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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Facet Preferencing by Chemical Substitution Controls Semi-Hydrogenation Selectivity in Ternary Pyrite-Type Intermetallic Compounds

Intermetallic compounds serve as model catalysts for selective hydrogenation reactions, offering precise control over the active site composition(s), geometric and electronic structure. The addition of a third element to form a ternary intermetallic alters the exposed crystal facet(s), demonstrating a strategy to impart improved catalytic behavior in intermetallic catalysts. The site-specific substitution of a small fraction of Pd atoms with Au in pyrite-type PdSb 2 results in the preferential exposure of the (100) facet over the (111) facet. Electron back scattered diffraction and density functional theory calculations confirm the facet change upon the substitution of Pd with Au to form the ternary Pd 1−x Au x Sb 2 (0.075 ≤ x ≤ 0.25). The (100) facet demonstrates higher net alkene selectivity due to significantly weaker alkene binding compared to the (111) facet. Distinct from our prior work on chemical substitution to directly alter the active site composition, this work demonstrates the indirect modification of active sites via preferential facet exposure.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Ternary Phosphides Ba M 2 P 2 : Tailoring Crystal and Electronic Structures Enables Highly Efficient HER Electrocatalysis

Binary transition metal phosphides and their solid solutions have emerged as promising hydrogen evolution reaction (HER) catalysts. Although many research endeavors have adopted strategies to vary compositions to optimize catalytic performance, they mainly focus on binary structures, which represent only a small fraction of the abundant phase space of structure types among transition metal phosphides. Here, the largely unexplored class of ternary and multinary ordered phosphides in catalysis comprises two or more metals with quite different chemical nature, concealing the structure–property relationships essential for advancing catalyst design. Here, we explored phosphides crystallizing in one of the most abundant ordered intermetallic structure types, —the ThCr 2 Si 2 type, —where square nets of 3d transition metal M and P atoms are separated by layers of electropositive Ba cations. Four ternary BaM 2 P 2 (M = Fe, Fe/Cu, Fe/Ni, Ni) catalysts were synthesized and characterized. BaNi 2 P 2 showed high HER activity in acidic electrolyte, which required an overpotential, η 10 , of only 62 mV to drive current density j = –10 mA/cm 2 and high stability with a potential drop rate of 0.25 mV/h. BaNi 2 P 2 outperformed other Ni-based catalysts, such as Ni 2 P and Ni 5 P 4 . Notably, at current densities above –170 mA/cm 2 , BaNi 2 P 2 outperformed the standard Pt electrode measured under identical conditions. Electronic structure analysis revealed a volcano-type activity trend among the four BaM 2 P 2 catalysts based on their d-band center positions, highlighting the role of electropositive Ba cations in shifting the Ni-3d orbitals into an optimal position.

BaNi2P2↗
DOE OSTI2024

Mechanistically Guided Materials Chemistry: Synthesis of Ternary Nitrides, CaZrN 2 and CaHfN 2

Recent computational studies have predicted many new ternary nitrides, revealing synthetic opportunities in this underexplored phase space. However, synthesizing new ternary nitrides is difficult, in part because intermediate and product phases often have high cohesive energies that inhibit diffusion. Here, we report the synthesis of two new phases, calcium zirconium nitride (CaZrN 2 ) and calcium hafnium nitride (CaHfN 2 ), by solid state metathesis reactions between Ca 3 N2 and MCl 4 (M = Zr, Hf). Although the reaction nominally proceeds to the target phases in a 1:1 ratio of the precursors via Ca 3 N 2 + MCl4 → CaMN 2 + 2 CaCl 2 , reactions prepared this way result in Ca-poor materials (Ca x M 2–x N2, x < 1). A small excess of Ca 3 N 2 (ca. 20 mol %) is needed to yield stoichiometric CaMN 2 , as confirmed by high-resolution synchrotron powder X-ray diffraction. In situ synchrotron X-ray diffraction studies reveal that nominally stoichiometric reactions produce Zr 3+ intermediates early in the reaction pathway, and the excess Ca 3 N 2 is needed to reoxidize Zr 3+ intermediates back to the Zr 4+ oxidation state of CaZrN 2 . Analysis of computationally derived chemical potential diagrams rationalizes this synthetic approach and its contrast from the synthesis of MgZrN 2 . These findings additionally highlight the utility of in situ diffraction studies and computational thermochemistry to provide mechanistic guidance for synthesis.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Computational discovery of ultra-strong, stable, and lightweight refractory multi-principal element alloys. Part II: comprehensive ternary design and validation

