Vacancy-Tolerant Oxide Electrolytes

Updated 30 December 2025

Vacancy-tolerant oxide electrolytes are materials that support high ionic transport through engineered lattice vacancies while maintaining robust phase stability.
Controlled vacancy formation reduces ion migration barriers and tailors electronic properties, as seen in systems like LiBO₂ and BaHfO₃.
Design strategies such as doping, lattice strain, and nonstoichiometric engineering optimize vacancy concentrations to improve conductivity in electrochemical devices.

Vacancy-tolerant oxide electrolytes are a class of materials engineered to maintain high ionic conductivity and phase stability in the presence of significant concentrations of lattice vacancies. These vacancies—typically A-site, B-site, or anion (oxygen)—play a central role in facilitating fast ionic transport and tuning electronic properties. The compositional, structural, and thermodynamic strategies governing vacancy management in oxides are critical for designing high-performance solid electrolytes and protective coatings in batteries, fuel cells, and other electrochemical systems.

1. Fundamental Concepts and Definitions

Vacancy tolerance refers to a material’s ability to accommodate high vacancy concentrations without detrimental ordering or phase decomposition, and ideally while retaining a conductive (often disordered) crystal lattice. Oxide electrolytes exploit vacancy-mediated transport: the migration of cations (e.g., Li⁺, H⁺) or anions (e.g., O²⁻) through hopping pathways created and amplified by controlled vacancy formation on specific lattice sites. The balance between mobile vacancy density, lattice disorder, and electronic insulation is foundational in vacancy-tolerant systems, enabling applications in environments demanding both high ionic conductivity and robust electronic behavior.

2. Vacancy Formation Energetics and Generation Methods

Vacancy formation energy ( $E_f$ ) quantifies the thermodynamic cost to remove an atom from its lattice site, creating a vacancy. High $E_f$ values (e.g., $E_f(B_{vac}) \approx 8.3$ eV for t-LBO, $7.9$ eV for m-LBO) indicate low equilibrium vacancy densities, so non-equilibrium routes such as neutron irradiation or transmutation reactions are often employed to generate concentrations exceeding $10^{22}$ cm⁻³ (Nguyen et al., 15 Mar 2025).

A-site and B-site doping, as well as controlled deficiency in the desired sublattice, can be engineered to reduce $E_f$ selectively. In BaHfO₃, introducing low-valence cations ( $\mathrm{K}^+$ , $\mathrm{Rb}^+$ , $\mathrm{Cs}^+$ ) or Ba vacancies decreases the oxygen-vacancy formation energy to $E_{vac} < 4.0$ eV and $1.35$ eV, respectively, relative to $6.69$ eV for the pristine lattice, dramatically boosting vacancy concentrations and their utility for proton conduction (Feng et al., 26 May 2025).

3. Vacancy-Induced Structural and Electronic Effects

Vacancies can exert pronounced influence on both the ionic transport pathways and the electronic structure. In LiBO₂, boron vacancies have dual effects:

In tetragonal-LBO (t-LBO), B vacancies widen the band gap ( $E_g$ from $7.3$ to $7.6$ eV), strengthening electronic insulation—ideal for solid electrolyte applications where electronic leakage across 4–5 V cells must be suppressed.
In monoclinic-LBO (m-LBO), B vacancies induce a defect band $0.85$ eV wide, 1–2 eV below the conduction band minimum, narrowing the activation gap for $p$ -type conduction and enabling semiconducting thin film coatings (Nguyen et al., 15 Mar 2025).

Perovskite oxides such as LSTZ₀.₇₅ exhibit grain boundaries hosting 20–30% A-site and 10% B-site vacancies, with negligible Li⁺ depletion even at GBs. Such atomic-scale vacancy tolerance preserves bulk-like ionic conductivity across polycrystalline interfaces—contrasting sharply with insulating GBs in related LLTO where Li depletion dominates (Lee et al., 2022).

Doped zirconias show conductivity peaking at moderate vacancy concentrations ( $c \sim 4$ –$6$%) and then falling at higher $c$ due to strong vacancy-vacancy ordering (⟨111⟩ pairs, ⟨112⟩ strings), an intrinsic fluorite-lattice effect independent of cation type (Marrocchelli et al., 2010).

4. Ionic Migration, Vacancy Ordering, and Lattice Dynamics

Vacancies serve as low-energy “sinks” for ion hopping, lowering migration barriers for mobile species. Climbing-image nudged-elastic-band (CI-NEB) calculations demonstrate:

B-vacancy t-LBO: $E_a$ for Li⁺ drops from $0.85$ eV (pristine) to $0.42$ eV, while B-vacancy m-LBO falls from $0.72$ eV to $0.38$ eV (Nguyen et al., 15 Mar 2025).
In BaHfO₃, Grotthuss-mode H⁺ migration barriers remain $0.28$–$0.77$ eV, controlled by local A-site doping and vacancy-induced distortions (Feng et al., 26 May 2025).

