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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Focused Ion Beam Preparation of Low Melting Point Metals: Lessons Learned From Indium

Indium (In) and other low melting point metals are used as interconnects in a variety of hybridized circuits and a full understanding of the metallurgy of these interconnects is important to the reliability and performance of the devices. Here, this paper shows that room temperature focused ion beam (FIB) preparation of cross-sections, using Ga + or Xe + can result in artifacts that obscure the true In microbump structure. The use of modified milling strategies to minimize the increased local sample temperature are shown to produce cross-sections that are representative of the In bump microstructure in some sample configurations. Furthermore, cooling of the sample to cryogenic temperatures is shown to reliably eliminate artifacts in FIB prepared cross-sections of In bumps allowing the true bump microstructure to be observed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A multifunctional technology platform for sorbent construction using polyacrylonitrile scaffolds

Polyacrylonitrile (PAN) is a synthetic polymer that shows high potential for use in a wide range of environmental remediation applications. PAN can be implemented in various ways within a batch or continuous process stream for use as a passive scaffold holding active gettering materials in place or where the PAN scaffold (e.g., beads, fiber mats, membranes) is functionalized with active chelating groups (e.g., amine, hydrazide, amidoximes, carboxyl). Application spaces covered in this review include remediation of heavy metals (e.g., Ag, As, Cd, Cr6+, Cu, Pb, Sb, and Se), high-dose fission products (e.g., 90Sr, 137Cs), radioiodine (i.e., 129I), noble gases (i.e., Xe, 85Kr), rare earths (e.g., Ce, Y), and actinides (e.g., Am, Pu, U). Methods for producing PAN composite sorbents are discussed. Options are also discussed for removing the PAN matrix following chemisorption of an active contaminant to minimize waste volumes requiring disposal.

polyacrylonitrile, composite sorbents, sulfides, a↗
DOE OSTI2022

Sequential Bond Dissociation Energies of Th + (CO) x , x = 3–6: Guided Ion Beam Collision-Induced Dissociation and Quantum Computational Studies

Collision-induced dissociation (CID) of [Th,xC,xO] + , x = 3–6, with Xe is performed using a guided ion beam tandem mass spectrometer (GIBMS). Products are formed exclusively by the loss of CO ligands. Analyses of the kinetic energy-dependent CID product cross sections yield bond dissociation energies (BDEs) of (CO) x–1 Th + –CO at 0 K as 1.09 ± 0.05, 0.82 ± 0.07, 0.63 ± 0.05, and 0.70 ± 0.05 eV, respectively. Different structures of [Th,xC,xO] + were explored using various electronic structure methods, and BDEs for CO ligand loss from precursor [Th,xC,xO] + complexes were computed. Both experimental and theoretical results corroborate that the structures of [Th,xC,xO] + , x = 3–6, formed experimentally are homoleptic thorium cation carbonyl complexes, Th + (CO) x . The nonmonotonic trend in experimental BDEs is reproduced theoretically, although ambiguities in the spin states of the x = 4–6 complexes (doublet or quartet) remain. BDEs calculated at the coupled cluster with single, double, and perturbative triple excitations (CCSD(T))/cc-pVXZ//B3LYP/cc-PVXZ (X = T and Q) level and a complete basis set (CBS) extrapolation agree reasonably well with the experimental values for all complexes. Thorium oxide ketenylidene carbonyl cations, OTh + CCO(CO) y , y = 1–4, were calculated to be the most stable structures of [Th,xC,xO] + , x = 3–6, respectively; however, these are not observed in our experiment. Potential energy profiles (PEPs) having either quartet or doublet spin calculated at the B3LYP/cc-pVQZ level suggest that the failure to observe OTh + CCO(CO) y , y = 1–4, is the result of a barrier corresponding to the C–C bond formation, making the formation of OTh + CCO(CO) y inaccessible kinetically under the present experimental conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

MOFX-DB: An Online Database of Computational Adsorption Data for Nanoporous Materials

