Mazharul M. Islam

The ionic conductivity in lithium-boron oxide materials and its relation to structural, electronic and defect properties: insights from theory

We review recent theoretical studies on ion diffusion in (Li(2)O)(x)(B(2)O(3))(1-x) compounds and at the interfaces of Li(2)O :B(2)O(3) nanocomposite. The investigations were performed theoretically using DFT and HF/DFT hybrid methods with VASP and CRYSTAL codes. For the pure compound B(2)O(3), it was theoretically confirmed that the low-pressure phase B(2)O(3)-I has space group P3(1)21. For the first time, the structure, stability and electronic properties of various low-index surfaces of trigonal B(2)O(3)-I were investigated at the same theoretical level. The (101) surface is the most stable among the considered surfaces. Ionic conductivity was investigated systematically in Li(2)O, LiBO(2), and Li(2)B(4)O(7) solids and in Li(2)O:B(2)O(3) nanocomposites by calculating the activation energy (E(A)) for cation diffusion. The Li(+) ion migrates in an almost straight line in Li(2)O bulk whereas it moves in a zig-zag pathway along a direction parallel to the surface plane in Li(2)O surfaces. For LiBO(2), the migration along the c direction (E(A) = 0.55 eV) is slightly less preferable than that in the xy plane (E(A) = 0.43-0.54 eV). In Li(2)B(4)O(7), the Li(+) ion migrates through the large triangular faces of the two nearest oxygen five-vertex polyhedra facing each other where E(A) is in the range of 0.27-0.37 eV. A two-dimensional model system of the Li(2)O :B(2)O(3) interface region was created by the combination of supercells of the Li(2)O (111) surface and the B(2)O(3) (001) surface. It was found that the interface region of the Li(2)O:B(2)O(3) nanocomposite is more defective than Li(2)O bulk, which facilitates the conductivity in this region. In addition, the activation energy (E(A )) for local hopping processes is smaller in the Li(2)O :B(2)O(3) nanocomposite compared to the Li(2)O bulk. This confirms that the Li(2)O:B(2)O(3) nanocomposite shows enhanced conductivity along the phase boundary compared to that in the nanocrystalline Li(2)O.

Electronic Properties of Vanadium-Doped TiO2

The electronic properties of vanadium-doped rutile TiO(2) are investigated theoretically with a Hartree-Fock/DFT hybrid approach. The most common oxidation states (V(2+), V(3+), V(4+), and V(5+)) in different spin states are investigated and their relative stability is calculated. The most stable spin states are quartet, quintet, doublet, and singlet for V(2+), V(3+), V(4+), and V(5+) doping, respectively. By comparing the formation energy with respect to the parent oxides and gas-phase oxygen (ΔE), we conclude that V(4+) (ΔE=145.3 kJ mol(-1)) is the most likely oxidation state for vanadium doping with the possibility of V(5+) doping (ΔE=283.5 kJ mol(-1)). The energetic and electronic properties are converged with dopant concentrations in the range of 0.9 to 3.2%, which is within the experimentally accessible range. The investigation of electronic properties shows that V(4+) doping creates both occupied and unoccupied vanadium states in the band gap and V(5+) doping creates unoccupied states at the bottom of the conduction band. In both cases there is a significant reduction of the band gap by 0.65 to 0.75 eV compared to that of undoped rutile TiO(2).

Interstitial Lithium Diffusion Pathways in γ-LiAlO2: A Computational Study

Although the Li diffusion in single crystalline γ-LiAlO2 was studied with temperature-dependent Li-7 NMR spectroscopy and conductivity measurements recently, the exact diffusion pathways are not yet clearly identified. Therefore, the present study aims at elucidating the diffusion pathways in γ-LiAlO2 theoretically from first principles. Competing pathways for Li diffusion are investigated using the climbing-image nudged-elastic-band approach with periodic quantum-chemical density functional theory (DFT) method. Li can migrate between two regular LiO4 tetrahedral sites via Li point defect (VLi) and via a Li Frenkel defect (VLi + Lii). On the basis of calculated activation energies for Li diffusion pathways, it is concluded that Li conductivity is strongly dependent on the distribution of Li vacancies and interstitial Li in the lattice. For Frenkel defects where Lii is far away from the migrating Li atom, the calculated activation energies for jumps to nearest-neighbor vacant sites agree with experimental values.

