Investigating Incomplete Stage Transition in Aluminum Ion Batteries for Performance Enhancement and the Artificial Intelligence Forecast for Capacity Oscillation towards High-Rate Discharge Batteries

Investigating Incomplete Stage Transition in Aluminum Ion Batteries for Performance Enhancement and the Artificial Intelligence Forecast for Capacity Oscillation towards High-Rate Discharge Batteries | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 22 February 2025 V1 Latest version Share on Investigating Incomplete Stage Transition in Aluminum Ion Batteries for Performance Enhancement and the Artificial Intelligence Forecast for Capacity Oscillation towards High-Rate Discharge Batteries Authors : Xuanming Chen , Ka Chun Li , King Cheong Lam 0000-0002-3079-3254 , Wai Keung Loh , Chak-yin Tang , Yuk Ming Tang 0000-0001-8215-4190 , Wing Cheung Law , Chi Pong Tsui , Ji-Yan Y. Dai 0000-0001-8938-7835 , Frank Leung-Yuk Lam , Xijun Hu 0000-0001-5561-5246 , and Chi Ho Wong 0000-0002-6026-0600 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.174026524.43483000/v1 615 views 160 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract While aluminum-ion batteries (AIBs) have been widely reported that intercalating AlCl₄ ions in each graphite layer in the fully charged state (i.e. a stage 1 configuration) is suffered, the incomplete stage transition hinders both intercalation efficiency and energy density. This issue prevents these batteries from reaching their theoretical potential as next-generation fast-charge batteries. In the lack of a comprehensive computational model capable of analyzing the transient evolution across stage transitions, we have developed a Monte Carlo algorithm to investigate the scientific mechanisms underlying stage transitions in AIBs. Our simulations dynamically model these transitions while accounting for various factors such as temperature, binding energy, diffusion barriers, electrostatic interaction, screening effects, and charge transfer dynamics within the intercalated electrode. Our findings indicate that these factors can be manipulated to either achieve a complete transition to stage 1 or facilitate incomplete transitions. In addition, our model offers insights into nanoscience regarding the unexpected concerns of excessively increasing the dielectric constant. As the demand for batteries evolves, high-rate discharge capabilities are becoming crucial, especially for extreme applications that require quick bursts of power, like electric sports cars. Hence, we conduct a case study on rapidly discharged AIB over numerous usage cycles, where we experimentally observe capacity oscillation. To enhance our ability to predict this oscillation, we harness the power of the LSTM networks to identify essential forecasting parameters, paving the way to envision potential problems operating under high-rate discharge modes. Article category: Full paper Subcategory: Aluminum Ion Batteries, artificial intelligence, Monte Carlo computations, Materials design Title: Investigating Incomplete Stage Transition in Aluminum Ion Batteries for Performance Enhancement and the Forecast for Capacity Oscillation towards High-Rate Discharge Modes 2 Xuanming Chen, 2 Ka Chun Li, 1 King Cheong Lam, 1 Wai Keung Loh, 3 Chak-yin Tang, 3 Yuk Ming Tang, 3 Wing Cheung Law, 3 Chi Pong Tsui, 4 Jiyan Dai, 2 Leung Yuk Frank Lam*, 2 Xijun Hu*, 1 Chi Ho Wong* 1 Division of Science, Engineering and Health Studies, The School of Professional Education and Executive Development, The Hong Kong Polytechnic University, Hong Kong, China not-yet-known not-yet-known not-yet-known unknown 2Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Hong Kong, China not-yet-known not-yet-known not-yet-known unknown 3Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, China 4 Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, China Email: [email protected] , [email protected] , [email protected] Keywords: Aluminum-ion batteries, incomplete stage mechanism, high-rate discharge, AI forecast. Abstract: While aluminum-ion batteries (AIBs) have been widely reported that intercalating AlCl₄ ions in each graphite layer in the fully charged state (i.e. a stage 1 configuration) is suffered, the incomplete stage transition hinders both intercalation efficiency and energy density. This issue prevents these batteries from reaching their theoretical potential as next-generation fast-charge batteries. In the lack of a comprehensive computational model capable of analyzing the transient evolution across stage transitions, we have developed a Monte Carlo algorithm to investigate the scientific mechanisms underlying stage transitions in AIBs. Our simulations dynamically model these transitions while accounting for various factors such as temperature, binding energy, diffusion barriers, electrostatic interaction, screening effects, and charge transfer dynamics within the intercalated electrode. Our findings indicate that these factors can be manipulated to either achieve a complete transition to stage 1 or facilitate incomplete transitions. In addition, our model offers insights into nanoscience regarding the unexpected concerns of excessively increasing the dielectric constant. As the demand for batteries evolves, high-rate discharge capabilities are becoming crucial, especially for extreme applications that require quick bursts of power, like electric sports cars. Hence, we conduct a case study on rapidly discharged AIB over numerous usage cycles, where we experimentally observe capacity oscillation. To enhance our ability to predict this oscillation, we harness the power of the LSTM networks to identify essential forecasting parameters, paving the way to envision potential problems operating under high-rate discharge modes. 