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Point Defects and Non-stoichiometry in Li2TiO3
Abstract
The intermediate-temperature, monoclinic β-phase of Li2TiO3 shows a stoichiometry range from 47 to 51.5 mol % TiO2. This broad stoichiometric range may be exploited for industrial applications, such as breeder material in a fusion reactor or a microwave dielectric. Here, density functional theory is employed to calculate formation energies for the intrinsic defect species, allowing the identification of the mechanisms responsible for accommodating both excess Li2O and TiO2 across a wide range of temperatures and oxygen partial pressures. The results predict that while the exact mode of accommodating non-stoichiometry depends on factors such as the temperature and oxygen partial pressure, cation disorder plays a major role in the incorporation of non-stoichiometry and that oxygen defects are of relatively minor importance.
... Both Li and Ti cations are located in octahedral sites with three crystallographically inequivalent Li positions, namely Li(1), Li (2) and Li(3), occupying the 8f, 4d and 4e Wyckoff sites, respectively, while two non-equivalent titanium positions Ti (1) and Ti(2) reside on 4e sites. β-Li2TiO3 has a layered-type framework that is a stacking of LiTi2 layers composed of Li(3) and Ti cations sharing 4e position and of single Li layers fully occupied by Li(1) and Li(2) ions [22,23]. ...
... Both Li and Ti cations are located in octahedral sites with three crystallographically inequivalent Li positions, namely Li(1), Li(2) and Li (3), occupying the 8f, 4d and 4e Wyckoff sites, respectively, while two non-equivalent titanium positions Ti(1) and Ti(2) reside on 4e sites. β-Li 2 TiO 3 has a layered-type framework that is a stacking of LiTi 2 layers composed of Li(3) and Ti cations sharing 4e position and of single Li layers fully occupied by Li(1) and Li (2) ions [22,23]. ...
... The activation energy estimated from the linear fit is found to be ~0.66 eV, which indicates a quasi-Debye behavior of the relaxation process of charge carriers in the LTO lattice. The mechanism of ionic motion has been discussed by several workers [23,74,75]. Li2TiO3 has a three-dimensional path for Li + ion diffusion, in which the ionic migration can occur in the (00l) plane, that is, LiTi2 layer, and along the c axis [74]. ...
Li2TiO3 nanopowders were synthesized by hydrothermal process using anatase TiO2 and LiOH H2O as raw materials. Li2TiO3 crystallizes in the layered monoclinic structure (space group C2/c) with average crystallite size of 34 nm. Morphology, elemental composition and local structure of products were carried out using HRTEM, FESEM, EDS, Raman and FTIR spectroscopy. Transport properties investigated by d.c. (4-probe measurements) and a.c. (complex impedance spectroscopy) show the activation energy of 0.71 and 0.65 eV, respectively. The ionic transport properties of Li+ ions in nanocrystalline Li2TiO3 characterized by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) validate the good electrochemical properties of this anode material for lithium-ion batteries.
... Li 2 TiO 3 exists in three modifications: the metastable cubic α-phase which can be synthesized hydrothermally and is stable at low temperatures which then transforms irreversibly to the monoclinic βphase between 300 and 600 °C and is stable up to 1150-1215 ˚C in which experiences a reversible transition to cubic γ-Li 2 TiO 3 [8,[14][15][16][17]. A higher order structural phase transition of monoclinic phase at about 450 ˚C was also reported by Hoshino et al. using X-ray diffraction method at high temperatures [18]. ...
... Improvement in sintering behavior in nonstoichiometric Li 2+x TiO 3 [8] [31]. Murphy et al. [16] used density functional theory to calculate formation energies for the intrinsic defect species and therefore identify the mechanisms responsible for accommodating both excess Li 2 O and TiO 2 across a wide range of temperatures and oxygen partial pressures. Huang et al. [11] studied the effects of ZnO addition with 10-50 mol.% and reported new microwave dielectric material of 0.7Li 2 TiO 3 -0.3ZnO ...
... All present peaks are assigned to monoclinic β-Li 2 TiO 3 phase (JCPDS card: 330831) with rock salt structure. The formation of solid solution between Li 2 TiO 3 and ZnO has been reported by Huang etal.[16] in which higher values of ZnO content in (1-x)Li 2 TiO 3 -xZnO ceramic system (x = 0.1-0.5) were investigated in order to alter the τ f value of ceramic to zero. ...
The densification behavior, structural and microstructural evolution and microwave dielectric properties of Li2TiO3 + xZnO (x = 0, 0.5, 1, 1.5, 2, 3, and 5 mol%) ceramics have been investigated using X-ray diffraction, Field Emission Scanning Electron Microscopy, Raman spectroscopy and microwave resonant measurement. The Maximum density of 3.33 g/cm3 was obtained in Li2TiO3 + 2ZnO ceramic at low sintering temperature of 1100˚C. SEM investigations revealed good close packing of grains when x = 2 and preferential grain growth when x ≥ 3. The maximum values of Q × f = 31800 GHz and εr = 22.5 were obtained in Li2TiO3 + 3ZnO and Li2TiO3 + 2ZnO compositions, respectively. The observed properties are attributed to the microstructural evolution and grain growth (first case) or high density of the obtained ceramic (second case).
... The preliminary results of impedance spectroscopy studies by Vitnis et al. [43] reveals that Li 2 TiO 3 is a poor lithium ion conductor that exhibits a negligibly low electronic charge transport component. Recently, the defect disorder of Li 2 TiO 3 was determined using the DFT method by Murphy [44] and Murphy and Hine [45]. It has been shown that the preferred occupation sites for tritium in the Li 2 TiO 3 lattice are the octahedral sites near the lithium layers [46]. ...
... The results of Murphy's studies on defect disorder of Li 2 TiO 3 are represented schematically in Figs. 7 and 8 for Li 2 Oand TiO 2 -rich solid solutions at 1000 K in terms of electronic defects and the predominant ionic defects [45]. ...
... The related n-p transition point corresponds to p(O 2 ) ¼ 10 À5 Pa and p(O 2 ) ¼ 10 À15 Pa for TiO 2 -rich and Li 2 O-rich systems, respectively. The diagrams derived by Murphy [44] and Murphy and Hine [45] may be used as a preliminary approach in processing the Li 2 TiO 3 e based materials with desired charge and mass transport that is required for enhanced performance in terms of the release of tritium. ...
... 36 The formation of heterogeneous structures between TiO 2 and titanate could modify the electronic structures of the pristine semiconductors. 23,37 Furthermore, the strong light scattering effects and the high surface area-to-volume ratio of the diamond nanoparticles may be conducive to the absorption of light. However, it shows that the absorption capacity was decreased when the concentration of the CH 3 COOLi solution was too high (curve c in Fig. 4A). ...
... 15,23 Furthermore, the energy level structures of TiO 2 and Li 2 TiO 3 match well. 37 It is well known that a higher photocurrent response indicates a higher efficiency in the separation of the photo-generated electrons and holes, and thus suggests a better photo-catalytic activity. 13 When the concentration of CH 3 COOLi in aqueous solution was increased to 0.2 M, the photocurrent density of the sample decreased (curve c in Fig. 5A) and the results were similar to those derived from the UV-vis diffuse reflectance absorption spectra. ...
... Li 2 TiO 3 is a kind of wide bandgap semiconductor (3.3 eV), and both the conduction band and valence band of Li 2 TiO 3 have appropriate energy levels matching with TiO 2 . 37,40 The good matching of band edges between TiO 2 and Li 2 TiO 3 is important to form a heterojunction. 20 Under light illumination, electrons photo-excited from the conduction band of Li 2 TiO 3 pass to the lower lying conduction band of TiO 2 , while the photo-excited holes in the valence band of TiO 2 transfer oppositely to that of Li 2 TiO 3 . ...
Heterogeneous Li2TiO3/TiO2 nanocomposite was successfully prepared from as-anodized amorphous TiO2 nanotube arrays in CH3COOLi solution by using a facile hydrothermal method. Morphology transformation from nanotubes to diamond-shape nanoparticles can be attributed to water-induced dissolution and recrystallization process of the nanotube arrays in a weak acid salt solution. Scanning electron microscopy, X-ray photoelectron spectroscopy and X-ray diffraction results showed that a large amount of Li2TiO3/TiO2 diamond-shape nanoparticles were formed on the surface of TiO2 nanotube arrays. UV–vis diffuse reflectance spectra indicated the improved visible light absorbance. The enhanced photoelectrochemical water splitting was demonstrated under UV–vis light illumination, and the photocurrent density of the electrode prepared in 0.1 M CH3COOLi was greater than that of other electrodes. The semiconductor characteristics were studied by electrochemical impedance spectroscopy in detail. This work is expected to guide next studies to design and fabricate photocatalysts for efficient photoelectrochemical water splitting.
... Studies based on density functional theory (DFT) showed that structural and thermodynamic properties, as well as the lithium diffusion pathway and elastic properties of Li-based materials can also accurately be achieved [15][16][17]. Classical simulations based on empirical potential (force field) revealed the most probable Li-diffusion pathway in Li 2 TiO 3 [17][18][19]. It is well known that lattice parameters, mechanical, thermal and transport properties of any material are modified by a substitution of a foreign ion in the host structure (action known as doping) [20][21][22][23]. ...
... The fact that the formal charges of the host ions in Li 2 TiO 3 are fractional, inhibits the research of the defects formation for its use in classical MD in other materials [24][25][26][27][28] making use of the existing empirical potentials [18]. Indeed, the actually available force fields are limited to the undoped compounds such as Li 2 TiO 3 [17][18][19]. ...
... the structural behaviour, and the transport properties but also thermal and luminescence spectra among other related properties of these materials. Non-stoichiometric samples play a role in diffusion, thermal and optical properties in Li 2 MO 3 [3,7,19,[69][70][71]. The force field provides here, can be used to explore the properties of nonstoichiometric samples, where the Li 2 O/TiO 2 molecular ratio play a role in the thermal behaviour of Li 2-x TiO 3-y samples [70]. ...
An extension of the existing force field for classical simulations was derived, and applied to Li 2 TiO 3 , Li 2 SnO 3 , Li 2 SiO 3 and other oxides such as SiO 2 and SnO 2. Using density functional theory, bulk properties such as elastic constant tensor components, Bulk, Shear and Young's modulus were computed. This force field was subsequently applied to calculate the bulk properties of some lithium-based materials (Li 2 MO 3 where M = Sn 4+ , Si 4+ and Ti 4+), as well as to explore their elastic stability and isotropy. The doped Li 2 MO 3 materials reveals the improvements-deteriorations effect of their mechanical properties as well as ductile/stiffness character. The capability of the force fields parameters is verified by testing the structural and mechanical properties of monoclinic Li 2 Si 2 O 5 , Li 2 Ti 6 O 13 and the unreported monoclinic Li 2 Sn 6 O 13. The results in general are in good agreement with previous experimental and theoretical studies. We propose that monoclinic Li 2 Sn 6 O 13 can also be obtained experimentally via Sn/Ti ion exchange.
... To obtain the temperature dependent defect concentrations we used the approach of Murphy and Hine [42] for calculating defect concentrations, which has been implemented into a python script. In this approach, defect (D) concentration, is related to the defect formation Gibbs energy, Δ , as: ...
... where the sum is over the considered defects (D) and their charges ( ), and ℎ are the electron and hole concentrations, respectively. For more detail of how the different concentrations are calculated see Ref. [42]. The term excess represents the excess charge in the system that can come from external sources or by doping. ...