Machine learning and data mining coupled with molecular modeling have become powerful tools for materials discovery. Metal-organic frameworks (MOFs) are a rich area for this due to their modular construction and numerous applications. Here, we make data from several previous large-scale studies in MOFs and zeolites from our groups (and new data for N 2 and Ar adsorption in MOFs) easily accessible in one place. The database includes over 3 million simulated adsorption data points for H 2 , CH 4 , CO 2 , Xe, Kr, Ar, and N 2 in over 160 000 MOFs and zeolites, textural properties like pore sizes and surface areas, and the structure file for each material. We include metadata about the Monte Carlo simulations to enable reproducibility. The database is searchable by MOF properties, and the data are stored in a standardized JSON format that that is interoperable with the NIST adsorption database. We also identify several MOFs that meet high performance targets for multiple applications, such as high storage capacity for both hydrogen and methane or high CO 2 capacity plus good Xe/Kr selectivity. Here, by providing this data publicly, we hope to facilitate machine learning studies on these materials, leading to new insights on adsorption in MOFs and zeolites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Two-Dimensional Energy Histograms as Features for Machine Learning to Predict Adsorption in Diverse Nanoporous Materials

A major obstacle for machine learning (ML) in chemical science is the lack of physically informed feature representations that provide both accurate prediction and easy interpretability of the ML model. In this work, we describe adsorption systems using novel two-dimensional energy histogram (2D-EH) features, which are obtained from the probe-adsorbent energies and energy gradients at grid points located throughout the adsorbent. The 2D-EH features encode both energetic and structural information of the material and lead to highly accurate ML models (coefficient of determination R2 ~ 0.94–0.99) for predicting single-component adsorption capacity in metal–organic frameworks (MOFs). Here, we consider the adsorption of spherical molecules (Kr and Xe), linear alkanes with a wide range of aspect ratios (ethane, propane, n-butane, and n-hexane), and a branched alkane (2,2-dimethylbutane) over a wide range of temperatures and pressures. The interpretable 2D-EH features enable the ML model to learn the basic physics of adsorption in pores from the training data. We show that these MOF-data-trained ML models are transferrable to different families of amorphous nanoporous materials. We also identify several adsorption systems where capillary condensation occurs, and ML predictions are more challenging. Nevertheless, our 2D-EH features still outperform structural features including those derived from persistent homology. The novel 2D-EH features may help accelerate the discovery and design of advanced nanoporous materials using ML for gas storage and separation in the future.

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

Pressure Effects on the Relaxation of an Excited Ethane Molecule in High-Pressure Bath Gases

Here, we use molecular dynamics to calculate the rotational and vibrational energy relaxation of C 2 H 6 in Ar, Kr, and Xe bath gases over a pressure range of 10 to 400 atm and at temperatures of 300 K and 800 K. The C 2 H 6 is instantaneously excited by 80 kcal/mol randomly distributed into both vibrational and rotational modes. The computed relaxation rates show little sensitivity to the identity of the noble gas in the bath. Vibrational relaxation rates show a non-linear pressure dependence at 300 K. At 800 K the reduced range of bath gas densities covered by the range of pressures do not yet show any non-linearity in the pressure dependence. Rotational relaxation is characterized with two relaxation rates. The slower rate is comparable to the vibrational relaxation rate. The faster rate has a linear pressure dependence at 300 K but an irregular, nonlinear pressure dependence at 800 K. To understand this, a model was developed based on approximating the periodic box used in the molecular dynamics simulations by an equal-volume collection of cubes where each cube is sized to allow only single occupancy by the noble gas or the molecule. Combinatorial statistics then leads to a pressure and temperature dependent analytic distribution of the bath gas species the molecule encounters in a collision. This distribution, the dissociation energy of molecule/bath gas complexes and bath gas clusters, and the computed energy release per collision combine to show that only at 300 K is the energy release sufficient to dissociate likely complexes and clusters. This suggests that persistent and pressure-dependent clusters and complexes at 800 K may be responsible for the non-linear pressure dependence of rotational relaxation.