1. Introduction As the demand for efficient and sustainable energy storage solutions continues to grow, a state-of-the-art battery that can survive in long-term high-power usage scenarios has become increasingly essential [1] . Currently, lithium-ion batteries (LiBs) still maintain their status as the dominant technology for electric vehicles and other energy storage applications [1] . However, LiBs face challenges related to resource availability, safety, and performance [2] . Lithium is not an abundant material, raising concerns about supply chain vulnerabilities [2] . In addition, LiBs are prone to safety risks, such as overheating and thermal runaway, which can result in fires [2] . The extraction and processing of lithium are also cost-intensive, increasing the production costs of LiBs [1,2] . As other battery technologies emerge with faster charging capabilities [3,4] , LiB may fall behind in terms of marketability and adoption in high-performance applications. The limitations associated with LiBs have prompted the search for alternative systems, such as aluminum-ion batteries (AIBs). Considering these limitations, AIBs have emerged as a promising alternative. AIBs offer distinct advantages including fast-charging capability, etc [3,4] . Compared to lithium, aluminum is abundant, inexpensive, safe, and exhibits high gravimetric density, making it a compelling candidate for next-generation battery technology [3] . Despite these potential advantages, the development of AIBs is hindered by complex reactions with the electrolyte [3] and the significant challenge of achieving complete filling of AlCl₄ ions in every graphite layer (i.e., reaching a pure stage 1) [5-7] . Most AIBs generally achieve stage 3 or the mixed stage 2.5 when fully charged [5-7] , while reaching stage 1 poses notable challenges. Some research teams have made commendable strides in this nanoscience [6] , but the exploration of the scientific mechanisms behind stage transitions continues to be a valuable focus for further study. The detection and characterization of intercalation stages are always conducted using Raman spectroscopy, which provides valuable insight into the interaction between graphite and the intercalated ions [6] . Pure graphite exhibits a characteristic vibrational mode, known as the G-band, which appears at ~1580 cm -1 [6,7] . During intercalation, the interior layers (without AlCl 4 ions) and bounded layers (with AlCl 4 ions) alter the vibrational modes of the graphite lattice, resulting in the emergence of additional peaks in the Raman spectrum [6,7] . In stage 4, where a reasonable level of intercalation occurs, two peaks at cm -1 are expected in the Raman spectrum [6,7] . As the system progresses to stage 3, more bounded layers increase the intensity of the new peak [6,7] . As intercalation advances to stage 2 or stage 1, the interior layers are rare, resulting in a new single peak in the Raman spectrum [6-7] . By the time stage 1 is achieved, the Raman spectrum undergoes a complete transformation, with the peaks corresponding to the fully intercalated graphite system. Tracking these vibrational spectrums as a function of applied voltage allows researchers to monitor the stage transition. Several studies have investigated potential explanations for the difficulty in achieving Stage 1 intercalation [5-7]. The nanoscience has been discovered that the introduction of nitrogen atoms into the graphite structure has been shown to hinder stage 1 intercalation [6] . Although nitrogen doping has been found to enhance the electrochemical performance of other battery systems, its effect on AIBs is likely to be counterproductive. The presence of nitrogen atoms [8,9] triggers the production of chlorine gas that destabilizes the intercalation process [6] . Nevertheless, battery engineering is a complex issue where any observation may be explained with a single scientific concept. To fully understand the stage transition, dynamic simulations are necessary to facilitate transitions between stages 4, 3, 2, and 1, while also allowing for the emergence of mixed stages during these transitions. Furthermore, the analysis of the AlCl₄ shape reveals that the tetrahedral AlCl₄ ion is more favorable in AIBs compared to the planar AlCl₄ ion but how the geometry of AlCl 4 ion impacts the stage transition remains unclear [10] . We will develop a simulation to compare how the tetrahedral ion and planar ion ions affect the stage transitions. Current mainstream simulation methods, including Density Functional Theory (DFT) and Molecular Dynamics (MD) [11,12] , remain inadequate for modeling the stage transition in AIBs. These mainstream methods are designed for simulating the dynamics of AlCl₄ ions and graphite within a single, or a pure intercalation stage only, rather than capturing the transient evolution from one stage to another. Hence, the development of new simulation approaches is essential for understanding the factors that govern stage transitions. Achieving these goals could enhance energy density, cycle life, and charging efficiency of AIBs that unlash their theoretical potential for energy applications. On the other hand, the demand for batteries is evolving to include not only standard applications but also burst mode capabilities [13,14] . High-rate discharge batteries are increasingly sought after for devices that require short bursts of power at ultra-high C rates, particularly in turbocharged electric vehicles [13,14] . These electric burst modes are desired for repeated use, such as in motorsport, where quick bursts of power are needed lap after lap. Increasing the frequency of burst mode usage within a fixed timeframe is essential, meaning that the charging and discharging process must be looped as quickly as possible. In spite of the fast-charging potential of AIBs [4] , rapid discharge may trigger non-equilibrium dynamics of AlCl₄ ions, which may