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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Diffuse back-illumination temperature imaging (DBI-TI), a novel soot thermometry technique

To meet stringent emissions regulations on soot emissions, it is critical to further advance the fundamental understanding of in-cylinder soot formation and oxidation processes. Among several optical techniques for soot quantification, diffuse back-illumination extinction imaging (DBI-EI) has recently gained traction mainly due to its ability to compensate for beam steering, which if not addressed, can cause unacceptably high measurement uncertainty. Until now, DBI-EI has only been used to measure the amount of soot along the line of sight, and here, we extend the capabilities of a DBI-EI setup to also measure in-cylinder soot temperature. This proof of concept of diffuse back-illumination temperature imaging (DBI-TI) as a soot thermometry technique is presented by implementing DBI-TI in a single cylinder, heavy-duty, optical diesel engine to provide 2-D line-of-sight integrated soot temperature maps. The potential of DBI-TI to be an accurate thermometry technique for use in optical engines is analyzed. The achievable accuracy is due in part to simultaneous measurement of the soot extinction, which circumvents the uncertainty in dispersion coefficients that depend on the optical properties of soot and the wavelength of light utilized. Analysis shows that DBI-TI provides temperature estimates that are closer to the mass-averaged soot temperature when compared to other thermometry techniques that are more sensitive to soot temperature closer to the detector. Furthermore, uncertainty analysis and Monte Carlo (MC) simulations provide estimates of the temperature measurement errors associated with this technique. The MC simulations reveal that for the light intensities and optical densities encountered in these experiments, the accuracy of the DBI-TI technique is comparable or even better than other established optical thermometry techniques. Thus, DBI-TI promises to be an easily implementable extension to the existing DBI-EI technique, thereby extending its ability to provide comprehensive line-of-sight integrated information on soot.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Theoretical predictive screening of noble-metal-containing M 3 AuC 2 (M = Ti, V, and Cr) MAX phases

Using first-principles density functional theory (DFT), the ground state physical properties of the newly synthesized noble-metal-containing Ti 3 AuC 2 MAX phase have been investigated. The effect of transition-element Ti replacement (V and Cr) on physical properties, including structural, elastic, electronic, thermal, and optical are presented. The optimized lattice parameters of Ti 3 AuC 2 MAX phase are in good agreement with the experimental values and decrease when we replace Ti with V and then Cr. The magnetic properties of M 3 AuC 2 are predicted by using generalized gradient approximation (GGA) incorporating onsite electron correlation parameter (Hubbard U parameter) within DFT. Out of three studied MAX phases, V 3 AuC 2 and Cr 3 AuC 2 phases exhibit magnetism. The thermodynamical stability of M 3 AuC 2 (M = Ti, V, and Cr) phases is discussed by the formation enthalpy with respect to their most competing phases. The electronic structure reveals that these phases have metallic nature and are electrically anisotropic. The M-element replacement has an effect on the bonding properties of M 3 AuC 2 . The bonding between M-C is in the order of Cr 3 AuC 2 > V 3 AuC 2 > Ti 3 AuC 2 according to their peak positions and heights of density of states in the occupied site, which is also confirmed from the charge density distribution. The elastic properties indicate that M 3 AuC 2 phases are ductile, machinable, less stiff, and better resistant to thermal shock and are elastically anisotropic. To understand the properties of M 3 AuC 2 for the extreme environment, we employed a quasi-harmonic Debye model at the pressure and temperature range of 0–50 GPa and 0–1600 K, respectively. Additionally, we evaluated thermal conductivity and melting temperature to further understand the potential of these MAX phases in coating applications at elevated temperature. In relation to optical properties, these MAX phases have a reasonable absorption coefficient in the visible as well as in the ultra-violet regions. The reflectivity of M 3 AuC 2 phases is polarization dependent and of 45 % against the visible region, which reveals its potential as coating material to minimize solar heating.

