Active Material Particles Research Articles

PVDF and PEO Catholytes in Solid‐State Cathodes Made by Conventional Slurry Casting

AbstractAll‐solid‐state Li batteries are desired for better safety and energy density than Li‐ion batteries. However, the lack of a penetrating liquid electrolyte requires a much different approach to the design of cathodes. The solid catholyte must enable good Li+ conduction, form good interfaces with active material particles, and have the strength to bind the cathode together during repeated volume changes. Catholyte formulation is often simply adapted from Li‐ion design principles, adding a Li salt to the PVDF binder. Here we show that such a PVDF binder at 10 wt % loading is a starved catholyte condition that compromises cell performance. By substituting a 70 : 30 blend of PVDF:PEO, performance is improved while maintaining nearly the same areal loading of LFP active material. Increasing the catholyte fraction to 16 % can also improve performance, but in this case the benefit of including PEO is lessened, with PVDF alone being an adequate catholyte. EIS analysis shows that PEO helps to form charge transfer interfaces at 10 % catholyte, but that its inclusion can degrade interfaces when there is ample catholyte at 16 %. It is also shown that catholyte agglomeration can impede bulk Li conduction, indicating that microstructural factors are of critical importance.

Interrogating the Role of Stack Pressure in Transport‐Reaction Interaction in the Solid‐State Battery Cathode

AbstractAs solid‐state batteries (SSBs) emerge as leading contenders for next‐generation energy storage, chemo‐mechanical challenges and instabilities at solid‐solid interfaces remain a critical bottleneck. Ensuring sufficient interfacial contact within composite cathode architectures often requires the application of high stack pressures, posing a significant hurdle in the development of viable, large‐scale SSBs. In this work, the impact of stack pressure is investigated on the performance of solid‐state composite cathodes comprised of single‐crystal LiNi0.5Mn0.3Co0.2O2 (SC‐NMC532) active material particles and a Li6PS5Cl (LPSCl) solid electrolyte phase. By unraveling the complex interplay between stack pressure and microstructure‐dependent mechanisms, the profound influence on interfacial resistances, cathode utilization dynamics, current constriction effects, and lithiation heterogeneities are revealed. Through a comprehensive examination of coupled reaction kinetics and transport interactions at the electrode and particle length scales, the implications of stack pressure at different C‐rates and microstructural arrangements are elucidated, thereby delineating the limiting mechanisms that are prevalent at low stack pressures. This work underscores the critical role of optimizing the cathode microstructure to mitigate the chemo‐mechanical challenges associated with SSB operation at low stack pressures, offering valuable insights and design guidelines for the development of high‐performance SSBs.

Visualizing and Quantifying Electronic Accessibility in Composite Battery Electrodes using Electrochemical Fluorescent Microscopy

Electronic connections between active material particles and the conductive carbon binder domain govern high-energy commercial Li-ion batteries' rate capability and lifetime (LIB). This work develops an in situ electrochemical fluorescent microscopy (EFM) technique that maps fluorescence intensity to these local electronic connections. Specifically, rapid redox kinetics of an electrofluorophore translates to reaction distributions limited by the electronic accessibility of battery electrode regions and individual active material particles. This technique can visualize hot spots, dead zones, and isolated particles on the electrode surface. EFM characterization of a series of LiNi0.33Mn0.33Co0.33O2 electrodes across processing parameters finds a significant negative correlation between the number of disconnected active particles and the rate capability. This low-cost technique provides quantitative mesoscale characterization of commercial LIB electrodes with fast throughput (<60 s) to facilitate rapid research and development and provide manufacturing quality control.

Review on the Polymeric and Chelate Gel Precursor for Li-Ion Battery Cathode Material Synthesis.

The rapid design of advanced materials depends on synthesis parameters and design. A wide range of materials can be synthesized using precursor reactions based on chelated gel and organic polymeric gel pathways. The desire to develop high-performance lithium-ion rechargeable batteries has motivated decades of research on the synthesis of battery active material particles with precise control of composition, phase-purity, and morphology. Among the most common methods reported in the literature to prepare precursors for lithium-ion battery active materials, sol-gel is characterized by simplicity, homogeneous mixing, and tuning of the particle shape. The chelate gel and organic polymeric gel precursor-based sol-gel method is efficient to promote desirable reaction conditions. Both precursor routes are commonly used to synthesize lithium-ion battery cathode active materials from raw materials such as inorganic salts in aqueous solutions or organic solvents. The purpose of this review is to discuss synthesis procedure and summarize the progress that has been made in producing crystalline particles of tunable and complex morphologies by sol-gel synthesis that can be used as active materials for lithium-ion batteries.