Abstract Here the discovery of refractory multi-principal element alloys (MPEAs) with high-temperature strength and stability is pursued within a constrained and application-relevant design space. A comprehensive approach is developed and applied to explore all 165 ternary systems in the Al-Ce-Fe-Hf-Mo-Nb-Ta-Ti-V-W-Zr family. A subset of ternary systems that contain large areas in composition–temperature space with high strength and robust BCC phase stability is found. Twelve sets of high-performing alloys are identified, each set optimized for one combination of phase constraint, optimization target, and temperature range. Preliminary mechanical tests support the viability of the method. This work highlights the importance of considering phase stability, exploring non-equiatomic regions of composition space, and applying application-relevant constraints. Parts I and II provide three down-selection techniques for identifying high-performing BCC refractory MPEAs, design guidelines, and many candidates predicted to have BCC phase stability and strengths 2–3 times higher than any reported to date.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Band gap and electronic structure of defects in the ternary nitride BP 3 N 6 : experiment and theory

Recent advances in methods to access nitride systems by a high-pressure high-temperature approach have made possible the one-step synthesis of mixed ternary non-metal nitrides. As a prerequisite to use in a practical device, it is important to understand important bulk electronic properties, such as the band gap, as well as characterizing the presence and effect of defects that are present. In this work, the novel ternary nitride BP 3 N 6 is studied using techniques sensitive to the partial electronic density of states, specifically X-ray absorption spectroscopy and X-ray emission spectroscopy. Complementary full-potential all-electron density functional theory (DFT) calculations allow important bulk electronic parameters, such as the band gap, to be elucidated. The band gap of BP 3 N 6 has been determined to be 3.9 ± 0.2 eV and 4.1 ± 0.4 eV at the B K- and N K-edges, respectively. This is close to a theoretical value of 4.3 eV predicted by the PBEsol exchange–correlation functional and considerably less than a value of 5.8 eV predicted by the modified Becke–Johnson exchange–correlation functional. X-Ray excited optical luminescence (XEOL) measurements are performed to interrogate the presence of point defects in this system. Together with DFT calculations, these measurements reveal the presence of nitrogen vacancies which lead to multiple mid-gap trap states.

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

Performance enhancement of aqueous ionic liquids with lower critical solution temperature (LCST) behavior through ternary mixtures

Thermally responsive ionic liquids (ILs) exhibit liquid–liquid phase separation when mixed with water and heated above a lower critical solution temperature (LCST), resulting in a water-rich (WR) and an IL-rich (ILR) phase. These binary IL–water mixtures can be employed in a variety of thermodynamic processes such as forward osmosis (FO) desalination, for which two solution properties are desirable: low phase separation temperature and high osmotic strength (osmolality). However, these two properties are interlinked, with ILs that exhibit higher osmotic strengths typically requiring higher phase separation temperatures. This behavior tends to arise from the hydrophilicity of the IL cations, which enhances osmotic strength while also elevating the phase separation temperature. In this work, we highlight a pathway to overcome this tradeoff by developing ternary IL mixtures (two ILs with varying cation hydrophilicity mixed with water), which lowers the phase separation temperature while maintaining and even enhancing the osmotic strength of the solution. We characterize the mixing behavior (osmolality, phase separation temperature, WR phase purity, and WR to ILR phase mass ratio) of four ILs as a function of their concentration in solution. We find that an enhancement of up to 81.6% in the osmolality with a concomitant reduction of up to 15.4% in the phase separation temperature can be achieved using this approach. The ternary mixture is also shown to improve the phase separation kinetics by nearly 95% compared to the binary mixture. Overall, this work highlights a new pathway to improve the performance of LCST ILs for water and energy applications.