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

Dynamics of Radiation Damage Buildup in Ultrathin Hexagonal Boron Nitride Films under Ion Bombardment

Two-dimensional hexagonal boron nitride (hBN) is attractive for several emerging applications. Ion bombardment can be used to modify the hBN properties. However, the understanding of radiation damage buildup in hBN remains limited. Here, we investigate the effects of the dose rate and ion mass on radiation damage buildup by studying 40 nm-thick hBN films bombarded at room temperature with 500 keV 4 He, 15 N, 40 Ar, and 129 Xe ions and comparing with results for ion bombardment of polycrystalline hBN ceramics. Raman spectroscopy is used to quantify damage buildup, and transmission electron microscopy is used for microstructural analysis. Experiments are complemented by molecular dynamics simulations of the formation and evolution of point defects. Lighter ions are found to be more efficient at disordering hBN than heavier ions. This observation points to a critical role of intracascade defect processes. In contrast, a negligible dose rate effect observed suggests limited intercascade defect dynamic annealing processes for these irradiation conditions. These findings provide a fundamental basis for hBN defect engineering.

2D materials↗
DOE OSTI2025

Ultrafast Photoflash Synthesis of High-Entropy Oxide Nanoparticles

High-entropy metal oxides (HEOs) have recently received growing attention for broad energy conversion and storage applications due to their tunable properties. HEOs typically involve the combination of multiple metal cations in a single oxide lattice, thus bringing distinctive structures, controllable elemental composition, and tunable functional properties. Many synthesis methods for HEOs have been reported, such as solid-state reactions and carbon thermal shock methods. These methods frequently are energy-intensive or require relatively expensive heating equipment. In this work, we report an ultrafast photoflash synthesis method for HEO nanoparticles on diverse substrates. The energy input is provided by a commercial Xe photoflash unit, which triggers exothermic reactions to convert metal salt precursors to HEO nanoparticles within tens of milliseconds. The formation of HEO nanoparticles is attributed to the ultrafast heating (∼106 K/s) and cooling (∼105 K/s) rates of the photoflash and overall high temperature (>1000 K) during the ultrafast synthesis process. When the synthesized CoNiFeCrMn oxide (HEO) is tested as an oxygen evolution reaction electrocatalyst, it shows similar activity to similar materials prepared by other methods. We believe this photoflash synthesis provides a simple method for many others to synthesize diverse HEOs and explore their properties and potential applications.

exothermic reaction synthesis↗
DOE OSTI2026

Unveiling Swift Heavy Ion Track Morphology in Sr-Based High-Entropy Perovskites

The incorporation of multiple cations on a single lattice site in the high-entropy oxides is considered the key driving factor for modifying the known atomic-level response to energetic ion irradiation due to the presence of structural disorder; however, these effects are not well-understood yet. In this work, we present atomic-level insight into irradiation-induced nanoscale phase transformations in a perovskite-structured high-entropy oxide, Sr(Zr 0.2 Sn 0.2 Ti 0.2 Hf 0.2 Nb 0.2 )O 3 (Sr(HE)O 3 ), subjected to 774 MeV swift Xe heavy ions, where damage is dominated by inelastic ion−lattice interactions. While these ions generally are known to create nanoscale disordered channels, “ion tracks”, along the penetration direction in the material, this study shows the formation of discontinuous and partially recrystallized ion tracks in Sr(HE)O 3 . Compared to SrTiO 3 irradiated under identical energy loss conditions, the ion tracks in Sr(HE)O 3 exhibit significantly reduced diameters and a markedly different interfacial structure. Notably, the crystalline−amorphous interface in Sr(HE)O 3 shows minimal lattice distortion, confined to approximately 2−3 monolayers, in contrast to the extended disordered shell commonly observed in SrTiO 3 . Using in situ atomic-resolution electron microscopy, we further demonstrate that the amorphous/disordered regions within Sr(HE)O 3 ion tracks remain highly stable under electron irradiation, whereas tracks in SrTiO 3 readily recrystallize. This enhanced stability is attributed to the dominance of structural and chemical complexity arising from multiple B-site cations, which suppress defect migration and templated recrystallization driven by electronic excitations and local heating. Overall, this study highlights how high-entropy oxide chemistry fundamentally reshapes irradiation damage evolution, offering insights into defect formation and phase stability under extreme conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Glass-Bonded Monazite Waste Forms for Lanthanide and Actinide Immobilization: From Theoretical Design to Scale-Up Production and Characterization

