Lithiation Phase Maps in Battery Electrodes

• Lithiation phase maps are detailed representations that track the spatial and temporal evolution of chemical, structural, and mechanical phases during lithium insertion into electrode materials.
• They integrate advanced operando imaging, computational phase-field models, and deep learning analysis to reveal phase boundaries, stress evolution, and reaction kinetics in battery electrodes.
• Insights from these maps drive materials optimization by correlating electrode geometry, phase kinetics, and mechanical stress, thereby informing design strategies for improved battery durability and performance.

Lithiation phase maps describe the spatial and temporal evolution of chemical, structural, and mechanical phases that arise during lithium insertion into electrode materials. In the context of phase-transforming battery electrodes, lithiation phase maps record the spatial distribution of distinct phases (e.g., crystalline/amorphous, Li-rich/Li-poor, or different intercalation stages) and link these patterns to electrochemical, mechanical, and architectural properties of electrodes. The concept encompasses atomistic, mesoscale, and continuum scales and serves as a fundamental descriptor for predicting lithiation pathways, stress evolution, phase boundary kinetics, degradation, and reversibility during battery cycling. Recent advances including operando imaging, computational phase-field modeling, and deep learning–based image analysis have yielded highly resolved lithiation phase maps, driving progress in both mechanistic understanding and materials optimization for next-generation lithium-ion and lithium-metal batteries.

1. Fundamental Mechanisms in Lithiation Phase Maps

Lithiation phase maps track the development of phase boundaries and the spatial progression of reaction fronts as lithium inserts into or is extracted from active materials such as silicon, graphite, transition metal oxides, or phosphates. In crystalline silicon, lithiation proceeds via the movement of a sharp phase boundary (∼1 nm) that separates the unreacted crystalline core from an amorphous, lithiated shell (a–LiₓSi) (1107.5739). High-resolution TEM directly reveals such sharp interfaces, and real-time curvature measurements enable mapping of local lattice strains and stresses. In V₂O₅ nanoparticles, STXM-based phase mapping (supported by deep learning segmentation) quantitatively resolves multi-phase regions—e.g., ε–Li₀.₃V₂O₅, ε–Li₀.₄₅V₂O₅, δ–Li₀.₉V₂O₅ (Lin et al., 24 Jul 2025).

Phase-field and Cahn–Hilliard reaction models capture the transition from homogeneous "solid-solution" diffusion to two-phase shrinking-core or core–shell morphologies, naturally predicting the nucleation and inward movement of diffuse or sharp phase boundaries under different thermodynamic and kinetic regimes (Zeng et al., 2013, Zhao et al., 2015, Fleck et al., 2018). The formation and propagation of these boundaries are central to the construction and interpretation of lithiation phase maps.

2. Multiscale Mapping Methodologies

Lithiation phase maps are generated using a variety of experimental, computational, and data-science methodologies, each tailored to probe different length scales and phenomena.

• Operando Imaging: Spatially resolved operando techniques—including focused synchrotron X-ray diffraction (Tardif et al., 2020), neutron imaging and diffraction (Strobl et al., 13 Nov 2024), and STXM (Lin et al., 24 Jul 2025)—provide direct phase mapping within electrodes. Diffraction signatures of unique LiₓC₆ stages in graphite or phase-specific attenuation profiles in neutron imaging are translated to phase fractions and local lithium stoichiometry using empirically or theoretically derived calibration relationships (e.g., $d = 2\pi/q$, $x = f(q)$).
• Mathematical Modeling: Phase-field and Cahn–Hilliard reaction models yield simulated phase maps by integrating governing equations that couple lithium concentration evolution, reaction kinetics, and (when appropriate) elastic and fracture fields (Zhao et al., 2015, L'vov et al., 2021, Yousfi et al., 30 Oct 2024). The models are implemented using numerical PDE solvers, with realistic electrode architectures obtained via stochastic geometry, Laguerre tessellation, or experimental 3D reconstructions.
• Deep Learning–Enabled Analysis: For complex or large-scale imaging data, Mask R-CNN segmentation isolates battery nanoparticles (Lin et al., 24 Jul 2025). These masks are combined with spectral decomposition (e.g., SVD) of hyperspectral data to produce per-particle phase composition maps. Mathematical aggregation over all pixels within each mask, weighted by phase assignment coefficients, yields spatially resolved lithiation states and enables correlation of phase maps with particle geometry.
• Quantitative Formulation Example: For segmented nanoparticles,

$$C_{hw}^N = \sum_i x^i\, \mathcal{M}_{hw}^N\, \phi_{hw}^i$$

where $C_{hw}^N$ is the lithiation map of particle $N$, $x^i$ are stoichiometry coefficients, $\mathcal{M}_{hw}^N$ the segmentation mask, and $\phi_{hw}^i$ the phase map from SVD (Lin et al., 24 Jul 2025).

3. Correlation Between Geometry, Stress, and Phase Patterns

Lithiation phase maps serve not only as descriptors of Li distribution, but also as predictors of stress, mechanical degradation, and overall battery performance.

• Stress Evolution: In phase-transforming materials such as Si, sharp concentration gradients at the phase boundary produce mechanical stresses up to ∼0.5 GPa during lithiation (compressive in the amorphous shell, tensile upon delithiation) (1107.5739). Inhomogeneous phase transformation and the associated stress jumps lead to fracture, damage, and microstructural fragmentation, as can be quantitatively mapped by coupling in situ curvature measurements with phase front position.
• Particle Geometry–Lithiation Correlation: Deep learning-enabled phase mapping allows statistical correlation of geometric descriptors (perimeter, area, aspect ratio, circularity, convexity, solidity, orientation, perimeter-to-area ratio) with lithiation state (Lin et al., 24 Jul 2025). Smaller, more isotropic, and convex particles are found to lithiate more uniformly, while elongated or irregular geometries correlate with phase heterogeneity and greater stress concentration. The perimeter-to-area ratio emerges as a key parameter linking available surface for Li diffusion to lithiation uniformity.
• Elastic and Crack Propagation Effects: Phase-field simulations including large-strain and fracture mechanics (Zhao et al., 2015, Yousfi et al., 30 Oct 2024) demonstrate that interfaces—especially those at particle boundaries or crack surfaces—host steeper concentration gradients and higher local reaction rates, driving stress accumulation, interface propagation, and potentially crack growth.