impact battery capacity. These capacity instabilities may lead to inconsistent energy output for repeated use, compromising applications that rely on stable power delivery, as the attainable capacity for the next recharge may become uncertain. To investigate if the capacity shows uncertainly, we fabricate an aluminum-ion battery to conduct a case study on ultra-high discharge speeds. We examine how rapid discharge affects the attainable capacity available for the next recharge, and essentially, develop an artificial intelligence model to forecast the attainable capacity after each recharge. To achieve high accuracy in LSTM networks, large data sets are always essential [15] . However, battery life under extreme conditions, such as high-rate discharge, often suffers. Therefore, it’s important to maintain a high accuracy of LSTM networks [15] while managing these limited battery data. These predictive capabilities will facilitate the proactive development of electric burst mode applications in AIBs. 2. Computational Methodologies (experimental section is listed in section 5) 2.1. Ab-initio Assisted Monte Carlo simulations of Stage Transition By the consideration of the binding energy between tetrahedral aluminum chloride ions and graphite, the electrostatic interactions among aluminum chloride ions, charge transfer between aluminum chloride ions and graphite, and the diffusion barrier within the graphite structure [16] , a Hamiltonian equation is formulated to represent the complex interactions and processes under investigation under an applied voltage. where is the average separation between AlCl 4 ions within the bounded layers , q is -1.6x10 -19 C, is the square of dimensionless Bader-charge number, is the binding energy between the AlCl 4 ion and graphite electrode, is the layer-to-layer distance of graphite, is the stage number, is the weight percentage of AlCl₄ intercalations, is the relative permittivity, is the dielectric constant in vacuum space, refers to the delta function in which = 1 if the applied voltage is larger than or equal to the threshold voltage of attaining the stage number ; otherwise = 0. Our simulation is configured based on the volume of the graphite electrode to examine the weight percentage of aluminum chloride ions (wt%) within the range of 5% to 44% where the range of wt% and the fitting of binding energies as a function of wt% and the layer-to-layer distance of graphite d are selected from the literature [16] . For each wt%, the simulation starts with stage 4 (the lowest intercalation of species) as the initial condition at every temperature. In this initial setup, AlCl₄ ions are randomly distributed within the bounded layers correspondingly. The density of AlCl₄ ions varies based on wt% and the stage number. For example, the AlCl₄ ions are initially sandwiched in graphite layers (k, k+4, k+8…) which refers to stage 4 intercalations [16] . The structural formula is [AlCl 4 ) m C v ], where m and v are the stoichiometric numbers [16] . We use to structural formula in the literature directly [16] : For stage 1, m=4,8,12,16 and v=288; For stage 2, m=2,4,6,8 and v=288; For stage 3, m=2,4,6,8 and v=432; For stage 4, m=1,2,3,4 and v=288; The size of Monte Carlo simulation is expanded to 100 times along x-, y-, and z-axis directions through scaling the size of [AlCl 4 ) m C v ]. The trial distance between AlCl₄ ions can be roughly derived from the structural formula. We apply a standard strategy to create energetically unfavorable sites, followed by Monte Carlo iterations to reach a ground state. Periodic boundary condition is applied to the 3D domain. The initial energetically unfavorable condition is created by arbitrarily compressing this trial distance by d trial = ~1%. The iterative motion of AlCl 4 ion within the bounded layers is one-tenth of d trial . The extent of the arbitrary compression primarily influences the computational time but does not affect the results. Following the initial configuration, the random selection of bounded layers begins, and the Monte Carlo simulation is allowed to relax until an equilibrium state at each wt%. A random number R stage34 , R stage234, R stage123, R stage12 are generated between 0 to 1, respectively. For every wt% analyzed, the system, starting from stage 4, proposes a trial transition to either stage 3 (R stage < 0.5) or stage 4 (R stage34 ≥ 0.5). A trial transition is accepted only if it results in a more negative Hamiltonian value, indicative of a lower energy state. If this trial condition is not satisfied, the system reverts to the previous stage. During the iterative process, if the system has reached stage 3, three potential outcomes were assessed, which are trial progression to stage 2 (R stage234 0.666). The acceptance of a trial transition is governed by the criterion of achieving a more negative Hamiltonian. If this condition is not met, the system returns to stage 3. In cases where the system transitioned to stage 2, similar possibilities are implemented. The trial state could either progress to stage 1 (R stage123 0.666). Each trial transition is evaluated based on its ability to minimize the Hamiltonian, thereby favoring system stability. If the system has reached stage 1, two potential outcomes are possible: reversion to stage 2 (R stage12 > 0.5) or retention at stage 1 (R stage12 ≤ 0.5). As with previous cases, the trial transition is accepted only if the system results in a more negative Hamiltonian value. not-yet-known not-yet-known not-yet-known unknown Whenever a trial stage number is accepted at any stage, the separation between the AlCl₄ ions will vary depending on the wt% number, where the AlCl₄ ions are freely adjusted themselves if the thermal energy is larger than the diffusion barriers within graphite. Since stage transition is a collective phenomenon [5-7,16], the