The development of nuclear waste forms for both existing and future nuclear wastes is critical to ensuring global environmental safety. This study focuses on waste management from molten salt reactors, where fuel exists in a salt form and could be processed in real time for the removal of neutron poisons such as xenon isotopes (e.g., 135 Xe) and rare earth elements (REEs, e.g., 149 Sm). To ensure safe, stable, and long-term disposal in geological repositories, REEs must be incorporated into a durable waste form. Iron-phosphate glasses are a promising candidate due to their low melting points, high chemical durability, and their ability to incorporate high concentrations of REEs. In this study, we successfully prepared iron-phosphate glass waste forms with high Nd loadings (up to 37 mass %) in batch sizes ranging from small (23 g) to large (1600 g). The resulting materials contained up to 75 mass % NdPO 4 , contributing to their mechanical resilience and exceptional chemical durability. These findings highlight the potential of iron-phosphate glasses as high-efficiency, chemically durable waste forms and demonstrate the successful transition from theoretical design to scaled-up production.

amorphous materials↗
DOE OSTI2020

Crystallizing Atomic Xenon in a Flexible MOF to Probe and Understand Its Temperature-Dependent Breathing Behavior and Unusual Gas Adsorption Phenomenon

Flexible metal–organic frameworks (MOFs) hold great promise as smart materials for specific applications such as gas separation. These materials undergo interesting structural changes in response to guest molecules, which is often associated with unique adsorption behavior not possible for rigid MOFs. Understanding the dynamic behavior of flexible MOFs is crucial yet challenging as it involves weak host–guest interactions and subtle structural transformation not only at the atomic/molecular level but also in a nonsteady state. Here we report an in-depth study on the adsorbate- and temperature-dependent adsorption in a flexible MOF by crystallizing atomic gases into its pores. Mn(ina)2 shows an interesting temperature-dependent response toward noble gases. Its nonmonotonic, temperature-dependent adsorption profile results in an uptake maximum at a temperature threshold, a phenomenon that is unusual. Full characterization of Xe-loaded MOF structures is performed by in situ single-crystal and synchrotron X-ray diffraction, IR spectroscopy, and molecular modeling. The X-ray diffraction analysis offers a detailed explanation into the dynamic structural transformation and provides a convincing rationalization of the unique adsorption behavior at the molecular scale. The guest and temperature dependence of the structural breathing gives rise to an intriguing reverse of Xe/Kr adsorption selectivity as a function of temperature. The presented work may provide further understanding of the adsorption behavior of noble gases in flexible MOF structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Global Ocean Cooling of 2.3°C During the Last Glacial Maximum

Abstract Quantitative constraints on past mean ocean temperature (MOT) critically inform our historical understanding of Earth's energy balance. A recently developed MOT proxy based on paleoatmospheric Xe, Kr, and N 2 ratios in ice core air bubbles is a promising tool rooted in the temperature dependences of gas solubilities. However, these inert gases are systematically undersaturated in the modern ocean interior, and it remains unclear how air‐sea disequilibrium may have changed in the past. Here, we carry out 30 tracer‐enabled model simulations under varying circulation, sea ice cover, and wind stress regimes to evaluate air‐sea disequilibrium in the Last Glacial Maximum (LGM) ocean. We find that undersaturation of all three gases was likely reduced, primarily due to strengthened high‐latitude winds, biasing reconstructed MOT by −0.38 ± 0.37°C (1σ). Accounting for air‐sea disequilibrium, paleoatmospheric inert gases indicate that LGM MOT was 2.27 ± 0.46°C (1σ) colder than the pre‐industrial era.