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

Alkali triel chalcogenide nanocrystals: a molecular reactivity approach to ternary phase selectivity

Alkali-metal-based materials are promising building blocks for energy conversion and storage technologies. Here, we use a molecular reactivity-based solution-phase approach to selectively synthesize multiple phases and specific polymorphs of lithium- and sodium-containing triel chalcogenide nanocrystals, LiTrCh 2 , NaTrCh 2 , and NaTr 3 Ch 5 , where Tr = Ga and In and Ch = S, Se, and Te. Analogous to the case of binary II–VI and III–V tetrahedral semiconductors, where the two commonly isolated zinc blende and wurtzite polymorphs are separated by only 1–50 meV f.u. −1 , we find that LiTrCh 2 nanocrystals easily adopt tetragonal (chalcopyrite) and orthorhombic polymorphs separated by only 2.7–6.2 meV f.u. −1 Because of this small energy difference, soft colloidal synthesis succeeds in accessing either one of these polymorphs, depending on the specific dichalcogenide precursor used. Highly reactive diethyl diselenide favors the thermodynamically more stable tetragonal I$\bar{4}2$d phase, whereas mildly reactive diphenyl diselenide favors the kinetic, metastable orthorhombic Pna2 1 phase. Density functional theory calculations confirm the relative energies among multiple LiTrCh 2 polymorphs and also model the observed powder X-ray diffraction pattern of a new C2 NaIn 3 Te 5 phase. 7 Li, 69 Ga, and 77 Se solid-state NMR spectra are consistent with phase-pure ternary LiGaSe 2 nanocrystals. A majority of the nanocrystal compositions are visible-light emitters. This work opens the door to new Li/Na-based ternary triel chalcogenide nanostructures for energy storage and conversion applications.

Pavel, Md Riad Sarkar [Iowa State Univ., Ames, IA ↗
DOE OSTI2021

The Li–F–H ternary system at high pressures

Evolutionary crystal structure prediction searches have been employed to explore the ternary Li-F-H system at 300 GPa. Metastable phases were uncovered within the static lattice approximation, with LiF 3 H 2 , LiF 2 H, Li 3 F 4 H, LiF 4 H 4 , Li 2 F 3 H and LiF 3 H lying within 50 meV/atom of the 0 K convex hull. All of these phases contain H n F¯ n+1 (n = 1; 2) anions, and Li + cations. Other structural motifs such as LiF slabs, $H$ $^{+}_{3}$ molecules and F δ- ions are present in some of the low enthalpy Li-F-H structures. The bonding within the H n F¯ n+1 molecules, which may be bent or linear, symmetric or asymmetric, is analyzed. The five phases closest to the hull are insulators, while LiF 3 H is metallic and predicted to have a vanishingly small superconducting critical temperature. Li 3 F 4 H is predicted to be stable at zero pressure. Furthermore, this study lays the foundation for future investigations of the role of temperature and anharmonicity on the stability and properties of compounds and alloys in the Li-F-H ternary system.

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

Computational discovery of stable and metastable ternary oxynitrides

Materials design from first principles enables exploration of uncharted chemical spaces. Extensive computational searches have been performed for mixed-cation ternary compounds, but mixed-anion systems are gaining increased interest as well. Central to computational discovery is the crystal structure prediction, where the trade-off between reliance on prototype structures and size limitations of unconstrained sampling has to be navigated. We approach this challenge by letting two complementary structure sampling approaches compete. We use the kinetically limited minimization approach for high-throughput unconstrained crystal structure prediction in smaller cells up to 21 atoms. On the other hand, ternary—and, more generally, multinary—systems often assume structures formed by atomic ordering on a lattice derived from a binary parent structure. Thus, we additionally sample atomic configurations on prototype lattices with cells up to 56 atoms. Using this approach, we searched 65 different charge-balanced oxide–nitride stoichiometries, including six known systems as the control sample. The convex hull analysis is performed both for the thermodynamic limit and for the case of synthesis with activated nitrogen sources. We identified 34 phases that are either on the convex hull or within a viable energy window for potentially metastable phases. We further performed structure sampling for “missing” binary nitrides whose energies are needed for the convex hull analysis. Among these, we discovered metastable Ce3N4 as a nitride analog of the tetravalent cerium oxide, which becomes stable under slightly activated nitrogen condition µN > +0.07 eV. Given the outsize role of CeO2 in research and application, Ce3N4 is a potentially important discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Composition Dependent Electrochemical Properties of Earth-Abundant Ternary Nitride Anodes

