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246 records · Page 2

Pressure-Stabilized MnSb2 with Complex Incommensurate Magnetic Order

Marcasite-type compounds have been proposed as promising hosts of exotic magnetic quantum states, yet experimental realizations in stoichiometric, disorder-free systems remain limited. Here, we report the high-pressure stabilization and magnetic characterization of MnSb2, a marcasite-type compound that is thermodynamically metastable under ambient pressure. Single crystals were synthesized using a cubic multianvil press at 3.3 GPa and 490 °C for 24 h, and powder and single-crystal X-ray diffraction confirm the orthorhombic Pnnm structure. These crystals are stable at ambient pressure for a long time up to between 450 and 500 K. Heat-capacity measurements reveal phase transitions at approximately T0 ∼ 118 K and T1 ∼ 220 K. Neutron diffraction uncovers an unconventional magnetic state below T1 ∼ 220 K. Magnetic powder neutron diffraction refinements reveal possible multiple magnetic configurations that provide comparably acceptable fits to the experimental data. While most solutions are consistent with a spin-density-wave (SDW) description, helical models systematically yield inferior agreement factors. Across a broad range of models, the Mn ordered moment reaches a maximum value of approximately 2 μB and remains predominantly collinear, with minimal canting along the c-axis. At 200 K, the magnetic propagation vector is q = (0, 0.3975, 0.3783); upon cooling, the b component increases toward 0.5, reflecting a temperature-dependent evolution of the modulation. The need for modification of the magnetic model between high and low temperatures further highlights the complex and strongly temperature-dependent nature of the magnetic order in this system. These results establish MnSb2 as a pressure-stabilized marcasite magnet with a tunable, complex magnetic state and a compelling stoichiometric platform for exploring unconventional magnetic behavior, including potential altermagnetism.

Xu, Mingyu [Michigan State University , , , ,; Iow

Anisotropic multi- Q order in Co x TaS 2

The cobalt-intercalated transition metal dichalcogenide Co x TaS 2 hosts a rich landscape of magnetic phases that depend sensitively on x. While the stoichiometric compound with x = 1/3 exhibits a single magnetic transition, samples with x≤0.325 display two transitions with an anomalous Hall effect (AHE) emerging in the lower temperature phase. Here, we resolve the spin structure in each phase by employing a suite of magneto-optical probes that include the discovery of anomalous magneto-birefringence: a spontaneous time-reversal sensitive rotation of the principal optic axes. A symmetry-based analysis identifies the AHE-active phase as an anisotropic (2+1)Q state, in which magnetic modulation at one wavevector (Q) differs in symmetry from that at the remaining two. The (2+1)Q state naturally exhibits scalar spin chirality as a mechanism for the AHE and expands the classification of multi-Q magnetic phases.

Kruppe, Jonathon [University of California, Berkel

Analysis of Surface and Bulk Behavior in Ni-Pd Alloys

The most salient features of the surface structure and bulk behavior of Ni-Pd alloys have been studied using the BFS method for alloys. Large-scale atomistic simulations were performed to investigate surface segregation profiles as a function of temperature, crystal face, and composition. Pd enrichment of the first layer was observed in (111) and (100) surfaces, and enrichment of the top two layers occurred for (110) surfaces. In all cases, the segregation profile shows alternate planes enriched and depleted in Pd. In addition, the phase structure of bulk Ni-Pd alloys as a function of temperature and composition was studied. A weak ordering tendency was observed at low temperatures, which helps explain the compositional oscillations in the segregation profiles. Finally, based on atom-by-atom static energy calculations, a comprehensive explanation for the observed surface and bulk features will be presented in terms of competing chemical and strain energy effects.