... Using these convergence criteria, non-defective supercells of ZrO 2 were relaxed under constant pressure. The resulting structure was used as the starting point to which defects were introduced, and subsequently relaxed again, this time under constant volume conditions to simulate low defect concentrations [178,179]. Finally, all DFT calculations on doped and defective structures in this thesis employed the Pulay method for density mixing [180] to take into consideration changes in electronic behaviour of the system caused by the defect and to speed up convergence. ...
... Brouwer diagrams, also known as Kröger-Vink diagrams, were produced using a method out-lined by Murphy et al. [178,188] through which it is possible to determine defect concentrations as a function of oxygen partial pressure. We start from the statement that the chemical potential of ZrO 2 is equivalent to the sum of chemical potentials µ of its constituent species, Zr and O: ...
Zirconium alloys are used as a cladding material in most nuclear reactors worldwide due to properties uniquely suited to the operating environment of a reactor. In this thesis, density functional theory (DFT) simulations were conducted to investigate the behaviour of fission product dopants in the inner cladding oxide, and to examine the role this layer plays in limiting corrosion in the context of pellet-cladding interaction (PCI). Simulations in undoped monoclinic, tetragonal and cubic ZrO2 yielded structure properties in addition to intrinsic defect energies, volumes and defect equilibria. Fully-charged Schottky defects 2{V_O^**:V_Zr^''''}^x had the smallest formation energies in each phase, followed by O Frenkels and then Zr Frenkels. Defective cubic ZrO2 simulations are sensitive to finite-size effects, and would often break symmetry or collapse into the tetragonal phase when defect clusters were introduced. Free energy calculations predicted a transition from monoclinic to tetragonal as temperature was increased, but not from tetragonal to cubic. Iodine defects adopt oxidation states of +1 (I_O^***, I_i^* and I_Zr^''') or -1 (I_O^*) in ZrO2, with fewer defects in the 0 oxidation state (I_O^**). At high oxygen partial pressures (p_O2), iodine defects in tetragonal ZrO2 fall significantly. Iodine defects in monoclinic ZrO2 changed by small amounts as p_O2 was increased. This demonstrated competition between iodine and oxygen in ZrO2, and that it is dependent on both p_O2 and phase. High p_O2 in the tetragonal phase provides the greatest barrier to iodine ingress. During reactor power ramps, the quantity of fission products implanted in the oxide layer will increase. Decay rates of Te and I isotopes were found to be commensurate with time to failure in irradiation tests. Defect equilibria and volumes of Te, I, Xe and Cs were obtained in tetragonal ZrO2 to investigate the effect of nuclear transmutation while dopant atoms are present. Defect evolution on the O site is predicted to be Te_O^** -> I_O^* -> Xe_O^** -> Cs_O^**. On the Zr site, Brouwer diagrams predict Te_Zr^''' -> I_Zr^''' -> Xe_Zr^'''' ->Cs_Zr^'''. These defects have large defect volumes and will generate stresses which may promote crack formation.
... Both Li and Ti cations are located in octahedral sites with three crystallographically inequivalent Li positions, namely Li(1), Li (2) and Li(3), occupying the 8f, 4d and 4e Wyckoff sites, respectively, while two non-equivalent titanium positions Ti (1) and Ti(2) reside on 4e sites. β-Li2TiO3 has a layered-type framework that is a stacking of LiTi2 layers composed of Li(3) and Ti cations sharing 4e position and of single Li layers fully occupied by Li(1) and Li(2) ions [22,23]. ...
... The activation energy estimated from the linear fit is found to be ~0.66 eV, which indicates a quasi-Debye behavior of the relaxation process of charge carriers in the LTO lattice. The mechanism of ionic motion has been discussed by several workers [23,74,75]. Li2TiO3 has a three-dimensional path for Li + ion diffusion, in which the ionic migration can occur in the (00l) plane, that is, LiTi2 layer, and along the c axis [74]. ...
Li2TiO3 nanopowders were synthesized by hydrothermal process using anatase TiO2 and LiOHH2O as raw materials. Li2TiO3 crystallizes in the layered monoclinic structure (space group C2/c) with average crystallite size of 34 nm. Morphology, elemental composition and local structure of products were carried out using high-resolution transmission electron microscopy, field-emission scanning electron microscopy, Raman and Fourier transform infrared spectroscopy. Transport properties investigated by d.c. (4-probe measurements) and a.c. (complex impedance spectroscopy) show the activation energy of 0.71 and 0.65 eV, respectively. The ionic transport properties of Li+ ions in nanocrystalline Li2TiO3 characterized by cyclic voltammetry and impedance spectroscopy validate the good electrochemical properties of this anode material for lithium-ion batteries.
... where the μ O 2 (g) at a nonstandard condition T and pO 2 is obtained from the rigid-dumbbell ideal gas model [26], [42], [43]. This approach ensures the consistency of the μ i of constituent elements for subsequent defect formation energy calculations. ...
Transition metal oxides such as MoO
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and NiO have shown potential as hole-selective passivating contact for crystalline silicon (c-Si) solar cells. Among them, NiO is a notoriously poor hole-conducting semiconductor. Doping metal oxide with multivalent metal cations is an effective method to modify their electronic properties because dopant-induced favorable defect states play a crucial role in charge carrier transport in device applications. We use first-principles density functional theory to identify suitable metal cations that favorably affect the hole-conducting properties of NiO. We identify Al, Mg, and Zn as suitable dopants for NiO, improving ohmic contact properties with c-Si. Subsequently, Al-doped NiO (Al
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with c-Si, in contrast to undoped NiO where no ohmic contact could be formed. This in-depth computational study followed by the experimental synthesis of Al
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O films removes a critical barrier for the future applications of NiO-based carrier-selective passivating contacts for c-Si and other types of solar cells and provides a path for the optimization of other functional materials.
... In fact, the Li1 and Li2 positions are remarkably similar and have almost identical vacancy formation energies. 16 In the pure lithium layer, a Li1 ion is surrounded by an equal number of Li1 and Li2 ions. By contrast, a Li2 ion is surrounded by Li1 ions only. ...
Lithium metatitianate, Li2TiO3, is a leading candidate for application as a tritium breeding material in a future fusion reactor. Following transmutation of lithium, the tritium must escape the crystal in order to be extracted for use in the fusion plasma. The rate limiting step to tritium release from the Li2TiO3 pebbles is diffusion through the crystal grains. In this work, the activation barriers for tritium diffusion have been calculated using density functional theory (DFT). The results show that tritium can diffuse as an interstitial with a barrier of 0.52 eV. However, when a tritium ion becomes bound to a lithium vacancy defect, the energy required for either the tritium to detrap from the vacancy or for the cluster to diffuse increase to >1 eV. Overall, these results suggest that the introduction of lithium vacancies due to Li burn-up may lead to an increase in tritium retention in the pebbles.
... Two Li1, one Li2, one Li3, and four O atoms surround an interstitial Li4 atom (Figure 2a), as predicted computationally. 50 Here, in the case of a Li4 atom, we denote the nearest-neighbor Li1 atoms with short and long interatomic distances in the average crystal structure of β-Li 2 TiO 3 as Li1 and Li1′, respectively. In the refined average structure of β-Li 2 TiO 3 at RT, the Li4−Lii interatomic distances, r(Li4−Lii) [i = 1, 2, 3], were short: r(Li4−Li1) = 1.77(5) ...
Monoclinic lithium metatitanate, β-Li2TiO3, is a member of the Li2MO3 (M = Ti, Mn, Sn, Ru, and/or Ir) series and an important cation conductor for various energy applications such as Li-ion batteries and nuclear fusion reactors. Comprehensive knowledge of the crystal structure is vital to understand the Li-ion diffusion mechanism, and several possibilities were proposed previously. However, the exact crystal structure and Li-ion diffusion paths of β-Li2TiO3 are still unclear. Here, the results of a neutron diffraction study of high-purity ⁷Li-enriched β-Li2TiO3 are reported. The occupancy factor 0.033(3) and the atomic coordinates of the interstitial Li ion in the Li–O layer are successfully refined by Rietveld analysis of the time-of-flight neutron diffraction data. The three-dimensional network of Li-ion diffusion pathways is visualized by a combined technique of high-temperature neutron-diffraction and maximum-entropy methods. An interstitialcy diffusion mechanism, in which a lithium ion migrates through both the interstitial tetrahedral and lattice octahedral sites, is proposed for the Li2MO3 series.
... Using these convergence criteria, non-defective supercells of monoclinic (2x2x2 unit cells), tetragonal (3x3x2 unit cells) and cubic (2x2x2 unit cells) ZrO 2 were relaxed under constant pressure. The resulting structures were used as the starting point to which defects were introduced, and subsequently relaxed again, this time under constant volume conditions to simulate low defect concentrations [33,34]. Supercells were constructed such that their dimensions were as similar as possible in order to minimise directional defect self-interaction across the periodic boundaries (see Table 1 for supercell details). ...
Incorporation energies and defect equilibria in monoclinic, tetragonal and cubic phases of ZrO2 are predicted, using density functional theory calculations, for iodine dopant concentrations between 10⁻⁵ and 10⁻³ atoms per formula unit of ZrO2. Data are presented for monoclinic and tetragonal polymorphs, in the form of Brouwer diagrams, to show the defect response at oxygen pressures ranging from 10⁻³⁵ to 10⁰ atm. The oxygen pressure required for stoichiometry in monoclinic ZrO2 is approximately 10−7.5 atm, at both low and high iodine concentrations, whereas for tetragonal ZrO2, it increases from 10⁻¹⁰ to 10−6.5 atm as the iodine concentration is increased from 10⁻⁵ to 10⁻³ atoms/formula unit. The dominant defects in monoclinic ZrO2 are IO• charge-compensated by I‴Zr at low oxygen pressures, and a combination of I‴Zr, IO••• and Ii• defects at high oxygen pressures. In tetragonal ZrO2, the dominant defects at low oxygen pressures are e′, VO•• and IO•. At high oxygen pressures, h• and I‴Zr are dominant, with additional charge-compensation from V″Zr defects when iodine concentrations are low. The concentration of IO defects in the tetragonal phase decrease with increasing oxygen pressure above stoichiometry, demonstrating competition between iodine and oxygen for occupancy of the anion site. This has implications for fuel and cladding designs that are resistant to iodine-SCC.
... Murphy. 39 For shallow and resonant defects, a band-filling correction ܧ( ி ሻ was applied to regain the dilute limit due to the relatively high carrier concentrations present in supercell calculations. 38,40 Thermodynamic Limits The thermodynamic transition levels (q/q′) were defined as: ...
Transparent conducting oxides have widespread application in modern society but there is a need to move away from the current ‘industry champion’ tin doped indium oxide (In2O3:Sn) due to high costs. Antimony doped tin(IV) oxide (ATO) is an excellent candidate but is limited by its opto-electical properties. Here, we present a novel and scalable synthetic route to ATO thin films that shows excellent electrical properties. Resistivity measurements showed that at 4 at.% doping the lowest value of 4.7 x 10-4 Ω.cm was achieved primarily due to a high charge carrier density of 1.2 x 1021 cm-3. Further doping induced an increase in resistivity due to a decrease in both the carrier density and mobility. Ab-initio hybrid density functional theory (DFT) calculations show the thermodynamic basis for the tail off of performance beyond a certain doping level, and the appearance of Sb(III) within the doped thin films.
... Since these materials have a large number of industrial applications several studies have been carried out to understand their electronic and thermodynamic properties [5,7,17e19]. Defect and energetic studies have also been carried out on these lithium rich ceramics as presence of defects, affects the conductivity of lithium ions and also the dielectric properties of these ceramics [6,20,21]. ...
