Atomistic simulation studies of inserted Li+, Na+ and Mg2+ in nanosphere TiO2 for metal ion batteries

This study employs classical molecular dynamics (MD) simulations, utilizing an amorphization and recrystallization (A + R) modelling framework, to comprehensively investigate the structural, thermodynamic, and ion transport behaviours of TiO₂ nanospheres intercalated with lithium (Li + ), sodium (Na + ), and magnesium (Mg 2+ ) ions. Atomistic models of mixed-phase TiO₂ nanospheres (15,972 atoms) were constructed, thermally amorphized at 7000 K, and then randomly intercalated with Li + , Na + , and Mg 2+ at molar fractions (x) of 0.11, 0.15, 0.19, and 0.23. These systems underwent controlled annealing and gradual cooling from 1500 K to 0 K to induce recrystallization and stabilization, mimicking synthesis and cycling conditions relevant to high-performance Li-, Na-, and Mg-ion batteries. Interatomic forces were described by the Born model with long-range Coulombic and short-range Buckingham potentials, incorporating a core-shell model for oxygen polarizability. The simulations revealed that both the type and concentration of intercalated ions critically influenced the structural stability and ionic transport efficiency of the TiO₂ nanospheres. Mg 2+ ions exhibited superior retention within the TiO₂ matrix compared to Li + and Na + , indicating strong thermodynamic stability and preference for embedded positions. Conversely, higher concentrations of Li + ions displayed enhanced surface migration due to their smaller radius and weaker electrostatic interactions, while Na + ions showed intermediate diffusional behaviours. Li + consistently demonstrated the highest diffusivity across all concentrations and temperatures, attributed to its smaller ionic radius (0.76 Å) and monovalent nature, resulting in weaker electrostatic interactions with the host lattice. Despite theoretical predictions of higher diffusion barriers for Mg 2+ , simulated activation energies were remarkably low (0.08–0.21 eV for Mg 2+ , 0.19–0.25 eV for Na + , and 0.18–0.37 eV for Li + ), suggesting kinetic advantages in an idealized, defect-controlled environment. Further analysis through slow cooling protocols showed that while Li + and Na + ions initially expelled at high temperatures re-diffused into the Ti O framework or near-surface sites below 1000 K, Mg 2+ ions remained stably intercalated throughout the cooling process, highlighting their excellent thermal stability. Microstructural evaluations confirmed the formation of well-ordered crystalline domains, predominantly brookite and rutile polymorphs, interspersed with functional tunnel-like defects and vacancies, which enhance ion mobility and structural robustness. MgₓTiO₂ systems, particularly at high concentrations (x = 0.23), exhibited the most thermodynamically stable structures, forming distinct multiphase crystalline architectures favourable for mechanical and thermal resilience. These findings underscore the potential of LiₓTiO₂, NaₓTiO₂, and MgₓTiO₂ nanospheres as promising anode materials for next-generation metal-ion batteries, offering a balanced combination of structural robustness, efficient ion transport, and thermal resilience for high-power and long-life energy storage applications.