Ordering

Highly Ordered Eutectic Mesostructures via Template‐Directed Solidification within Thermally Engineered Templates

Template-directed self-assembly of solidifying eutectics results in emergence of unique microstructures due to diffusion constraints and thermal gradients imposed by the template. Here, the importance of selecting the template material based on its conductivity to control heat transfer between the template and the solidifying eutectic, and thus the thermal gradients near the solidification front, is demonstrated. Simulations elucidate the relationship between the thermal properties of the eutectic and template and the resultant microstructure. The overarching finding is that templates with low thermal conductivities are generally advantageous for forming highly organized microstructures. When electrochemically porosified silicon pillars (thermal conductivity < 0.3 Wm −1 K −1 ) are used as the template into which an AgCl-KCl eutectic is solidified, 99% of the unit cells in the solidified structure exhibit the same pattern. In contrast, when higher thermal conductivity crystalline silicon pillars (≈100 Wm −1 K −1 ) are utilized, the expected pattern is only present in 50% of the unit cells. The thermally engineered template results in mesostructures with tunable optical properties and reflectances nearly identical to the simulated reflectances of perfect structures, indicating highly ordered patterns are formed over large areas. This work highlights the importance of controlling heat flows in template-directed self-assembly of eutectics.

36 MATERIALS SCIENCE

Thermal Data-driven Model Reduction for Enhanced Battery Health Monitoring

Electric aviation faces a major challenge of avoiding potentially catastrophic consequences of the battery’s thermal runaway while keeping the weight of the battery low. Detection of early warning signals of battery failures requires accurate monitoring of the battery’s health throughout its lifespan. However, identifying the parameters of the battery from field data is notoriously difficult. We investigate this problem within the framework of modeling the temperature dynamics of a Li-ion cell during tests simulating loading in electric aircraft flights. It is found that the parameters of a higher-fidelity physics-based thermal model cannot be identified from the simulated flight data. To resolve this issue, we reduce the higher-fidelity thermal model to a model with fewer parameters. The resulting reduced-order model can predict temperature dynamics accurately and is identifiable throughout the cell’s lifespan which allows using the model’s parameters to monitor the state-of-health of the aging cell and detect anomalies in thermal behavior.

Li ion batteries

Enabling Mission Flexibility to Battery Driven Deep Space Endeavors With Generalized Battery-Health-Monitoring Using Physics-Based and Data-Driven Reduced-Order Models

The needs and requirements for an electrochemical energy storage for deep space exploration is well explored. It is often understood that different mission sites and environmental conditions require different battery chemistries or technologies. Additionally, various engineering solutions are deployed to overcome specific chemical challenges. One often overlooked need is the “health” monitoring of an electrochemical storage system. The term generalized health monitoring, as envisioned in this work, refers to the monitoring of various aspects such as electrode health, electrolyte health, reaction pathway health, cooling system health, sensor health, and BMS health [1]. Generalized health monitoring allows mission leads, engineers, and scientists to incorporate flexibility in mission designs, make on-the-fly mission changes, and extend the duration of science missions. Moreover, it enables automation and data-driven decision-making without compromising safety and performance. Recently, our group developed a hierarchy of thermal reduced-order models (TROM) by combining a physics-based modeling approach and data-driven model reduction techniques applied to flight data [2]. The resulting TROMs were found to be not only accurate but also identifiable from the flight data. Consequently, the coefficient of variance of the model parameters is small over the course of hundreds of flights, allowing for monitoring the parameter evolution trajectories as the battery ages and degrades. These parameters constitute the metrics of the generalized health of a battery. Monitoring their evolution allows such models to be used for anomaly detection and prognostics, improving early detection of abnormal behavior and thus enabling timely maintenance, longer battery life, and enhanced battery safety. For this presentation, the practicality of the thermal model will be validated on a pack of 14cells under various topology configurations such as 1S14P, 2P7S, 7S2P, and 1P14S. It is well known that manufacturing and non-uniform aging lead to variability in the performance of a cell, which is exacerbated by cell balancing during active load. Additionally, in extreme scenarios, the paramount objective is to complete the mission, regardless of the stresses on the battery. Topology-induced balancing issues further stress the battery. The goal of this study is to determine if the noise (identifiability) in the reduced-order thermal model parameters is sensitive to topology, cell spacing, cooling strategy, and manufacturing or age variability. The variability in cells is considered by assuming a multimodal distribution for microscopic parameters of a cell (such as porosity, tortuosity, reaction kinetics, volumetric thermal conductivity, and volumetric heat capacity). The compounded effect of manufacturing variability, topological selection, cooling strategies, and cell balancing ages each cell in a battery differently. The study aims to clarify whether the challenge in extracting maximum information depends on the minimum number of sensors or models used for data extraction.