Simulating solid-state battery cathode manufacturing via wet-processing with resolved active material geometries

Prior to the development of a solid-state battery cell, researchers have limited knowledge about the microstructure of the electrodes and how they are affected by manufacturing. Therefore, numerical simulations can be considered as a powerful tool to link the fabrication process to the final microstructure of the electrode. In this paper, a numerical simulation of a wet-processed solid-state battery cathode with a formulation of 75 % LiNi9Mn0.5Co0.5O2 (NMC), 17.5 %LPSCl, 5 % Timcal C65 and 2.5 % Polyisobutene (PIB) is presented. From nano-computed tomography images, realistic shapes of active material particles are extracted and used in the simulation, which is well-calibrated to experimental data. In particular, we study the effects of calendering on the microstructure of the simulated cathode and deduce structure-property relations.

Development, characterization and validation of a novel physics-informed equivalent circuit model for silicon–graphite battery cells

The widespread deployment of electric vehicles (EVs), as well as the growing requirements both from manufacturers and consumers, necessitate an increase in energy density with regard to current lithium-ion batteries (LIBs). In this regard, one of the most promising alternatives is the addition of silicon to conventional graphite anodes, thus giving rise to energy-dense LIBs. However, this entails a significant increment in modeling, parameterization and computational complexities due to the interactions between both negative electrode materials. In this article, we present a novel physics-informed equivalent circuit model for cells with blended electrodes, which is able to provide accurate results with respect to a state-of-the-art electrochemical model, not only for the output voltage (≤25 mV RMS), but also internal states, namely active material particle surface concentrations (≤1.2 %) and current distribution (≤2.6 %) at a much lower computational cost. Furthermore, this formulation also allows for a notable simplification of model parameterization. Hence, we describe thorough static and dynamic parameterization processes from half-cell experimental data and impedance measurements. Finally, we validate the proposed model in constant-current as well as dynamic operation, highlighting the influence that the choice of hysteresis model has on the latter. We understand that the presented model is an interesting alternative for the modeling of cells with blended electrodes, and is also suitable for its implementation in Battery Management Systems (BMSs) in EVs.

Tuning the cathode/solid electrolyte interface for high‐performance solid‐state Na‐ion batteries

AbstractThis study examines and compares the impact of various interfacial modification strategies in optimizing the contact resistance between the rigid ceramic electrolyte and cathode active material (AM) in solid‐state sodium‐ion batteries (SSBs). All the cells are fabricated using Na3.1V2P2.9Si0.1O12, Na3.456Mg0.128Zr1.872Si2.2P0.8O12, and Na as a cathode AM, solid electrolyte (SE) and anode, respectively. The AM/SE interface is modified by (1) wetting the interface with organic liquid electrolyte (LE), (2) slurry casting and sintering a thin layer of composite cathode, and (3) infiltrating AM precursors inside the porous SE structure followed by drying and sintering. Despite exhibiting a stable cyclability performance, the SSBs prepared using the LE modification and composite cathode approach possess a low AM loading of &lt; 1 mg·cm−2. On the other hand, the SSBs with infiltrated‐cathode exhibit a superior discharge capacity of ∼ 102 mAh·g−1 at 0.2C and less than 5% capacity fading after 50 cycles at room temperature. Notably, these cells contain a high AM loading of 2.12 mg·cm−2. The microstructural analysis reveals the presence of AM particles inside the pores of the porous SE, allowing for the efficient insertion/removal of sodium ions. The porous scaffold of SE not only provides continuous sodium‐ion conduction pathways inside the cathode structure but also renders stability by accommodating stress induced by volume change during repeated cycling. The outcomes of this work demonstrate the effectiveness of the wet‐chemical infiltration technique in improving the AM loading and storage capacity performance of SSBs working at 25°C.