Seltzer, A. M.↗
DOE OSTI2022

Ba +2 ion trapping using organic submonolayer for ultra-low background neutrinoless double beta detector

If neutrinos are their own antiparticles the otherwise-forbidden nuclear reaction known as neutrinoless double beta decay can occur. The very long lifetime expected for these exceptional events makes its detection a daunting task. In order to conduct an almost background-free experiment, the NEXT collaboration is investigating novel synthetic molecular sensors that may capture the Ba dication produced in the decay of certain Xe isotopes in a high-pressure gas experiment. The use of such molecular detectors immobilized on surfaces must be explored in the ultra-dry environment of a xenon gas chamber. Here, using a combination of highly sensitive surface science techniques in ultra-high vacuum, we demonstrate the possibility of employing the so-called Fluorescent Bicolor Indicator as the molecular component of the sensor. We unravel the ion capture process for these molecular indicators immobilized on a surface and explain the origin of the emission fluorescence shift associated to the ion trapping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Fluorescence imaging of individual ions and molecules in pressurized noble gases for barium tagging in 136Xe

Abstract The imaging of individual Ba 2+ ions in high pressure xenon gas is one possible way to attain background-free sensitivity to neutrinoless double beta decay and hence establish the Majorana nature of the neutrino. In this paper we demonstrate selective single Ba 2+ ion imaging inside a high-pressure xenon gas environment. Ba 2+ ions chelated with molecular chemosensors are resolved at the gas-solid interface using a diffraction-limited imaging system with scan area of 1 × 1 cm 2 located inside 10 bar of xenon gas. This form of microscopy represents key ingredient in the development of barium tagging for neutrinoless double beta decay searches in 136 Xe. This also provides a new tool for studying the photophysics of fluorescent molecules and chemosensors at the solid-gas interface to enable bottom-up design of catalysts and sensors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Non-linear enhancement of ultrafast X-ray diffraction through transient resonances

Diffraction-before-destruction imaging with ultrashort X-ray pulses can visualize non-equilibrium processes, such as chemical reactions, with sub-femtosecond precision in the native environment. Here, a nanospecimen diffracts a single X-ray flash before it disintegrates. The sample structure can be reconstructed from the coherent diffraction image (CDI). State-of-the-art X-ray snapshots lack high spatial resolution because of weak diffraction signal. Bleaching effects from photo-ionization significantly restrain image brightness scaling. We find that non-linear transient ion resonances can overcome this barrier if X-ray laser pulses are shorter than in most experiments. We compared snapshots from individual ≈ 100 nm Xe nanoparticles as a function of pulse duration and incoming X-ray fluence. Our experimental results and Monte Carlo simulations suggest that transient resonances can increase ionic scattering cross sections significantly beyond literature values. This provides a novel avenue towards substantial improvement of the spatial resolution in CDI in combination with sub-femtosecond temporal precision at the nanoscale.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Effect of metal/dielectric substrates on photopolymerization of BITh thin films

Abstract We have studied effects of metal–dielectric substrates on photopolymerization of [2,2ʹ-Bi-1H-indene]-1,1ʹ-dione-3,3ʹ-diyl diheptanoate (BITh) monomer. We synthetized BITh and spin-coated it onto a variety of dielectric, metallic, and metal–dielectric substrates. The films were exposed to radiation of a UV–Visible Xe lamp, causing photo-polymerization of monomer molecules. The magnitude and the rate of the photo-polymerization were monitored by measuring the strength of the ~ 480 nm absorption band, which existed in the monomer but not in the polymer. Expectedly, the rate of photo-polymerization changed nearly linearly with the change of the pumping intensity. In contrast with our early study of photo-degradation of semiconducting polymer P3HT, the rate of photo-polymerization of BITh is getting modestly higher if the monomer film is deposited on top of silver separated from the monomer by a thin insulating MgF 2 layer preventing a charge transfer. This effect is partly due to a constructive interference of the incident and reflected light waves, as well as known in the literature effects of metal/dielectric substrates on a variety of spectroscopic and energy transfer parameters. At the same time, the rate of photopolymerization is getting threefold larger if monomer is deposited on Ag film directly and charge transfer is allowed. Finally, Au substrates cause modest (~ 50%) enhancement of both monomer film absorption and the rate of photo-polymerization.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Experimental and computational investigation of the bond energy of thorium dicarbonyl cation and theoretical elucidation of its isomerization mechanism to the thermodynamically most stable isomer, thorium oxide ketenylidene cation, OTh + CCO