Lithium metatitanate (LTO) and lithium metazirconate (LZO) are lithium rich ceramics which can be used as tritium breeder materials for thermonuclear reactors. In-situ x-ray diffraction and ab-initio studies at high pressure show that LTO has a higher bulk modulus than that of LZO. In fact these studies indicate that they are the least compressible of the known lithium rich ceramics like Li2O or Li4SiO4, which are potential candidates for blanket materials. These studies show that the TiO6 octahedra are responsible for the higher bulk modulus of LTO when compared to that of LZO. It has also been shown that the compressibility and distortion of the softer LiO6 octahedra can be controlled by altering the stacking sequence of the more rigid covalently bonded octahedra. This knowledge can be used by chemists to design new lithium based ceramics with higher bulk modulus. It was observed that LTO was stable upto 34 GPa. Ab initio DFT calculations helped to understand the anisotropy in compressibility of both LZO and LTO. This study also shows, that even though the empirical potentials developed by Vijaykumar et al. successfully determine the ambient pressure structure of lithium metatitanate, they cannot be used at non ambient conditions like high pressure [1].
Understanding the intrinsic defect chemistry of tritium breeder materials proposed for use in future fusion reactors is imperative, as certain defects may act as traps leading to retention of tritium in the ceramic matrix. In this paper, we use combined density functional theory simulations with simple thermodynamics to explore the intrinsic defect chemistry of octalithium plumbate (Li8PbO6) as a function of both temperature and oxygen partial pressure. Importantly, we consider vibrational contributions to the energies of the reference states used in the calculations of the defect formation energies. Our results indicate that including these temperature effects can modify the predicted defect chemistry for materials at a high temperature. For Li8PbO6, the defect chemistry is predicted to be dominated by the VLi–1 defect, which will likely act as a trap for tritium. The charge compensating mechanism is predicted to change as a function of the conditions, with the Lii⁺¹ interstitial defect providing compensation at low temperatures and the VO²⁺ vacancy defect occurring close to the Li2O saturation limit.
The tritium breeder and structural materials are necessary components in the blanket to realize tritium (T) self‐sustainment of nuclear fusion. The long‐term exposure between tritium breeders and structural materials will cause surface corrosion in irradiation environments and then further affect the tritium release behavior. In this study, chemical compatibility between Li2TiO3 ceramic pebbles and advanced structural materials was studied systematically at 700 °C for 300 h under He+0.1 % H2 environment, respectively. The color of the Li2TiO3 ceramic pebbles changes from white to dark grey and black. Moreover, the grain size of Li2TiO3 ceramic pebbles increases to more than 5 μm, and the crushing load decreased slightly. For the structural materials, the Al‐rich oxide layer with about 188.7 nm of 14Cr‐5Al oxide dispersion strengthened (ODS) steel and Cr‐Fe rich oxide layer with about 1.04 μm of 14Cr‐ODS steel were observed on the cross‐section. The effective diffusion coefficient of O element in Li2TiO3 ceramic moved into ODS steel at 700 °C was calculated to be 3.3 × 10⁻¹⁶cm²/s and 1.02 × 10⁻¹⁴ cm²/s. Unfortunately, when SiC ceramics were contacted with the pebbles, the crystal phase transformed into SiO2, which severely limits its application. Therefore, these results will provide guidance for the selection of structural materials in the future.
The transfer of heat through the breeder region of a future fusion reactor is a key component of its thermal efficiency. Development of advanced ceramic breeder materials based on Li2TiO3 seek to exploit its ability to accommodate significant non-stochiometry, however, it is not clear how deviations for the 50:50 mix of Li2O and TiO2 will affect key properties of the material, including the thermal conductivity. Therefore, in this work molecular dynamics simulations are employed to examine how the thermal conductivity of Li2TiO3 changes with stoichiometry. The results suggest that while there is a significant decrease in the thermal conductivity at room temperature, at higher temperatures the impact of deviations from stoichiometry is limited.
Doping and forming solid solution is an effective approach to tailor densification and grain growth. In this study, submicron Li2(Ti,Zr)O3 solid solution ceramics was successfully fabricated by a modified solid‐state route for the first time. The use of appropriate starting powders can greatly reduce the synthesis temperature, and the preparation of Li2(Ti,Zr)O3 with submicron grain size is possible. The substitution of Ti by Zr will inhibit the phase transition from cubic to monoclinic structure, as well as the grain growth and pore removal. By doping 10‐at.% Zr, the grain size was significantly decreased from several μm to 400 nm at 900°C, which contributes to a high conductivity eight times that of pure Li2TiO3. Moreover, after being heated at 900°C for 10 days, the grain size of Li2(Ti,Zr)O3 only increases to 5 μm; however, the grains of Li2TiO3 grows up to 16 μm with abnormal grain growth. The compositions of Li2(Ti,Zr)O3 are high uniform with no element segregation, indicating the sluggish grain growth rate is caused by the slow diffusion of Zr rather than segregation‐induced solute drag. By adding excess Li and two‐step sintering, the Li‐rich Li2(Ti,Zr)O3 ceramic pebbles with high crush load of 50–60 N and small grain size of 300–500 nm were successfully fabricated. This work demonstrates a simple method for the synthesis of Li2(Ti,Zr)O3, which makes this material more widely accessible for exploration and also help accelerate its engineering application to be an advanced solid breeder.
Historically, defects in semiconductors and ionic conductors have been studied using very different approaches. In the solid state ionics community, non-stoichiometry and defect thermochemistry are often probed directly through experiments. The dependency of defect concentrations on chemical conditions (typically oxygen pressure) are modeled using a physical chemistry framework and compactly represented by the well-known Brouwer diagrams. In contrast, defects in electronic materials are now studied primarily with computational approaches --- often density functional theory (DFT) --- based in semiconductor physics in which the energy of defect formation also has an explicit dependence on the Fermi-level, making the defect energy diagram multidimensional. As charged defects begin to attract the attention of experts from both schools of thought for applications in thermoelectrics, solar cells, batteries, fuel cells and other electrochemical devices, a consistent understanding of charged defects addressing the apparent gaps in the two approaches is necessary.
This account reviews both methods using a common notation and thermodynamics to clarify misunderstandings between the fields. We demonstrate the equivalence between the Brouwer diagrams obtained from DFT calculated defect energy diagrams with those constructed using the simple analytical theory described in physical chemistry textbooks. We show how the explicit Fermi-level dependence of defect energy in semiconductor physics appears as an electron concentration in the mass action law using a constant defect energy defined in a standard state, \Delta G^\minuso_d. This quantity \Delta G^\minuso_d can also be visualized on a defect energy diagram. Furthermore, we develop the utility of a Brouwer band diagram to compactly map defect and charge concentration as well as important electronic dopability information in compound semiconductors over a multi-dimensional chemical potential space into a single 2-dimensional plot.
Semiconductors and ion conductors often have distinct mechanisms to compensate for the additional charge introduced by extrinsic (or impurity) doping with aliovalent species. Whereas such extrinsic doping in ionic conductors (e.g. Gd doped CeO_(2-x)) results in formation of intrinsic ionic defects (e.g. V_O), in the case of traditional semiconductors (e.g. P doped Si) free electronic charge carriers are formed. Using the example of thermoelectric Mg3Sb2, which can exhibit both these mechanisms depending on chemical conditions, we explain charge compensation of extrinsic dopants (e.g. doping efficiency) using the simple mass action laws for intrinsic defect reactions.
Li2TiO3 has a broad stoichiometric range and wide application prospects such as cathode, tritium breeder, and microwave dielectric materials. Particularly, Li2TiO3 shows a faster tritium release performance and exceptional chemical and radiation stabilities, making it one of the most promising solid breeder materials. Li‐rich Li2TiO3 has been developed for years as an advanced breeder material due to its enhanced tritium production and better stability in hydrogen atmosphere. However, the defect chemistry responsible for accommodating excess Li and how the non‐stoichiometry improves the material's performance is still unclear. In this work, the crystal structure and non‐stoichiometry‐induced defects in Li‐rich Li2TiO3 were investigated by means of X‐ray diffraction, electron spin resonance, and X‐ray photoelectron spectroscopy. Results show that oxygen vacancies and cation disorder both play a major role in the incorporation of excess Li. The sintering atmosphere (air/vacuum) has a negligible effect on the formation of the non‐stoichiometry‐induced defects but will influence the concentration of the oxygen vacancies. The better stability in the reduction atmosphere may be ascribed to the oxygen vacancies inside the Li‐rich Li2TiO3 crystals.
Inevitably, all crystalline materials will contain imperfections that have the ability to modify the properties of the host material. Key to the development of advanced materials is the ability to predict the concentrations of different defects in any given environmental conditions and how the change in the defect population alters the material’s properties. Modern first principles atomistic simulation techniques, such as density functional theory (DFT), are now widely employed for the simulation of point defects, however, to develop true insight into a material’s defect chemistry, it is essential to link the energies calculated to thermodynamic variables that fully describe its operating conditions. The Defect Analysis Package (DefAP), an open-source Python code, has been designed to fulfil this role. The primary function of the package is to predict the concentrations of defects in materials as a function of key thermodynamic variables, such as temperature and availability of different species, expressed through chemical potentials. Through simple thermodynamic equations, DefAP allows the rapid exploration of a material’s defect chemistry allowing direct comparison with experimental observations. Rapid exploration is supported through the use of autoplotting with carefully considered automatic data labelling and simplification options enabling production of publication quality plots. DefAP offers a wide range of options for the calculation of defect and carrier concentrations that can be customised by the user to suit the material studied and an extensive suite of options have been designed for the study of extrinsic defects (e.g. dopants or impurities). The capabilities of DefAP are demonstrated in this paper by studying intrinsic defects in YBa2Cu3O7, P doping in Si, Am accumulation in PuO2, and simultaneous build-up of T and He in Li2TiO3.
The high alpha-activity of plutonium dioxide (PuO2) results in significant ingrowth of radiogenic helium (He) in the aged material. To safely store/dispose PuO2 or use in applications such as space exploration, the impact of He accumulation needs to be understood. In this work, defect energies obtained using a density functional theory (DFT) + U + D3 scheme are used in a point defect model constructed for PuO2 to predict the method of He incorporation within the PuO2 lattice. The simulations predict that the preferred incorporation site for He in PuO2 is a plutonium vacancy, however, the point defect model indicates that helium will be accommodated as an interstitial irrespective of He concentration and across a wide stoichiometric range. By considering the charge imbalance that arises due to incorporation of Am3+ ions it is shown that He accommodation in oxygen vacancy sites will dominate in PuO2-x as the material ages.
TRISO fuel particles are candidates for use in next generation reactors including gas reactors, fluoride salt-cooled high temperature reactors, and micro-reactors. The UCO fuel kernel consists of a uranium dioxide (UO2) and uranium carbide mixture. The addition of UC2 helps suppress the formation of carbon monoxide gas, which led to failures during initial TRISO development. The addition of uranium carbide alters the chemistry of the UO2 pellet, which is known to influence performance parameters such as fission gas diffusivity, although the impact has not been quantified and no models exist that take the change in chemistry into account. Therefore, better understanding and more accurate models of the impact of chemistry on fuel performance are of high priority. In this paper, a first-principles density functional theory (DFT) and empirical potential based multi-scale study has been carried out to model the diffusivity of fission gas xenon (Xe) in UCO TRISO fuel kernels. The focus is on the UO2 component in the UCO fuel kernels, as that represents the largest volume fraction of the fuel kernels. The study relies on DFT and empirical potential calculations to determine Xe and point defect properties, which are then used in thermodynamic and kinetic models to predict diffusion for intrinsic conditions. In addition, the information is utilized in cluster dynamics simulations using the Centipede code to estimate the impact of irradiation on defect transport. The presence of UC2 or UC2−x in the UCO fuel kernels is shown to have a substantial impact on the UO2 non-stoichiometry by inducing oxygen vacancies and driving UO2 sub-stoichiometric, which causes much slower Xe diffusion in UCO compared to light water reactor UO2 fuel. The application of this model in fuel performance simulations using the Bison code is also demonstrated.