4. Kinetics, Phase Boundary Phenomena, and Nonuniform Reaction

Lithiation phase maps reveal complex kinetic and thermodynamic phenomena that are not apparent from bulk or average measurements.

• Nonuniform Fronts and Reaction Hot-Spots: When reaction kinetics are fast compared to bulk diffusion, lithiation proceeds as a shrinking-core or core–shell process, often yielding a sharp interface. In slow-kinetic or highly diffusional systems, nucleation and growth of phase domains lead to rough, nonuniform fronts (Zhao et al., 2015, L'vov et al., 2021). The mapping of the reaction rate as a function of local gradient (with maximal rates at phase interfaces) is both a simulation and an experimental observable (Tardif et al., 2020, Strobl et al., 13 Nov 2024).
• Influence of Phase Transitions on Homogeneity: Operando X-ray and neutron mapping across thick graphite electrodes exposes the coexistence of multiple LiₓC₆ phases during battery operation, with heterogeneity maxima often found at stage transitions and surprisingly homogeneous profiles seen at the LiC₆/LiC₁₂ interface—attributed to slowed exchange kinetics (Tardif et al., 2020, Strobl et al., 13 Nov 2024).
• Sequential Symmetry Breaking: When phase-separation thermodynamics are operative, lithiation proceeds via sequential symmetry breaking (SB) events—localized transitions from a homogeneous to a bi-phasic regime (Sheintuch et al., 2021). Porous electrode models reduced to "solid two-zone" approximations successfully capture the timing, composition, and spatial fraction involved in each SB event as a function of imposed current and "noise" (parameter nonuniformity or potential gradient).

5. Mathematical and Physical Formalism

Lithiation phase maps are constructed and interpreted using a suite of mathematical tools:

Formalism	Description	Example Source
Cahn–Hilliard (CHR) equation	Captures phase separation and front propagation	(Zeng et al., 2013)
Modified Butler–Volmer kinetics	Surface and interface reaction rates as function of local potential	(Zhao et al., 2015)
Stoney equation	Maps wafer curvature to film stress	(1107.5739)
Normalized Absolute Averaged Deviation (NAAD)	Quantifies lithium heterogeneity across electrode	(Tardif et al., 2020)
Deep learning aggregation	Composes per-particle phase maps from segmentation and SVD	(Lin et al., 24 Jul 2025)

Other frameworks, including the Ising model for configurational phase stability in graphite (Pande et al., 2016), Allen–Cahn/phase-field approaches (decoupling order parameter evolution and diffusion), and molecular dynamics informed by embedded-atom potentials (Godet et al., 2019), yield additional quantitative insight. Electro-chemo-mechanical coupling is explicit in most modern phase-field models (Zhao et al., 2015, Yousfi et al., 30 Oct 2024), incorporating terms such as

$$\dot{\phi} = \frac{1}{\tau} \left( -\frac{\delta F}{\delta \phi} + \beta_\phi \text{(SBM surface term)} \right)$$

with $\phi$ the order parameter, $F$ the free energy, and SBM surface terms enforcing interface conditions.

6. Applications to Battery Design and Optimization

Interpretation of lithiation phase maps informs multiple aspects of electrode and cell engineering:

• Design for Homogeneous Lithiation: The mapping of lithiation as a function of geometry motivates the rational design of active materials—favoring reduced size, isotropic shapes, higher convexity, and greater surface-to-volume ratio to minimize nonuniform phase transformation and associated stress (Lin et al., 24 Jul 2025).
• Cycle Life and Reversibility: Identification of critical stress thresholds for fracture and crack propagation assists in establishing operational limits (e.g., voltage windows, degree of lithiation) to avoid catastrophic electrode damage (1107.5739, Jiang et al., 2016).
• Mitigation of Interfacial Degradation: Correlating phase map evolution with regions of SEI formation, lithium plating, and dead lithium enables targeted improvement in ultra-thick electrodes (Strobl et al., 13 Nov 2024).
• Mechanics–Electrochemistry Coupling: Phase maps and simulations that account for coupled stress and Li chemistry tune the rate capability and cycle durability in composite electrodes (Zhao et al., 2015, Fleck et al., 2018, Yousfi et al., 30 Oct 2024).

7. Future Trends and Outlook

Ongoing advances in multimodal operando imaging, large-scale phase-field simulation, and machine learning–driven image analysis are rapidly increasing the spatial and temporal resolution of lithiation phase maps, enabling:

• Real-time, in situ mapping of phase evolution in thick, architected electrodes with microscale (or better) resolution (Strobl et al., 13 Nov 2024).
• Integration of 3D compositional maps with mechanical field measurements (e.g., stress, strain) for fully coupled chemo-mechanical modeling.
• Statistical learning of particle-size, shape, and connectivity effects on lithiation pathways and stress evolution at the ensemble scale (Lin et al., 24 Jul 2025).
• Predictive modeling of degradation and lifetime based on observed and simulated evolution of phase maps under realistic operating conditions.

Such developments are anticipated to accelerate materials selection, optimization of electrode architectures, and the development of operational protocols maximizing uniformity, reversibility, and performance in advanced lithium-based energy storage systems.