Growing energy storage demands on lithium-ion batteries necessitate exploration of new electrochemical materials as next-generation battery electrode materials. In this work, we investigate the previously unexplored electrochemical properties of earth-abundant and tunable Zn 1-x Sn 1+x N 2 (x = -0.4 to x = 0.4) thin films, which show high electrical conductivity and high gravimetric capacity for Li insertion. Enhanced cycling performance is achieved compared to previously published end-members Zn 3 N 2 and Sn 3 N 4 , showing decreased irreversible loss and increased total capacity and cycle stability. The average reversible capacity observed is >1050 mAh/g for all compositions and 1220 mAh/g for Zn-poor (x = 0.2) films. Extremely Zn-rich films (x = -0.4) show improved adhesion; however, Zn-rich films undergo a phase transformation on the first cycle. Zn-poor and stoichiometric films do not exhibit significant phase transformations which often plague nitride materials and show no required overpotential at the 0.5 V plateau. Cation composition x is explored as a mechanism for tuning relevant mechanical and electrochemical properties, such as capacity, overpotential, phase transformation, electrical conductivity, and adhesion. The lithiation/delithiation experiments confirm the reversible electrochemical reactions. Without any binding additives, the as-deposited electrodes delaminate resulting in fast capacity degradation. We demonstrate the mechanical nature of this degradation through decreased electrode thinning, resulting in cells with improved cycling stability due to increased mechanical stability. Combining composition and electrochemical analysis, this work demonstrates for the first time composition dependent electrochemical properties for the ternary Zn 1-x Sn 1+x N 2 and proposes earth-abundant ternary nitride anodes for increased reversible capacity and cycling stability.

25 ENERGY STORAGE↗
DOE OSTI2021

Ternary SiGeSn alloy nanocrystals via nonthermal plasma synthesis

We report on the synthesis of ternary SiGeSn nanocrystals (NCs) produced via nonthermal plasma synthesis from silane (SiH 4 ), germane (GeH 4 ), and tetramethylstannane (Sn(CH 3 ) 4 ) precursor sources. Detailed structural, chemical, and vibrational analyses show that all three elements are incorporated both on the NC surface and within the NC core. Incorporation of Sn into the NC core is realized using a secondary injection of SiH 4 and GeH 4 precursor gases in the after-glow region of the plasma, which kinetically traps Sn in the core. We demonstrate compositional tunability of the SiGeSn NCs in which the Si and Ge ratios can be varied broadly at low Sn concentrations. We also show tunability of the Sn content up to ~2 atomic percent as revealed by ICP-MS analysis. More generally, this report demonstrates how nonthermal plasma synthesis can be used to produce metastable ternary nanostructured alloys involving thermodynamically insoluble constituents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

La 4 Co 4 X ( X = Pb , Bi , Sb ) : A demonstration of antagonistic pairs as a route to quasi-low-dimensional ternary compounds

