11.1 Mechanisms of lithium dendrite growth in solid electrolytes

Lithium dendrite growth in solid electrolytes is a major hurdle for solid-state batteries. It starts with lithium nucleation at defects and grows due to ion concentration gradients and electric fields. Understanding this process is crucial for developing safer, more efficient batteries.

The formation of these dendrites is influenced by various factors, including temperature, pressure, and electrolyte composition. Thermodynamics and kinetics play key roles, with energy barriers and rate-determining steps affecting the growth process. Mastering these mechanisms is essential for preventing battery failure and improving performance.

Lithium Dendrite Formation

Nucleation and Growth Mechanisms

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• Lithium dendrite formation in solid-state electrolytes involves deposition and growth of lithium metal structures
• Initial stage starts with nucleation of lithium at defect sites or inhomogeneities on electrode-electrolyte interface
• Concentration gradient of lithium ions and electric field distribution within solid electrolyte drive dendrite growth
• Butler-Volmer equation describes relationship between current density and overpotential, influencing rate of lithium deposition and dendrite growth
• Mechanical stress accumulation at electrode-electrolyte interface leads to formation of voids or cracks, providing pathways for dendrite propagation
• Competition between surface diffusion and bulk diffusion of lithium atoms determines morphology of growing dendrites
  • Surface diffusion promotes smoother, more compact structures
  • Bulk diffusion tends to result in more branched, dendritic growth
• Factors affecting kinetics and thermodynamics of dendrite formation
  • Temperature: Higher temperatures generally increase diffusion rates and can alter growth patterns
  • Pressure: Increased pressure can suppress void formation and influence dendrite morphology
  • Electrolyte composition: Additives or dopants can modify interfacial properties and dendrite growth behavior

Thermodynamics and Kinetics

• Gibbs free energy drives the overall process of lithium dendrite formation
  • ΔG = ΔH - TΔS, where ΔG is the change in Gibbs free energy, ΔH is the enthalpy change, T is temperature, and ΔS is the entropy change
• Activation energy barriers exist for various steps in dendrite formation process
  • Nucleation requires overcoming an energy barrier to form stable lithium clusters
  • Growth involves overcoming energy barriers for lithium ion transport and incorporation into the dendrite structure
• Rate-determining steps in dendrite formation can vary depending on conditions
  • Mass transport of lithium ions through the electrolyte
  • Charge transfer at the electrode-electrolyte interface
  • Surface diffusion of adatoms on the growing dendrite
• Tafel equation describes the relationship between overpotential and current density in electrochemical systems
  • η = a + b log(i), where η is overpotential, a and b are constants, and i is current density
• Arrhenius equation relates reaction rate constants to temperature
  • k = A exp(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is activation energy, R is the gas constant, and T is temperature

Interfacial Instabilities in Dendrite Growth

Morphological Instabilities

• Mullins-Sekerka instability describes morphological instability of planar interface during solidification or electrodeposition, leading to dendrite formation
  • Small perturbations on a flat interface can grow exponentially under certain conditions
  • Characterized by a critical wavelength below which perturbations are damped and above which they grow
• Surface energy anisotropy at electrode-electrolyte interface results in preferential growth directions for dendrites
  • Crystallographic orientation of the substrate can influence initial dendrite growth direction
  • Anisotropic surface energies can lead to faceted dendrite structures
• Local variations in lithium ion concentration and electric field strength at interface create hotspots for dendrite nucleation
  • Concentration gradients can arise due to non-uniform ion transport or consumption
  • Electric field inhomogeneities can be caused by surface roughness or local charge accumulation
• Space charge layer formation at interface leads to enhanced local electric fields, promoting dendrite growth
  • Debye length characterizes the thickness of the space charge layer
  • Non-uniform space charge distribution can create preferential sites for dendrite initiation

Mechanical and Interfacial Factors

• Mechanical stress concentrations at interface cause localized deformations, creating favorable sites for dendrite initiation
  • Stress can arise from volume changes during cycling or from external pressure
  • Stress concentration factors can be influenced by interface geometry and material properties
• Stability of solid electrolyte interphase (SEI) layer and its uniformity significantly influence likelihood of dendrite nucleation and growth
  • SEI composition and structure affect lithium ion transport kinetics
  • Inhomogeneities in SEI can create localized high-current density regions
• Interfacial adhesion between electrode and electrolyte impacts dendrite growth behavior
  • Strong adhesion can help suppress void formation and reduce dendrite initiation sites
  • Weak adhesion can lead to delamination and create pathways for dendrite propagation
• Wetting properties of lithium on the solid electrolyte surface influence dendrite morphology
  • Contact angle measurements can provide insights into wetting behavior
  • Surface modifications can be used to alter wetting properties and control dendrite growth