Augmenting the sinter-ability of powder is helpful to address problems such as Li sublimation and rapid grain growth related to the sintering of lithium-bearing ceramics as tritium breeder materials. In the present work, the sintering behavior of pure phase Li2TiO3 powders with and without BeO doping synthesized by urea assisted solid-state method was probed employing dilatometry analysis in the O2 atmosphere. Results revealed surprisingly low sintering onset temperature (∼715 °C) of un-doped Li2TiO3. Increasing sintering temperature to about 970 °C resulted in an anomalous monoclinic-to-cubic phase transformation characterized by unusually low transformation temperature and irreversible nature. Such phase transformation of Li2TiO3 has been usually reported in temperature range 1150–1250 °C which is significantly higher than observed in the present work. Interestingly, after BeO doping, a further reduction in sintering temperature with improved densification and suppression of the phase transformation was observed.
The β decay of ²⁴¹Pu to ²⁴¹Am results in a significant ingrowth of Am during the interim storage of PuO2. Consequently, the safe storage of the large stockpiles of separated Pu requires an understanding of how this ingrowth affects the chemistry of PuO2. This work combines density functional theory (DFT) defect energies and empirical potential calculations of vibrational entropies to create a point defect model to predict how the defect chemistry of PuO2 evolves due to the incorporation of Am. The model predicts that Am occupies Pu sites in (Pu,Am)O2±x in either the +III or +IV oxidation state. High temperatures, low oxygen-to-metal (O/M) ratios, or low Am concentrations favor Am in the +III oxidation state. Am (+III) exists in (Pu,Am)O2±x as the negatively charged (AmPu1–) defect, requiring charge compensation from holes in the valence band, thereby increasing the conductivity of the material compared to Am-free PuO2. Oxygen vacancies take over as the charge compensation mechanism at low O/M ratios. In (Pu,Am)O2±x, hypo- and (negligible) hyperstoichiometry is found to be provided by the doubly charged oxygen vacancy (VO²⁺) and singly charged oxygen interstitial (Oi1–), respectively.
The Li4TiO4 ceramic is a promising solid-state tritium breeder material for the production of tritium fuel in the designs of fusion reactors. Tritium extraction efficiency is one of the key factors that determines the performance of the breeder material. Vacancies are known to trap tritium and adversely affect tritium extraction. Understandings of tritium-trapped defect configurations in Li4TiO4 are limited so far. In this work, the oxygen/lithium vacancy (VO/Li) and the vacancy-tritium defect complex (VO/Li +T) in Li4TiO4 are studied by first-principles density functional theory. The atomic configurations, formation energies and electronic structures of various charged defect species are obtained. We find that 2+ and 0 are the dominate charge states of VO, 1- is the dominate charge state of VLi, 1+ is the dominate charge state of the defect complex (VO+T), and 0 is the dominate charge state of (VLi +T). Tritium atoms trapped in VO are bonded to Ti atoms, and those trapped in VLi are bonded to O atoms.
Gamma-phase lithium aluminate (γ-LiAlO2) in the form of annular pellets is used as a breeding material in tritium-producing burnable absorber rods (TPBARs) for the production of tritium by thermal neutron irradiation of ⁶Li. Significant radiation damage occurs in γ-LiAlO2 due to neutrons, and tritium and helium (He) nuclei, which recoil through the crystal. The radiation-damaged crystal is rich with vacancies and impurities such as carbon (C) that can act as tritium trapping sites. The presence of C impurities can hinder ³H diffusivities significantly. Here, we studied the effect of C impurities on ³H diffusivity and energy barriers in γ-LiAlO2 using first-principles density functional theory. In addition, we studied the He diffusion in an undefective γ-LiAlO2. We calculated the energy barrier for diffusion in γ-LiAlO2 to be 0.98 eV for substitutional ³H in the presence of a C impurity. At 600 K, the corresponding diffusion coefficient was calculated to be 7.98×10-14m²/s. Similarly, we calculated the energy barrier for He diffusion to be 0.12 eV, which was along the crystallographic c-direction. The corresponding diffusion coefficient for He at 600 K was calculated to be 6.8×10-7m²/s. This work may open further theoretical and experimental avenues on impurity effects and release of He from γ-LiAlO2.
An increased knowledge of the chemistry of PuO2 is imperative for the design of procedures to store, dispose, or make use of PuO2. In this work, point defect concentrations in PuO2 are determined by combining density functional theory (DFT) defect energies and empirical potential calculations of vibrational entropies. The obtained defect concentrations are expressed as a function of temperature and oxygen partial pressure and used to calculate non-stoichiometry in PuO2±x. The results show that the defect chemistry of PuO2 is dominated by oxygen vacancies and interstitials. Hyper-stoichiometric PuO2-x is accommodated by both the uncharged oxygen vacancy (VO×) and positively charged oxygen vacancy (VO²⁺) at small values of x, with VO× increasingly dominant with increasing x. The negatively charged oxygen interstitial (Oi²⁻) is found to accommodate hyper-stoichiometry (PuO2+x), but reluctance to form hyper-stoichiometric PuO2+x is observed, with oxygen interstitials present only in very low concentrations irrespective of conditions. The small degree of hyper-stoichiometry found is favoured by low temperatures.
Li2TiO3 with excess Li was developed as an advanced tritium breeder material for fusion reactors. To improve tritium release performance, the breeder pebbles should have a uniform microstructure with small grains. In this work, Li-rich Li2TiO3 ceramic pebbles were fabricated by an efficient spraying-rolling method and were sintered under air and vacuum atmospheres. Results show that the powder calcination temperature has a significant influence on crush load but negligible effect on grain growth. Excess Li2CO3 in pebbles was not just a lithium source to form the Li-rich phase, but also an effective sintering aid to improve sinterability. Small-grained pebbles with dense and homogeneous structure could be obtained by sintering at a low temperature of 1123 K in air. However, when sintered in vacuum, the pebbles exhibit a porous microstructure with very low crush strength. It is indicated that sintering in air is more suitable for the fabrication of Li-rich Li2TiO3 ceramic pebbles.
Ni as an alloying addition in Zircaloy leads to an increase in hydrogen pick-up fraction. Atomic scale simulations of tetragonal ZrO2, based on density functional theory, are used to identify a possible mechanism for this observation. First, defect formation energies associated with Ni but also Fe and Cr are used to predict relative defect cluster and defect charge concentrations using Brouwer diagrams. At low oxygen partial pressures (PO2), expected in the vicinity of the oxide metal interface, a cluster consisting of an oxygen vacancy adjacent to a charge neutral Ni⁰ atom is identified as the most populous cluster. Further simulations show that a hydrogen molecule will dissociate in the vicinity of this cluster. No other cluster is both sufficiently populous and acts in this way. This differentiates Ni from the other alloying elements.
Li2TiO3 (LTO) is a promising Ti-based material showing interesting electrochemical performance, good structural stability, cost-effectiveness, and non-toxic electrode material for energy storage and conversion. In this work, thin films of LTO have been deposited by the pulsed laser deposition (PLD) technique on Au/Ti/SiO2/textured Si multilayer substrates maintained at different temperatures (Ts) in a partial pressure of 0.4 mPa, and the microstructural properties are investigated. The as-deposited films are textured and contain TiO2 impurities. The LTO thin films grown at Ts of 600 °C are observed to be phase pure with a predominant (002) orientation related to the β-Li2TiO3 phase with C2/c symmetry. As electrodes for lithium microbatteries, LTO thin films delivered a specific discharge capacity of 46 μAh cm−2 μm−1 in the voltage range 0.0–1.0 V vs. Ag/AgCl and retained 91% capacity after 30 discharge cycles; as electrodes for supercapacitors, LTO thin films displayed a specific capacitance of 283 mF cm−2 at a current density of 1 mA cm−2 and retained 94% capacitance over 1000 cycles. The dual nature of the films demonstrates that the LTO films are suitable electrodes for supercapattery application.
Molybdenum contamination of silicon can have serious detrimental consequences for the efficiency of solar cells, raising durability concerns for novel solar cell designs that utilize MoO3 in contact with Si. Density functional theory simulations of Mo defects in Si revealed that Mo is preferentially accommodated in tetrahedrally coordinated interstitial sites and that the contamination may reach a sufficiently high concentration to cause a 20% relative solar cell efficiency degradation if processing steps are performed between 950 and 1300 K. The formation energy of the most energetically favored Mo defect in Si has a minimum value of 1.58 eV at the valence band maximum and a maximum of 2.10 eV at higher Fermi levels, indicating that higher Mo defect concentrations may occur in p-type Si than intrinsic or n-type Si. The diffusion processes for Mo in Si were investigated, and it was identified that interstitial diffusion dominates over a vacancy-mediated mechanism under all equilibrium conditions. Migration barriers were calculated to be 2.29 eV for charge neutral and 2.03 eV for charge +1 defects, occurring under n-type and p-type doping, respectively, indicating that Mo diffusion is faster in p-type Si, and hence potentially more effectively gettered than it would be in n-type Si.
Titanium oxide lithium ion sieve (Ti-LIS)is regarded as the most promising adsorbent due to its highest theoretical lithium adsorption capacity and excellent stability among various other lithium ion sieves. A new kind of Ti-LIS precursor with Mo-doped was prepared by a facile calcination method. The related lithium ion sieve (Mo-Ti-0.15 (H))with a high O 2– content (61.58%)was obtained by acid pickling. Mo-Ti-0.15 (H)possesses a quite high adsorption capacity, up to 78 mg g ⁻¹ in LiOH solution (lithium 1.8 g L ⁻¹ )at room temperature, which is much higher than that of the other lithium ion sieves reported. In addition, the adsorption isotherm and kinetic of the Mo-Ti-0.15 (H)belong to the Langmuir isotherm and pseudo-second order kinetic equations. Finally, the Mo-Ti-0.15 (H)shows a good stability and excellent selectivity, which was demonstrated by batch experiments.
Lithium metatitanate, Li2TiO3, is a material that is being considered for the breeder blanket region of fusion reactors, and as a cathode material in lithium batteries. We employ atomistic simulations to study the point defect processes and lithium diffusion in Li2TiO3. It is calculated that the activation energy of migration of Li ions via the vacancy mechanism is 0.51 eV along the ab plane. The energetically favorable intrinsic defect type is Li Frenkel (1.25 eV/defect). This is important as the formation of Li vacancies is required as they act as vehicles for Li diffusion in the vacancy mechanism. The solution of trivalent dopants can contribute further Li vacancies, however, the synthesis routes should be determined experimentally.