2D Discrete Element Simulation of Electrode Structural Evolutions in Li‐Ion Battery During Drying and Calendering

Drying and calendering are critical steps in the manufacture of electrodes for lithium‐ion battery that affect their mechanical and electrochemical properties. A 2D representative volume element (RVE) model, including active material and carbon binder domain particles of different shapes and sizes, is developed. The evolution of the RVE structure is simulated using the discrete element method, providing insight into changes in velocity, coordination number, porosity, pore size distribution, tortuosity, and stress. Based on this analysis, a three‐step drying scheme is proposed in accordance with the experimental drying results. In addition, the calendering process significantly improves the mechanical integrity and electronic conductivity of the electrode. Through simulations and experimental observations of changes in surface morphology and porosity, an optimal compression ratio of about 20% is determined for the electrode.

Microstructure impact on chemo-mechanical fracture of polycrystalline lithium-ion battery cathode materials

Anisotropic volume change of layered oxide cathode active material such as Ni-rich nickel–manganese–cobalt-oxide (NMC) during cycling significantly contributes to mechanical degradation, emerging as a primary factor leading to instability issues in these high-capacity cathode active materials for lithium-ion batteries. Despite their commendable energy density, these challenges hinder the broader application of NMC, underscoring the need for rational analysis and innovative solutions to address the associated mechanical instability. In this contribution, we utilize a chemo-mechanically coupled cohesive fracture model, complemented by its 3D finite element implementation, to simulate and analyze the performance and cracking behavior of polycrystalline high-Ni nickel–manganese–cobalt cathode active materials. Thereby the two-way coupling between mechanics and diffusion is regarded both in the bulk and at grain boundary. In particular, novel algorithms are introduced to model the electrolyte penetration along the inter-granular cracks, capturing its intricate impact on particle performance. Utilizing simulations on synthetic and reconstructed microstructure samples derived from experimental images, extensive parameter studies were conducted. These investigations unveiled the intricate influence of various microstructure aspects, encompassing grain morphology, grain/particle sizes, and texture. The findings indicate that secondary active material particles exhibiting smaller grains and radially elongated primary particles, coupled with radially oriented high-diffusivity planes, demonstrate enhanced resistance to inter-granular mechanical damage.

Structural Analysis of Cathode Slurry Under Flow Using New Probe for Rheo-Impedance Measurements

A battery slurry will experience a variety of shear stresses as it goes through the manufacturing process. The full characterization of a slurry for quality control is challenging due to the complex and changing relationship between active material particles, binder, and the carbon black conductive network as a function of these different shear environments. Rheology is a powerful tool for measuring suspension stability and the viscosity at different shear stresses. However, it cannot characterize the structure of the carbon black conductive network because the rheological properties are dominated by the larger active material particles. Poor distribution or aggregation of the carbon black additive will create an electrode with higher electrical resistance, resulting in more heat generation and a shorter cycle life. Electrochemical impedance spectroscopy is an information dense technique that probes the sample using an alternating current or potential at a range of frequencies. Amongst its many applications, EIS can discriminate between simultaneous events that take place over different time scales, such as the measurement of conductivity within a solid electrode vs the ionic conductivity of the electrolyte. Combining these techniques into a simultaneous measurement will characterize the rheological behavior and the structure of the carbon black conductive network under flow and temperature conditions that are relevant for a manufacturing environment. A novel probe for the simultaneous measurement of rheological properties and electrochemical impedance spectroscopy (Rheo-EIS) is herein presented. A structural analysis of Li-ion battery cathode slurries and carbon paste is used to demonstrate the technique.

Influence of Mechanical Degradation in Polycrystalline NMC Particles on the Electrochemical Performance of Lithium-Ion Batteries

Lithium-ion batteries (LIBs) have gained widespread popularity for energy storage systems owing to their high coulombic efficiency and energy density. Within the cathode electrode materials of LIBs, the structural integrity of secondary particles, composed of randomly oriented single-crystal primary active particles, is crucial for sustained performance. The fracture of these particles can occur due to both mechanical stress and chemical interactions within the solid. Modeling LIBs presents a multiphysics challenge as it involves addressing the electro-chemo-mechanical phenomena and their interactions across various length scales. During electrochemical cycling, volume changes in active particles induce mechanical stresses, while the mechanical state of the battery influences the diffusion of lithium.This study proposes a numerical modeling framework to investigate the degradation of active material particles and its impact on electrochemical performance. The model integrates mechanical and electrochemical processes, solving nonlinear equations related to surface charge transfer, lithium diffusion, and mechanical stresses. By incorporating phase field damage, the model tracks crack evolution and mechanical failure of active particles. The coupled equations are solved within a finite element framework using COMSOL Multiphysics.Notably, the model offers numerical insights into intergranular and transgranular fracture within secondary active material particles. The infiltration of liquid electrolyte into cracks is identified as a positive effect, reducing electrochemical overpotential by increasing electrochemically active surface area from particle cracking. However, prolonged cycling with particle cracking poses a notable threat to battery performance and capacity. This comprehensive numerical modeling approach provides valuable insights into the intricate interplay of mechanical and electrochemical factors governing LIB performance and degradation.