Current Density and Overpotential Effects

Dendrite Growth Kinetics

• Current density and overpotential determine rate and morphology of lithium dendrite growth in solid electrolytes
• Higher current densities lead to faster dendrite growth and more branched structures due to increased lithium ion flux
  • Diffusion-limited aggregation (DLA) model can describe dendritic growth at high current densities
  • Transition from compact to dendritic growth occurs above a critical current density
• Sand's time equation relates critical current density to time required for dendrite initiation, providing insights into dendrite growth kinetics
  • $t_{Sand} = \frac{\pi D}{4} \left(\frac{zFC_0}{J_{lim}}\right)^2$
  • Where t_Sand is the Sand's time, D is the diffusion coefficient, z is the ion charge, F is Faraday's constant, C_0 is the initial concentration, and J_lim is the limiting current density
• Overpotential influences driving force for lithium deposition and affects dendrite growth mode
  • Tip-growing dendrites typically form at higher overpotentials
  • Root-growing dendrites are more common at lower overpotentials
• Transition from mossy to dendritic growth occurs at critical current densities, as described by Chazalviel model
  • Mossy growth characterized by compact, rounded structures
  • Dendritic growth results in more elongated, branched structures

Current Manipulation Techniques

• Pulsed current techniques manipulate dendrite morphology by controlling balance between deposition and relaxation periods
  • On-time allows for lithium deposition
  • Off-time promotes relaxation and redistribution of lithium ions
• Relationship between current density, overpotential, and dendrite growth non-linear and influenced by factors such as temperature and electrolyte properties
  • Butler-Volmer equation describes non-linear relationship: $i = i_0 \left[e^{\frac{\alpha_a n F \eta}{RT}} - e^{-\frac{\alpha_c n F \eta}{RT}}\right]$
  • Where i is current density, i_0 is exchange current density, α_a and α_c are transfer coefficients, n is number of electrons transferred, F is Faraday's constant, η is overpotential, R is gas constant, and T is temperature
• Current ramping techniques can be used to control dendrite nucleation and growth
  • Gradually increasing current density can promote more uniform lithium deposition
  • Helps prevent sudden onset of dendrite formation at high current densities
• Asymmetric cycling protocols can influence dendrite growth behavior
  • Different charge and discharge rates can affect the balance between lithium deposition and stripping
  • Can be used to promote more reversible lithium plating/stripping cycles

Electrolyte Microstructure and Defects

Grain Boundaries and Crystalline Defects

• Microstructure of solid electrolytes, including grain boundaries, pores, and crystalline defects, significantly affects lithium ion transport and dendrite formation
• Grain boundaries in polycrystalline electrolytes act as preferential pathways for dendrite growth due to enhanced ionic conductivity or mechanical weakness
  • Triple junctions where three grains meet can be particularly susceptible to dendrite penetration
  • Grain boundary engineering can be used to control dendrite propagation paths
• Point defects influence local lithium ion concentration and mobility, potentially promoting or inhibiting dendrite nucleation
  • Vacancies can enhance lithium ion diffusion (Schottky defects)
  • Interstitials can create local stress fields and affect ion transport (Frenkel defects)
• Presence of impurities or secondary phases in electrolyte creates heterogeneous nucleation sites for dendrites
  • Intentionally introduced dopants can modify electrolyte properties to suppress dendrite growth
  • Unintentional impurities can create localized regions of high ionic conductivity or mechanical weakness

Porosity and Mechanical Properties

• Porosity in electrolyte leads to non-uniform current distribution and localized hotspots for dendrite growth
  • Closed pores can create regions of stress concentration
  • Open pores can provide direct pathways for dendrite propagation
• Mechanical properties of electrolyte play crucial role in resisting dendrite penetration
  • Elastic modulus: Higher modulus materials generally provide better resistance to dendrite penetration
  • Fracture toughness: Increased toughness can help prevent crack propagation and dendrite growth
• Engineered microstructures control dendrite growth pathways and improve battery performance
  • Aligned grain boundaries can create tortuous paths for dendrite propagation
  • Artificially introduced defects can act as "dendrite traps" to limit growth
• Composite electrolytes combine properties of multiple materials to enhance dendrite resistance
  • Ceramic fillers in polymer electrolytes can improve mechanical strength and ionic conductivity
  • Layered structures can create barriers to dendrite propagation while maintaining high ionic conductivity