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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Implications of AI and Data Center Service Demand on Energy, Water, and Economic Systems

This talk focuses on the challenges posed by the rapid growth of data centers (DCs), which rely heavily on electricity, water, land, and mineral resources, and have significant interactions with economic growth. The U.S. leads in DC deployment, but understanding how resource demands and constraints impact DC expansion requires strategic multisector analysis. To address this, the talk introduces a new conceptual framework and modeling capability within GCAM-USA, allowing integrated analysis of DC service demand, electricity, and direct and indirect water needs under varied scenarios. Insights include state-level water and electricity trends for DCs, uncertainty bounds, and the broader implications for resources and economics.

Data Centers↗
DOE OSTI2026

Active learning of a crystal plasticity flow rule from discrete dislocation dynamics simulations

Continuum-scale material deformation models, such as crystal plasticity (CP), can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e. mesoscale) models. The procedure to generate and extract the relevant information is however typically complex and ad hoc, involving decision and intervention by domain experts, leading to long development times. In this study, we develop a principled approach for calibration of continuum-scale models using lower scale information by representing a CP flow rule as a Gaussian process model. This representation allows for efficient parameter space exploration, guided by the uncertainty embedded in the model through a process known as Bayesian optimization (BO). We demonstrate a semi-autonomous BO loop which instantiates discrete dislocation dynamics simulations whose initial conditions are automatically chosen to optimize the uncertainty of a model CP flow rule. Our self-guided computational pipeline efficiently generated a dataset and corresponding model whose error, uncertainty, and physical feature sensitivities were validated with comparison to an independent dataset four times larger, demonstrating a valuable and efficient active learning implementation readily transferable to similar material systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Atomistic modeling of LiF microstructure ionic conductivity and its influence on nucleation and plating

We report the formation and degradation of the solid electrolyte interphase (SEI) and its underlying transport properties play an essential role in the overall performance of lithium-ion batteries. This paper presents classical molecular dynamics studies on polycrystalline inorganic lithium fluoride (LiF) layers to model and predict the SEI transport properties. The ionic conductivity is obtained from the lithium-ion diffusivity in polycrystalline structures of LiF using the Nernst-Einstein relation. The predicted molecular dynamics data are used in a continuum scale phase-field model to evaluate the plating kinetics under fast charging conditions. The analysis emphasizes that the SEI ionic conductivity properties impact the plating dynamics, where SEI's low ion conductivity value is prone to large plating and subsequent capacity degradation. The combination of atomic and continuum scale studies shown herein lays a foundation to tune in SEI transport properties to decrease the amount of lithium plating and improve the performance of fast-charging batteries.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2021

Micromechanics-based Modeling of Laminated SiC/SiC Ceramic Matrix Composites

The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses.

Ceramic Matrix Composites↗
DOE OSTI2021

Long-range hydrogen-binding effects of carbide interfaces in iron

A micromechanics model was developed to evaluate the elastic binding energy between carbide precipitates and hydrogen interstitials using Eshelby's equivalent inclusion method. In this work, density functional theory (DFT) simulations were performed to obtain the material-specific quantities, e.g., lattice constants and the elastic constants, for the continuum model. Using this model, we find that for coherent carbide precipitates, hydrogen atoms are more likely to bind on the broad surfaces of the disk-like precipitates, which is consistent with experimental observations. For semicoherent and incoherent precipitates, our model suggests that it is possible for semicoherent precipitates to have significant hydrogen binding capability while there is no hydrogen-binding capability of incoherent precipitates, which also agrees with experimental findings. In addition, several factors that influence the binding energies between hydrogen atoms and carbide precipitates were quantitatively analyzed, including the precipitate size, morphology, orientation, and interface. These collective results include both the position and the value of the strongest hydrogen-binding interaction for a wide range of carbide stoichiometries, which contributes to our understanding of hydrogen trapping in steel-based materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Low-cost fin-tube heat exchanger design for building thermal energy storage using phase change material

Heat transfer in phase change materials (PCMs) is complex because the melting and freezing fronts change as functions of stored or released heat. In prior attempts to optimize heat exchangers (HXs) in one or two dimensions, complex geometry has often been used to maximize the melt and freeze front area. This complex geometry is difficult and hence expensive to construct. This paper proposes a multiple-scale 3D finite element modeling approach to design fin-tube HXs for low-cost latent thermal energy storage applications. Further, the optimal fin and tube designs were determined at three scales (unit-scale, medium-scale, and large-scale) by modeling the melt and freeze front in three dimensions and using measured bulk thermal properties. The finite element model was validated by comparing it with the experimental data for a referenced design of a similar type. The results indicate that commercially available organic PCMs with low conductivity (<0.3 W/m·K) can have charge and discharge times appropriate for building thermal energy storage (i.e., 4–5 h) with fin-tube HX designs at costs <$26/kWh, even when the temperature difference (5.56°C) between the heat transfer fluid and the PCM phase change temperature is small. However, as the HX increases in length, the temperature reduction along the tube limits some larger-scale designs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2026