Automation

The Benard Problem: A Comparison of Finite Difference and Spectral Collocation Eigen Value Solutions

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2 nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2 nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

J Raymond Lee Skarda

Strong Kitaev Interaction in BaCo 2⁢ (AsO 4 ) 2

The inelastic neutron scattering results and their analysis unequivocally point to a dominant Kitaev interaction in the honeycomb-lattice cobaltate BaCo 2 ⁢(AsO 4 ) 2 . Our anisotropic-exchange model closely describes all available neutron scattering data in the material’s field-polarized phase. Furthermore, the density-matrix renormalization group results for our model are in close accord with the unusual double-zigzag magnetic order and the low in-plane saturation field of BaCo 2 ⁢(AsO 4 ) 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Block-Type Antiferromagnetism in Single Chain Quasi-One-Dimensional K 3 ⁢Fe 2 ⁢Se 4

One-dimensional (1D) structures provide a unique platform to study the correlated quantum interactions and phase transitions such as unconventional magnetism and superconducting states. Here, we report that iron chalcogenide K 3 ⁢Fe 2 ⁢Se 4 exhibits an unusual block-type canted antiferromagnetic (AFM) order with a clear single chain quasi-1D structure, which is structurally different from the two-leg ladder BaFe 2 ⁢Se 3 , through both experimental measurements and density matrix renormalization group (DMRG) calculations. The narrow bandgap semiconductor K 3 ⁢Fe 2 ⁢Se 4 has a quasi-1D edge-shared FeSe4 tetrahedra chain structure and orders antiferromagnetically below 110 K. The magnetic moments couple antiferromagnetically along the quasi-1D chain direction of the 𝑏 axis and form an up-down-down-up (↑−↓−↓−↑)–like spin structure with a commensurate propagation vector 𝒌=⁢(0,0,0), where block-type spin ↑−↑ or ↓−↓ coupling are between the longer Fe-Fe bonds of the quasi-1D chain. DMRG results show that block antiferromagnetic state is stable in K 3 ⁢Fe 2 ⁢Se 4 and reveal that the block-ordered arrangement of Fe 2.5+ ions spins arise from the competition between ferromagnetic and AFM interaction in the presence of strong electronic correlation. Our research results not only report the discovery of a clear block-type canted antiferromagnetic structure in a real quasi-1D chain material but also provide a theoretical approach to understand the block-type antiferromagnetism in quasi-1D iron chalcogenides.

antiferromagnetism

High-Order Methods in NASA’s Next Generation of Computational Fluid Dynamics Tools