Insights into Li+ Migration Pathways in α-Li3VF6: A First-Principles Investigation

Magnetic, structural, and defect properties of lithium vanadium hexafluoride (α-Li3VF6) are investigated theoretically with periodic quantum chemical methods. It is found that the ferromagnetic phase is more stable than the antiferromagnetic phase. The crystal structure contains three inequivalent Li sites (Li(1), Li(2), and Li(3)), where Li(1) occupies the middle position of the triplet Li(2)-Li(1)-Li(3). The calculated Li vacancy formation energies show that vacancy formation is preferred for the Li(1) and Li(3) sites compared to the Li(2) position. The Li exchange processes between Li(1) ↔ Li(3), Li(1) ↔ Li(2), and Li(2) ↔ Li(3) are studied by calculating the Li(+) migration between these sites using the climbing-image nudged elastic band approach. It is observed that Li exchange in α-Li3VF6 may take place in the following order: Li(1) ↔ Li(3) > (Li(1) ↔ Li(2) > Li(2) ↔ Li(3). This is in agreement with recently published results obtained from 1D and 2D (6)Li exchange nuclear magnetic resonance spectroscopy.

Energy ordering of grain boundaries in Cr2O3: insights from theory

The grain boundaries (GBs) of corundum Cr2O3 are known to play an important role in the diffusion of ions within the oxide, which is an important phenomenon for the corrosion of stainless steels. The extent of the growth of oxide layers in stainless steel depends upon which interfaces are preferred within Cr2O3. Therefore, we have constructed four different grain boundary planes (rhombohedral, basal, prismatic and pyramidal) and their various associated interface symmetries known in literature for corundum Al2O3. Their structural, electronic, and energetic properties are investigated theoretically with periodic boundary conditions using the DFT + U approach. We find that the prismatic screw GB with a Cr–O plane interface is the energetically preferred GB with the rhombohedral GB with screw symmetry and Cr vacancy termination being the second energetically preferred GB. The increase of the number of in-plane Cr atoms at the interface of prismatic GB enhances the stability, which is also evident in the electronic density of states.

Theoretical Investigation of Migration Pathways for Li Diffusion in h-LiTiS2

Abstract Lithium diffusion in highly lithiated hexagonal titanium disulphide (h-LixTiS2, x=0.88, 1.0) is investigated theoretically with periodic quantum-chemical methods. The calculated lithiation energies confirm that Li preferentially occupies the octahedral site rather than the tetrahedral site. Surprisingly, uncorrected density-functional theory (DFT) methods give better agreement with experiment for the structural parameters than the dispersion-corrected DFT-D approaches. Among the considered point defects, VLi, VTi, and Tii, Li point defects are thermodynamically preferred in h-LixTiS2. A moderate relaxation is observed for the atoms surrounding the Li defect or Ti defect site, whereas a pronounced relaxation of the nearest neighboring atoms of a Ti Frenkel defect occurs. Competing pathways for Li diffusion in h-LixTiS2 are investigated using the climbing-image Nudged-Elastic-Band (cNEB) approach. Li+ ions can migrate within the crystallographic ab plane either in a direct pathway through shared edges of neighboring octahedra or via vacant tetrahedral sites. The possibility of three-dimensional Li+ diffusion along the c direction is investigated via inclusion of Ti point defects and Ti Frenkel defects.

Diffusion Pathways and Activation Energies in Crystalline Lithium-Ion Conductors

Geometric information about ion migration (diffusion pathways) and knowledge about the associated energy landscape (migration activation barriers) are essential cornerstones for a comprehensive understanding of lithium transport in solids. Although many lithium-ion conductors are discussed, developed, and already used as energy-storage materials, fundamental knowledge is often still lacking. In this microreview, we give an introduction to the experimental and computational methods used in our subproject within the research unit FOR 1277, “Mobility of Lithium Ions in Solids (molife)”. These comprise, amongst others, neutron diffraction, topological analyses (procrystal-void analysis and Voronoi– Dirichlet partitioning), examination of scattering-length density maps reconstructed via maximum-entropy methods (MEM), analysis of probability-density functions (PDFs) and one-particle potentials (OPPs), as well as climbing-image nudged-elastic-band (cNEB) computations at density-functional theory (DFT) level. The results of our studies using these approaches on ternary lithium oxides and sulfides with different conduction characteristics (fast/slow) and dimensionalities (one-/two-/three-dimensional) are summarized, focusing on the close orbit of the research unit. Not only did the investigations elucidate the lithiumdiffusion pathways and migration activation energies in the studied compounds, but we also established a versatile set of methods for the evaluation of data of differing quality.