trial stage number at each Monte Carlo step is applied to all the intercalated ions. On the other hand, the Boltzmann factor is employed to evaluate the effects of high temperatures on stage transitions. In high-temperature conditions, the system may accept any trial stage number, even if it leads to a less negative change in the Hamiltonian (dH). If another random number Rthermal within 0 and 1 is less than exp(-dH/kBT) [17], the energetically less favorable state is accepted; otherwise, it rejects the trial stage transition, where k is the Boltzmann constant and T is temperature. This thermal excitation follows the Metropolis algorithm [17], enabling the acceptance of energetically less favorable states if they are thermodynamically permissible at elevated temperatures. Unless otherwise stated, tetrahedral AlCl₄ ions are the intercalated species. To investigate the shape impact of tetrahedral AlCl₄⁻ ions compared to planar AlCl₄⁻ ions, we utilized ab-initio method to compare the binding energies of the AlCl₄⁻ ion, the dielectric constants and the layer-to-layer distances of the intercalated graphite, etc. The calculations employed the GGA-PBE functional [18] , with a SCF tolerance set to 10µeV [18] and a k-space interval of 0.025 (1/Å). The maximum number of SCF cycles is capped at 1000, and ultrasoft pseudopotential is assigned [18] . Geometric optimization is performed under these conditions to relax the AlCl₄⁻ ion within graphite [16,19] . 2.2. LSTM Network for the Capacity Prediction We conduct a parametric analysis of the LSTM network [15] to predict the maximum attainable capacity for the next recharge of our AIB following each burst-mode discharge cycle. The analysis involves key parameters, including a maximum epoch, a gradient threshold, and an initial learning rate, etc [21] . To further enhance the LSTM performance, we adjust the learning rate drop factor and the mini-batch size [21] . The first few warm-up cycles are excluded in the experimental data. For the training process, we capture pronounced features from the first ~70% charge & burst-mode discharge cycles, while the last ~30% cycles are reserved to validate the prediction accuracy. 3. Results and Discussion 3.1. Parametric studies of stage transitions We explore an extreme scenario in which we assume the AlCl 4 ions can smoothly insert into graphite as an initial condition to satisfy = 1. The remaining question is whether the inserted AlCl 4 ions will remain in the same bounded layers at stage 4. To investigate this, we relax the system to equilibrium to assess whether the AlCl 4 ions prefer to stay there. If stage transitions occur, our model indicates that, despite efforts to initially insert all the AlCl 4 ions at stage 4, the ions do not favor remaining in the proposed stage. A higher dielectric constant typically indicates that a material can store more electric energy and meanwhile it reduces the effective electrostatic repulsion between charged particles by providing better screening of electrostatic forces [22] . A larger dielectric constant of the intercalated graphite delays the transition from stages 4 to 3 and from stage 3 to 2 as plotted in Figure 1a. Stage transitions require collective movement among the AlCl 4 species and the graphite layers. A higher dielectric constant enhances the screening of electrostatic forces between the AlCl 4 ions, promoting a crowded arrangement of the AlCl 4 species within the same stage configuration [16] . Parallelly, the densely packed arrangement of the AlCl₄ ion results in a more negative binding energy (per species) within the same stage [16] . This configuration enables the accumulation of more AlCl₄⁻ ions, which in turn delays the transition from stage 4 to stage 3 and from stage 3 to stage 2. In contrast, the AlCl 4 ions become sufficiently crowded at high concentrations (i.e., ~28% or above), diminishing the delay of transition from stage 2 to stage 1. Our model allows for the experimental observation that no stage 1, 2, or 3 configurations are observed at low weight percentages [5-7] because the insertion of high weight percentage AlCl₄ ions in a stage-4 configuration encounters significant electrostatic repulsion within each intercalated layer. A high dielectric constant hinders the complete transition to stage 3, stages 2 and stage 1 accordingly, as illustrated in Figure 1a. To understand this phenomenon, we compare the binding energies of four different stages where the binding energies for stages 1, 2, and 3 are always less negative than that of stage 4 at the same weight percentage (e.g. wt = 16.5%) [16] . The scientific aspect is that, at the same weight percentage of AlCl 4 ions, the transition from stage 4 to stage 3 would increase the average separation of AlCl₄ as more bounded layers becomes available for intercalation. In other words, f orward transitions under fixed wt%, such as from stage 4 to stage 3, from stage 3 to stage 2 or from stage 2 to stage 1, lead to a decrease in the number of AlCl 4 ions per bounded layer. Hence, o nce the stage-4 system proposes stage 3 under the same wt%, the lower concentration of intercalated species in each filled layer now rearranges to allow for greater separation, further minimizing the electrostatic repulsion in each intercalated layer [22] in stage 3. If the dielectric constant is very large, increasing the average separation between AlCl 4 ion from stage 4 to stage 3 does not offer significant benefits in terms of reducing repulsion [22] . This increases the likelihood that some AlCl₄ ions will retain its configuration in stage 4. The same scientific aspect can be applied to incomplete stage transition from 3-2 and 2-1. This raises concerns about the AIB design, as pursuing an excessively high dielectric constant to enhance capacitance may inadvertently make it more difficult to