312 MAX phases↗
DOE OSTI2024

Suppressed electric quadrupole collectivity in 49 Ti

Single-step Coulomb excitation of 46,48,49,50 Ti is presented. A complete set of E2 matrix elements for the quintuplet of states in 49 Ti, centred on the core excitation, was measured for the first time. A total of nine E2 matrix elements are reported, four of which were previously unknown. $^{49}_{22}$Ti 27 shows a 20% quenching in electric quadrupole transition strength as compared to its semi-magic $^{50}_{22}$Ti 28 neighbour. This 20% quenching, while empirically unprecedented, can be explained with a remarkably simple two-state mixing model, which is also consistent with other ground-state properties such as the magnetic dipole moment and electric quadrupole moment. A connection to nucleon transfer data and the quenching of single-particle strength is also demonstrated. The simplicity of the 49 Ti- 50 Ti pair (i.e., approximate single-j 0 7/2 valence space and isolation of yrast states from non-yrast states) provides a unique opportunity to disentangle otherwise competing effects in the ground-state properties of atomic nuclei, the emergence of collectivity, and the role of proton-neutron interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Intricate Magnetic Landscape in Antiferromagnetic Kagome Metal TbTi 3 Bi 4 and Interplay with Ln 2– x Ti 6+ x Bi 9 (Ln: Tb···Lu) Shurikagome Metals

Here we present the discovery and characterization of the kagome metal TbTi 3 Bi 4 in tandem with a new series of compounds, the Ln 2–x Ti 6+x Bi 9 (Ln: Tb–Lu) shurikagome metals. We previously reported on the growth of the LnTi 3 Bi 4 (Ln: La–Gd 3+ , Eu 2+ , Yb 2+ ) family, a chemically diverse and exfoliable series of kagome metals with complex and highly anisotropic magnetism. However, unlike the La–Gd analogs, TbTi 3 Bi 4 cannot be synthesized by our previous methodology due to phase competition with crystals of Ln 2–x Ti 6+x Bi 9 (x ~ 1.7–1.2). Here we discuss the phase competition between the LnTi 3 Bi 4 and Ln 2–x Ti 6+x Bi 9 families, helping to frame the difficulty in synthesizing LnTi 3 Bi 4 compounds with small Ln species and providing a strategy to circumvent the formation of Ln 2–x Ti 6+x Bi 9 . Detailed characterization of the magnetic and electronic transport properties on single crystals of TbTi 3 Bi 4 reveals a highly complex landscape of magnetic phases arising from an antiferromagnetic ground state. A series of metamagnetic transitions creates at least 5 unique magnetic phase pockets, including a 1/3 and 2/3 magnetization plateau. Further, the system exhibits an intimate connection between the magnetism and magnetotransport, exhibiting sharp switching from positive (+40%) to negative magnetoresistance (–50%). Like the LnTi 3 Bi 4 kagome metals, the Ln 2–x Ti 6+x Bi 9 family exhibits quasi-2D networks of titanium and chains of rare earth. Finally, we present the structures and some basic magnetic properties of the Ln 2–x Ti 6+x Bi 9 family alongside our characterization of the newly discovered TbTi 3 Bi 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Plasmonic Hot-Carrier Generation and Catalysis in Ti 3 C 2 O 2 from Real-Time TDDFT Simulations

Photoinduced hot electrons are central to plasmon-driven catalysis. Atomically thin Ti 3 C 2 O 2 , with high carrier density and broad optical absorption, offers a promising platform for plasmon-driven reactions. However, comprehensive investigations of its plasmon resonance, hot-carrier generation, and plasmonic catalytic performance remain limited. In this work, real-time time-dependent density functional theory (rt-TDDFT) was employed to study Ti 3 C 2 O 2 ’s plasmon excitation and hot-carrier generation from nonradiative plasmon damping. The temporal evolution of the dipole moment reveals plasmon resonance in Ti 3 C 2 O 2 , followed by strong plasmon damping that redistributes the stored energy to generate hot carriers. Ti 3 C 2 O 2 with low oxygen vacancy concentration (O v -Ti 3 C 2 O 2 ) exhibits plasmonic behavior resembling the pristine surface, and the plasmon-generated hot electrons can markedly reduce the dissociation barrier of CO 2 at the oxygen vacancy. These findings provide fundamental insights into the plasmonic properties of Ti 3 C 2 O 2 and how they drive its catalytic performance in surface reactions, which is valuable for advancing plasmon-driven catalysis.