We outline how pairs of strongly immiscible elements, referred to here as antagonistic pairs, can be used to synthesize ternary compounds with low or quasi-reduced-dimensional motifs intrinsically built into their crystal structures. By identifying third elements that are mutually compatible with a given antagonistic pair, ternary compounds can be formed in which the third element segregates the immiscible atoms into spatially separated substructures. Quasi-low-dimensional structural units, such as sheets, chains, or clusters are a natural consequence of the immiscible atoms seeking to avoid close contact in the solid state. Further, as proof of principle, we present the discovery, crystal growth, and basic physical properties of La 4 ⁢Co 4 ⁢$\mathrm{X}$ (X = Pb, Bi, Sb), a family of intermetallic compounds based on the antagonistic pairs Co-Pb and Co-Bi. La 4 ⁢Co 4 ⁢$\mathrm{X}$ adopts an orthorhombic crystal structure (space group Pbam) containing quasi-two-dimensional Co slabs and La-X polyhedra that stack in an alternating manner along the α axis. Consistent with our proposal, the La atoms separate the Co and X substructures, ensuring there are no direct contacts between the members of the immiscible (antagonistic) pair. Within the Co slabs, the atoms occupy the vertices of corner sharing tetrahedra and triangles, and this bonding motif produces narrow electronic bands near the Fermi level that favor magnetism. The Co is moment bearing in each La 4 ⁢Co 4 $\mathrm{X}$ compound studied, and we show that whereas La 4 ⁢Co 4 ⁢Pb behaves as a three-dimensional antiferromagnet with T N =220K, La 4 ⁢Co 4 ⁢Bi and La 4⁢ Co 4 ⁢Sb have behavior consistent with low-dimensional magnetic coupling and ordering, with T N =153K and 143 K, respectively. In addition to the Pb-, Bi-, and Sb-based La 4 ⁢Co 4 ⁢$\mathrm{X}$ compounds, we also were likely able to produce an analogous La 4 ⁢Co 4 ⁢Sn in polycrystalline form, although we were unable to isolate single crystals. We anticipate that identifying and using mutually compatible third elements together with an antagonistic pair represents a generalizable design principle for discovering new materials and new structure types containing low-dimensional substructures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Machine learning accelerated prediction of Ce-based ternary compounds involving antagonistic pairs

The discovery of novel quantum materials within ternary phase spaces containing antagonistic pairs such as Fe with Bi, Pb, In, and Ag, presents significant challenges yet holds great potential. In this work, we investigate the stabilization of these immiscible pairs through the integration of Cerium (Ce), an abundant rare-earth and cost-effective element. By employing a machine learning (ML)-guided framework, particularly crystal graph convolutional neural networks (CGCNN), combined with first-principles calculations, we efficiently explore the composition/structure space and predict 9 stable and 37 metastable Ce-Fe-X (X=Bi, Pb, In, and Ag) ternary compounds. Our findings include the identification of multiple new stable and metastable phases, which are evaluated for their structural and energetic properties. These discoveries not only contribute to the advancement of quantum materials but also offer viable alternatives to critical rare earth elements, underscoring the importance of Ce-based intermetallic compounds in technological applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Combinatorial investigation of the Mn–Ge–N chemical system containing ternary nitrides Mn 3 GeN and MnGeN 2

By changing nitrogen chemical potential during synthesis of Mn–Ge–N ternary nitrides, both wurtzite MnGeN 2 and antiperovskite Mn 3 GeN ternary phases are prepared. Antiperovskite films are optically opaque and conductive, while wurtzite films with Mn/(Mn + Ge) ≤ 0.5 transmit light above ~ 2 eV. Alloys of Mn 3 GeN with Si and Al are also investigated. Mn 3 (Ge 1−x Al x )N alloys with 0.07 ≤ x ≤ 0.16 exhibit a cubic (rather than tetragonal) structure. Mn 3 (Ge 1−x Si x )N with x ≤ 0.05 maintains the tetragonal structure but becomes cubic when x > 0.05. This study shows that care must be taken in the synthesis of Mn–Ge–N and similar nitrides, especially when materials are integrated into devices not amenable to structural and chemical probing.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Investigations into the Ternary NaF-KF-UF4 Salt System – Phase A