achieve stage 1. We temporarily set the Bader charge C Bader to 1 to eliminate unnecessary factors that could obscure our observations Temperature also plays a role in stage transition, with evidence in Figure 1b. At low wt%, temperature has a minimal effect on trigging transition from stage 4 to stage 3. At medium wt%, the transition from stage 3 to stage 2 becomes more temperature dependent. While the average diffusion barrier for the four different paths of AlCl 4 ions is ~9meV only [16] . Therefore, higher thermal energy facilitates the redistribution of AlCl₄ ions from stage 3 to stage 2, allowing us to observe the transition from stage 3 to stage 2 earlier at 400 K (400K is equivalent to temperature becomes more complex at high weight percentages. At a first glance, higher temperatures should promote the redistribution of AlCl₄ ions again, but from stage 2 to stage 1, the AlCl₄ ions are densely packed within the fixed volume of the graphite electrode, leaving little space for them to be redistributed effectively. As a result, in this crowded configuration, thermal energy loses its advantage in facilitating the stage transition, unlike in the more-space scenario from stage 3 to stage 2. In addition, stage transition is a collective phenomenon involving both graphite and AlCl₄ ions. When AlCl₄ ions attempt to complete the stage 1 configuration, their chaotic motion at high temperatures disrupts the coordinated collective action of the ions. This disruption continues until enough AlCl₄ ions are present in the bounded layers to regain the ordered action of the ions, ultimately delaying the transition to stage 1. By comparing Figures 1a and 1b at the same temperature of 330 K, it can be observed that the average stage number in the relative permittivity of ε(wt) for weight percentages of approximately 32-42% is about 1.2 (Figure 1b - black curve). This is higher than the average stage number of 1.03 for ε = 6 within the same weight percentage range (Figure 1a - black curve). It is because, the relative permittivity ε(wt ~ 40%) is about 11 in Figure 2b, which is higher than ε = 6, as listed in the supplementary materials. This further supports the notion that a higher dielectric constant could impede a complete transition to stage 1 in AIB. We also observe the relative permittivity increase with the intercalated concentration (supplementary materials), and the magnitude of the relative permittivity is comparable to what has been observed in Li-ion batteries [22]. DFT calculations have generated the average distance between the AlCl 4 ions. Therefore, there is no need to double count the mean free path (MFP) by setting in the iterative steps, where is the size of particle, is the particle density. Moreover, each data point in Figure 1 and 2 are averaged 5000 times. A good signal-to-noise ratio across stage transitions has been demonstrated in Figure S1 in supplementary materials. The DFT-computed values of relative permittivity may vary slightly based on the choice of DFT functionals. However, the key aspect is to compare the ratios of relative permittivity and to anticipate how these ratios influence stage transitions. Two configurations of AlCl₄ ions are analyzed [16,23]: planar (black line) and tetrahedral (red line) in Figure 2a. For weight percentages below approximately 20%, there is no noticeable difference in the average stage number between planar and tetrahedral AlCl₄. However, as the weight percentage above 30%, tetrahedral AlCl₄ ions show a greater likelihood of completing the stage 1 transition [16] because the planar AlCl 4 intercalated graphite shows a larger dielectric constant regardless of the stage numbers (supplementary materials). This difference suggests that the geometry of the AlCl₄ ions influences their intercalation behavior, particularly in tight distributions. The tetrahedral AlCl₄ ion exhibits a binding energy that is approximately 10% more negative than that of the planar AlCl₄ ion, fluctuating with weight percentage. Tetrahedral AlCl₄ ions likely benefit from better geometric compatibility or stronger interactions with graphite with help of a higher local charge density at the tetrahedral sites [16] , ending stage 3 later (extend from wt percentages, specifically during the transition from stage environment for the planar AlCl₄ configuration is possible because the planar shape at monoatomic thick allows for intercalating a bit more species per layer, while the 3D geometry of tetrahedral AlCl₄ occupies more space within the intercalated layers. Consequently, the tetrahedral case ends the stage 2 earlier. As a result, the tetrahedral configuration initiates the transition from stage ~2 to stage ~1 at approximately 27.5% weight percentage, while the planar configuration begins this transition at around 29%. The geometric effect of AlCl 4 ion is not observed during the transition from stage 4 to stage ~3, and stage available space, preventing any noticeable impact on low weight percentages. The dielectric constant of the intercalated graphite in the planar case is slightly larger than that in the tetrahedral case because of the shorter layer-to-layer distance of the planar AlCl 4 intercalated graphite (supplementary materials). Up to this point, the dimensionless Bader charge number C Bader is set at 1. This temporary boundary condition is used to more conveniently observe how temperature, dielectric constant, and the geometry of the AlCl₄ ion affect the effectiveness of a complete stage-1 transition. While this observation has been made, we now consider the charge transfer between the intercalated AlCl₄ and graphite, which ultimately affects the effective charge of the AlCl₄ ion (i.e., C Bader ≠1). The presence of charge transfer can reduce C Bader to approximately 0.85 [16] . From the perspective of electrostatic interaction, the