Two-phase Transformation Research Articles

In-depth approach and establishment from a structural perspective of LiFePO4 cathodes for lithium-ion batteries by a two-step sintering

Most synthesis of olivine LiFePO4 (LFP) studies have emphasized the importance of a two-step sintering process for the formation of a uniform carbon coating. However, in this study, it is found that, as an advantage of the two-step sintering process, stable carbonization not only improves lithium-ion conductivity by forming a coating layer but also increases the uniformity of the internal crystal structure. In addition to basic crystallinity and structure analysis using X-ray diffraction (XRD), in-depth calculations are performed to explain the formation mechanism of crystal structure according to the two-step sintering process and the temperature of the first sintering step. In particular, lattice defects and structural uniformity are closely investigated from the crystal structure perspective by comparing lattice micro-strain and dislocation density. Improvement in lithium-ion conductivity from structural uniformity is also demonstrated through cyclic voltammetry (CV) analysis. As a result, it is confirmed that LFP, which undergoes a high-temperature two-step sintering, has high capacity and excellent cycle retention at high rates. Furthermore, ex-situ XRD analysis demonstrates the performance difference according to lithium-ion mobility by comparing the LiFePO4/FePO4 two-phase transformation reaction of two-step sintered LFP and the plateau stability during charging.

Method for determining phase shift using two-phase interpolation transformation

This study focuses on a method for accurately determining the phase shift between two harmonic signals. The proposed technique compares the waveform of the combined signal, which is obtained by applying a two-phase interpolation transformation, with a set of predefined reference functions. This study aims to develop a method for accurately measuring the phase shift between two harmonic signals to reduce the measurement errors caused by phase asymmetry in signal transmission channels and minimize the costs associated with parameter control. The sources of error in the proposed measurement method are identified and addressed. The task involves setting up the measurement objective to determine the phase shift between two harmonic signals. This section presents the analyses of known methods for measuring phase shifts using of analog-to-digital conversion. The next step involves selecting indicators and criteria to determine how closely the investigated signal matches the reference function. Then, we propose the synthesis of an algorithm to find the extremum of the sum of squares deviations for the set of reference functions and the investigated signal, relying on the golden ratio method. Finally, the paper will analyze possible sources of error that could affect the measurement outcome. The methods used are the following: methodology for conducting digital signal processing and measuring error estimation, numerical methods for extremum search, and methodology for single-factor experiments. The following results were obtained. A proposed compensation method for measuring phase shift is based on comparing the shape of the normalized signal, which is obtained as a result of the summation of harmonic signals after their semiperiodical transformation, with a set of normalized reference functions synthesized by computational means. A list of measurement and auxiliary operations, which should be ideally conducted to implement this measurement method, has been determined. An analysis of the components of measurement errors was conducted. Conclusions. The scientific novelty of the obtained results lies in the following: a method for measuring the phase shift of a signal has been developed, which, in our opinion, should be classified as a compensatory measurement method. This will significantly reduce the error component caused by the phase asymmetry of signal transmission channels and reduce the costs of controlling parameters (up to 10%) without decreasing the quality of control; a list of the measuring and auxiliary operations necessary for the implementation of the proposed measurement method has been identified; sources of errors have been determined.

Multifunctional-Element doping of NASICON-Structured cathode enables High-Rate and stable sodium storage

The NASICON cathode of sodium ion battery (SIB) exhibits a stable structure and good electrochemical performance. Na3V2(PO4)3 (NVP), as a typical NASICON cathode, has been widely used in SIBs due to its high capacity and long cycle life. However, the high proportion of vanadium in NVP escalates its cost, which deviates from the initial objective of affordable sodium-ion batteries. In this work, a multifunctional-element substitution of vanadium sites in NVP is introduced by the cost-effective transition metals (Mn and Al), which optimizes the host structure, promotes the transmission of sodium ions and improves the cycle stability. The introduction of Mn can enhance its electrochemical activity and increase the reaction potential, and the doping of Al can improve structural support and cycle stability by the enhanced covalent skeleton. It was found that the Na3.7VAl0.3Mn0.7(PO4)3 cathode shows a high capacity of 87.77 mAh g−1 even at 40C (93.2 % retention compared to 1C), and the capacity retention reaches 96.33 % after 1000 cycles at 2C. In-situ XRD analysis demonstrate that the Na3.7VAl0.3Mn0.7(PO4)3 cathode exhibits a solid solution reaction mechanism instead of the previous two-phase transformation process during the Na+ (de)insertion. Furthermore, we conducted assessments on the efficacy of diverse phosphate cathodes within a coin-type full-cell configuration, which initially exhibits a high energy density of 343.9 Wh kg−1 and excellent capacity retention of 91.58 % after 150 cycles at 0.5C. These characteristics position it as a promising candidate for NASICON cathode materials in the field of research and development.