Vacancy-vacancy interactions, especially in fluorite and bixbyite oxides, lead to correlation and clustering at high concentrations. This ordering raises activation barriers (effective $E_{assoc}(c)$ as high as $0.2$ eV), impeding conductivity at excessive vacancy levels (Marrocchelli et al., 2010), while in multi-cation LN-HEOs, phase competition between disordered fluorite (high-T, high entropy, random Vo) and bixbyite (ordered, high Vo) determines percolative transport capacity (Caucci et al., 28 Dec 2025).

5. Thermodynamics, Phase Stability, and Configurational Entropy

The interplay between formation enthalpy $\Delta H_f$ , configurational entropy $S_{config}$ , and synthesis temperature $T$ dictates phase stability, vacancy ordering, and functional performance. In LN-HEOs with tunable Ce fraction ( $x_{Ce}$ ) and oxygen non-stoichiometry ( $\delta$ ), disordered fluorite is stabilized at higher $x_{Ce}$ and $T$ due to the large anion sublattice entropy, with crossover to bixbyite phase only at lower $x_{Ce}$ and $\delta > 0.20$ (Caucci et al., 28 Dec 2025).

$S_{config,anion} = -k_B [\delta\ln\delta + (1-\delta)\ln(1-\delta)]$

The entropy gain at $T = 1750$ K for $\delta = 0.20$ offsets fluorite’s enthalpic penalty, so processing protocols (calcination/sintering above 1400 K, rapid quenching) are used to kinetically freeze favorable vacancy disorder and inhibit large-scale ordering (Caucci et al., 28 Dec 2025). Excessive vacancy ordering (e.g., 25% in bixbyite) raises migration barriers and quenches ionic conductivity.

6. Design Principles and Optimization Strategies

Key guidelines for engineering vacancy-tolerant oxide electrolytes include:

Match dopant ionic radius closely to host (e.g., Sc³⁺ ≈ Zr⁴⁺ in zirconia) to minimize cation–vacancy ordering (Marrocchelli et al., 2010).
Restrict total vacancy concentration to $c \lesssim 5$ –$6$% in single-phase fluorite oxides, or target $0.15 \leq \delta \leq 0.20$ in high-entropy systems to maximize conductivity without imposing vacancy ordering (Caucci et al., 28 Dec 2025).
Employ mixed-dopant strategies or lattice strain to disrupt vacancy-vacancy ordering.
Use nonstoichiometric or low-valence A-site dopants in perovskites and Ba-deficient BaHfO₃ to boost mobile vacancy density, but control local lattice distortions to keep migration barriers low (Feng et al., 26 May 2025).
For grain-boundary engineering, drive vacancy segregation via off-stoichiometric sintering while maintaining conductive perovskite motifs and avoiding blocking phases (Lee et al., 2022).
Leverage neutron irradiation or chemical transmutation to generate stable sublattice vacancies for high rate oxide-ion or cation transport in challenging environments (Nguyen et al., 15 Mar 2025).

7. Electrochemical and Mechanical Stability Under Operating Conditions

The distribution and mobility of vacancies affect chemical potentials, oxygen partial pressures, and thus the degradation landscape in devices. Analytical models for SOECs (YSZ/GDC bilayers) show how extreme oxygen partial pressures develop at interfaces due to spatial variation in vacancy and carrier concentrations, directly correlating with degradation (reductive phase-separation, interfacial cracking). Control variables include carrier diffusivities (tuned via dopant levels), cell current density, and operating temperature—each parameter intricately coupled to vacancy tolerances and performance (Zhang et al., 2020).

Operating at higher temperatures and moderate current densities, and reducing resistive mismatches between layers, flattens chemical potential gradients and avoids critical $P_{O_2}$ excursions, enhancing the lifetime and stability of vacancy-rich oxide electrolytes.

In summary, vacancy-tolerant oxide electrolytes represent a mechanistically and thermodynamically optimized approach to enabling high-diffusivity ionic transport with minimal electronic leakage, stable phase structure, and resistance to environmental perturbations. The design parameters—structural, compositional, kinetic, and thermodynamic—are increasingly well understood through ab initio simulations and advanced spectroscopies, providing a foundation for systematic materials development for batteries, fuel cells, and other ion-conducting devices (Nguyen et al., 15 Mar 2025, Marrocchelli et al., 2010, Lee et al., 2022, Feng et al., 26 May 2025, Zhang et al., 2020, Caucci et al., 28 Dec 2025).