The effect of six potential contaminants (Cu, In, Ga, Se, Sn, and Zn) and five potential dopants (Ti, Mn, Sc, V, and Y) on the electronic and optical properties of molybdenum oxide (MoO3) contact layers for solar cells was investigated using point defect analysis based on density functional theory simulations. Of the contaminants investigated, Sn, In, and Ga were found to be highly insoluble at all relevant temperatures and pressures and therefore not a concern for solar cell manufacturing. Zn, Cu, and Se exhibit some solubility, with the latter two appearing to introduce detrimental defect states near the valence band. This contamination can be avoided by increasing the O2 partial pressure during MoO3 deposition. Of the five potential aliovalent dopants, Sc, Ti, and Y were disregarded because of their limited solubility in MoO3, whereas V was found to be highly soluble and Mn somewhat soluble. The effect of Mn and V doping was shown to be strongly dependent on the O2 partial pressure during deposition, with a high pO2 favoring the formation of substitutional defects (potentially beneficial in the case of Mn doping because of the addition of defect states near the conduction band), whereas low pO2 favoring interstitial defects.
The defect energetics in γ-LiAlO2, Li2TiO3, and Li2ZrO3 materials used in tritium-producing burnable absorber rods and fusion solid breeder applications was investigated using density functional theory calculations. A comprehensive analysis of the charged defects was performed for cation and anion vacancies, interstitials, antisite defects, and ³H interstitial and substitutional defects to understand the defect structures at different charge states and their stability as a function of the electron chemical potential across the electronic band gap of crystals at operating temperature and oxygen partial pressure conditions. Through investigation of the local bonding configurations and projected electronic density of states of the ³H related charged defects, including ³H interstitial (³Hint), ³Hint bound with an oxygen interstitial, and substitutional ³H defects on the Li, O, and M (M = Al, Ti, and Zr) sites (³HLi, ³HO, and ³HM), the ³H states of these defects were distinguished, i.e. triton (³H⁺), neutral ³H (³H⁰), and tritide (³H⁻). The two stable ³H related defects under the Li2O-LiOH rich condition at T = 1000 K, between P(O2) = 10⁻⁵ and 10⁻²⁵ atm were found to be ³H interstitial (³Hint) with charge of +1 and neutral ³HLi (substitutional ³H on the Li site) in γ-LiAlO2, Li2ZrO3, and Li2TiO3 materials. For Li2TiO3, the stability of the ³HO with charge of +1 and ³HM with charge of −3 becomes comparable to that of ³Hint atm at P(O2) = 10⁻²⁵ atm. Overall, our results indicate the energy cost to form the stable ³H defect species (³Hint with charge of +1 and neutral ³HLi) in γ-LiAlO2 material are higher than those of Li2TiO3 and Li2ZrO3 materials at T = 1000 K, between P(O2) = 10⁻⁵ and 10⁻²⁵ atm. Interactions between the point defects and the ³H species as a function of the electron chemical potential across the band gap of the materials were also examined. All the three materials exhibit strong interactions between the ³Hint and the O vacancy, Li vacancy, and O interstitial defects with the strongest interactions found in the case of γ-LiAlO2 phase, indicating a higher tendency to trap ³H at such point defects in γ-LiAlO2.
Tritium trapping at point defects is a major issue concerning tritium extraction efficiency in solid state breeder materials in future fusion reactors. Here, tritium trapping behaviors at oxygen vacancies in Li4SiO4 have been investigated by density functional theory simulations. Formation energies have been calculated to determine the stability of defects in various charge states. Density of states, charge distribution and atomic charge has been calculated to investigate the mechanism of defect formation. The results showed that the neutral and 2 + charged oxygen vacancies are the most stable species and are both diamagnetic. The 1 + charged paramagnetic oxygen vacancy (E′ center) is less stable. In addition, the tritium-trapped O-vacancy is most stable when the defect complex is 1 + charged. The trapped tritium is bonded to Si forming a T-SiO3 unit. Other charge states of the complex may lead to unstable defect structures and high formation energies, forcing tritium to escape the vacancy.
Displacement cascades were conducted on β-Li2TiO3 to determine threshold displacement energies and understand primary damage. Two different PKA energies and three different crystallographic directions were used for the study. Ti seemed to have the lowest threshold displacement energy. The evolution of the damage showed an oscillating behavior suggesting that subcascades form even for the low PKA energies considered in this work. This observation suggested that, either high angle scattering or short range channeling occurs during radiation damage. The primary damage was found to consist mainly of Li Frenkel pairs, OLi and LiO antisites. Almost all the defects showed a strong, identical dependence on the PKA direction, independent of the PKA energy. In particular, PKA directions of [100] produced maximum defects, while [001] the lowest. LiTi and TiLi showed directional dependence only for high energy cascades. The primary damage state had significant fractions of Lii close to O atoms, and Oi close to Li atoms. This observation suggests that Li atoms are trapped by O atoms due to Coulombic interactions. Such a trapping behavior may also be observed for positively charged T, thus reducing T yield. For the PKA energies and the time scales examined in this work, no clusters were found to occur.
With superior thermo-physical and thermo-chemical properties, γ-LiAlO2 has high compatibility with other blanket materials and is used in the form of an annular pellet in tritium-producing burnable absorber rods (TPBARs) to produce tritium by thermal neutron irradiation of ⁶Li. In radiation damaged γ-LiAlO2, different types of vacancies, defects of its constituent elements and other trapping sites hinder the diffusion process of tritium. In this study, the first principles density functional theory approach is used to study the diffusion mechanisms of tritium defect and its species, such as interstitial and substitutional tritium defects, oxygen-tritium vacancy defects, and interaction of tritium with oxygen-vacancies in defective and non-defective γ-LiAlO2. The obtained results provide an understanding of how such defects hamper the diffusivity and solubility of tritium. By calculating several different diffusion pathways, our results show that the smallest activation energy barrier is 0.63 eV for substitutional tritium diffusion with a diffusion coefficient of 3.25x10⁻¹² m²/s. The smallest oxygen-tritium diffusion barrier is found to be 2.17 eV which is around 3.5 times higher than tritium diffusion barrier alone.
Additives are widely used to control the microstructure of materials via their effect on defect chemistry during sintering. As the primary nuclear fuel, the properties of UO2 are crucial for safe and efficient reactor operation. UO2 has been manipulated by fuel vendors through doping to enhance grain size to provide improved fission gas retention and plasticity. In this work the common phenomenon that governs the effect of Mg, Ti, V, Cr, Mn, and Fe doping of UO2 for enhanced grain growth is revealed, elucidating experimental observations. A combined density functional theory and empirical potential description of defect free energy is used to calculate the doped UO2 defect concentrations as a function of temperature. At high (sintering) temperatures all dopants studied transition to a positively charged interstitial defect. Furthermore, a number of dopants (Ti, V, Cr, and Mn) do so in sufficiently high concentrations to greatly increase the negatively charged uranium vacancy concentration. High uranium vacancy concentrations can enhance grain growth and fission gas diffusion. Mg and Fe also enhance uranium vacancy concentrations but to a lesser extent, while Al has no impact. The enhanced uranium vacancy concentrations, associated with solution of dopants interstitially, is proposed as the mechanism responsible for the enlarged grains seen experimentally in (Ti/V/Cr/Mg)-doped systems. Mn- and V-doped UO2 have been predicted to have higher uranium vacancy concentrations than the more widely used Cr-doped UO2, leading to higher grain growth and fission gas diffusivity.
Control of the defect chemistry in UO2±x is important for manipulating nuclear fuel properties and fuel performance. For example, the uranium vacancy concentration is critical for fission gas release and sintering, while all oxygen and uranium defects are known to strongly influence thermal conductivity. Here the point defect concentrations in thermal equilibrium are predicted using defect energies from density functional theory (DFT) and vibrational entropies calculated using empirical potentials. Electrons and holes have been treated in a similar fashion to other charged defects allowing for structural relaxation around the localized electronic defects. Predictions are made for the defect concentrations and non-stoichiometry of UO2±x as a function of oxygen partial pressure and temperature. If vibrational entropy is omitted, oxygen interstitials are predicted to be the dominant mechanism of excess oxygen accommodation over only a small temperature range (1265 K–1350 K), in contrast to experimental observation. Conversely, if vibrational entropy is included oxygen interstitials dominate from 1165 K to 1680 K (Busker potential) or from 1275 K to 1630 K (CRG potential). Below these temperature ranges, excess oxygen is predicted to be accommodated by uranium vacancies, while above them the system is hypo-stoichiometric with oxygen deficiency accommodated by oxygen vacancies. Our results are discussed in the context of oxygen clustering, formation of U4O9, and issues for fuel behavior. In particular, the variation of the uranium vacancy concentrations as a function of temperature and oxygen partial pressure will underpin future studies into fission gas diffusivity and broaden the understanding of UO2±x sintering.
Molybdenum trioxide (MoO3) is a promising material for energy conversion applications, including recent uses as a hole selective contact in silicon photovoltaic devices. The electrical and chemical properties of MoO3 are known to be strongly sensitive to the presence of intrinsic and extrinsic defects, which in turn are dependent on the fabrication route and processing conditions used to form the device layers. Of particular interest to this study were intrinsic defects comprising oxygen vacancies and extrinsic defects involving possible contaminant silicon atoms. Density functional theory simulations were used to predict defect concentrations as a function of processing temperature and oxygen partial pressure. A rigorous method is outlined to calculate defect formation energies for all intrinsic defects in MoO3, resolving conflicting information arising from previous studies. Brouwer diagrams were constructed and used to show that the charge neutral oxygen vacancy is dominant under most of the temperature and oxygen partial pressure conditions investigated. It was also shown that at commonly-used processing temperatures and oxygen partial pressures, silicon interstitials in MoO3 can introduce a spin-polarised defect state 0.5 eV above the MoO3 valence band maximum. Their concentration in MoO3 may reach 1.3 ppm with processing conditions of 700 K and 10⁻⁶ atm oxygen partial pressure, and this concentration is predicted to increase dramatically with higher temperatures and/or lower oxygen partial pressures. Our findings highlight the possibility of silicon contamination in hole-selective contact layers for silicon photovoltaic devices, with a potential increase in the parasitic absorption due to silicon defects in the contact layers reducing energy conversion efficiency.
The Mn⁴⁺,Zn²⁺:Li2TiO3red phosphors are synthesized through the high temperature solid state reaction method. The XRD, SEM, ICP, absorption spectra, excitation and emission spectra are described. The Zn²⁺ acts as the luminescence adjustment ion to enhance the red emission efficiency. The phosphors have the crystal structure consisting of [TiO6] and [LiO6] octahedral sites and the Zn-O-Zn bonds. Concentration dependence on Zn²⁺ in Mn⁴⁺,Zn²⁺: Li2TiO3 is presented. Results indicate the suitable concentration of Zn²⁺ can enhance the emission efficiency. In the region of 682–697 nm when excited by 475 nm, the external quantum efficiency are obtained to be 18%, correlative with the transition of ²Eg (²T1)→⁴A2g of Mn⁴⁺. The crystal field strength (Dq) and the Racah parameters (B and C) are estimated to evaluate the nephelauxetic effect of Mn⁴⁺. The white-LED performances and thermal stability are also presented.
Li2Ti1-x(Mg1/3Nb2/3)xO3 ceramics were prepared by conventional solid state process. Their structural evolution, grain growth kinetics and microwave dielectric properties have been studied in this paper. The results show that continuous solid solution could be formed within the experiment compositional range. The structure changed from long range ordered monoclinic into short range ordered cubic phase as the increase in x. Small levels of substitution for Ti⁴⁺by (Mg1/3Nb2/3)⁴⁺ slightly decreased the dielectric permittivity, while considerably improved the Q×f value. The temperature coefficient of resonant frequency changed from positive into negative value. The grain growth kinetics during sintering process and Q × f value of the sintered body were affected by different calcining temperature of mixed powders. Excellent combined microwave dielectric properties with εr ∼21.0, Q × f ∼ 200 000GHz and τf value of -1ppm/°C could be obtained after optimizing calcining temperature for the x=0.24 composition after sintering at 1250°C/2h.