Evolution of Mn-doped LiFePO4 during cycling: Fast synchrotron operando Mössbauer studies

Due to the chemical and thermal stability, lithium iron phosphate is a popular cathode material, the properties of which can be improved by doping. This work presents a study of the charge/discharge mechanisms for the LiFe1-XMnXPO4/C cathodes using synchrotron operando Mössbauer measurements. Both an increase in the cycling rate and Mn-substitution in the LiFePO4 structure lead to a gradual switch of lithium intercalation mechanisms between the two-phase transformation and the formation of an extended solid solution domain at the Fe1-XMnXPO4/LiFe1-XMnXPO4 interface. The role of doping in improving the cycling of LiFe1-XMXPO4/C cathodes during both charge and discharge and their cycling mechanism are discussed.

Experimental research on the transformation of gas-oil two-phase flow pattern in large vertical annulus

Criteria for gas-oil two-phase flow transformation are essential guidelines that are used as auxiliary equations for the calculation of two-phase flows in gas-oil based drilling fluids within wellbores. The currently used flow pattern transformation criteria, which are based on gas-water two-phase flow experiments in circular pipes or small annuli, have limited applicability when calculating the gas-liquid two-phase flows in oil-based drilling fluids. In this study, experiments were carried out on the transformation of gas-oil two-phase flow patterns in a large annulus (φ100 mm × φ60 mm × 12 m) under different viscosities (16–39 mPa s). The flow characteristics of gas-liquid two-phase flows were measured using electrical capacitance volume tomography (ECVT) at different superficial gas-liquid velocities. It was found that as the liquid phase viscosity increased, the slug flow area gradually expanded, and the superficial gas velocity at which the annular mist flow appeared decreased. When the superficial Reynolds number of the liquid phase exceeded the critical value (approximately 135), the slug flow no longer appeared in the wellbore, and the bubble flow was directly transformed into the churn flow. Based on the results of the dimensionless analysis in the experiments, the criteria for flow-type transitions among different flow patterns were established by considering the influence of the liquid-phase viscosity. Both the average relative errors between the predicted and experimental values of the superficial gas velocity during the bubble-slug, bubble-churn, slug-churn, and churn-annular transitions, at the same superficial liquid velocities, were less than 3.5, 4.5, 3, and 7%, respectively.

Tuning the electrochemical behaviors of N-doped LiMnxFe1–xPO4/C via cation engineering with metal-organic framework-templated strategy

LiFePO4, as a prevailing cathode material for lithium-ion batteries (LIBs), still encounters issues such as intrinsic poor electronic conductivity, inferior Li-ion diffusion kinetic, and two-phase transformation mechanism involving substantial structural rearrangements, resulting in unsatisfactory rate performance. Carbon coating, cation doping, and morphological control have been widely employed to reconcile these issues. Inspired by these, we propose a synthetic route with metal–organic frameworks (MOFs) as self-sacrificial templates to simultaneously realize shape modulation, Mn doping, and N-doped carbon coating for enhanced electrochemical performances. The as-synthesized LiMnxFe1–xPO4/C (x = 0, 0.25, and 0.5) deliver tunable electrochemical behaviors induced by the MOF templates, among which LiMn0.25Fe0.75PO4/C outperforms its counterparts in cyclability (164.7 mA h g−1 after 200 cycles at 0.5 C) and rate capability (116.3 mA h g−1 at 10 C). Meanwhile, the ex-situ XRD reveals a dominant single-phase solid solution mechanism of LiMn0.25Fe0.75PO4/C during delithiation, contrary to the pristine LiFePO4, without major structural reconstruction, which helps to explain the superior rate performance. Furthermore, the density functional theory (DFT) calculations verify the effects of Mn doping and embody the superiority of LiMn0.25Fe0.75PO4/C as a LIB cathode, which well supports the experimental observations. This work provides insightful guidance for the design of tunable MOF-derived mixed transition-metal systems for advanced LIBs.