Integrated Computational Materials Engineering (ICME) Capability Maturity Levels for Ecosystems Enabling Digital Transformation

Digital engineering (DE) and integrated computational materials engineering (ICME) are widely recognized as critical enablers of faster, more affordable, and more reliable aerospace systems. However, many organizations have struggled to realize the promised return on investment (ROI) from digital initiatives. A primary reason is the absence of a shared, decision-focused framework that distinguishes simple digitization of existing workflows from true digital transformation that fundamentally changes how engineering decisions are made. This paper introduces an ICME capability maturity framework that fills this gap. The framework defines six cumulative ICME capability maturity levels (CMLs), explicitly tied to decision authority, engineering integration, optimization, and uncertainty management across material, process, structure, and performance scales. It is designed to complement established readiness metrics such as technology readiness levels (TRLs), manufacturing readiness levels (MRLs), and integration readiness levels (IRLs), by addressing a missing dimension: the conditions required for model-informed decision authority across scales. A unifying figure and capability table illustrate the six-level ICME Capability Maturity Framework, showing how organizations progress from digitization—with limited or negative ROI—to true digital transformation, where ICME-enabled workflows deliver measurable improvements in decision quality, cycle time, risk reduction, and reuse. The framework is intended for both technical practitioners and executive leadership, providing a common language to assess current state, guide roadmaps, align software ecosystem investments, and set realistic expectations for digital transformation outcomes. A regulatory-relevant statement clarifying the relationship between ICME capability and existing certification frameworks is provided.

ICME↗
NASA NTRS2015

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

International Conference on Envronmental Systems (ICES), Seattle WA NCTS 20964-15. The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earths magnetosphere as a laboratory tostudy the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10-4 Pa (10-6 torr)and the surrounding temperature achieving -180 C. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperatureversus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDAFLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 C of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 C and the heater power goal is to be within 5 of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Thermal↗
DOE OSTI2024

Recent Advances on Computational Modeling of Supported Single-Atom and Cluster Catalysts: Characterization, Catalyst–Support Interaction, and Active Site Heterogeneity

To satisfy the need for catalyst materials with high activity, selectivity, and stability for energy conversion, material design and discovery guided by theoretical insights are a necessity. In the past decades, the rise in theoretical investigations into the properties of catalyst materials, reaction mechanisms, and catalyst design principles has shed light on the catalysis field. Quantitative structure–activity relationships have been developed through incorporating spectroscopic simulations, electronic structure calculations, and reaction mechanistic studies. Here, in this review, we report the state-of-the-art computational approaches to catalyst materials characterization for supported single-atom and cluster catalysts utilizing spectroscopic simulations, i.e., XANES simulation, and material properties investigation via electronic-structure calculations. Furthermore, approaches regarding reaction mechanisms, focusing on active site heterogeneity, are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2015

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earth's magnetosphere as a laboratory to study the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10 (sup -4) pascals (10 (sup -6) torr) and the surrounding temperature achieving -180 degrees Centigrade. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperature versus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDA/FLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 degrees Centigrade of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 degrees Centigrade and the heater power goal is to be within 5 percent of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Correlation↗
NASA NTRS2016