The missions of the National Aeronautics and Space Administration (NASA) routinely produce unique requirements and challenges for development and application of Computational Fluid Dynamics (CFD) methods. NASA presently embodies four distinct Mission Directorates: Aeronautics Research, Exploration Systems, Science, and Space Operations. These missions generate requirements for systems that operate in a wide variety of environments. They range from the high-speed flight of aerodynamically optimized vehicles operating in the earth’s atmosphere to spacecraft designed for missions that don’t favor aerodynamic optimization, some operating in the atmosphere of planets and planetary moons such as Mars and Venus or Saturn’s moon Titan. Systems supporting these vehicles, such as rocket and jet propulsion, reaction control systems, fluid and thermal transfer systems, etc. can also generate their own unique set of flow phenomena that challenge today’s CFD methodology. Through the NASA Engineering and Safety Center (NESC), NASA annually conducts state-of-the-discipline assessments in fifteen distinct engineering disciplines. These assessments are performed by the NASA Technical Fellows that lead Technical Discipline Teams (TDT) of recognized experts in these fifteen areas. In the Aerosciences discipline, three topics have been identified as the top challenges for the discipline: aero-plume interaction prediction, unsteady separated flows, and aerothermodynamic prediction. These challenge areas are defined by the Agency’s high-risk projects and problems on which the NESC is requested to perform independent testing, analysis, and assessments. When viewed as a whole, these tests, analyses, and assessments provide a clear view of the recurring technical challenges facing Agency engineers and researchers and can be used to guide future research and technology development. The present state-of-the-art in the application of CFD at NASA is the use of Reynolds-Averaged Navier- Stokes (RANS) solvers, primarily executed in a steady-state mode of operation. In isolated cases, Unsteady RANS (URANS) solvers have been employed when steady RANS solutions produce poorly converging or oscillating results or in cases, such as aeroelastic analysis, which require unsteady aerodynamic simulation. For most traditional external and internal aerodynamic flows, structured overset grids or unstructured grids are employed to minimize geometric modeling and grid generation times. Grid adaptation, primarily as a series of coarse-grain intermediate processing steps is also seeing use on particularly complex flow problems and configurations. In the case of aerothermodynamic flows, engineers have been forced to continue to employ structured grid techniques as the present unstructured grid methodology has proven inadequate in the prediction of surface heating. In the area of aero-plume interaction modeling, two-gas, frozen chemistry simulation is generally the state-of-the- art, with some production solvers capable of predicting flows with only a single gas component. Prediction of flows falling into the afore-mentioned top Aerosciences technical challenges have severely stressed the present state-of-the-art in CFD prediction and for some problems, such as unsteady separated flows and aero-plume interaction cases, engineers have begun employing Large Eddy Simulation (LES) and Hybrid RANS/LES techniques. In some isolated aero-propulsion interaction cases, chemically reacting flow simulations have been applied. These methods are highly evolutionary and engineers have little experience in their application, so they cannot be heavily relied upon in today’s application environment. Therefore, this leads one to muse over which numerical technologies will be included in the CFD tools that will be employed 30 years in the future. This presentation will describe specific technical problems that have stressed NASA’s traditional CFD methods to their breaking point and will link these issues to the Agency’s top Aerosciences technical challenges. The discussion will then shift to the characteristics of future CFD solvers that will be required to attack these challenges and how these characteristics differ from the present state-of-the- art. High-order methods certainly appear to have a place in the development of future CFD tools and some of the physical characteristics of our most challenging problems suggest that high-order methods are the only way to effectively solve them. But there are some relatively severe implementation issues that face these methods, particularly in the area of general applicability and robust operation as an engineering tool. Desired characteristics of next-generation CFD solvers will be discussed and the author’s view of which emerging numerical technologies might be employed to address these attributes will also be presented

David M Schuster

Anion-dependent phase behavior of methylimidazolium-based ionic liquids mixed with water: Correlation between local molecular structure and mesoscale behaviors

The mesoscopic phase behavior of decylmethylimidazolium (C 10 mim) ionic liquids (ILs) bearing three monovalent anions—thiocyanate (SCN − ), nitrate (NO 3 − ), and chloride (Cl − )—mixed with water at relatively high IL contents (50–95 wt%) was investigated. Small-angle and wide-angle X-ray scattering (SAXS/WAXS) were employed to follow the evolution of both local and mesoscale structures across this composition range. In the absence of water, C 10 mimSCN and C 10 mimCl behaved as disordered liquids, whereas C 10 mimNO 3 spontaneously formed a hexagonally ordered cylindrical mesophase and displayed a sticky-solid macroscopic appearance. Upon addition of water, C 10 mimSCN remained a viscous liquid and only weakly ordered lamellar domains were observed. This limited ordering is attributed to the lack of hydrogen bonding and weak interaction energy between SCN − anions and C 10 mim + cations. In contrast, the trigonal-planar NO 3 − and point-like Cl − anions promoted the formation of well-defined hexagonal mesophases up to 35–45 wt% water. The formation of hydrogen bonding of the two anions with imidazolium ring protons likely enabled the creation of compact ion clusters that effectively exclude water molecules from the immediate vicinity of the IL aggregates. These findings demonstrate that the interaction energy between ion pairs dictate IL-water interactions and therefore control the transition from disordered liquids to ordered mesophases in IL/water mixtures with high IL contents. In conclusion, the combined SAXS/WAXS analysis reveals a correlation between local intermolecular structure and the emergence of mesoscopic order, providing a systematic framework for tailoring mesoscale structures in alkylimidazolium-based IL/water systems.