Ti, F Codoped Sodium Manganate of Layered P2-Na 0.7 MnO 2.05 Cathode for High Capacity and Long-Life Sodium-Ion Battery

Ti, F Codoped Sodium Manganate of Layered P2-Na _0.7 MnO _2.05 Cathode for High Capacity and Long-Life Sodium-Ion Battery

Single-machine scheduling of multiple projects with controllable processing times

This paper studies the single-machine multiple-project scheduling problem with controllable processing times, in which the cost of a project refers to the total compression cost of its jobs plus the weighted number of tardy jobs in a schedule satisfying some given precedence constraints. It involves four specific problems: (i) minimizing the total cost of an arbitrary number of projects, (ii) being the same as (i) except the jobs from the same project having a common due date, (iii) having a fixed number of projects and minimizing the cost of one project subject to the cost of each of other projects not exceeding a given threshold, and (iv) being the same as (iii) except all jobs having identical weights. We show that a special version of (i) in which each project has only two jobs and all jobs have unit weights and cannot be compressed is strongly NP-hard (it implies the strong NP-hardness of (i)), (ii) is weakly NP-hard and admits a pseudo-polynomial algorithm and a fully polynomial time approximation scheme, (iii) is pseudo-polynomially solvable by a two-phase transformation, and (iv) is weakly NP-hard even if there are only two projects and all jobs have identical maximum compression amounts and identical processing times.

Experimental and Numerical Research on Water Transport during Adsorption and Desorption in Cement-Based Materials

The durability of cement-based materials is related to water transport and storage in their pore network under different humidity conditions. To understand the mechanism and characteristics of water adsorption and desorption processes from the microscopic scale, this study introduces different points of view for the pore space model generation and numerical simulation of water transport by considering the “ink-bottle” effect. On the basis of the pore structure parameters (i.e., pore size distribution and porosity) of cement paste and mortar with water-binder ratios of 0.3, 0.4 and 0.5 obtained via mercury intrusion porosimetry, randomly formed 3D pore space models are generated using two-phase transformation on Gaussian random fields and verified via image analysis method of mathematical morphology. Considering the Kelvin-Laplace equation and the influence of “ink-bottle” pores, two numerical calculation scenarios based on mathematical morphology are proposed and applied to the generated model to simulate the adsorption-desorption process. The simulated adsorption and desorption curves are close to those of the experiment, verifying the effectiveness of the developed model and methods. The obtained results characterize water transport in cement-based materials during the variation of relative humidity and further explain the hysteresis effect due to “ink-bottle” pores from the microscopic scale.

Homeostatic Solid Solution in Layered Transition-Metal Oxide Cathodes of Sodium-Ion Batteries.

Two-phase transformation reaction is ubiquitous in solid-state electrochemistry; however, it usually involves inferior structure rearrangement upon extraction and insertion of large-sized Na+, thus leading to severe local strain, cracks, and capacity decay in sodium-ion batteries (SIBs). Here, a homeostatic solid solution reaction is reported in the layered cathode material P'2-Na0.653Ni0.081Mn0.799Ti0.120O2 during sodiation and desodiation. It is induced by the synergistic incorporation of Ni and Ti for the reinforced O(2p)-Mn(3d-eg*) hybridization, which leads to mitigated Jahn-Teller distortion of MnO6 octahedra, contracted transition-metal oxide slabs, and enlarged Na layer spacings. The thermodynamically favorable solid solution pathway rewards the SIBs with excellent cycling stability (87.2% capacity retention after 500 cycles) and rate performance (100.5 mA h g-1 at 2500 mA g-1). The demonstrated reaction pathway will open a new avenue for rational designing of cathode materials for SIBs and beyond.

Inductor Saturation Compensation in Three-Phase Three-Wire Voltage-Source Converters Via Inverse System Dynamics

In three-phase three-wire (3P3W) voltage-source converter (VSC) systems, utilization of filter inductors with deep saturation characteristics is often advantageous due to the improved size, cost, and efficiency. However, with the use of conventional synchronous frame current control methods, the inductor saturation results in significant dynamic performance loss and poor steady-state current waveform quality. This article proposes an inverse dynamic model-based compensation (IDMBC) method to overcome these performance issues. For this purpose, two-phase exact modeling of the 3P3W VSC control system is obtained. Based on the modeling, the inverse system dynamic model of the nonlinear system is obtained and employed such that the nonlinear plant is converted to a virtual linear inductor system for linear current regulators to perform satisfactorily. Further, to control phase currents in the synchronous frame, a two-phase coordinate transformation is proposed. The IDMBC method is tested via dynamic command response and waveform quality simulations and experiments that employ saturable inductors reaching down from full inductance at zero current to 1/9th inductance at full current. The results obtained demonstrate the suitability of the method for 3P3W VSCs employing saturable inductors.