CO2 reduction↗
DOE OSTI2020

Porous Ti-MOF-74 Framework as a Strong-Binding Nitric Oxide Scavenger

Combining synthesis, infrared spectroscopy, and ab initio modeling we show that the titanium-based porous framework Ti-MOF-74 has potential as an environmental nitric oxide (NO) scavenger, exhibiting an extraordinarily strong binding affinity and selectivity over other flue-gas components. The robustness upon exposure to water vapor and high flue-gas stack temperatures suggests that this material can perform well in an industrial environment. In-depth analysis of the Ti-NO bond indicates that the NO forms a strong covalent bond with the Ti. The process of this NO bond formation involves a reaction with the OH- capping groups of the Ti to form NO x groups, after which the excess NO binds to the open Ti metal sites. Ti-MOF-74 thus becomes, to the best of our knowledge, the first known porous framework that binds NO significantly stronger than water, providing novel avenues for environmental and physiological scavenging applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Facilitating Hydrogen Dissociation over Dilute Nanoporous Ti–Cu Catalysts

The dissociation of H 2 is an essential elementary step in many industrial chemical transformations, typically requiring precious metals. Here, we report a hierarchical nanoporous Cu catalyst doped with small amounts of Ti (npTiCu) that increases the rate of H 2 –D 2 exchange by approximately one order of magnitude compared to the undoped nanoporous Cu (npCu) catalyst. The promotional effect of Ti was measured via steady-state H 2 –D 2 exchange reaction experiments under atmospheric pressure flow conditions in the temperature range of 300–573 K. Pretreatment with flowing H 2 is required for stable catalytic performance, and two temperatures, 523 and 673 K, were investigated. The experimentally determined H 2 –D 2 exchange rate is 5–7 times greater for npTiCu vs the undoped Cu material under optimized pretreatment and reaction temperatures. The H 2 pretreatment leads to full reduction of Cu oxide and partial reduction of surface Ti oxide species present in the as-prepared catalyst as demonstrated using in situ ambient pressure X-ray photoelectron spectroscopy and X-ray absorption spectroscopy. The apparent activation energies and pre-exponential factors measured for H 2 –D 2 exchange are substantially different for Ti-doped vs undoped npCu catalysts. Density functional theory calculations suggest that isolated, metallic Ti atoms on the surface of the Cu host can act as the active surface sites for hydrogen recombination. Furthermore, the increase in the rate of exchange above that of pure Cu is caused primarily by a shift in the rate-determining step from dissociative adsorption on Cu to H/D atom recombination on Ti-doped Cu, with the corresponding decrease in activation entropy that it produces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Proton, Electron, and Hydrogen-Atom Transfer Thermodynamics of the Metal–Organic Framework, Ti-MIL-125, Are Intrinsically Correlated to the Structural Disorder

Interfacial charge transfer reactions involving protons and/or electrons are fundamental to heterogeneous catalysis and many other reactions relevant to energy, chemical, and biological sectors. Metal–organic frameworks (MOFs) with redox-active metal-oxo nodes have emerged as candidate materials to examine these reactions with near-atomic-level precision, given their crystalline nature. Here, we employed a colloidally stable, Ti-based MOF, Ti-MIL-125, with different crystal sizes to examine catalytically relevant charge transfer thermodynamics. The Ti 8 (μ 2 -O) 8 (μ 2 -OH) 4 nodes structurally mimic TiO 2 , which has shown some PCET reactivity toward reactions of H 2 , O 2 , and others. In this report, we have demonstrated that a change in crystal size induces different amounts of structural disorder to the Ti-oxo node, further changing the thermodynamics of proton/electron/hydrogen-atom transfer reactions. Using electrochemical open-circuit potential (E OCP ) measurements, we have determined that all crystallites undergo a 1H + /1e – redox reaction, which, given the stoichiometry, can be considered as a net H atom transfer (HAT) reaction. The thermodynamics of this HAT reaction, the Ti 3+ O–H bond dissociation free energy (BDFE), was dependent on the crystal size of the MOF, as the decrease in crystal size induced more structural disorder. Our computational calculations have indicated that this difference in BDFE is due to a local change in the geometry of Ti cations, rather than the commonly invoked defects, such as the “missing-linker” defect sites. Individual proton/electron transfer (PT/ET) thermodynamics were also highly dependent on the crystal sizes. These were probed using pK a or band gaps (E g ), respectively. These findings suggest that, particularly when MOFs are nanosized with a large amount of structural disorder, they should no longer be considered “true” single-site catalysts; this is an implicit, but widespread assumption within the MOF-based catalysis field. Implications of these findings will be contrasted with structurally similar metal oxides like TiO 2 and other redox-active MOFs.