Tool for Generation of MAC/GMC Representative Unit Cell for CMC/PMC Analysis

This document describes a recently developed analysis tool that enhances the resident capabilities of the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) 4.0. This tool is especially useful in analyzing ceramic matrix composites (CMCs), where higher fidelity with improved accuracy of local response is needed. The tool, however, can be used for analyzing polymer matrix composites (PMCs) as well. MAC/GMC 4.0 is a composite material and laminate analysis software developed at NASA Glenn Research Center. The software package has been built around the concept of the generalized method of cells (GMC). The computer code is developed with a user friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermomechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated to increase the user friendliness, as well as to make it more robust in terms of input preparation and code execution. Finally, classical lamination theory has been implemented within the software, wherein GMC is used to model the composite material response of each ply. Thus, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. The primary focus of the current effort is to provide a graphical user interface (GUI) capability that generates a number of different user-defined repeating unit cells (RUCs). In addition, the code has provisions for generation of a MAC/GMC-compatible input text file that can be merged with any MAC/GMC input file tailored to analyze composite materials. Although the primary intention was to address the three different constituents and phases that are usually present in CMCs-namely, fibers, matrix, and interphase-it can be easily modified to address two-phase polymer matrix composite (PMC) materials where an interphase is absent. Currently, the tool capability includes generation of RUCs for square packing, hexagonal packing, and random fiber packing as well as RUCs based on actual composite micrographs. All these options have the fibers modeled as having a circular cross-sectional area. In addition, a simplified version of RUC is provided where the fibers are treated as having a square cross section and are distributed randomly. This RUC facilitates a speedy analysis using the higher fidelity version of GMC known as HFGMC. The first four mentioned options above support uniform subcell discretization. The last one has variable subcell sizes due to the primary intention of keeping the RUC size to a minimum to gain the speed ups using the higher fidelity version of MAC. The code is implemented within the MATLAB (The Mathworks, Inc., Natick, MA) developmental framework; however, a standalone application that does not need a priori MATLAB installation is also created with the aid of the MATLAB compiler.

Materials Engineering↗
DOE OSTI2019

Surface Engineering by Simultaneous Action of Multiple External Fields (Final Technical Report)

This research project aims at enabling surface engineering strategies based on the fundamental understanding and predictive modeling of the surface morphological response of solid materials subjected to the combined action of multiple external forces. Surface morphological response to mismatch strain in strained-layer heterostructures also is analyzed. Our research focuses on the surface morphological evolution and stability of electrically conducting (metallic, such as Cu) and semiconducting (such as Si) solids under the simultaneous application of mechanical stresses, electric fields, and temperature gradients. We emphasize on identifying the conditions under which the multiply driven surface morphology is stable and on exploring the complexity of the corresponding various morphologically stable surface patterns. We also emphasize on the driven evolution of nanoscale features aiming at stabilizing and controlling nanoscale patterns on surfaces by their manipulation through simultaneously applied multiple external forces. Specifically, we address systematically the morphological response to the combined action of multiple external forces of bulk solid surfaces, surfaces of thin films grown epitaxially on thick or thin substrates, as well as nanoscale surface features such as coherently strained islands grown epitaxially on substrate surfaces. The research is based on a modeling approach that combines theoretical analyses of surface morphological stability with self-consistent dynamical simulations of surface evolution based on properly parameterized continuum and multiscale surface transport models.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Development of Machine-Learned Interatomic Potentials to Predict Structure, Transport, and Reactivity in Platinum-Based Fuel Cells

Machine-learned interatomic potentials (MLIPs) have rapidly progressed in accuracy, speed, and data efficiency in recent years. However, training robust MLIPs in multicomponent systems remains a challenge. In this work, we train an MLIP to describe hydrated Nafion ionomers and platinum catalysts, which are important components of fuel cells, by constructing a diverse training set to describe the bulk polymer and interfacial catalyst–polymer interactions well. We use our trained MLIP to study the properties of the platinum–Nafion system, including polymer structure, proton mobility in a bulk Nafion polymer and near a platinum-Nafion interface, and reactions near and far from the interface, finding excellent results for structure and reactions contained within our training set. Transport seems to be well described, with both vehicular transport and Grotthuss hopping captured, although converged calculations of diffusivities were not computed because they require calculations of tens of nanoseconds that are challenging with current state-of-the-art MLIPs. The combined insights that this model provides can be leveraged to optimize fuel cell performance, and the approach can be applied to other chemical processes and devices where structure, transport, and reactivity all contribute to the overall observed performance.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

United States Multi-Sector Dynamics land use and land cover base maps to support Human-Earth System Modeling

Datasets are land use and land cover (LULC) rasterized base maps at 30-m resolution for the conterminous United States (CONUS) for the years 2008, 2011, 2016, and 2019. Separate base maps are provided where LULC classifications are thematically congruent with Community Land Model (CLM), Land Use Harmonization (LUH2), and Global Change Analysis Model (GCAM), and a detailed decomposition of all combined land classes into a Multisector Dynamics (MSD) LULC product. Base maps were developed using empirically derived satellite (National Land Cover Dataset, MODIS) and combined observation datasets (Crop Data Layer, Protected Areas Database) and represent the most up-to-date accurate information on LULC in the CONUS. The four datasets encompass four different landcover classification systems: MSD Layers - The raw landcover classes obtained from reclassifying NLCD and USDA Crop data layers into a respective landcover class GCAM Layers - The MSD classes mosaiced, reclassified, and combined into the respective GCAM landcover classes CLM Layers - Similar process to GCAM layers, but mosaiced, reclassified, and combined MSD layers to their respective PFT classes LUH2 Layers - Similar process to both GCAM and CLM Layers, but mosaiced, reclassified and combined the MSD layers to align with the respective states