A knowledge gap exists in the data and understanding of fresh fuel salt and irradiated multicomponent fuel salt systems thermophysical properties. Quantifying these properties is necessary for the design and construction of test reactors, as well as the licensing of future commercial molten-salt reactors. To facilitate thermal property determination on a proposed fuel salt composition for Seaborg Technologies, several samples containing depleted uranium tetrafluoride (UF4), sodium fluoride (NaF), and potassium fluoride (KF) were blended, and a melt temperature analysis was performed. From the melting temperature analysis, it was determined that sample Seaborg-7, a ternary salt composition of 26.4UF4-24.7KF-48.9NaF (mol%), was very near a ternary eutectic point. Therefore, thermal properties such as melting temperature, salt stability, density, heat capacity, thermal diffusivity, and viscosity were experimentally determined on the Seaborg-7 salt. These measurements document the baseline properties of fresh fuel salt as a function of temperature, where future experiments on irradiated fuel salt will provide a holistic perspective on the change of thermophysical properties during reactor operations. Several precision instruments were used to collect property data, and instrument calibrations and data collection were performed and documented in a standardized and reproducible manner with meticulous detail. This process ensured that the measurement procedures and resulting data can readily be duplicated elsewhere. The Seaborg-7 salt was shown to be stable at temperatures up to 900°C, as no mass change was observed upon repeated heating and cooling. The peak melting temperature was determined to be 547°C (557°C endset). The enthalpy of fusion (??H?_fus^o) was determined to be 167.5 ± 2.7 J/g while the enthalpy of crystallization (??H?_c^o) was determined to be -147.8 ± 13.3 J/g. In addition to the eutectic melting peak, upon heating, several pre eutectic peaks were observed, occurring at 470°C (onset) and 499°C (peak). Specific heat capacity measurements showed a slightly increasing trend with respect to temperature in the solid phase, while the liquid-specific heat capacity showed a somewhat flat trend with an average value of 106.1 ± 1.24 J/mol·K between 600 to 800°C. Three independent trials using the Seaborg-7 salt determined the density to be ?(T) = 4.908 – 0.000363·T(°C), validated between 32 to 200°C, and ?(T) = 4.808 – 0.00113·T(°C), validated between ~575 to 850°C. Thermal diffusivity was determined for the liquid state and is represented by the linear equation y = 0.1581 + 0.000207·T(°C) between 550 to 850°C. The viscosity was determined from 600 to 800°C and is represented by the exponential fit equation, ? (mPa·s) = 736.58e^(-0.006·T(°C)). This report documents the conclusion of fuel salt thermophysical property measurements for the Seaborg SPP, Phase A project.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1978

Normal state properties of the ternary molybdenum sulfides

By making a large number of normal state and superconducting properties measurements, all on the same ternary molybdenum sulfide samples, we obtain values for Fermi surface and superconducting parameters. From these we conclude that sputtered ternary molybdenum sulfides are not completely in the dirty superconductor limit, and that they are d-band metals with a high electron carrier density.

Woollam, J. A.↗
NASA NTRS1991

On the capacity of ternary Hebbian networks

Networks of ternary neurons storing random vectors over the set -1,0,1 by the so-called Hebbian rule are considered. It is shown that the maximal number of stored patterns that are equilibrium states of the network with probability tending to one as N tends to infinity is at least on the order of (N exp 2-1/alpha)/K, where N is the number of neurons, K is the number of nonzero elements in a pattern, and t = alpha x K, alpha between 1/2 and 1, is the threshold in the neuron function. While, for small K, this bound is similar to that obtained for fully connected binary networks, the number of interneural connections required in the ternary case is considerably smaller. Similar bounds, incorporating error probabilities, are shown to guarantee, in the same probabilistic sense, the correction of errors in the nonzero elements and in the location of these elements.

Baram, Yoram↗
NASA NTRS1993

Case study of binary and ternary synthetic discriminant function filters with similar in-class and out-of-class images

A simulation study is reported of the performance of two designs of ternary synthetic discriminant function (SDF) filters. The filters are compared to binary SDFs in terms of the probability of correct identification P(ID) between in-class and out-of-class image sets. Compared to binary synthetic discriminant function (BSDF) filters, both ternary SDF filters designs offer improved performance in P(ID) and thus allow extension of the maximum filter direction range when evaluated in the presence of white image noise. Larger distortion range filters translate to fewer correlations required to perform image identification, and thus higher system speed. The TSDF(SNR) filters had the highest of system performance, while TSDF(d) filters were able to improve discrimination to a degree, but their optimal designs had essentially the same SNR performance as the BSDF filters.

Downie, John D.↗