Zr-Nb alloys are known to perform better in corrosion and hydrogen pick-up than other Zr alloys but the mechanism by which this happens is not well understood. Atomistic simulations using density functional theory of both tetragonal and monoclinic ZrO2 were performed, with intrinsic defects and Nb dopants. The overall defect populations with respect to oxygen partial pressure were calculated and presented in the form of Brouwer diagrams. Nb is found to favour 5 + in monoclinic ZrO2 at all partial pressures, but can exist in oxidation states ranging from 5 + to 3 + in the tetragonal phase. Nb⁵⁺ is charge balanced by Zr vacancies in both phases, suggesting that contrary to previous assumptions, Nb does not act as an n-type dopant in the oxide layer. Clusters containing oxygen vacancies were considered, Nb²⁺ was shown to exist in the tetragonal phase with a binding energy of 2.4 eV. This supports the proposed mechanism whereby low oxidation state Nb ions (2 + or 3+) charge balance the build-up of positive space-charge in the oxide layer, increasing oxygen vacancy and electron mobility, leading to near-parabolic corrosion kinetics and a reduced hydrogen pick-up. Previous experimental work has shown that tetragonal ZrO2 transforms to the monoclinic phase during transition, and that during transition a sharp drop in the instantaneous hydrogen pick-up fraction occurs. The oxidation of lower charge state Nb defects to Nb⁵⁺ during this phase change, and the consequent temporary n-doping of the oxide layer, is proposed as an explanation for the drop in hydrogen pick-up during transition.
Lithium metatitanate (Li2TiO3) doped magnesium hydride (MgH2) has been investigated in this paper. Desorption properties of the sample with catalyst are compared to the pure MgH2. Particularly, MgH2 doped with 5 mol % Li2TiO3 started to desorb hydrogen at 170 °C with a peak temperature at 211 °C, which is 100 °C and 80 °C lower than that of the as-milled MgH2. The reversibility and cyclability of sample with catalyst have also been investigated. Compared with the raw material, the desorption activation energy was reduced from 113 kJ/mol to 84 kJ/mol. Furthermore, the catalytic mechanism was discussed according to the experimental results.
One of the main sources of error associated with the calculation of defect formation energies using plane-wave density functional theory (DFT) is finite size error resulting from the use of relatively small simulation cells and periodic boundary conditions. Most widely used methods for correcting this error, such as that of Makov and Payne, assume that the dielectric response of the material is isotropic and can be described using a scalar dielectric constant ε. However, this is strictly only valid for cubic crystals, and cannot work in highly anisotropic cases. Here we introduce a variation of the technique of extrapolation based on the Madelung potential that allows the calculation of well-converged dilute limit defect formation energies in noncubic systems with highly anisotropic dielectric properties. As an example of the implementation of this technique we study a selection of defects in the ceramic oxide Li2TiO3 which is currently being considered as a lithium battery material and a breeder material for fusion reactors.
Plane-wave density functional theory was used to study the properties of oxygen vacancies and interstitials, with differen charge states, in MgO. The calculated properties were the relaxed configurations, the Frenkel defect formation energies an the energies of the migration barriers, and all properties were found to be strongly dependent on the defect charge state.
The lowest energy configuration of the O2− interstitial was found to be the cube centre; however, the O− and O0 interstitials formed dumb-bell configurations. The Frenkel defect energies were also strongly dependent on the defect charge with the neutral pair energy calculated to be 3 eV lower than the doubly charged Frenkel pair defect energy. The migratio barriers of the oxygen vacancies were found to increase as the net charge of the oxygen vacancies decreased, which suggest that vacancies with trapped electrons are much less mobile than the F2+ vacancies modelled by classical potentials. The migration of the oxygen interstitials showed particularly interesting behaviour.
The O0 interstitial was found to have a higher migration barrier than the O2− interstitial but a very low barrier (0.06 eV) was found for the O− interstitial. The results have significant implications for the reliability of classical radiation damage simulations.
Solid solutions Li2 +xTi1 – 4xNb3xO3 have the cation-disordered, rock-salt structure at high temperature and the cation-ordered, low Li2TiO3 structure at lower temperatures. The ordering transition was studied by X-ray powder diffraction on samples heated isothermally as a function of time, temperature and composition and subsequently quenched to room temperature. A nucleation and growth mechanism was observed. In the early stages, ordered domains were surrounded by cation-disordered material; in the later stages, all of the material was ordered but was divided into domains that were in antiphase relationship to each other. Reduction in total area of antiphase boundaries provided the driving force for continued domain growth in the later stages. The kinetic data fitted a cubic growth law, similar to that used to fit grain growth during sintering of ceramics. The activation energies were large, 1.8–2.3 eV and indicated that diffusion of the multivalent cations, Ti4+ and/or Nb5+, provided the rate-limiting step.
We address the calculation within density functional theory (DFT) of defect formation energies in alumina, a ceramic oxide often considered an archetype for a wide variety of other similar oxides. We examine the conditions under which calculated defect formation energies, especially those of charged defects, are independent of the principal approximations of the plane-wave DFT formalism, most significant of which is the finite-sized supercell in which the calculation must be performed. We introduce a variation on existing methods of extrapolation to infinite system size to reduce dependence of the result on finite-size errors in the electrostatic and elastic energies of a periodic supercell containing a defect. We also show how the results can be made relatively insensitive to the choice of exchange-correlation functional and pseudopotential by a suitable treatment of the chemical potentials of the atomic species. Our results for formation energies of charged defects are less sensitive than traditional approaches to supercell size and choices of exchange-correlation functional and pseudopotential, and differ notably from previous results.
Stoichiometric magnesium aluminate spinel, MgAl2O4, contains equimolar proportions of Al2O3 and MgO. Spinel can, however, exhibit significant deviations from this stoichiometric composition. There is considerable disagreement concerning which species compensate for either excess Al2O3 or MgO non-stoichiometry. Here, we use empirical and quantum mechanical (density functional theory) atomistic simulation techniques to investigate the defect chemistry accommodating non-stoichiometry. The incorporation of excess Al2O3 was found to be a lower energy process than the solution of excess MgO. Elevated magnesium and aluminium cation vacancy defect concentrations are predicted in Al2O3 rich spinels, whilst MgO excess is facilitated by a combination of oxygen vacancy and magnesium interstitial defects.
We review here the theory of the early stages of oxidation of the (110) surface of Ni 1−x Al x , based on ab initio calculations using a plane-wave pseudopoten-tial method. The clean surface and several oxidized surfaces have been investigated, with oxygen coverages up to 2 ML of oxygen (1 ML = 3 O atoms per 2 surface Al atoms). The theory to date is a description in terms of equilibrium thermodynamics, with a comparison of the free energies of several surfaces of different composition, implemented at the atomic scale. Three environmental parameters are singled out as control variables in this treatment, namely the alloy composition x (assumed to be near 0.5), the temperature T and the partial pressure of oxygen p O2 . With certain reasonable approximations an analytic formula for the surface energy σ is derived in terms of these variables and some constants that are calculated ab initio together with others that are derived from experimental thermodynamic tables. At oxygen pressures just above the threshold for bulk oxidation of NiAl, the calculations explain the observed formation of a thin film of alumina in place of NiAl surface layers, with the consequent dissolution of Ni into the bulk. Ab initio calculations illustrate how the energetics of supplying Al to the surface depends on bulk stoichiometry, which alters the relative stability of different surface oxidation states so as to favour oxidation more if the alloy is Al-rich than if it is Ni-rich.
Crystal structures of TiO(OH)(2) and Li(2)TiO(3) have been studied in detail and refined using X-ray powder diffraction data. Both compounds possess a high concentration of defects in the structure. The crystal structure of the Li(2)TiO(3) salt obtained at 700 degrees C reveals stacking faults of LiTi(2) metal layers, which leads to the appearance of short-range order in three possible space groups: C2/c, C2/m, P3(1)12. The possibility to stabilise this imperfect state increases the mobility of the Li(+) ions in the structure and allows the complete exchange of lithium by hydrogen in acid water solutions with formation of TiO(OH)(2). The crystal structure of TiO(OH)(2) belongs to the layered double hydroxide structure type with the 3R(1) sequence of oxygen layers and can be described as a stacking of charge-neutral metal oxyhydroxide slabs [(OH)(2)OTi(2)O(OH)(2)]. TiO(OH)(2) is the first layered double hydroxide structure formed by a cation with oxidation state +4 only.
We present an improved method to calculate defect formation energies that overcomes the band-gap problem of Kohn-Sham density-functional theory (DFT) and reduces the self-interaction error of the local-density approximation (LDA) to DFT. We demonstrate for the silicon self-interstitial that combining LDA with quasiparticle energy calculations in the G0W0 approach increases the defect formation energy of the neutral charge state by approximately 1.1 eV, which is in good agreement with diffusion Monte Carlo calculations (E. R. Batista, Phys. Rev. B 74, 121102(R) (2006)10.1103/PhysRevB.74.121102; W.-K. Leung Phys. Rev. Lett. 83, 2351 (1999)10.1103/PhysRevLett.83.2351). Moreover, the G0W0-corrected charge transition levels agree well with recent measurements.
A new approach to the construction of first-principles pseudopotentials is described. The method allows transferability to be improved systematically while holding the cutoff radius fixed, even for large cutoff radii. Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced. The potentials have a separable form well suited for plane-wave solid-state calculations, and show promise for application to first-row and transition-metal systems.
A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.
We have investigated the (001) surface structure of lithium titanate (Li2TiO3) using auger electron spectroscopy (AES), low-energy electron diffraction (LEED), and scanning tunneling microscopy (STM). Li2TiO3 is a potential fusion reactor blanket material. After annealing at 1200 K, LEED demonstrated that the Li2TiO3(001) surface was well ordered and not reconstructed. STM imaging showed that terraces are separated in height by about 0.3 nm suggesting a single termination layer. Moreover, hexagonal patterns with a periodicity of 0.4 nm are observed. On the basis of molecular dynamics (MD) simulations, these are interpreted as a dynamic arrangement of Li atoms.
Li2MnO3 is the parent compound of the well‐studied Li‐rich Mn‐based cathode materials xLi2MnO3·(1‐x)LiMO2 for high‐energy‐density Li‐ion batteries. Li2MnO3 has a very high theoretical capacity of 458 mA h g−1 for extracting 2 Li. However, the delithiation and lithiation behaviors and the corresponding structure evolution mechanism in both Li2MnO3 and Li‐rich Mn‐based cathode materials are still not very clear. In this research, the atomic structures of Li2MnO3 before and after partial delithiation and re‐lithiation are observed with spherical aberration‐corrected scanning transmission electron microscopy (STEM). All atoms in Li2MnO3 can be visualized directly in annular bright‐field images. It is confirmed accordingly that the lithium can be extracted from the LiMn2 planes and some manganese atoms can migrate into the Li layer after electrochemical delithiation. In addition, the manganese atoms can move reversibly in the (001) plane when ca. 18.6% lithium is extracted and 12.4% lithium is re‐inserted. LiMnO2 domains are also observed in some areas in Li1.63MnO3 at the first cycle. As for the position and occupancy of oxygen, no significant difference is found between Li1.63MnO3 and Li2MnO3. The atomic structures of Li2MnO3 after delithiation and re‐lithiation are directly observed using spherical aberration‐corrected scanning transmission electron microscopy. It is found that after electrochemical treatments, a new stacking sequence of LiMn2 planes appears and the regularly arrayed LiMn2 planes become disordered. LiMnO2 and some new domains are also found in the delithiated state in the first cycle.