Substitution of a Microstructure-Simulation with a Data-Driven Approach for Modelling Mechanical Degradation of Electrodes

One significant aspect of battery aging involves the mechanical degradation of battery electrodes. The intercalation of ions into the active material particles of a lithium-ion battery creates a concentration profile along the radial direction of the active material particle, influenced by transport properties and kinetics. Mechanical stresses arise due to the spatial constraints of intercalated ions, leading to the mechanical degradation of the electrode.Common cathode materials used in practical applications, such as Lithium Nickel Manganese Cobalt Oxide (NMC) or Lithium Iron Phosphate (LFP), undergo a transition from a lithium-poor phase to a lithium-rich phase during the intercalation process. Along this phase boundary, high mechanical stresses occur due to the inconsistency of the concentration profile, resulting in particle fractures. This can lead to electrical isolation and, consequently, the electrochemical inertization of the active particle material, manifested as a reduced battery capacity on a macroscopic scale.Simulating these processes poses computational challenges. Given current computational power, accurately simulating a sufficient number of cycles for a microstructure simulation, which describes transport processes within a battery, is computationally prohibitive. Therefore, this study employs data-driven models. To predict radial concentration profiles within the particle, a physics-informed neural network (PINN) proves useful by extending the cost function with the transport equation. Classical neural networks (ANN) are utilized to calculate the electrical voltage of active material particles. These models are trained with results from microstructure simulations to develop a grey-box model, enabling the inclusion of mechanical degradation in the electrode simulation.Mechanical stresses and degradations are thus investigated under various galvanostatic discharge rates to define an aging-resistant operational window for the battery.

Improving Electrical Conductivity of LiFePO4 through Advanced Synthesis and Multidoping Techniques

Extensive research has been conducted to enhance the electrical conductivity of LiFePO4. Several techniques, including doping with metal cations, synthesizing nanocrystalline grains, and carbon coating, have been employed [1]. Recent advances in material synthesis have revolutionized LiFePO4, such as depositing conductive carbon coatings on active material particles and exploring surface doping techniques. These advanced approaches have significantly improved the mass transfer rate [2]. High-capacity LiFePO4 materials close to the theoretical specific capacitance have been obtained.Efforts are currently underway to improve the electronic and ionic conductivity of LiFePO4 to enhance its efficiency. However, before it can be widely used, the material's low electronic conductivity and suboptimal performance in high-speed regimes must be overcome. Doping with supervalent cations is an effective method for narrowing the energy gap and increasing the electrical conductivity of LiFePO4 [3]. Additionally, the synthesis of nanocrystalline grains and the deposition of conductive carbon coatings on the particle surface contribute to an increase in mass transfer rate, removing critical performance limitations of LiFePO4. Reducing the size of LiFePO4 to the nanoscale has been identified as a strategic method to shorten the diffusion length of Li-ions and accelerate electron-conducting pathways during charging and discharging cycles, ultimately improving the overall performance of the material.This work compares the doping process of LiFePO4 cathode material using two methods: solid-phase synthesis in a planetary ball mill and spray pyrolysis in an inert gas atmosphere. The studies on the synthesis and modification of LiFePO4 have significant potential to overcome existing limitations and unlock its full potential for integration into high energy density batteries. The above multidoping methods enable the production of doped LiFePO4 materials with specific capacitance approaching theoretical values. Acknowledgments This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP19677233).