Food↗
DOE OSTI2022

Coupling of multiscale imaging analysis and computational modeling for understanding thick cathode degradation mechanisms

Here, using a thick NMC811 (LiNi 0.8 Mn 0.1 Co 0.1 O 2 ) electrode as an example, we present a macro- to nanoscale 2D and 3D imaging analysis approach coupled with 4D (space + time) computational modeling to probe its degradation mechanism in a lithium-ion battery cell. Particle cracking increases and contact loss between particles and carbon-binder domain are observed to correlate with the cell degradation. This study unravels that the reaction heterogeneity within the thick cathode caused by the unbalanced electron conduction is the main cause of the battery degradation over cycling. The increased heterogeneity in the system will entail more cathode regions where the degree of active material utilization is uneven, leading to higher probabilities of particle cracking. These findings shed light on the crucial role of the electronic and ionic transportation networks in the performance deterioration of the thick cathode. They also provide guidance for cathode architecture optimization and performance improvement.

25 ENERGY STORAGE↗
DOE OSTI2024

Machine-learning-assisted deciphering of microstructural effects on ionic transport in composite materials: A case study of Li 7 La 3 Zr 2 O 12 -LiCoO 2

The effective diffusivity of ionic species in multiphase materials is critical for the design and function of composite materials for electrochemical energy storage. In practice, effective diffusivity depends sensitively not only on the intrinsic diffusivities of constituting materials but also on their topological arrangement; nevertheless, these coupled contributions are oversimplified in most analytical models. Here, we combine atomistically informed mesoscale modeling and machine learning (ML) analysis to unravel how such features affect effective diffusivity in two-phase composites. Using the Li 7 La 3 Zr 2 O 12 -LiCoO 2 composite solid-state battery cathode as a model system, we compute effective diffusivity for 600 distinct dense polycrystalline microstructures with different topological configurations of grains, grain boundaries, and heterointerfaces. We verify that in addition to atomic-scale variabilities, microstructural feature diversity can significantly impact effective transport properties. Across the ensemble of test microstructures, this often results in bimodal distributions of effective diffusivity that encompass two qualitatively distinct operating mechanisms, which we identify via flux analysis. An ML approach reveals that the most critical determining factors for effective diffusivity are the connectivity of bulk phases and their heterointerfaces. The role of ionic mobility at the heterointerfaces is also discussed. These insights highlight the combined importance of microstructure and interface engineering in tuning the transport properties of ionic species in composite materials. In conclusion, our framework can also be extended for understanding generic microstructure-property relationships in other complex multiphase materials.

25 ENERGY STORAGE↗
DOE OSTI2025

Computational Modeling to Advance Novel Medical Isotopes for Radiotheranostics: A DOE-NIH Joint Workshop Executive Summary

The DOE-NIH Joint Workshop on Computational Modeling to Advance Novel Medical Isotopes for Radiotheranostics, held on September 27, 2024, brought together experts from government, academia, and industry to address critical challenges in radionuclide production and clinical translation. Here, the workshop emphasized interdisciplinary collaboration, particularly between the Department of Energy (DOE) and the National Institutes of Health (NIH), to strengthen the domestic isotope supply, streamline regulatory pathways, and further integrate computational tools into radiopharmaceutical therapy (RPT). Key discussions explored the role of AI-driven modeling, machine learning, and digital twin technologies in optimizing dosimetry, dynamically personalizing treatments, and reducing time to clinical adoption. Advances in predictive computational modeling were highlighted as essential for improving radionuclide yield, purity, and synthesis efficiency. Regulatory considerations and equitable access were central themes, with participants advocating for harmonized global standards, adaptive trial designs, and expanded infrastructure for clinical implementation. DOE computational and production infrastructure was emphasized. Future priorities identified include increased investment in radionuclide production infrastructure, expanded workforce development in radiopharmaceutical sciences and computational modeling, and the creation of robust public-private partnerships. The workshop concluded that continued strategic collaboration and sustained resources will be vital for advancing next-generation radiotheranostics, ensuring safe and effective therapies accessible to all patients.

digital twins↗
DOE OSTI2025

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTi⁢O3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