Negative Thermal Expansion Behavior Of Fe₂（MoO₄）₃ And Its Li/Na-Occupation Behaviors: A First-principles Study

The thermal expansion behavior of materials has a great impact on their applications in the fields such as the precision instruments, electronic devices and building materials. The occurrence of negative thermal expansion（NTE） materials makes it possible to control the thermal expansion coefficient, and especially plays an importance role in the design of zero-expansion materials and synthesis of low expansion materials. The orthorhombic Fe₂（MoO₄）₃ is not only a kind of NET material but also a kind of environment-friendly and potential battery material. At present, both the microscopic mechanism on the NTE behavior of the orthorhombic Fe₂（MoO₄）₃ and its Li and Na intercalation/deintercalation processes remain unclear. By combining the materials synthesis and experimental characterization, both the microscopic mechanism on the NTE behavior of the orthorhombic Fe₂（MoO₄）₃ and its Li and Na intercalation/deintercalation processes are systematically studied using the first-principles calculation.1. Monoclinic Fe₂（MoO₄）₃ sample is synthesized by hydrothermal method, and characterized via high temperature X-ray diffraction and thermogravimetric-differential scanning calorimetry. It is observed that the reversible phase transition between the low-temperature monoclinic and high-temperature orthorhombic phases occurs at about 510 ℃. The cell parameters at different temperatures are calculated by using the Rietveld refinement method. In the temperature range from 25℃ to 400℃, the a, b and c crystallographic axes with the monoclinic phase gradually expand. On the other hand, in the temperature range from 530℃ to 710℃, the orthorhombic phase exhibits a negative thermal expansion（NTE） behavior, in which the b and c axes gradually contract but the a axis contracts and then has a little expansion.2. Atomic and electronic structures are investigated using first-principles calculation. Results indicate that the Mo–O bonds are much stronger than the Fe–O bonds in Fe₂（MoO₄）₃ and the MoO4 tetrahedrons are more rigidly than FeO6 octahedrons. To reveal the relationship between NTE and polyhedral distortions, the phonon density of state of Fe₂（MoO₄）₃ is calculated using ab initio method. The experimental Raman spectrum positions can be identified in the calculated dispersion of the total phonon DOS. Meanwhile, by calculating the Grüneisen parameters for phonon branches at Γ point, the optical branch with the lowest vibration frequency is believed to have the largest negative Grüneisen parameter. Furthermore, we analyze the atoms vibration behaviors, and find that oxygen atoms have different vibrational eigenvectors and more obvious amplitude relative to Fe or Mo atoms. Therefore, it is concluded that the transverse vibration of the oxygen bridge atom between the MoO4 tetrahedron and FeO6 octahedron contributes to the negative thermal expansion of Fe₂（MoO₄）₃, together with the soft distortion of FeO6 octahedrons and the rigid rotation of MoO4 tetrahedrons.3. The Li and Na intercalation/deintercalation processes of the orthorhombic Fe₂（MoO₄）₃ are systematically studied using the first-principles calculation. By comparing the lattice parameters of AxFe₂（MoO₄）₃ and the formation energies of AxFe₂（MoO₄）₃（A = Li, Na） with respect to Fe₂（MoO₄）₃ and A2Fe₂（MoO₄）₃, it is found that the intercalation/deintercalation behaviors of Li and Na in the orthorhombic Fe₂（MoO₄）₃ exhibit the two-phase reaction and single-phase solid solution reactions processes. In addition, by comparing Li+/Na+ migration barriers along the [100], [010] and [001] directions, it is found that that LixFe₂（MoO₄）₃ exhibits the smaller volume change and faster ion diffusion than Nax Fe₂（MoO₄）₃ during the intercalation/deintercalation process and Li+ tends to migrate along the [010] direction in Fe₂（MoO₄）₃, and migration of Na+ in the [100] directions.