When and Where Lithium Plating Occurs, Its Correlation with Microstructure Heterogeneity, and the Mechanisms That Initiate and Self-Regulate Electrochemical Heterogeneity

A microstructure scale electrochemical LIB model was used to investigate lithium plating onset, material non-uniform utilization, and in-plane heterogeneities for an NMC-graphite full cell [1]. Model predicts active material particle surface roughness and size distribution (respectively, non-uniform curvature within and between particles) initiate in-plane heterogeneity, and that particle size heterogeneity at the separator interface controls the lithium plating preferential deposition (“Where”). These in-plane heterogeneities are then exacerbated by through-plane heterogeneities induced at fast charge as electrolyte depletion occurs and concentrates intercalation reaction near the anode-separator interface. Also, overall magnitude and occurrence of lithium plating is controlled by effective, or macroscale, microstructure parameters (“When”).As local states of charge start to diverge between nearby active material regions, overpotential differences induced by OCP difference kick in and contribute to reduce these SOC local heterogeneities. However, for staged materials such as graphite, with OCP profile alternating between plateaus and varying regions, this balancing mechanism is, respectively, inactive and active. This leads to a dynamic, non-monotonic, in-plane heterogeneity time evolution for state of charge and Faraday current density, for which their respective in-plane heterogeneity magnitude alternates. Such behavior has been modeled both for the whole electrode at the microstructure scale and at the particle scale. In-plane heterogeneities are usually considered to be detrimental, as they result in material non-uniform utilization (i.e., under and over stressed regions) and earlier degradations. However, this work provides a more granular approach as it discriminates between a harmful in-plane heterogeneity (non-uniform curvature) that triggers SOC in-plane heterogeneity, and a beneficial in-plane heterogeneity (Faraday current density) that contributes to reduce SOC in-plane heterogeneity.This work comprehensively explains the mechanisms that initiate, exacerbate, and regulate heterogeneity at the microstructure scale, while providing some design suggestions to reduce both in-plane and through-plane heterogeneities, as summarized in the graphical abstract.[1] F. L. E. Usseglio-Viretta, A. M. Colclasure, J. Allen, D. P. Finegan, P. Graf, and K. Smith, Microstructure Scale Lithium-ion Battery Modeling, Part I: on lithium plating prediction and heterogeneity, in preparation. Figure 1

Addressing Strain and Porosity Changes of Battery Electrodes Due to Reversible Expansion through DEM Simulations

In this work, discrete element method (DEM) simulations were used to probe changes in electrode porosity, electrode strain, and the resultant pressure changes for composite electrodes comprised of active material and binder particles. Through the results acquired by these simulations, three cases that are representative of two limiting cases for electrode operation, and one case for realistic electrode face pressure during operation were captured and the implications on design and performance are discussed. Predicting changes in the porosity is a unique insight that is difficult if not impossible to capture experimentally but is important for predicting changes in electrochemical performance during cycling, and should be addressed early on in the design phase for automotive and grid storage battery design and performance.

Theoretical design and performance of three-dimensional, pillared FeS2 cathodes

Three-dimensional (3D) electrode design can provide improved capacities and rate capabilities over conventional two-dimensional electrodes by enhancing electrical and ionic transport. Expanding upon our previous modeling efforts for conversion chemistry lithium-ion batteries, we develop a pseudo-four-dimensional (P4D) approach that is subsequently used to investigate the design of a pillared FeS2 electrode. The model considers transport in three dimensions with an additional “fourth” dimension corresponding to the solid-state lithium transport within the active material particles. Additionally, we allow for expansion of the active material during the conversion reaction to understand how internal stresses impact the electrochemical performance of the cell. By optimizing the model with respect to areal capacity, we are able to predict areal capacities up to 16.8mAh/cm2 for an areal current density of 1.78mA/cm2 and a 103% improvement for the three-dimensional electrodes over planar electrodes of equal volume. Despite the promising results, our simulations suggest that 3D design may be difficult for conversion cathode materials due to the large internal stresses that arise during conversion. Nevertheless, the model is robust and adaptable to other materials that may be more suitable for 3D electrodes due to a lesser change in volume during discharge.