Atomic scale simulations are used to predict how excess oxy-gen is accommodated across the group II monoxides. In all cases, the preference is to form a peroxide ion centered at an oxygen site, rather than a single oxygen species, although the peroxide ionic orientation changes from <100> to <110> to <111> with increasing host cation radius. The enthalpy for accommodation of excess oxygen in BaO is strongly negative, whereas in SrO it is only slightly negative and in CaO and MgO the energy is positive. Interestingly, the increase in mate-rial volume due to the accommodation of oxygen (the defect volume) does not vary greatly as a function of cation radius. The vibrational frequency of peroxide ions in the group II mon-oxides is predicted with the aim to provide test data for future experimental observations of oxygen uptake. Finally, calcula-tions of the dioxide structures have also been carried out. For these materials the oxygen vacancy formation energy is always positive (1.0–1.5 eV per oxygen removed) indicating that they exhibit only small oxygen defect concentrations.
The intrinsic point defects of β-Ga2O3 are investigated using density functional theory. We have chosen two different exchange-correlation potentials: the generalized gradient approximation (GGA) and a hybrid potential (HSE06). Defect formation energies were determined taking into account finite-size effects. Schottky, anti-Frenkel, and Frenkel energies have been extracted for T=0 K. We calculate formation entropies for an oxygen and a gallium vacancy and determine the Gibbs energy of Schottky disorder. Furthermore, we investigate the defect concentrations as a function of the oxygen partial pressure. The obtained purely intrinsic defect concentrations for charged defects are very small and result in a pO2 dependence of the electron concentration of [e′]∼ pO2−1/6, whereas experimentally [e′]∼ pO2−1/4 is found. So we assume that, experimentally, a small unintentional donor doping is unavoidable. A small extrinsic donor concentration [D·] = 1018 cm−3 (10 ppm) changes the electron concentration to [e′]∼ pO2−1/4 and gives an activation energy of the conductivity σ of 1.7 eV in good agreement to experimental values. So we propose as majority disorder 3[VGa′′′] = [D·] with electrons being minority defects.
Li2TiO3 is among the most promising candidates for solid breeder materials. However, its structural property, especially the possibility of non-stoichiometric composition, has not been well established yet. Therefore, the composition of Li2TiO3 has been further investigated by means of thermogravimetry, XRD etc. Also, thermal diffusivity measurement was carried out. Mass of Li2TiO3 was found to change after the change of the atmosphere from hydrogen to oxygen as observed by means of thermogravimetry. At the same time, the color was observed to change from dark blue to initial color, white. These behaviors suggest not only oxygen deficient but also lithium oxide deficient defects formation. Thus, the doubly non-stoichiometric composition, Li2−xTiO3−y, has been confirmed. Further, it was shown by thermal diffusivity measurement that 95Li2TiO3 (i.e. Li2O/TiO2=0.95) has a higher thermal conductivity than 100Li2TiO3.
Li2TiO3 is one of the most promising candidate solid breeder materials. However, its structural properties have not been established, especially for a non-stoichiometric composition. In the present paper, non-stoichiometric compositions of Li2TiO3 have been extensively investigated by means of thermogravimetry, X-ray diffraction and color change observations. For the Li2TiO3 samples used in the present study, Li2CO3 and TiO2 powders were mixed in the proportion corresponding to the molecular ratio Li2O/TiO2 of either 1.00, 0.95, 0.938, 0.90 or 0.80. In thermogravimetry, mass of the Li2TiO3 samples was found to decrease with time in a hydrogen atmosphere, then to increase after the change of the atmosphere from hydrogen to oxygen. The color of the samples was observed to change from white to dark blue under a hydrogen atmosphere. These results suggest not only oxygen deficient but also Li2O deficient defect formation. Thus, the doubly non-stoichiometric composition, Li2−xTiO3−y, has been confirmed.
Li2MnO3 component plays a key role in Li-rich Mn-based layered materials (mLi2MnO3·nLiMO2, M = Mn, Ni, Co, etc.) for achieving unusually high lithium storage capacity. However, detailed lithium storage mechanism in Li2MnO3, such as structure evolution and charge compensation are still not very clear. In this work, the redox mechanism, the delithiation process, the kinetics of lithium diffusion, and the oxygen stability of Li2MnO3 are investigated through density functional calculations. The ground-state Li/vacancy configurations of Li2–xMnO3(0 ≤ x ≤ 1) at five Li concentrations are determined, from which the delithiation potential is calculated as 4.6 V vs Li+/Li, and the charge compensation during Li removal is contributed mainly by oxygen. According to the Li/vacancy configuration in each ground state, the sequence of lithium removal is suggested from an energetic view. Both the Li+ in the lithium layer and in the transition-metal layer can be extracted. The first-principles molecular dynamics (FPMD) simulations indicate that the lithium layer is the main diffusion plane in this material, while the Li+ in the transition-metal LiMn2 layer can migrate into the lithium layer first, and then diffuse through the lithium plane or move back to the LiMn2 layer. The energy barriers of such migrations are in the range of 0.51–0.84 eV, according to the calculations with the nudged elastic band method. The release of O2 gas from Li2–xMnO3(0 ≤ x ≤ 1) happens spontaneously if x ≥ 0.5, from the point of view of enthalpy change. Further understanding on the evolution of oxygen in Li2–xMnO3 with x ≥ 0.5 is needed to find a way to stabilize the structure during electrochemical cycles.
Ultrafine Li2TiO3 nanopowder was synthesized by a sol–gel method. The effect of a slight A- and B-site cation nonstoichiometry on the structure, densification and microwave dielectric properties of Li2TiO3 was investigated. The phase presence and surface morphology were determined by XRD and SEM techniques, respectively. The average particle size calculated from the TEM micrograph of the powder was 6–12 nm. Compared with the conventional solid-state method, Li2TiO3 nanopowder synthesized by the sol–gel method could be densified at 1250 °C with less micro pores and cracks. In addition, the densification temperature of slightly A-site nonstoichiometric ceramics have been successfully reduced to 1050 °C. Also, it is found that a slight cation defect can improve density and microwave dielectric properties, while the addition of excess ions deteriorated them. When x = 0.08, well-densified ceramics with uniform grains and good dielectric microwave dielectric properties of εr = 23.2, Q × f = 56400 GHz, and a τf = 38.4 were achieved in Li2+xTiO3.
Sintering behavior, microstructure and microwave dielectric properties of Li2+xTiO3 (0≤x≤0.2) ceramics have been studied by X-ray diffraction (XRD), scan electron microscopy (SEM), Raman spectra, dilatometery and microwave resonant measurement in this research. Homogeneous non-stoichiometric composition with rock salt structure existed for Li2+xTiO3 (0≤x≤0.2) ceramics. The sintering temperature was successfully reduced and highly densified sample could be obtained with appropriate excessive amount of lithium (x=0.08). A transient reactive liquid phase sintering mechanism was proposed. The preferred orientation of grain growth and micro-cracks existed in the Li2TiO3 (x=0) sample disappeared in the lithium excessive samples with x≥0.08. The microwave dielectric properties varied significantly with the excessive amount of lithium. Optimized microwave dielectric properties were obtained for the x=0.08 composition: ɛr=24.6, Q×f=66,000GHz, and τf=22.1ppm/°C.
Li-ion batteries have contributed to the commercial success of portable electronics and may soon dominate the electric transportation market provided that major scientific advances including new materials and concepts are developed. Classical positive electrodes for Li-ion technology operate mainly through an insertion-deinsertion redox process involving cationic species. However, this mechanism is insufficient to account for the high capacities exhibited by the new generation of Li-rich (Li1+xNiyCozMn(1-x-y-z)O2) layered oxides that present unusual Li reactivity. In an attempt to overcome both the inherent composition and the structural complexity of this class of oxides, we have designed structurally related Li2Ru1-ySnyO3 materials that have a single redox cation and exhibit sustainable reversible capacities as high as 230 mA h g(-1). Moreover, they present good cycling behaviour with no signs of voltage decay and a small irreversible capacity. We also unambiguously show, on the basis of an arsenal of characterization techniques, that the reactivity of these high-capacity materials towards Li entails cumulative cationic (M(n+)→M((n+1)+)) and anionic (O(2-)→O2(2-)) reversible redox processes, owing to the d-sp hybridization associated with a reductive coupling mechanism. Because Li2MO3 is a large family of compounds, this study opens the door to the exploration of a vast number of high-capacity materials.
AgLi1
/
3Ti2
/3O2 and AgLi1/3Sn2/3O2 with delafossite structures were synthesized by treating the layered compounds Li2TiO3 and Li2SnO3 with molten AgNO3 (573 K for 5 h) through ion exchange of Li+ for Ag+. The band gaps of both AgLi1/3Ti2/3O2 and AgLi1/3Sn2/3O2 were estimated to be 2.7 eV from diffuse reflectance spectra. These delafossite-type metal oxides showed activity for O2 evolution from an aqueous silver nitrate solution under visible light irradiation. Moreover, these materials were also active for photocatalytic degradation of methylene blue under irradiation of monochromatic light at 420 nm. The visible light responses of AgLi1/3Ti2/3O2 and AgLi1/3Sn2/3O2 were due to the band gap excitation between conduction bands consisting of either Ti 3d or Sn 5s5p orbitals and valence bands consisting of Ag 4d orbitals.
The microstructure of Li2TiO3 ceramics, proposed as blanket material in deuterium–tritium fusion reactors, plays an important role for this application; grain size and grain shape determine to a considerable degree the properties in question. Electrical properties may reflect certain characteristics of the microstructure to some extent. In this communication impedance spectroscopy is applied to analyse electrical charge transport in ceramics of monoclinic β-Li2TiO3, synthesized in different conditions. Li+ ions are suggested to be the majority charge carriers. Typical activation energies for charge transport, deduced from the DC conductivity σDC, are EA∼0.6–0.9 eV and the bulk σDC (573 K)∼3×10−6 Ω−1cm−1. The DC and AC conductivities show some features of the microstructure. Anomalies in the DC conductivity at ∼570 K–900 K are indicative of a change in conduction which is tentatively assigned primarily to the formation of nuclei of the cubic γ-Li2TiO3 phase in this temperature region, well below the first order phase transition β→γ at 1425 K–1485 K.
A novel process method based on solid–liquid combustion synthesis has been developed to produce high purity monoclinic Li2TiO3 directly after combustion. The process does not call for any additional heat treatment for phase formation. The lattice parameters of Li2TiO3 were determined through Rietveld refinement of XRD pattern. Systematic studies were carried out to optimize the sintering temperature to obtain the desired microstructure and density in the sintered specimens. The morphology of Li2TiO3 powder and microstructures of sintered specimens were studied by scanning electron microscopy. The powder produced through this route could be sintered to 90% of theoretical density at relatively low temperatures (<1150 °C). The process developed in the present investigation is simple and convenient for mass production.
