast electronic conduction of carbon and the stable carbon surface. In addition, the working potentials of P-LLTO/C||LiFePO4 and P-LLTO/C||LiCoO2 full cells are all 0.7 V higher than that of the corresponding commercial full cells with LTO as an anode, meaning much higher power energy densities (307.6 W kg-1 at 2C and 342.4 W kg-1 at 1C vs 198.4 W kg-1 and 275.2 W kg-1 for LTO||LiFePO4 and LTO||LiCoO2 full cells based on electrode materials, respectively). This low-temperature synthesis method can extend to other solid-state ionic materials and electrode materials for electrochemical devices.

Novel equivalent circuit model for high-energy lithium-ion batteries considering the effect of nonlinear solid-phase diffusion

Efficient and accurate management of lithium-ion batteries (LIBs) highly relies on models that capture the in-cell nonlinear behaviors. As one of the most dominant dynamics inside high-energy LIBs, the solid-phase diffusion shows nonlinearity because the lithium diffusivity in solid phase is a physical parameter varying with the lithium concentration. Yet, this nonlinearity has not been well disclosed in the electrical modeling field of LIBs. This paper presents a novel equivalent circuit model in which the effect of nonlinear solid-phase diffusion is considered. First, the modeling process is illustrated, and it is worth noting that the circuit representation of solid-phase diffusion is established based on its physical principles at electrode particle level. Second, while paying special attention to the relaxation voltage offset, the model parameters are identified with the help of the multi-timescale characteristics of batteries during the voltage recovery period in pulse discharge test. Finally, the model is thoroughly validated by performing constant-current discharge and dynamic tests on the commercial high-energy LIBs. Results show that the proposed model remains robust to the state-of-health of batteries and outperforms the conventional second-order resistor–capacitor model. Moreover, the model keeps similar simplicity to the conventional one and can meet the real-time requirements in engineering.

Solid Phase Diffusion Bonding of Chromium Copper Alloys Using Formate Formation and Decomposition Reactions

Solid Phase Diffusion Bonding of Chromium Copper Alloys Using Formate Formation and Decomposition Reactions

Study of possibility for obtaining of fibrous aluminum-matrix composite materials reinforced by carbon

Compatibility problems in obtaining of composite materials are proposed to be eliminated by preliminary metallization of the carbon component and an application of a combined technological scheme of solid-phase diffusion of the aluminum matrix. The contact wetting angle is experimentally estimated, which allowed the selection of the coating composition for the most effective metallization at the preparatory stages of the desired composite material. The surface of carbon fibers is studied by the scanning electron microscopy. Studies of the structure of experimental samples made it possible to establish the possibility for obtaining of aluminum-matrix materials of the selected composition.

Fabrication of a novel molybdenum carbide composite coating with double-layer structure on cast iron via in situ solid-phase diffusion

The improvement of comprehensive properties including hardness, toughness, adhesion strength, and wear resistance of the hard coating is highly desirable for various applications. Herein, a new strategy involving in situ solid-phase diffusion (ISSD) is utilized to fabricate a novel molybdenum carbide composite coating (MCCC) with double-layer structure on cast iron (CI). MCCC is composed of two layers, the outermost layer (Layer I) is a completely dense Mo2C layer, and just beneath it is a Fe3Mo3C(Si) composite transitional layer (Layer II) which connects the outer layer and the CI substrate. The squares of the thickness of the Layer I, Layer II, and MCCC are found to be proportional to the ISSD time, thus following the classic parabolic law. The hardness, elastic modulus, and fracture toughness of the coating surface reach 24.6 ± 0.5 GPa, 483.5 ± 3.1 GPa, and 3.0 ± 0.1 MPa·m1/2. With the evolution of the microstructure in the coating along the thickness direction, the hardness and elastic modulus gradually decrease, while the fracture toughness gradually increases. Furthermore, the result of scratch test shows that the adhesion strength between Layer I and Layer II is approximately 93.4 N, while the adhesion strength between the coating and the substrate is greater than 93.4 N. Therefore, this work provides a new route for the fabrication of MCCC with double-layer structure capable of combining superhardness, excellent toughness, and superior adhesion strength.

Parameter identification of reduced-order electrochemical model simplified by spectral methods and state estimation based on square-root cubature Kalman filter

With the in-depth study of electrochemical models, the use of reduced-order electrochemical models on battery management systems becomes a possible future trend. In this paper, a two-step parameter identification method and the square-root cubature Kalman filter are employed. The pseudo-spectral method is used to solve the solid-phase diffusion equation, while the liquid-phase concentration equation is simplified by the Galerkin method. The reduced-order model maintains high accuracy while significantly reducing computational burden, the computation of a discharge voltage is within 1.5 s, which makes it possible to use the model for parameter identification and real-time state estimation. Next, the ant lion optimizer is applied to identify 21 parameters in the electrochemical model and 4 parameters in the thermal model respectively. Identification and validation results in constant current discharge and several dynamic tests demonstrate the high accuracy of the reduced-order model. Finally, the square-root cubature Kalman filter based on the identified parameters is developed to estimate the state of charge and temperature. The states are initialized with certain errors in two dynamic tests to verify the performance of the algorithm. The results show that the designed state observer has good convergence, robustness, and accuracy.

Study on the micro-interface behavior of 2024Al light alloy bonded by ultrasonic assisted solid phase diffusion welding with Ag interlayer under atmosphere

This paper introduces a new welding process. Based on the traditional solid phase diffusion welding, the ultrasonic energy field is introduced, and the acoustic plastic effect caused by ultrasonic vibration propagating in the solid phase medium is used to promote the plastic deformation of the base metal, so as to form an effective joining. Combined with the model analysis, the theory proves that the introduction of ultrasonic energy field can reduce the welding pressure and shorten the welding time. The plastic deformation was confirmed by the observation of dislocation and twinning in the weld seam with Ag as intermediate layer in atmospheric environment. The maximum shear strength of the welded joint is about 84.33 MPa. It was also found that the oxide Ag2O can help compounds with different crystal structures form bonds.

Reaction Behavior of Porous TiAl3 Intermetallics Fabricated by Thermal Explosion with Different Particle Sizes.

Porous TiAl3 intermetallics were prepared by the thermal explosion (TE) and space holder method with different particle sizes of Ti and Al powders, and their reaction behaviors were investigated. The results showed that with the increase in the particle size of the Ti and Al powders, the interfacial contact between the particles decreased, resulting in low interfacial energy and reaction activity, making the process difficult to initiate. Meanwhile, the heat flow rose from 358.37 J/g to 730.17 J/g and 566.74 J/g due to the extension of the solid–liquid diffusion time. The TiAl3 structures obviously expanded, and the formation of connected pore channels promoted the porosity. Only when the Ti and Al particle sizes were both small did the solid–solid diffusion significantly appear. At the same time, the TE reaction weakened, so the product particles had no time to fully grow. This indicates that the particle size of the raw materials controlled the TE reaction process by changing the solid–liquid diffusion reaction time and the degree of solid-phase diffusion.