Experimental investigation of water-gas mixed seepage parameters characteristics in broken coal medium

In order to study the mixed permeability characteristics of broken coal medium, the parameter changes during water-gas permeation are analyzed and discussed in this study. It includes the law of two-phase flow state transformation, the law of permeability evolution and the principle of effective stress action. Firstly, the water-gas mixed permeation test system was designed by independent design. Then the gas and liquid two-phase permeation parameters were measured in real time by using multiple sets of sensors. The results are as follows: In one hand, the two-phase seepage process in broken coal medium, the seepage apparent Reynolds number is mainly distributed between 1230–2207. The difference of two orders of magnitude between the kinematic viscosities of the two fluids leads to an asynchronous transition process between the liquid and gas phase flow regimes. On the other hand, there is a competitive relationship between the relative permeability ratio of water and gas phases. When the proportion of gas phase relative permeability is distributed in the interval 71.7%–85.1%, the proportion of gas phase relative permeability is dominant, and it is most sensitive to the influence of the compaction deformation process of the initial pore structure. At the same time, the permeability k decreases with the increase of the effective stress σov in all three stages of the compaction deformation of the skeleton of the broken coal medium, in accordance with the relationship: σov=0.678/k+0.608. The effective stress will directly determine the pore deformation process of the structure of the broken coal medium.

A two-phase quasi-affine transformation evolution with feedback for parameter identification of photovoltaic models

Metaheuristic algorithm is a prestigious technique for solving optimization problems. QUATRE is a simple but powerful algorithm. However, QUATRE also shows premature convergence and is easily trapped in local optima for complex optimization problems. This work presents a novel algorithm named two-phase QUasi-Affine Transformation Evolution with feedback (tfQUATRE). The proposed tfQUATRE is an enhanced quasi-affine transformation evolution algorithm. In tfQUATRE, a two-phase approach is introduced to improve the exploration and exploitation abilities by adjusting the search tendency at different phases. Moreover, the historical population is employed for the feedback approach to guide the search towards promising areas to maintain population diversity, which boosts the exploration ability. The comprehensive performance of tfQUATRE is evaluated in the simulations. First, the performance of tfQUATRE is evaluated under the CEC2017 test suite. The simulations prove that tfQUATRE is superior to 12 state-of-the-art algorithms. In addition, tfQUATRE is applied to extract the parameters of photovoltaic (PV) systems in real application. The experimental results confirm that the proposed tfQUATRE is more competitive than 17 recent counterparts.

(Student Battery Slam Best Presentation Award Winner) Investigation of Tunable Properties in Single-Crystal LiNi0.5Mn1.5O4 Cathode Materials