Density Functional Theory Evaluated for Structural and Electronic Properties of 1T-LixTiS2 and Lithium Ion Migration in 1T-Li0.94TiS2

Abstract In many applications it has been found that the standard generalized gradient approximation (GGA) does not accurately describe weak chemical bond and electronic properties of solids containing transition metals. In this work, we have considered the intercalation material 1T-LixTiS2 (0≤x≤1) as a model system for the evaluation of the accuracy of GGA and corrected GGA with reference to the availabile experimental data. The influence of two different dispersion corrections (D3 and D-TS) and an on-site Coulomb repulsion term (GGA+U) on the calculated structural and electronic properties is tested. All calculations are based on the Perdew-Burke-Ernzerhof (PBE) functional. An effective U value of 3.5 eV is used for titanium. The deviation of the calculated lattice parameter c for TiS2 from experiment is reduced from 14 % with standard PBE to −2 % with PBE+U and Grimme’s D3 dispersion correction. 1T-TiS2 has a metallic ground state at PBE level whereas PBE+U predicts an indirect gap of 0.19 eV in agreement with experiment. The 7Li chemical shift and quadrupole coupling constants are in reasonable agreement with the experimental data only for PBE+U-D3. An activation energy of 0.4 eV is calculated with PBE+U-D3 for lithium migration via a tetrahedral interstitial site. This result is closer to experimental values than the migration barriers previously obtained at LDA level. The proposed method PBE+U-D3 gives a reasonable description of structural and electronic properties of 1T-LixTiS2 in the whole range 0≤x≤1.

Stress Concentration in the Bulk Cr2O3: Effects of Temperature and Point Defects

Modeling the growth and failure of passive oxide films formed on stainless steels is of general interest for the use of stainless steel as structural material and of special interest in the context of life time extension of light water reactors in nuclear power plants. Using the approach, a theoretical investigation on the resistance to failure of the chromium-rich inner oxide layer formed at the surface of chromium-containing austenitic alloys (stainless steel and nickel based alloys) has been performed. The investigations were done for periodic bulk models. The data at the atomic scale were extrapolated by using the Universal Binding Energy Relationships (UBERs) model in order to estimate the mechanical behavior of a 10 μm thick oxide scale. The calculated stress values are in good agreement with experiments. Tensile stress for the bulk chromia was observed. The effects of temperature and structural defects on cracking were investigated. The possibility of cracking intensifies at high temperature compared to 0 K investigations. Higher susceptibility to cracking was observed in presence of defects compared to nondefective oxide, in agreement with experimental observation.

3D Li Diffusion in c-LixTiS2 (x = 0.69 and 0.75): A Theoretical Study

Abstract Lithium diffusion in the spinel type cubic titanium disulphide (c-LixTiS2, x = 0.69 and 0.75) is investigated theoretically with periodic density-functional theory (DFT) method. The calculated unit cell length and bond distances for a series of LixTiS2 (0 < x < 1) compounds are in agreement with the experimental data, with the maximum deviation of +0.06% for the lattice parameter and −1.2% for the bond length. In agreement with Vegards law, the unit cell length a is an almost linear function of x. The calculated average intercalation potentials for the series LixTiS2 (0 < x < 1) range between 1.6 to 1.9 V which is in the range of experimental findings. Competing pathways for Li diffusion in c-LixTiS2 (x = 0.69 and 0.75) are investigated using the climbing-image Nudged-Elastic-Band (cNEB) approach. Li+ ions can migrate along the 〈100〉 and 〈110〉 directions suggesting that Li+ diffusion in c-LixTiS2 is three-dimensional (3D). The calculated activation energy values for the considered migration pathways show that Li+ diffusion along the 〈100〉 directions is more preferable that that along the 〈110〉 directions.