Bond dissociation free energy↗
DOE OSTI2022

A theoretical investigation of the effect of Ga alloying on thermodynamic stability, electronic-structure, and oxidation resistance of Ti 2 AlC MAX phase

We present a systematic investigation of thermodynamic stability, phase-reaction, and chemical activity of Al containing disordered Ti 2 (Al-Ga)C MAX phases using machine-learning driven high-throughput framework to understand the oxidation resistance behavior with increasing temperature and exposure to static oxygen. The A-site (at Al) disordering of Ti 2 AlC with Ga shows significant change in the chemical activity of Al with increasing temperature and exposure to static oxygen, which is expected to enable surface segregation of Al, thereby, the formation of Al 2 O 3 and improved oxidation resistance. We performed in-depth convex hull analysis of ternary Ti-Al-C, Ti-Ga-C, and Ti-Al-Ga-C based MAX phase, and provide detailed contribution arising from electronic, chemical and vibrational entropies. The thermodynamic analysis shows change in the Gibbs formation enthalpy (ΔG form ) at higher temperatures, which implies an interplay of temperature-dependent enthalpy and entropic contributions in oxidation resistance Ga doped Ti 2 AlC MAX phases. A detailed electronic structure and chemical bonding analysis using crystal orbital Hamilton population method reveal the origin of change in phases stability and in oxidation resistance in disorder Ti2(Al 1-x Ga x )C MAX phases. Our electronic structure analysis correlate well with the change in oxidation resistance of Ga doped MAX phases. We believe our study provides a useful guideline to understand to role of alloying on electronic, thermodynamic, and oxidation related mechanisms of bulk MAX phases, which can work as a precursor to understand oxidation behavior of twodimensional MAX phases, i.e., MXenes (transition metal carbides, carbonitrides and nitrides).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Tuning the temperature range of superelastic Ni-Ti alloys for elastocaloric cooling via thermal processing

Abstract Caloric cooling enlisting solid-state refrigerants is potentially a promising eco-friendly alternative to conventional cooling based on vapor compression. The most common refrigerant materials for elastocaloric cooling to date are Ni-Ti based superelastic shape memory alloys. Here, we have explored tuning the operation temperature range of Ni 50.8 Ti 49.2 for elastocaloric cooling. In particular, we have studied the effect of thermal treatments (a.k.a. aging) on the transformation temperature, superelasticity, and elastocaloric effects of Ni 50.8 Ti 49.2 shape memory alloy tubes. The isothermal compressive test revealed that the residual strain of thermally-treated Ni-Ti tubes at room temperature approaches zero as aging time is increased. Short-time aging treatment at 400 °C resulted in good superelasticity and elastocaloric cooling performance with a large tunable austenite finish ( A f ) temperature range of 24.7 °C, as determined from the A f temperature of the samples that were aged 5–120 min. The main reason of the property change is the formation of a different amount of Ni 4 Ti 3 precipitates in the NiTi matrix. Our findings show that it is possible to tailor the A f temperature range for development of cascade elastocaloric cooling systems by thermally treating a starting single composition Ni-Ti alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Superconducting phase of Ti x O y thin films grown by molecular beam epitaxy

Here we investigate the complex relationship between the growth conditions and the structural and transport properties of Ti x O y thin films grown by molecular beam epitaxy. Transport properties ranging from metallicity to superconductivity and insulating states are stabilized by effectively tuning the O/Ti ratio via the Ti flux rate and the O partial pressure P Ox for films grown on (0001)-Al 2 O 3 substrates at 850° C. A cubic c-TiO 1±δ buffer layer is formed for low O/Ti ratios, while a corundum cr-Ti 2 O 3 layer is formed under higher-oxidizing conditions. Metallicity is observed for c-TiO 1-δ buffer layers. The superconducting γ -Ti 3 O 5 Magnéli phase is found to nucleate on a c-TiO 1-δ buffer for intermediate POx conditions, and an insulator-superconducting transition is observed at 4.5 K (T$^{onset}_{C}$ = 6K) for 85 nm thick films. Strain relaxation of γ -Ti 3 O 5 occurs with increasing film thickness and correlates with a thickness-dependent increase in T C observed for Ti x O y thin films.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Low cost fabrication of sheet structure using a new beta titanium alloy, Ti-15V-3Cr-3Al-3Sn

