2.1 Mechanisms of ionic conduction in solids

Ionic conduction in solids is all about how ions move through solid materials. It's crucial for solid-state batteries and other cool tech. The key is understanding how ions hop through crystal structures and what helps or hinders their movement.

This part dives into the nitty-gritty of how ions actually get around in solids. We'll look at different ways ions can move, like jumping into empty spots or squeezing between atoms. It's like understanding the traffic rules for ions in a solid city!

Ionic conduction in solids

Fundamentals of ionic movement

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• Ionic conduction involves movement of ions through crystal lattice facilitated by defects in structure
• Rate of ionic conduction influenced by temperature, pressure, and concentration of mobile ions
• Solid electrolytes exhibit ionic conductivity while maintaining solid-state structure (unlike liquid electrolytes)
• Nernst-Einstein equation relates ionic conductivity to diffusion coefficient and charge carrier concentration in solids
  • Formula: $\sigma = \frac{nq^2D}{kT}$
  • Where σ = ionic conductivity, n = charge carrier concentration, q = charge, D = diffusion coefficient, k = Boltzmann constant, T = temperature

Anisotropy and chemical bonding

• Ionic conductivity in solids typically anisotropic varying depending on crystallographic direction
  • Example: β-alumina exhibits higher conductivity along basal planes compared to perpendicular direction
• Partial ionic character in chemical bonds crucial for understanding potential for ionic conduction
  • Materials with higher degree of ionic bonding (NaCl) generally show greater ionic conductivity than those with more covalent bonds (SiO2)

Mechanisms of ionic transport

Vacancy and interstitial mechanisms

• Vacancy mechanism ions move by jumping into neighboring vacant lattice sites
  • Common in many crystalline solids (NaCl, KCl)
• Interstitial mechanism ions move through interstitial sites in crystal structure
  • Prevalent in some metal halides (AgI, CuI)
• Interstitialcy mechanism combination of vacancy and interstitial mechanisms
  • Ion moves to interstitial site and displaces another ion into regular lattice position
  • Observed in some fast ion conductors (Li3N)

Collective and alternative mechanisms

• Collective mechanism multiple ions move simultaneously in cooperative manner
  • Often observed in superionic conductors (α-AgI, RbAg4I5)
• Knock-on mechanism ions displaced from lattice sites by high-energy particles
  • Creates cascade of ionic movements
  • Relevant in radiation environments or ion implantation processes
• Grain boundary diffusion ions move along grain boundaries in polycrystalline materials
  • Can be faster than bulk diffusion in some cases (YSZ, CGO)
  • Important for nanostructured materials with high grain boundary density

Role of point defects

Types and formation of point defects

• Point defects localized disruptions in crystal lattice facilitating ionic movement
• Schottky defects vacancy pairs of cations and anions maintaining charge neutrality
  • Common in alkali halides (NaCl, KCl)
• Frenkel defects ion displaced from lattice site to interstitial position
  • Creates vacancy-interstitial pair
  • Prevalent in silver halides (AgCl, AgBr)
• Concentration of point defects temperature-dependent following Arrhenius-type relationship
  • $n = N \exp(-\frac{E_f}{kT})$
  • Where n = defect concentration, N = number of lattice sites, Ef = defect formation energy

Influence of point defects on ionic conduction

• Doping intentionally introduces point defects to enhance ionic conductivity
  • Example: Yttria-stabilized zirconia (YSZ) where Y3+ replaces Zr4+ creating oxygen vacancies
• Formation and migration of point defects key factors in determining overall ionic conductivity
• Point defects interact with each other and other crystal imperfections
  • Influences ionic conduction pathways
  • Can lead to complex defect clusters or associations affecting conductivity

Activation energy in ionic conduction

Fundamentals of activation energy

• Activation energy minimum energy required for ion to move from one lattice site to another
• Arrhenius equation describes temperature dependence of ionic conductivity
  • $\sigma = \sigma_0 \exp(-\frac{E_a}{kT})$
  • Where σ = ionic conductivity, σ0 = pre-exponential factor, Ea = activation energy
• Activation energy consists of two components
  • Energy required to form a defect
  • Energy needed for ion migration

Factors affecting activation energy

• Lower activation energy generally results in higher ionic conductivity at given temperature
• Activation energy determined experimentally through temperature-dependent conductivity measurements
  • Arrhenius plot of ln(σT) vs 1/T yields slope proportional to Ea
• Crystal structure and composition significantly influence activation energy
  • Example: Li+ conduction in different structures: Li3N (0.25 eV) < LiI (0.4 eV) < Li2O (1.8 eV)
• Understanding activation energy crucial for designing and optimizing solid electrolytes
  • Guides material selection and modification strategies for enhanced ionic conductivity