effect of this reduction in C Bader is equivalent to the effect of an increase in dielectric constant [22] . Hence, a smaller C Bader hinders the pure transition to stage 1 at higher weight percentages, as shown in Figure 2b, which is consistent with the results of Figure 1. Figure 3 demonstrates that the mixed stage exists as a combination of different stages along the out-of-plane axis of graphite. For instance, in Figure 3, we illustrate the regional stage configuration of stage avoid mixing stages 2 and 3 within a bounded layer but they prefer to form a mixture configuration along the out-of-plane axis randomly. This finding aligns with the experimental Raman spectrum, which shows only relative intensity changes [6,7] . We also see a similar case of a mixed stage of ~3.3 in Figure 4, where 45 layers within the sample are selected for scientific observations. From an experimental point of view, nitrogen doping can destroy the complete stage-1 configuration in AIBs [6] . One of the explanations is related to the release of chlorine gas, which destabilizes the intercalation process [6] . On the other hand, a 2- to 3-fold increase in the dielectric constant of graphite is observed due to nitrogen doping [24] , while our model suggests that the approximately 4-fold increase in the dielectric constant may hinder the full transition to stage 1 (as illustrated in Figure 1), aligning with experimental expectations [6] . Both arguments offer a logical explanation, suggesting that multiple factors can impede a pure stage 1 transition. This shortfall underscores the necessity for further research into the intercalation process, particularly focusing on the conditions needed to achieve Stage 1. Despite a high dielectric constant favors energy storage in batteries. Pursuing an excessively high dielectric constant may compromise the complete Stage 1 configuration. Addressing this challenge could pave the way for the development of AIBs with greater intercalation efficiency, providing a more competitive alternative to LiBs. We do not run the Monte Carlo simulation under nitrogen doping because the dopant could create additional E-fields locally which violates the mean-field assumption of the Hamiltonian. 3.2. Maximize the Effect of Burst Mode Discharge in our AIBs We employ a short circuit to quickly discharge the AIB battery, mimicking a burst mode discharge. This study reveals the parameters that are critical for high-rate discharge applications in future battery management. The peak capacity of our AIB in Figure 5 is to the literature data [25, 26, 27] . As we continue the charge and burst-mode discharge sequence for up to same charging duration, exhibits a decay pattern together with oscillation mode as plotted in Figure 5. This capacity oscillation is rare during standard use, where AIBs are discharged slowly, as evidenced by findings from elsewhere. In other words, it is anticipated that high-rate discharge could trigger the capacity oscillation. Neglecting this oscillation in battery capacity could lead to complications in managing burst-mode discharge. This oscillation in capacity could pose issues, particularly in high-performance and reliable applications like motorsport. In such scenarios, a driver may want to activate a boost mode on the main straight during each lap. However, the capacity available for the high-rate discharge battery is inconsistent from lap to lap, leading to uncertainty in top speed. Short circuit discharge represents an extreme scenario of high-rate discharge. In this context, we expect that the phenomenon of capacity oscillation has reached its maximum (ΔC extreme : ~20% or Δcharge: case (ΔC extreme ) can provide valuable insights for designers regarding the extent of this issue, helping them understand how much attention and mitigation strategies are necessary to address the problem effectively. Suppressing the ΔC extreme via materials engineering or adjusting the charging duration to maintain consistent capacity after each recharge could be possible (out of scope here). Any phenomena associated with batteries are rarely explained by a single scientific discipline. One of the scientific disciplines for the capacity oscillation could be linked to non-equilibrium dynamics of AlCl 4 ions [28] . During high-rate discharge followed by immediate recharge, not all AlCl₄ ions can escape from the graphite electrode completely because of the mass of inertia, leaving a tiny proportion of AlCl₄ ions behind [28] . When the next recharge occurs, the presence of these residual ions increases the weight percentage of AlCl₄ during intercalation, which may temporarily increase the capacity for that recharge. However, imagine if excessive residual AlCl₄ ions are accumulated within the graphite electrode at the beginning of recharge, the excessive residual AlCl 4 ions in graphite could reduce the concentration gradient between two electrodes that hinders the diffusion of AlCl₄ during the next recharge, ultimately leading to a decrease in capacity for that cycle. 