A systematic first-principles calculation based on density functional theory is carried out to discuss the redox mechanism of Li2MnO3. The lattices of structural models having C2/m- and C2/c-type stacking sequences can be regarded as hexagonal, while their symmetry is monoclinic. Different stacking sequences of [Mn2/3Li1/3] layers do not cause differences in the energy or crystallographic structure, suggesting a disordered stacking sequence. A calculation for Li2−xMnO3 assuming topotactic lithium removal indicates that lithium removal can occur at a potential of about 4.6V with a wide potential plateau. The electronic structure of Li2−xMnO3 shows that the manganese ions remain in the charge state of Mn4+ and the charge of the removed lithium ions is compensated by the oxidation of oxygen.
We present a density functional theory (DFT) framework taking into account the finite temperature effects to quantitatively understand and predict charged defect equilibria in a metal oxide. Demonstration of this approach was performed on the technologically important tetragonal zirconium oxide, T-ZrO2. We showed that phonon free energy and electronic entropy at finite temperatures add a nonnegligible contribution to the free energy of formation of the defects. Defect equilibria were conveniently cast in Kröger–Vink diagrams to facilitate realistic comparison with experiments. Consistent with experiments, our DFT-based results indicate the predominance of free electrons at low oxygen partial pressure (PO2≤10−6 atm) and low temperature (T≤1500 K). In the same regime of PO2 but at higher temperatures, we discovered that the neutral oxygen vacancies (F-centers) predominate. The nature of the predominant defect at high oxygen partial pressure has been a long-standing controversy in the experimental literature. Our results revealed this range to be dominated by the doubly charged oxygen vacancies at low temperatures (T≤1500 K) and free electrons at high temperatures. T-ZrO2 was found to be hypostoichiometric over all ranges of T and PO2, mainly because of the doubly charged oxygen vacancies, which are responsible for inducing n-type conductivity via a self-doping effect. A range of 1.3 eV in the band gap of T-ZrO2 starting from the middle of the gap toward the conduction band is accessible to the chemical potential of electrons (Fermi level) by varying T and PO2 without extrinsic doping. The approach presented here can be used to determine the thermodynamic conditions that extremize certain desirable or undesirable defects to attain the optimal catalytic and electronic performance of oxides.
Understanding lithium diffusion properties in electrode materials is important for designing rechargeable lithium-ion batteries with improved performance. In this work, the lithium dynamics in layered Li2TiO3 were characterized using a combination of 6,7Li nuclear magnetic resonance (NMR) over a wide temperature range (150−500 K) and molecular dynamics (MD) simulations. The 7Li static NMR and stimulated echo experiments show slow and partial lithium diffusion in Li2TiO3. The high-field (21.1 T) 6Li magic-angle spinning NMR shows a new tetrahedral lithium site along with the three crystallographic octahedral sites in Li2TiO3 sample. MD simulations predict that lithium can occupy a tetrahedral site if two or more vacancies exist in the vicinity, which may result, for example, from the presence of a Ti defect in the LiTi2 layer. 6Li two-dimensional (2D) exchange NMR experiments show evidence of lithium diffusion between the pure Li and LiTi2 layers along the c axis. Although the 2D exchange NMR data are not sensitive to lithium diffusion in the ab plane, MD simulations show that lithium diffusion in the pure Li layer is equally probable. Combining these results, a detailed picture of the lithium diffusion pathways in Li2TiO3 is presented.
Lithium-based ceramics, such as lithium metatitanate, have been proposed for adoption in the breeder blanket region of a fusion reactor. In this article, we report a combination of empirical and density functional theory (DFT) simulations employing “on-the-fly” pseudopotentials for Li2TiO3. The smoothing parameters of the plane-wave pseudopotentials were optimized to ensure an appropriate level of precision for determination of structural, thermodynamic, and elastic properties. As the elastic properties of lithium metatitanate are not well-known, the efficacy of the DFT simulations employing the new pseudopotentials was explored using Li2O and TiO2 where experimental data are available. These pseudopotentials are then used to investigate the three intermediate temperature phases of Li2TiO3 (i.e., C2/c, C2/m, and P3112). Finally, we examine the elastic properties of Li2TiO3 using both DFT and an empirical potential model and find it to be, irrespective of space group, more resistant to deformation than other promising ceramic breeder materials.
Hybrid density functionals are very successful in describing a wide range of molecular properties accurately. In large molecules and solids, however, calculating the exact (Hartree-Fock) exchange is computationally expensive, especially for systems with metallic characteristics. In the present work, we develop a new hybrid density functional based on a screened Coulomb potential for the exchange interaction which circumvents this bottleneck. The results obtained for structural and thermodynamic properties of molecules are comparable in quality to the most widely used hybrid functionals. In addition, we present results of periodic boundary condition calculations for both semiconducting and metallic single wall carbon nanotubes. Using a screened Coulomb potential for Hartree-Fock exchange enables fast and accurate hybrid calculations, even of usually difficult metallic systems. The high accuracy of the new screened Coulomb potential hybrid, combined with its computational advantages, makes it widely applicable to large molecules and periodic systems.
A thorough understanding of ion dynamics in solids, which is a vital topic in modern materials and energy research, requires the investigation of diffusion properties on a preferably large dynamic range by complementary techniques. Here, a polycrystalline sample of Li(2)TiO(3) was used as a model substance to study Li motion by both (7)Li spin-alignment echo (SAE) nuclear magnetic resonance (NMR) and ac-conductivity measurements. Although the two methods do probe Li dynamics in quite different ways, good agreement was found so that the Li diffusion parameters, such as jump rates and the activation energy, could be precisely determined over a dynamic range of approximately eleven decades. For example, Li solid-state diffusion coefficients D(σ) deduced from impedance spectroscopy range from 10(-23) m(2) s(-1) to 10(-12) m(2) s(-1) (240-835 K). These values are in perfect agreement with the coefficients D(SAE) deduced from SAE NMR spectroscopy. As an example, D(SAE) = 2 × 10(-17) m(2) s(-1) at 433 K and the corresponding activation energy determined by NMR amounts to 0.77(2) eV (400-600 K). At room temperature D(σ) takes a value of 3 × 10(-21) m(2) s(-1).
Über Einkristallaufnahmen von Lithiummetastannat wurden die Strukturen folgender, durch die Analyse bestätigter Verbindungen ermittelt: Die Verbindungen erwiesen sich über Intensitätsrechnungen an Hand der Pulveraufnahmen als isotyp. Die monokline Elementarzelle gehört der Raumgruppe C C 2/c an und enthält acht Molekeln. Die Struktur läßt sich auch durch eine Zelle mit rhombischem Umriß und dreifachem Volumen beschreiben. Der manchen Netzsilicaten verwandte pseudo‐hexagonale Charakter des Gitters läßt sich an dem Verhältnis a‐Achse: b‐Achse = 1:√3 erkennen. Wie dort bilden die Sauerstoffionen eine kubisch‐dichteste Kugelpackung und treten in der Zelle als Schichten auf, während die Kationen in besonderer Anordnung die Zwischenschichten dazu bilden.
Na 2 PbO 3 tritt in einer zweiten Modifikation auf, die der kubischen Form von Li 2 TiO 3 entspricht.
Die Herstellung von Na 2 TiO 3 und Li 2 ZrO 3 wurde – wie bei den anderen Verbindungen über Reaktion von Alkalicarbonat und Metalloxyd im festen Zustand versucht. Die Pulveraufnahmen der nicht analysierten Reaktionsprodukte ergaben zwar ähnliche, aber doch an wesentlichen Stellen veränderte Reflexfolgen, so daß keine Isotypie mit den übrigen Verbindungen angenommen werden darf.
Colorless platelet crystals of monoclinic Li2TiO3 with a maximum size of 5.0 mm × 5.0 mm × 0.5 mm were successfully grown by a flux method at 1373 K using a LiBO2–Li2O system flux. The stoichiometric chemical composition of Li2TiO3 was determined by the SEM-EDX, ICP-AES and density measurement using the single crystal samples. The thermal conductivity of the Li2TiO3 single crystals was evaluated using hot-disk method. A single-crystal X-ray diffraction study confirmed the monoclinic Li2SnO3-type structure, space group C2/c and the lattice parameters of a = 5.0623(5) Å, b = 8.7876(9) Å, c = 9.7533(15) Å, β = 100.212(11)°, and V = 427.01(9) Å3. The crystal structure was refined to the conventional values of R = 2.4% and wR=3.3% for 2187 independent observed reflections. The cationic arrangement of (LiTi2) layers in Li2TiO3 was precisely revealed by the structure analysis.
A comparative study on the structure and stability of oxygen defects in ZnO is presented. By means of first-principles calculations based on local density functional theory we investigate the oxygen vacancy and different interstitial configurations of oxygen in various charge states. Our results reveal that dumbbell-like structures are thermodynamically the most stable interstitial configurations for neutral and positive charge states due to the formation of a strongly covalent oxygen-oxygen bond. For negative charge states the system prefers a split-interstitial configuration with two oxygen atoms in almost symmetric positions with respect to the associated perfect lattice site. The calculated defect formation energies imply that interstitial oxygen atoms may provide both donor- and acceptor-like defects.
This article describes recent technical developments that have made the total-energy pseudopotential the most powerful ab initio quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.
We propose a powerful scheme to accurately determine the formation energy and thermodynamic charge transition levels of point defects in nonmetals. Previously unknown correlations between defect properties and the valence-band width of the defect-free host material are identified allowing for a determination of the former via an accurate knowledge of the latter. These correlations are identified through a series of hybrid density-functional theory computations and an unbiased exploration of the parameter space that defines the Hyde-Scuseria-Ernzerhof family of hybrid functionals. The applicability of this paradigm is demonstrated for point defects in Si, Ge, ZnO, and ZrO2.
Electrical conductivity in the monoclinic Li2TiO3, cubic Li1.33Ti1.67O4, and in their mixture has been studied by impedance spectroscopy in the temperature range 20–730 °C. Li2TiO3 shows low lithium ion conductivity, σ300≈10–6 S/cm at 300 °C, whereas Li1.33Ti1.67O4 has 3×10–8 at 20 °C and 3×10–4 S/cm at 300 °C. Structural properties are used to discuss the observed conductivity features. The conductivity dependences on temperature in the coordinates of 1000/T versus loge(σT) are not linear, as the conductivity mechanism changes. Extrinsic and intrinsic conductivity regions are observed. The change in the conductivity mechanism in Li2TiO3 at around 500–600 °C is observed and considered as an effect of the first-order phase transition, not reported before. Formation of solid solutions of Li2–x
Ti1+x
O3 above 900 °C significantly increases the conductivity. Irradiation by high-energy (5 MeV) electrons causes defects and the conductivity in Li2TiO3 increases exponentially. A dose of 144 MGy yields an increase in conductivity of about 100 times at room temperature.
The phase equilibria of the pseudo-binary Li2O–TiO2 system and the stoichiometry shift of Li2TiO3 during the Li transmutation process are investigated. The structural properties, the thermal expansion, enthalpy, heat capacity, enthalpy of transformation and melting, thermal conductivity and the vapourisation behaviour of Li2TiO3 are assessed. The ternary Li–Ti–O system is treated with emphasis to the characteristic of Li2TiO3 under reducing conditions. The phase is reduced to LiTiO2 with the Ti valence +3 due to its transition metal character.
Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n + 1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The
simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and
computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum,
needed in statistical estimation problems.
We calculate absolute formation energies of native defects in GaAs. The formation energy and hence the equilibrium concentration of the defects depends strongly on the atomic chemical potentials of As and Ga as well as the electron chemical potential. For example, the Ga vacancy concentration changes by more than ten orders of magnitude as the chemical potentials of As and Ga vary over the thermodynamically allowed range. This result indicates that the rate of self-diffusion depends strongly on the surface-annealing conditions.
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
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