36 MATERIALS SCIENCE

Wild Blue Yonder Propulsion Schemes

This paper will include a discussion of the ORION concept, several gaseous core nuclear rockets, thermonuclear propulsion utilizing superconducting magnets, and finally a lightweight radioisotope power generation system for electric propulsion. With the exception of the latter concept, all of these schemes have much in common. The initial vehicle weights would be very large - on the order of several million pounds. The payload fractions are high - on the order of 25 to 50 percent of the takeoff weight - for near Earth missions. The development problems would be severe, and, correspondingly, the development costs would be extreme - on the order of many billions of dollars. In addition, the launching problems from Earth would be fantastic - with nuclear radiation hazards and political overtones added for good measure. However, the reward for success would be great. One can contemplate large payload fractions propelled on space missions - with thrust-to-weight ratios, at least in some cases, greater than unity and with specific impulses of several thousand seconds. The mission transportation costs would run in terms of dollars per pound of payload with clear opportunities for reasonable manned expeditions across the solar system. This is the carrot that leads the endorsement of such gigantic projects.

John C Evvard

A Machine Learning Framework for Error Compensation in Radiative Transfer Calculations

Radiative heat transfer influences the amount of heat flux transferred to the surface of the hypersonic vehicle, which is essential to evaluate the performance of thermal protection systems. The radiative heat flux is found to be computationally prohibitive while accounting for the variation in spatial, angular, and spectral domains. A new methodology has been recently developed to alleviate the cost of computation in the spectral domain by constructing flow-agnostic reduced-order models (ROMs). The developed spectral ROM databases provide grouping strategies that account for non-equilibrium absorption and emission as well as interaction between disparate species due to spectral overlap in associated radiative processes. However, the developed ROMs need to be optimized for a specific combination of interacting gas species and would need to re-calibrated in case individual species are added/omitted. In this work, we use various machine learning (ML) techniques to approximate the radiative intensities determined by a ROM optimized for a specific gas mixture. The ML model relies on the ROM databases developed for a single species which ignores any spectral overlap. Thus, radiation evaluation starts with a simple summation of radiative intensities predicted using these non-calibrated ROMs for the contributing species. The ML framework then provides a correction to account for the interplay in the frequency, i.e., emission of photons by one species and absorption by another, and yields mixture-specific radiation fields. Once trained on the individual ROM databases, the ML framework offers instantaneous corrections that serves as a time/cost effective alternative to the optimization of ROMs for a specific gas mixture. The ML framework is trained on both the high fidelity and ROM evaluated line of sight (LOS) data from Orion, Stardust, and FIRE II cases to obtain a general purpose correction model for earth re-entry scenarios when radiation contributions from both atomic nitrogen and atomic oxygen are considered. A geometric length scale parameter is used in the training process to account for errors introduced in the ROM databases as a consequence of high optical thickness. The efficacy of the ML framework is underscored through extensive analysis of train and test errors with respect to all the re-entry scenarios. The applicability of such an ML framework was further corroborated by embedding it in a state-of-the-art US3D - NERO system for determining the radiative heat flux transferred to the hypersonic vehicle surface.

Radiation

Mathematical Characterization of Battery Models

The purpose of this document is to demonstrate the use of the Extended Kalman Filter as a tool for battery state estimation and the estimation of battery state of charge. The mathematical details based on the equivalent circuit model are presented followed by an electrochemical engineering model. A simplified first-order model is used to demonstrate the procedure followed by second and third-order models. Next a simplified electrochemistry model is presented along with observer development. State observability is calculated for the simpler equivalent circuit models and the simplified electrochemistry model. An outline of the battery model parameter identification method is presented, and model performance based on experimental and flight data is demonstrated.