Collision-induced dissociation (CID) of [Th,2C,2O] + with Xe is performed using a guided ion beam tandem mass spectrometer (GIBMS). The only products observed are ThCO + and Th + by sequential loss of CO ligands. The experimental findings and theoretical calculations support that the structure of [Th,2C,2O] + is the bent homoleptic thorium dicarbonyl cation, Th + (CO) 2 , having quartet spin, which is both thermodynamically and kinetically stable enough in the gas phase to be observed in our GIBMS instrument. Analysis of the kinetic energy-dependent cross sections for this CID reaction yields the first experimental determination of the bond dissociation energy (BDE) of (CO)Th + –CO at 0 K as 1.05 ± 0.09 eV. A theoretical BDE calculated at the CCSD(T) level with cc-pVXZ (X = T and Q) basis sets and a complete basis set (CBS) extrapolation is in very good agreement with the experimental result. Although the doublet spin bent thorium oxide ketenylidene cation, OTh + CCO, is calculated to be the most thermodynamically stable structure, it is not observed in our experiment where [Th,2C,2O] + is formed by association of Th + and CO in a direct current discharge flow tube (DC/FT) ion source. Potential energy profiles of both quartet and doublet spin are constructed to elucidate the isomerization mechanism of Th + (CO) 2 to OTh + CCO. The failure to observe OTh + CCO is attributed to a barrier associated with C–C bond formation, which makes OTh + CCO kinetically inaccessible under our experimental conditions. Furthermore, chemical bonding patterns in low-lying states of linear and bent Th + (CO) 2 and OTh + CCO isomers are also investigated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Aliovalent gallium dopants remove Ti 3+ defects and improve photocatalytic and photoelectrochemical water oxidation properties of LaTiO 2 N

LaTiO 2 N is a promising semiconductor for the water splitting reaction due to its 2.1 eV band gap and stability against corrosion. However, its solar energy conversion is limited by Ti 3+ recombination defects introduced during ammonolysis. Here we show for the first time that Ti 3+ defects in LaTiO 2 N can be suppressed with incorporation of 2, 5, and 10% aliovalent gallium (Ga 3+ ) dopants during synthesis via the layered La 2 Ti 2 O 7 intermediate. Electron paramagnetic resonance (EPR) spectroscopy on the solid powders confirms a reduction in the Ti 3+ donor density from 2.97 × 10 17 cm −3 for the non-doped material to ∼6.24 × 10 16 cm −3 for 5% Ga-doped LaTiO 2 N. The remaining Ti 3+ defects are concentrated near the LaTiO 2 N surface, according to X-ray photoelectron spectroscopy. The defect reduction shifts the optical absorption edge from 2.02 to 2.09 eV and eliminates a broad absorption band at 1050 nm from the optical absorption spectra. It also removes a 1.0–1.7 eV sub-band gap photovoltage signal from surface photovoltage spectra. This suggests that empty Ti 3+ d-orbitals are located 1.0–1.7 eV above the LaTiO 2 N valence band edge. Removing these recombination states with increasing Ga 3+ content enhances the photoconversion efficiency of LaTiO 2 N during water oxidation. The optimized 2 wt% CoO x -loaded 5% Ga-doped LaTi O2 N material has a 16% AQE (400 nm) for O 2 production from aqueous silver nitrate solution and a ∼2.1 mA cm −2 water oxidation photocurrent at 1.23 V under 100 mW cm −2 Xe arc lamp illumination. The water oxidation photocurrent is stable during a 50 min test, and the Faraday efficiency for O 2 generation is 97%, confirming short-term corrosion stability of LaTiO 2 N. Altogether, these results provide a better understanding of the distribution, concentration, and impact of Ti 3+ defects on the optical, photovoltage, and photoelectrochemical properties of LaTiO 2 N. In combination with other defect control strategies, aliovalent Ga 3+ doping can help bring the solar energy conversion efficiency of LaTiO 2 N closer to the theoretical limit.

Wang, Li [University of California, Davis, CA (Uni↗