Development efforts have been undertaken to improve the processing and structural efficiencies of advanced cold-formable beta Ti alloys, using the standard, hot-formed and rivetted construction of Ti-6Al-4V sheet structures as a basis for comparison. Ti-15V-3Cr-3Al-3Sn (Ti-15-3) beta alloy is formable, brazable and weldable in the solution-treated condition, and after aging displays mechanical properties suitable for postulated service in the -65 to 600 F temperature range. A novel methodology using cold-formed Ti-15-3 stringers and Ti-6Al-4V face sheets that are joined by means of an out-of-furnace isothermal brazing process, followed by low temperature aging, can reduce production costs by as much as 28 per cent. Structural efficiency has been demonstrated in room and elevated temperature crippling tests of small skin-stringer assemblies.

Kaneko, R. S.↗
NASA NTRS1988

Synchronously pumped mode-locked Ti:Al2O3 lasers

Synchronously pumped mode-locked laser operation in a Ti:Al2O3 ring laser is demonstrated. The laser pump source was a frequency-doubled Nd:YAG laser-amplifier system producing a 60-micron-long macropulse that comprised a wavetrain of mode-locked 70-ps micropulses with a 10-ns spacing (100 MHz). The Ti:Al2O3 laser consisted of a 1-cm-long crystal with faces cut at the Brewster angle and placed in a ring laser cavity configuration with a 2 percent output coupling mirror. The cavity was adjusted for a 5-ns round trip transit time, which was close to half the temporal spacing of the pump pulse. When the crystal was pumped synchronously at 532 nm with a 30-mJ macropulse, which was approximately an order of magnitude above the laser threshold, mode-locked lasing at approximately 200 MHz was obtained. This macropulse pump energy corresponds to an average micropulse pump energy of about 5 microJ at the Ti:Al2O3 crystal face. The mode-locked operation of the Ti:Al2O3 was observed only after several microseconds into the macropulse, indicating a long build-up process over many cavity trips. During this time, relaxation oscillations were observed. When mode locking started, the relaxation oscillation frequency increased by an order of magnitude. Synchronous pumping has been limited to operation with dye lasers and used either a CW or pulsed mode-locked pump source. Recent work has demonstrated CW mode-locked operation of a Ti:Al2O3 laser. The result raises the possibility that pulsed synchronous pumping may be used to obtain significantly narrowed laser pulses in Ti:Al2O3.

Source record↗
NASA NTRS1988

Residual infrared absorption in Ti:Al2O3 crystals

The performance of Ti:Al2O3 lasers is impaired generally by an infrared absorption that occurs in the laser output wavelength region. On the basis of data for as-grown and annealed samples cut from Ti:Al2O3 crystals grown by the vertical-gradient-freeze (VGF) technique, we previously proposed that the residual absorption is due to Ti(3+) to Ti(4+) pairs. In this report, we present additional data that confirm this ion-pair model for the residual absorption, which can be attributed to excitation of the 3d electron of the Ti(3+) ion perturbed by the Coulomb field of the neighboring Ti(4+) ion and/or an associated Al vacancy.

