2.4 Types of charge carriers in solid electrolytes

Solid electrolytes contain various charge carriers, primarily ionic and electronic. Cations are the most common mobile carriers in battery electrolytes, while anions serve in some systems. Electronic carriers include electrons and holes, contributing to conductivity in certain electrolytes.

Charge carrier behavior is influenced by concentration, mobility, dopants, defects, and temperature. These factors directly impact the overall conductivity of solid electrolytes. Understanding and controlling these aspects is crucial for optimizing performance in applications like batteries and fuel cells.

Charge carriers in solid electrolytes

Types of charge carriers

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• Solid electrolytes contain various charge carriers primarily ionic and electronic in nature
• Cations act as the most common mobile charge carriers in solid electrolytes used for batteries (lithium ions in lithium-ion batteries)
• Anions serve as charge carriers in certain solid electrolyte systems (oxide ions in solid oxide fuel cells)
• Electronic charge carriers include electrons and holes which contribute to conductivity in some solid electrolytes
• Mixed ionic-electronic conductors (MIECs) contain both ionic and electronic charge carriers
  • Allow simultaneous transport of ions and electrons
  • Find applications in fuel cells and gas sensors

Factors affecting charge carrier behavior

• Concentration and mobility of charge carriers directly influence the overall conductivity of the solid electrolyte
  • Higher concentration generally leads to increased conductivity
  • Mobility depends on factors like ion size, charge, and crystal structure
• Dopants and defects in the crystal structure introduce additional charge carriers or enhance mobility of existing ones
  • Aliovalent doping creates vacancies or interstitials
  • Isovalent doping alters lattice parameters
• Temperature impacts charge carrier behavior
  • Higher temperatures generally increase mobility and conductivity
  • Follow Arrhenius-type relationship: $σ = A \exp(-E_a/kT)$ where σ is conductivity, A is a pre-exponential factor, E_a is activation energy, k is Boltzmann's constant, and T is temperature

Properties of mobile ions

Ion transport mechanisms

• Mobile ions in solid electrolytes move through crystal lattice via hopping mechanisms between vacant sites or interstitial positions
  • Vacancy mechanism involves ions jumping into neighboring vacant lattice sites
  • Interstitial mechanism involves ions moving between interstitial positions
• Activation energy for ion migration determines ease with which ions move through solid electrolyte structure
  • Lower activation energy results in higher ionic conductivity
  • Typical values range from 0.1 to 1 eV
• Size and charge of mobile ions influence their mobility and overall ionic conductivity of solid electrolyte
  • Smaller ions generally have higher mobility
  • Higher charge leads to stronger interactions with the lattice, reducing mobility

Structural influences on ion mobility

• Grain boundaries in polycrystalline solid electrolytes act as barriers or pathways for ionic conduction depending on composition and structure
  • Can block ion movement if poorly connected or aligned
  • Can provide fast conduction pathways if well-designed
• Structural features such as ion channels or layered structures facilitate movement of mobile ions in certain solid electrolyte materials
  • NASICON-type structures provide 3D pathways for ion conduction
  • Layered structures like β-alumina allow 2D ion movement
• Concentration of mobile ions affects ionic conductivity with higher concentrations generally leading to increased conductivity
  • Follows a non-linear relationship due to ion-ion interactions
  • Optimal concentration depends on specific material and application

Electronic charge carriers' role

Electronic conductivity mechanisms

• Electronic charge carriers (electrons and holes) contribute to overall conductivity in some solid electrolytes
• Band structure and energy gaps in solid electrolytes determine ease of electronic charge carrier movement
  • Smaller bandgap materials tend to have higher electronic conductivity
  • Larger bandgap materials (>4 eV) typically have negligible electronic conductivity
• Redox-active elements or impurities in solid electrolyte introduce electronic charge carriers
  • Transition metal ions with multiple oxidation states (Fe2+/Fe3+)
  • Oxygen vacancies in oxide-based electrolytes

Impact on electrolyte performance

• Presence of electronic charge carriers leads to undesired self-discharge in battery systems reducing overall efficiency
  • Causes capacity loss over time
  • Shortens battery shelf life
• Electronic conductivity in solid electrolytes often undesirable for battery applications as it can lead to internal short-circuiting
  • Compromises the electrolyte's ability to separate anode and cathode
  • Can result in safety issues such as thermal runaway
• Ratio of ionic to electronic conductivity (transference number) serves as crucial parameter in evaluating solid electrolyte performance
  • Ideal electrolytes have a transference number close to 1 (purely ionic conduction)
  • Calculated as t_ion = σ_ion / (σ_ion + σ_electron)
• Some solid electrolytes such as those used in fuel cells intentionally utilize electronic conductivity for specific electrochemical processes
  • Mixed ionic-electronic conductors in solid oxide fuel cell electrodes
  • Allow for expanded reaction zones and improved performance

Mixed ionic-electronic conductivity

Fundamentals of MIECs

• Mixed ionic-electronic conductors (MIECs) simultaneously transport both ionic and electronic charge carriers
• Total conductivity in MIECs equals the sum of ionic and electronic conductivities
  • σ_total = σ_ion + σ_electron
• MIECs classified based on dominant charge carrier type (ionic or electronic) and relative magnitudes of each conductivity
  • Predominantly ionic MIECs (t_ion > 0.5)
  • Predominantly electronic MIECs (t_electron > 0.5)
  • Balanced MIECs (t_ion ≈ t_electron)

Applications and optimization

• Wagner equation describes relationship between chemical potential gradients and charge carrier fluxes in MIECs
  • Relates oxygen chemical potential gradient to ionic and electronic conductivities
  • Used to analyze oxygen transport in MIEC membranes
• Applications of MIECs include solid oxide fuel cells gas sensors and electrochemical membranes
  • Cathode materials in solid oxide fuel cells (La0.6Sr0.4Co0.2Fe0.8O3-δ)
  • Oxygen transport membranes for gas separation (Ba0.5Sr0.5Co0.8Fe0.2O3-δ)
• Properties of MIECs tuned by adjusting composition microstructure and environmental conditions
  • Doping to alter defect concentrations
  • Controlling grain size and porosity
  • Modifying temperature and atmosphere
• Understanding and controlling balance between ionic and electronic conductivity crucial for optimizing MIEC performance in specific applications
  • Tailoring conductivity ratios for desired functionality
  • Balancing transport properties with stability and compatibility requirements