Thermal behaviors during lithium diffusion in Li_0.4WO₃ bronze studied by elastic and quasi-elastic neutron scattering

Polycrystalline Li_0.4WO₃ bronze has been synthesized by solid state reaction carried out in a silica tube at 10^-7 MPa and 973 K. The sample is characterized by temperature-dependent neutron elastic and quasielastic scatterings. The room-temperature neutron powder data Rietveld refinement confirmed the space group Im3̄ along with lithium occupancy found predominantly at the 6b crystallographic site. Upon increasing temperature above 300 K lithium at 6b site decreases and at 2a site increases, suggesting Li⁺ cation diffusion between these two sites demonstrated by quasielastic neutron scattering as well. The lattice thermal expansion anomaly is observed between 380 K and 450 K, which is explained in terms of lithium dynamic disorder (non-equilibrium) as complemented by elastic and quasielastic neutron scatterings. DFT calculations with different lithium distributions at two different crystallographic sites guide to understand the lattice expansion anomaly. The lattice thermal expansion is modeled using Grüneisen first-order approximation, where the Debye-Einstein-Anharmonicity approach provides the temperature-dependent vibrational energy. The DFT-calculated phonon density of states and bulk modulus help extract the characteristic Debye and Einstein frequencies.