Source record↗
NASA NTRS2007

[Ti II] and [Ni II] Emission from the Strontium Filament of eta Carinae

We study the nature of the [Ti II] and [Ni II] emission from the so-called strontium filament found in the ejecta of eta Carinae. To this purpose we employ multilevel models of the Ti II and Ni II systems which are used to investigate the physical condition of the filament and the excitation mechanisms of the observed lines. For the Ti II ion, for which no atomic data was previously available, we carry out ab initio calculations of radiative transition rates and electron impact excitation rate coefficients. It is found that the observed spectrum is consistent with the lines being excited in a mostly neutral region with an electron density of the order of 10(exp 7) per cubic centimeter and a temperature around 6000 K. In analyzing three observations with different slit orientations recorded between March 2000 and November 2001 we find line ratios that change among various observations, in a way consistent with changes of up to an order of magnitude in the strength of the continuum radiation field. These changes result from different samplings of the extended filament, due to the different slit orientations used for each observation, and yield clues on the spatial extent and optical depth of the filament. The observed emission indicates a large Ti/Ni abundance ratio relative to solar abundances. It is suggested that the observed high Ti/Ni ratio in gas is caused by dust-gas fractionation processes and does not reflect the absolute Ti/Ni ratio in the ejecta of eta Carinae. We study the condensation chemistry of Ti, Ni and Fe within the filament and suggest that the observed gas phase overabundance of Ti is likely the result of selective photo-evaporation of Ti-bearing grains. Some mechanisms for such a scenario are proposed.

Bautista, M. A.↗
NASA NTRS2012

TEM Observation of the Ti Interlayer Between SiC Substrates During Diffusion Bonding

Diffusion bonding was carried out to join SiC to SiC substrates using titanium interlayers. In this study, 10 m and 20 m thick physical vapor deposited (PVD) Ti surface coatings, and 10 and 20 m thick Ti foils were used. Diffusion bonding was performed at 1250 C for PVD Ti coatings and 1200 C for Ti foil. This study investigates the microstructures of the phases formed during diffusion bonding through TEM and selected-area diffraction analysis of a sample prepared with an FIB, which allows samples to be taken from the reacted area. In all samples, Ti3SiC2, Ti5Si3Cx and TiSi2 phases were identified. In addition, TiC and unknown phases also appeared in the samples in which Ti foils were used as interlayers. Furthermore, Ti3SiC2 phases show high concentration and Ti5Si3Cx formed less when samples were processed at a higher temperature and thinner interlayer samples were used. It appears that the formation of microcracks is caused by the presence of intermediate phase Ti5Si3Cx, which has anisotropic thermal expansion, and by the presence of an unidentified Ti-Si-C ternary phase with relatively low Si content.

Tsuda, Hiroshi↗
NASA NTRS2001

Fretting Wear of Ti-48Al-2Cr-2Nb

An investigation was conducted to examine the wear behavior of gamma titanium aluminide (Ti-48Al-2Cr-2Nb in atomic percent) in contact with a typical nickel-base superalloy under repeated microscopic vibratory motion in air at temperatures from 296-823 K. The surface damage observed on the interacting surfaces of both Ti-48Al-2Cr-2Nb and superalloy consisted of fracture pits, oxides, metallic debris, scratches, craters, plastic deformation, and cracks. The Ti-48Al-2Cr-2Nb transferred to the superalloy at all fretting conditions and caused scuffing or galling. The increasing rate of oxidation at elevated temperatures led to a drop in Ti-48Al-2Cr-2Nb wear at 473 K. Mild oxidative wear was observed at 473 K. However, fretting wear increased as the temperature was increased from 473-823 K. At 723 and 823 K, oxide disruption generated cracks, loose wear debris, and pits on the Ti-48Al-2Cr-2Nb wear surface. Ti-48Al-2Cr-2Nb wear generally decreased with increasing fretting frequency. Both increasing slip amplitude and increasing load tended to produce more metallic wear debris, causing severe abrasive wear in the contacting metals. Keywords