Battery

Coexistence of Synchronization and Stochasticity in Thermally Coupled Mott Oscillators

Synchronization is conventionally regarded as a mechanism for suppressing variability and enforcing order in coupled systems, from pendula and lasers to neurons and electronic oscillators. Here, we show that synchronization can also embed stochasticity at finer scales. We observe this phenomenon in thermally coupled VO 2 neuristors, where robust in-phase synchronization at the microsecond scale coexists with spike onset fluctuations at the nanosecond scale, with no fixed leader. The coexistence of order and disorder originates from stochastic domain-level physics of the insulator–metal and metal–insulator transitions, where local variations in transition temperature drive cycle-to-cycle randomness in nucleation, percolation, and relaxation. A stochastic domain model reproduces this effect by generating synchronized spike trains with random lead–lag jitter, and experimental interspike interval statistics confirm the persistence of fine-scale variability despite macroscopic phase locking. These findings establish that synchronization and stochasticity can coexist within the same physical platform, revealing hidden disorder within collective order. Furthermore, this insight reframes synchronization as not purely deterministic, but as a universal context where microscopic variability can persist, with implications for electronics, cryptography, and the fundamental physics of order–disorder coexistence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Insulating ground state and 2−𝑘 magnetic structure of candidate Weyl hydrogen-atom K2⁢Mn3⁢(AsO4)3

The ideal Weyl "hydrogen-atom" semimetal exhibits only a single pair of Weyl nodes and no other trivial states at the Fermi energy. Such a material would be a panacea in the study of Weyl quasi-particles, allowing direct unambiguous observation of their topological properties. The alluaudite-like K2⁢Mn3⁢(AsO4)3 compound was recently proposed as such a material. Here, we use comprehensive experimental work and first-principle calculations to assess this prediction. We find K2⁢Mn3⁢(AsO4)3 crystallizes in the 𝐶⁢2/𝑐 symmetry with a quasi-one-dimensional Mn sublattice, growing as small needle-like crystals. Bulk property measurements reveal magnetic transitions at ≈8 and ≈4 K, which neutron scattering experiments show correspond to two distinct magnetic orders, first a partially ordered ferrimagnetic 𝐤𝟏=(0,0,0) structure at 8 K and a second transition of 𝐤𝟐=(1,0,0) at 4 K to a fully ordered state. Below the second transition, both ordering vectors are necessary to describe the complex magnetic structure with modulated spin magnitudes. Both of the best-fit magnetic structures in this work are found to break the symmetry necessary for the generation of Weyl nodes, though one of the magnetic structures allowed by 𝐤𝟏 does preserve this symmetry. However, the crystals are optically transparent and ellipsometry measurements reveal a large band gap, undermining expectations of semimetallic behavior. Density functional theory calculations predict an insulating antiferromagnetic ground state, in contrast to previous reports, and suggest potential frustration on the magnetic sublattice. Given the wide tunability of the alluaudite structure, we consider ways to push the system closer to a semimetallic state.

Taddei, Keith M [Argonne National Laboratory]

Contrasting structural reversibility and magnetic correlations in isostructural honeycomb magnets CrCl3 and 𝛼−RuCl3

We report a comparative neutron single crystal diffraction study of the structural and magnetic properties of layered halides CrCl3 and 𝛼−RuCl3. They host a honeycomb arrangement of transition metal ions with distinct electronic configurations and undergo a first-order structural transition between high-temperature 𝐶⁢2/𝑚 and low-temperature 𝑅⁢‾‾‾3. Both compounds show a step-like change in the 𝑐-lattice parameter across the structure transition. In contrast, the in-plane lattice response is quite different: 𝛼−RuCl3 exhibits an abrupt hysteretic change across the transition accompanied by progressive crystalline degradation upon thermal cycling, whereas CrCl3 shows a smooth in-plane lattice evolution and remains structurally robust. Magnetically, CrCl3 orders into an A-type antiferromagnetic structure at 𝑇𝑁=14 K and exhibits pronounced diffuse magnetic scattering extending up to about 40 K. 𝛼−RuCl3 shows no observable magnetic diffuse scattering above its zigzag antiferromagnetic ordering temperature 𝑇𝑁=7.6 K. These results suggest that the contrasting structural responses arise from an interplay between interlayer sliding energetics, stacking-strain coupling, and elastic accommodation of the stacking transition. The distinct chemical bonding and electronic configurations of the two compounds provide a microscopic basis for their different lattice responses to the structure transition and magnetic correlations.

Morgan, Zachary [ORNL] (ORCID:0000000243625911)

An analysis of digital phase-locked loops

This report focuses on second-order digital phase-locked loops (DPLLs) with uniformly sampled input, an amplitude-insenstive phase extractor and a conventional loop filter.

Thomas, J. B.