Polyacrylonitrile as a binder realizes high-rate activated-carbon-based supercapacitors

Highly polar CN functional groups on polyacrylonitrile (PAN) facilitate strong hydrogen bonding and dipole-dipole interactions with hydroxyl groups on the surfaces of active materials and current collectors. Here we report that the strong interaction between PAN and carbon black (CB) particles facilitates a uniform distribution of CB particles within the electrode and forms a well-connected conductive network on the surface of active material particles. This significantly enhances electron transport within the electrode, offering superior rate performance and cycling stability beyond traditional binders like polyvinylidene fluoride (PVDF). Activated carbon (AC) electrodes containing 7.70 wt.% PAN binder (AC-7.7PAN) deliver areal capacitances over 0.60 F cm⁻2 at a scan rate of 500 mV s⁻1, and exhibits a high gravimetric energy density (Eg) of 26.20 Wh kg⁻1 and high areal energy density (Ea) of 0.33 mWh cm⁻2 at a current density of 1 A g⁻1. An AC-7.7PAN coin-cell supercapacitor maintains up to 62 % of its initial capacitance at a scan rate of 200 mV s⁻1, while a controlled AC-7.7PVDF coin-cell keeps only 37 % under the same conditions. The AC-7.7PAN coin-cell retains 91 % of its capacity even after 50,000 charge/discharge cycles at a constant current of 5 A g⁻1. The ability of PAN to evenly distribute conductive agents might be attractive for other power-type electrochemical electrodes, for which effective electron transport are extremely required.

A Formula to Customize Cathode Binder for Lithium Ion Battery

AbstractThe binder plays a crucial role in binding the solid electrode components and fixing them to the current collector, ensuring good contact and transformation. The high‐energy‐density cathode poses several challenges for the Polyvinylidene fluoride (PVDF) binder, such as high electrode potential, mass loading, and binding force. Although various new binders are proposed to optimize the electrochemical performance of cathode, the design focus and mechanisms often lack universality. This study introduces a design strategy for the cathode binder from the perspective of molecular structure design. The performance of the binder is optimized by adjusting the soft‐hard and hydrophilic‐hydrophobic balances of the polymer, and the effectiveness of this strategy is verified in the LiCoO2 (LCO) system. The optimized copolymer binder improves the cycling stability of the LCO electrode under high load and low binder content conditions and even achieves stable operation at a high charging voltage of 4.6 V. The mechanism for improving the performance of LCO electrodes is that the optimized binder stabilizes the electrode structure, the active material particle structure, and the active material interface. This design strategy provides a valuable reference for customizing cathode binders.

Modeling Rate Dependent Volume Change in Porous Electrodes in Lithium-Ion Batteries

Automotive manufacturers are working to improve individual cell, module, and overall pack design by increasing the performance, range, and durability, while reducing cost. One key piece to consider during the design process is the active material volume change, its linkage to the particle, electrode, and cell level volume changes, and the interplay with structural components in the rechargeable energy storage system. As the time from initial design to manufacture of electric vehicles decreases, design work needs to move to the virtual domain; therefore, a need for coupled electrochemical-mechanical models that take into account the active material volume change and the rate dependence of this volume change need to be considered. In this study, we illustrated the applicability of a coupled electrochemical-mechanical battery model considering multiple representative particles to capture experimentally measured rate dependent reversible volume change at the cell level through the use of an electrochemical-mechanical battery model that couples the particle, electrode, and cell level volume changes. By employing this coupled approach, the importance of considering multiple active material particle sizes representative of the distribution is demonstrated. The non-uniformity in utilization between two different size particles as well as the significant spatial non-uniformity in the radial direction of the larger particles is the primary driver of the rate dependent characteristics of the volume change at the electrode and cell level.

Diffusion-induced stress amplification in phase-transition materials for electrodes of lithium-ion batteries

This work sheds the light on the stress amplification in active material particles of electrodes caused by the localized lithium concentration inhomogeneity due to phase transitions. This is a significant issue usually neglected in the literature, as generally the ideal Fickian diffusion model is used to describe the lithium diffusion, which particularly fails when dealing with phase change materials, resulting in the underestimation of the stress. In turn, this results in the underestimation of the fracture behavior of the electrode and the battery degradation, ultimately.To overcome these limitations, this work proposes a mechanical-transport model where the lithium transport is modeled according to the non-ideal solution theory with an equivalent diffusion coefficient depending on the potential of the host material vs Li/Li+. The results show that the proposed model correctly describes the concentration distribution within the particle of phase-change materials (graphite is chosen as a case study), in agreement with the existent experimental measurements. The differences with respect to the traditional Fickian diffusion model is substantial as the stress is up to 85% higher with the proposed model and the concentration distribution can capture the inhomogeneity caused by phase transitions.