Miyoshi, Kazuhisa↗
DOE OSTI2020

Materials Data on Ti(FeO2)3 by Materials Project

Ti(FeO2)3 is beta indium sulfide-derived structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are four inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one TiO6 octahedra, and edges with four FeO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.80–2.29 Å. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one TiO6 octahedra, and edges with three FeO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.79–2.21 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six FeO4 tetrahedra, edges with two equivalent TiO6 octahedra, and edges with two FeO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.86–2.10 Å. In the fourth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six FeO4 tetrahedra, edges with two equivalent TiO6 octahedra, and edges with two FeO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.88–2.08 Å. There are twelve inequivalent Fe+2.67+ sites. In the first Fe+2.67+ site, Fe+2.67+ is bonded to four O2- atoms to form FeO4 tetrahedra that share corners with two TiO6 octahedra and corners with nine FeO6 octahedra. The corner-sharing octahedra tilt angles range from 53–60°. There are a spread of Fe–O bond distances ranging from 1.89–1.99 Å. In the second Fe+2.67+ site, Fe+2.67+ is bonded to four O2- atoms to form FeO4 tetrahedra that share corners with five TiO6 octahedra and corners with five FeO6 octahedra. The corner-sharing octahedra tilt angles range from 48–66°. There are a spread of Fe–O bond distances ranging from 1.96–2.10 Å. In the third Fe+2.67+ site, Fe+2.67+ is bonded to four O2- atoms to form FeO4 tetrahedra that share corners with four FeO6 octahedra and corners with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–63°. There are a spread of Fe–O bond distances ranging from 1.86–2.01 Å. In the fourth Fe+2.67+ site, Fe+2.67+ is bonded to four O2- atoms to form FeO4 tetrahedra that share corners with four TiO6 octahedra and corners with seven FeO6 octahedra. The corner-sharing octahedra tilt angles range from 47–63°. There are a spread of Fe–O bond distances ranging from 1.86–1.99 Å. In the fifth Fe+2.67+ site, Fe+2.67+ is bonded to four O2- atoms to form FeO4 tetrahedra that share corners with four TiO6 octahedra and corners with five FeO6 octahedra. The corner-sharing octahedra tilt angles range from 50–62°. There are a spread of Fe–O bond distances ranging from 1.93–2.13 Å. In the sixth Fe+2.67+ site, Fe+2.67+ is bonded to four O2- atoms to form FeO4 tetrahedra that share corners with four TiO6 octahedra and corners with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 53–60°. There are a spread of Fe–O bond distances ranging from 1.89–2.01 Å. In the seventh Fe+2.67+ site, Fe+2.67+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one FeO6 octahedra, and edges with three TiO6 octahedra. There are a spread of Fe–O bond distances ranging from 1.99–2.24 Å. In the eighth Fe+2.67+ site, Fe+2.67+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six FeO4 tetrahedra, edges with two TiO6 octahedra, and edges with three FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 1.96–2.16 Å. In the ninth Fe+2.67+ site, Fe+2.67+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one TiO6 octahedra, and edges with five FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 2.01–2.12 Å. In the tenth Fe+2.67+ site, Fe+2.67+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one TiO6 octahedra, and edges with five FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 2.11–2.18 Å. In the eleventh Fe+2.67+ site, Fe+2.67+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one FeO6 octahedra, and edges with three TiO6 octahedra. There are a spread of Fe–O bond distances ranging from 1.91–2.10 Å. In the twelfth Fe+2.67+ site, Fe+2.67+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six FeO4 tetrahedra, an edgeedge with one TiO6 octahedra, and edges with five FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 1.99–2.11 Å. There are twenty-four inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to four Fe+2.67+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to two Ti4+ and one Fe+2.67+ atom. In the fourth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Fe+2.67+ atoms. In the fifth O2- site, O2- is bonded in a rectangular see-saw-like geometry to two Ti4+ and two Fe+2.67+ atoms. In the sixth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to two Ti4+ and two Fe+2.67+ atoms. In the seventh O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Fe+2.67+ atoms. In the eighth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms. In the ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms. In the tenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Fe+2.67+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal planar geometry to two Ti4+ and one Fe+2.67+ atom. In the twelfth O2- site, O2- is bonded in a 3-coordinate geometry to one Ti4+ and two Fe+2.67+ atoms. In the thirteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Fe+2.67+ atoms. In the fourteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to two Ti4+ and one Fe+2.67+ atom. In the sixteenth O2- site, O2- is bonded in a distorted trigonal pyramidal geometry to one Ti4+ and three Fe+2.67+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Ti4+ and three Fe+2.67+ atoms. In the eighteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to two Ti4+ and two Fe+2.67+ atoms. In the nineteenth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Ti4+ and three Fe+2.67+ atoms. In the twentieth O2- site, O2- is bonded in a trigonal planar geometry to three Fe+2.67+ atoms. In the twenty-first O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms. In the twenty-second O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Ti4+ and three Fe+2.67+ atoms. In the twenty-third O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms. In the twenty-fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two Fe+2.67+ atoms.

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