The commercialization of lithium-ion batteries has played a pivotal role in the development of consumer electronics and electric vehicles. In recent years, much research has focused on the development and modification of the active materials of electrodes to obtain higher energies for a broader range of applications. High-voltage spinel materials including LiNi0.5Mn1.5O4 -δ (LNMO) have been considered as promising cathode materials to address the increasing demands for improved battery performance due to their high operating potential, high energy density, and stable cycling lifetimes.Spinel LNMO can adopt two crystallographic structures depending on the synthesis conditions: an ordered P4332 structure which contains Ni and Mn on separate octahedral sites and a disordered Fdm structure which contains Ni and Mn in a random arrangement on octahedral sites. The disordered spinel phase requires higher synthesis temperatures than the ordered phase to form and is often associated with the loss of oxygen from the material lattice, as well as the reduction of a small amount of electrochemically inactive Mn4+ to active Mn3+ for overall charge compensation. The differences in structure and Mn oxidation state of LNMO cathode materials can influence the electrochemical performance. Increased structural disorder can increase Li+ transport properties through reducing two-phase transformation domains, leading to improved rate performances. Through manipulation of synthetic parameters, the structural and electronic properties of LNMO can be well controlled during formation. The molten salt synthesis method has become one of the most prominent techniques to synthesize single-crystal layered and spinel materials.In this work, the molten salt synthesis method is used as a technique to tune both the morphology and Mn3+ content of high-voltage LNMO cathodes. The resulting materials are thoroughly characterized by a suite of analytical techniques, including synchrotron X-ray core-level spectroscopy, which are sensitive to the materials properties at multiple length scales. The multidimensional characterization allows us to build a materials library according to the molten salt phase diagram as well as to establish the relationship between synthesis, materials properties, and battery performance. Results of this work show that Mn3+ content is primarily dependent on the synthesis temperature and increases as temperature is increased. Particle morphology is mostly dependent on the composition of the molten salt flux, which can be tailored to obtain well-defined octahedrons enclosed by (111) facets, plates with predominant (11) facets, irregularly shaped particles, or mixtures of these. The electrochemical measurements indicate that the Mn3+ content has a larger contribution to the battery performance of LNMO than morphological characteristics and that a significant amount of Mn3+ could become detrimental to the battery performance. However, with similar Mn3+ contents, morphology still plays a role in influencing the battery cycle life and rate performance.We also employ high spatial resolution, synchrotron X-ray nanodiffraction techniques to identify the presence and quantify the percentage of the ordered versus disordered spinel phases at the individual particle level as LNMO single-crystal particles likely contain local regions of both ordered and disordered regimes which standard lab X-ray diffractometers may be unable to distinguish. The relationship between structural ordering and Mn3+ content is critical to the understanding of the intrinsic chemomechanical and electrochemical properties of LNMO. The insights of molten salt synthesis parameters on the formation and performance of LNMO, with deconvolution of the roles of Mn3+, crystal structure, and morphology, are crucial for continuing studies in the rational design of LNMO cathode materials for high energy Li batteries.

High-performance Na3V2(PO4)2F2.5O0.5 cathode: Hybrid reaction mechanism study via ex-situ XRD and sodium storage properties in solid-state batteries

Presently, sodium-vanadium fluorophosphates are highly competitive cathode materials for sodium ion batteries (SIBs) due to the high operating voltage and specific capacity. Herein, self-assembly Na3V2(PO4)2F2.5O0.5 microspheres with uniform polypyrrole (PPy)-coating modification (NVPFO@PPy) are successfully constructed via a facile solvothermal method combined with chemical oxidation for the first time. Benefiting from the improved reaction kinetics and large electrolyte–electrode contact area, the NVPFO@PPy composite exhibits superior rate capability (119 mAh g−1 at 0.2 C and 71 mAh g−1 at 10 C) and cycling stability (78% capacity retention after 1000 cycles) in solid-state SIBs. Importantly, the solid-state full SIBs are built based on the NVPFO@PPy as cathode and NaTi2(PO4)3 (NTP) as anode together with gel polymer electrolyte, and it presents an attractive energy density of 198 Wh kg−1 at 1 C. Moreover, the hybrid reaction mechanism mixed with two-phase transformation and solid-state reaction of NVPFO@PPy composite is investigated in detail through ex-situ XRD analysis.

Imaging the Phase Transformation in Single Particles of the Lithium Titanate Anode for Lithium-Ion Batteries

Lithium uptake and release in lithium titanate (LTO) anode materials during a discharge and charge cycle is one of the fundamental processes of a lithium-ion battery (LIB), still not fully understood at the microscopic level. During the discharge cycle, LTO undergoes a phase transformation between Li4Ti5O12 and Li7Ti5O12 states within a cubic crystal lattice. To reveal the details of the microscopic mechanism, it is necessary to track the sequence of phase transformations at different discharge/charge states under operating conditions. Here, we use in situ Bragg coherent diffraction imaging (BCDI) and in situ X-ray diffraction (XRD) experiments to examine the lithium insertion-induced materials phase transformation within a single LTO particle and a bulk battery analogue, respectively. BCDI analysis from (111) Bragg peak shows the two-phase transformation manifesting as a distinct image phase modulation within a single LTO nanoparticle occurring in the middle of the discharge region then subsiding toward the end of the discharge cycle. We observe the biggest phase variation at the two-phase stage, indicating the formation of phase domains of 200 nm in size during the discharge process. We also observe a lattice contraction of >0.2% in a single LTO nanoparticle at the (400) Bragg peak measurement, larger than that in the corresponding bulk material. Our observation of this phase transformation at a single-particle level has implications for the understanding of the microscopic/mesoscale picture of the phase transformation in anode and cathode LIBs materials.