3.3: Parametric studies of the LSTM network for C extreme prediction High accuracy in LSTM networks depends on access to large data sets [29] . However, battery life can be limited during burst-mode discharge, creating a challenge for the C extreme prediction due to the lack of extensive datasets. Therefore, it’s crucial to develop methods that improve LSTM accuracy while operating within these data constraints. We train the first 70% of the time-series C extreme data to forecast the remaining 30%. When artificial intelligence forecasts the C extreme for each test cycle, we conduct 10 trials and then average the results of the best three cycles. Due to limited data in the burst-mode discharge, we manually identify which LSTM parameters massively impact the pursuit of high AI accuracy for extended usage [21] . Figure 6a illustrates that using a small hidden unit not only degrades the predicted capacity in the early cycles but also compromises accuracy over long-range cycles. Meanwhile, Figure 6b demonstrates that an inappropriate initial learning rate can result in negative capacities for long-range predictions. Figures 6a and 6b demonstrate that AI accuracy is highly dependent on the cycle number, with prediction errors increasing substantially at larger cycle numbers. In contrast, the other four factors, such as minimum batch size, epoch length, gradient threshold, and the drop period of the learning rate, affect AI accuracy in a more random manner, lacking a similar error dependence on the cycle number. Therefore, we have not plotted AI accuracy against these four factors for clarity. We identify the optimal parameters as follows: a batch size of 32 (within the range of 8 to 256), an epoch length of 500 (from 100 to 1000), hidden unit of 800 (from 100 to 1000), an initial learning rate of 0.2 (within 0.001 to 0.5), a gradient threshold of 1.0 (within 0.5 to 1.5), and a drop period for the learning rate of 125 (between 50 and 150). Using the identified factors, we present the optimal AI results in Figure 7, which reflect a reasonable level of accuracy. The success of the AI predictions is grounded in several key techniques. First, we analyzed the dependence of prediction errors on the cycle number, as long-range predictions can be particularly challenging. This analysis provides valuable insights into which parameters should be optimized finer on long-range predictions. Second, the burst mode discharge consistently reduces the battery voltage to 0V, resulting in a vertical line in the data. This consistency means that the final capacity point for each discharge remains the same, helping the AI to focus on the C extreme values only. Thirdly, we establish a constant charging rate, ensuring that the slope of the charging curve stays stable manually. The second and third techniques serve as data augmentation that minimizes uncertainty associated with a limited dataset, thereby improving AI predictions. Despite the presence of capacity oscillation during burst mode usage, this AI tool can still effectively predict the extreme capacity C extreme which will provide valuable insights for battery management in high-performance scenarios. Figure 1: (a) The intercalation process of AlCl₄-graphite-based batteries. The dielectric constant plays a major role in affecting the completeness of the stage transition. We assume that the dielectric constant is independent to the weight percentage of tetrahedral AlCl₄ ions, where the square of effective charge C Bader = 1. (b) The intercalation process of AlCl₄-graphite-based batteries is influenced by temperature, which affects the transitions from stage 3 to stage 2 and from stage 2 to stage 1. The dielectric constant as a function of the weight percentage of tetrahedral AlCl 4 ion is examined, with ε(wt) obtained from a linear fit of the four relative permittivity in each stage, as presented in Table 1 of the supplementary material. Figure 2. (a) The geometric effect of AlCl₄ ions on the stage transition in AIB. (b) Relationship between effective charge of AlCl₄ ions and average stage number in AIBs at the weight percentage of tetrahedral AlCl 4 ion of 40%. The x-axis represents the effective charge of the AlCl₄ ion, ranging from -1.0 to -0.85, while the y-axis shows the corresponding average stage number. The trend observed in the graph indicates that as the effective charge of the AlCl₄ ion becomes less negative, the average stage number increases (i.e. the impedance of pure stage-1 configuration). Figure 3: The regional stage configuration (not-to-scale) corresponding to an average incomplete stage number of approximately 2.5 at 330K. The purple color indicates stage 3, while green represents stage 2. White denotes unfilled conditions. The integers indicate the local stage number. The tetrahedral AlCl 4 ions are filled, where the Bader charge is about 0.8 Figure 4: This illustration presents the regional stage configuration (not-to-scale) with an average incomplete stage number of approximately 3.3 at 330K. In this depiction, purple indicates stage 3, red denotes stage 4, and white shows unfilled conditions. Integers represent the local stage number. The tetrahedral AlCl 4 ions are filled, where the Bader charge is about 0.8 Figure 5: The charge & burst-mode discharge sequence continues up to 48 cycles. Figure 6: (a) Impact of Hidden Unit (HU) on predicted capacity. Utilizing a small number of hidden units degrades predictive capability during early cycles and more seriously affects accuracy in long-range cycles. (b) Effect of initial learning rate on capacity predictions. not-yet-known not-yet-known not-yet-known unknown Figure 7: Optimal AI performance with selected parameters against the experiment. 4. Conclusion: Our Monte Carlo simulation focuses on the stage transitions in aluminum-ion batteries (AIBs), highlighting that the pursuit of an excessively high dielectric constant may inadvertently complicate the completion of the Stage 1 transition (or limit the intercalation efficiency). We also examine the factors such as temperature, the shape of AlCl 4 ion, and charge transfer within the intercalated graphite that affects the stage 1 transition. We also maximize the discharge rate for our aluminum-ion battery (AIB) and observe a capacity oscillation of approximately 20% experimentally. This indicates that battery management is necessary to maintain consistent capacity after each recharge during burst mode usage. The prediction of the capacity oscillation is feasible. Our study identifies optimal parameters and applies data augmentation techniques to enhance the accuracy of AI predictions in the context of capacity uncertainty, resulting in reasonable outcomes. 