Properties Analysis of Dual IPCs 240 with Three Branches Case Study in an Energy Transmission Line Connected to a Hydroelectric Mini-Power Plant

In this paper, the newly developed “Dual Interphase Power Controller (IPC) 240” technology is used to increase the reliability of transmission lines for small renewable energy plants. This asymmetric compensation method based on symmetrical components has used two IPC. The first one is placed at the sending end of the line and the second IPC at the receiving end of the line. During normal operation of the transmission line formed, the electrical service continuity is ensured at the load using reactances, which adjust according to the power angle. When a permanent single-phase fault occurs, triggering the circuit breakers of the infected phase, the two IPCs are reconfigured so that the first performs a three-phase / two-phase transformation and the second a two-phase/three-phase transformation of voltage to continue providing a sufficient power for the load. Data from a power transmission line (30 kV-5 MW) from a mini hydroelectric power station has been used in a virtual network under Matlab/Simulink to test the functions dedicated to this technology. The results of the tests obtained and presented show the feasibility of this technology. The efficiency is also guaranteed because the electricity service is 100% assured in the absence of contingency and almost 70% during the contingency of the single-phase short-circuit type.

Damage recognition based on Generalized Genetic Algorithm

A new optimization approach to solving problems concerning structural damage identification with finite element model is introduced. In this approach, the generalized genetic algorithm is applied to damage recognition with its advantage of directed evolution and two-phase transformation. To employ the method, objective function is constructed by the residual of modal frequency and incomplete modal mode. Meanwhile the recombination and mutation operators are also improved with sparsity constrain. The results show that modified generalized genetic algorithm performs better in convergence speed and accuracy than traditional optimization approach in damage identification.

Optimisation of Casting Geometries for A356 Alloy Composites Reinforced with Organic Materials using Box-Behnken Design Methodology

In an earlier article, the central composite design was applied to the determination of geometrical features of casts in a two-phase transformation process to produce the wheel covers of automobiles whereby the A356 alloy is reinforced with organic substances for composite property enhancement. This article reexamines the assumptions in that circumstance to revise and expand the optimisation through the response surface methodology to a new method, Box-Behnken design (BBD), to facilitate a comprehensive treatment of the sand casting product parameters. Casting geometrical optimisation can be modelled to involve lengths, breadths, widths, heights, densities of casts and weight loss, varied at three discrete levels. The parameters are translated into codes (–1,0,1) with specified actual, minimum and maximum values. The framework, validated by published literature data, indicates its feasibility in a real-life circumstance. This article assessed the effects of the casting geometry parameters on the responses. Besides, it examined the accuracy of the parameters to predict in the regression models deployed. It was concluded that the BBD and the regression models are adequate and predict correctly. The BBD can be applied by composite developers to improve casting dimensional accuracy and economics.

Two-Phase Composition (LiFePO4/FePO4) and Phase Transformation Dependence on Charging Current: In Situ and Ex Situ Studies

The study on the two-phase (LiFePO₄/FePO₄) transformation mechanism of LiFePO₄ during charge–discharge is reported. The study is conducted using ex situ and in situ X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) techniques. The Rietveld refinements are performed on ex situ XRD data of electrode materials collected at various stages of the first charge–discharge cycle. The results reveal the existence of solid solution at room temperature in the narrow nanophase region (0 < x < μ and 1 – η < x < 1). The biphase LiₓFePO₄ is a mixture of Li-deficient phase LiμFePO₄ and Li-rich phase Li₁₋ηFePO₄ in μ < x < 1 – η, where μ = 0.056 and η = 0.043. The present study is conducted on samples prepared by electrochemical reaction, which provides a more realistic situation than the previous study reported on samples prepared by the chemical process. Moreover, a similar study is also repeated by in situ XRD and XPS techniques, which also confirm the transformation of LiFePO₄ into the FePO₄ phase during charging and vice versa during discharging. Furthermore, the study also conducted on the fully charged state (at different current rates from 0.1 to 5C) of various electrodes by ex situ XRD found that phase transformation (LiFePO₄ to FePO₄) depends on the charging current rate. At the lower current, complete transformation of the LiFePO₄ phase into FePO₄ is observed, whereas at the higher current rate, a trace amount of residual phase LiFePO₄ along with FePO₄ is found in the fully charged state. Therefore, the findings of the study reveal the time-dependent lithium-ion diffusion phenomenon in LiFePO₄ causing lower capacity at the higher current rate.