5. Experiment: Battery Fabrication The aluminum-ion battery is constructed using anode materials (Aluminium) and cathode material (carbon), with an electrolyte designated as [BMIm]Cl/AlCl 3 . [20] The battery features a coin size of CR2032, and the separator is made purchased from Whatman GF/F (Glass Microfiber Filter). During the testing process, the battery is slowly charged and then quickly discharged over 50 cycles with the help of the workstation (Neware Battery Test System CT-4008T). The applied charging voltage is 3V, with the discharge ending at 0.00001A. To investigate the maximized change in capacity under an extreme condition of high-rate discharge, we create a scenario in which the battery is discharged rapidly through a short circuit (mimic burst-mode), followed by a breathing period of 1 minute before the subsequent charging. Each charging session is fixed at a long duration of 5 hours to regain the thermal equilibrium. The entire cycle test is performed at an environmental temperature of 290K. A glove-box environment is used to maintain an oxygen- and moisture-free atmosphere. Acknowledgements We thank the CPCE Research Fund (SEHS-2024-334(J) and SEHS-2024-332(J)). We acknowledge the Department of Industrial and System Engineering at The Hong Kong Polytechnic University for providing simulation support. not-yet-known not-yet-known not-yet-known unknown Author Contributions Conceptualization, C.H. Wong.; methodology, C.H. Wong, K.C.Lam; computation (Monte Carlo & AI), C.H.Wong, computation (ab-initio), C.H.Wong, X.Chen; Experiment (K.C.Lam); validation, C.H. Wong, X. Chen, K.C. Lam; formal analysis, C.H.Wong, X.Chen, X.Hu, L.Y.F Lam; data curation, C.H.Wong; resource, X.Hu, L.Y.F Lam, W.K. Loh, C.Y.Tang, Y.M.Tang, W.C.Law, C.P.Tsui; writing, C.H.Wong, K.C.Li, editing, C.H.Wong, J.Dai; visualization, C.H.Wong, X.Chen. The first two authors contributed equally to this work. 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Energy & Environmental Science, 17, 4929-4943 (2024) [29] Franyell Silfa, Jose Maria Arnau, Antonio González, Boosting LSTM Performance Through Dynamic Precision Selection, 2020 IEEE 27th International Conference on High Performance Computing, Data, and Analytics (HiPC), DOI: 10.1109/HiPC50609.2020.00046 Supporting Information Title: Investigating Incomplete Stage Transition in Aluminum Ion Batteries for Performance Enhancement and the Forecast for Capacity Oscillation towards High-Rate Discharge Modes 2 Xuanming Chen, 2 Ka Chun Li, 1 King Cheong Lam, 1 Wai Keung Loh, 3 Chak-yin Tang, 3 Yuk Ming Tang, 3 Wing Cheung Law, 3 Chi Pong Tsui, 4 Jiyan Dai, 2 Leung Yuk Frank Lam*, 2 Xijun Hu*, 1 Chi Ho Wong* Table 1: The dielectric properties and the layer-to-layer distance [16] of the intercalated graphite Tetrahedral AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) Planar AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) 16 6.2 8.36 16 8.9 6.22 28 9.1 8.52 28 14.7 6.30 37 11.2 8.69 37 19 6.37 44 12.9 8.76 44 22.4 6.46 Stage 2 Tetrahedral AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) Planar AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) 10 8.5 6.07 10 15.9 4.72 16 11.9 6.09 16 21.9 4.79 23 16.0 6.12 23 28.9 4.83 28 18.9 6.11 28 34.0 4.93 Stage 3 Tetrahedral AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) Planar AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) 7.5 11.8 5.11 7.5 14.3 4.29 11 15.7 5.16 11 28.7 4.33 16 21.5 5.2 16 25 4.36 21 27.5 5.22 21 31.3 4.42 Stage 4 Tetrahedral AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) Planar AlCl 4 (wt%) Relative permittivity Interlayer distance(Å) 5 16.1 4.72 5 18.9 3.97 8 21.2 4.74 8 23.7 3.98 13 29.5 4.76 13 31.9 4.00 16 34.6 4.78 16 36.8 4.01 Figure S1: The average stage number as a function of weight percentage of tetrahedral AlCl 4 ion under different trials. The slopes across the stage transition are consistent. Left: Bader charge = 1; Right: Bader charge = 0.86. Information & Authors Information Version history V1 Version 1 22 February 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords ai forecast aluminum-ion batteries high-rate discharge incomplete stage mechanism Authors Affiliations Xuanming Chen The Hong Kong University of Science and Technology View all articles by this author Ka Chun Li The Hong Kong University of Science and Technology View all articles by this author King Cheong Lam 0000-0002-3079-3254 The Hong Kong Polytechnic University View all articles by this author Wai Keung Loh The Hong Kong Polytechnic University View all articles by this author Chak-yin Tang The Hong Kong Polytechnic University View all articles by this author Yuk Ming Tang 0000-0001-8215-4190 The Hong Kong Polytechnic University View all articles by this author Wing Cheung Law The Hong Kong Polytechnic University View all articles by this author Chi Pong Tsui The Hong Kong Polytechnic University View all articles by this author Ji-Yan Y. Dai 0000-0001-8938-7835 The Hong Kong Polytechnic University View all articles by this author Frank Leung-Yuk Lam The Hong Kong University of Science and Technology View all articles by this author Xijun Hu 0000-0001-5561-5246 The Hong Kong University of Science and Technology View all articles by this author Chi Ho Wong 0000-0002-6026-0600 [email protected] The Hong Kong Polytechnic University View all articles by this author Metrics & Citations Metrics Article Usage 615 views 160 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Xuanming Chen, Ka Chun Li, King Cheong Lam, et al. Investigating Incomplete Stage Transition in Aluminum Ion Batteries for Performance Enhancement and the Artificial Intelligence Forecast for Capacity Oscillation towards High-Rate Discharge Batteries. Authorea . 22 February 2025. 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