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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Computational Investigation of Oxidative Etch Pitting in FiberForm and Its Impact on Material Properties

Oxidation-driven carbon erosion does not occur uniformly but rather through the development of localized etch pits at active surface sites. These active sites form due to atomic defects on the carbon surface, making them significantly more reactive than the surrounding, non-defective areas. As a result, these sites are the first to react during ablation, leading to their removal. This process creates new defects in neighboring atoms, increasing their reactivity and causing localized carbon removal around these active sites. In this way, the highly reactive defective areas serve as nucleation points for the formation and growth of etch pits, which can have adverse effects on structural integrity of FiberForm. To better understand how these etch pits impact the material properties of carbon fiber microstructures, we have developed a new capability within the direct simulation Monte Carlo (DSMC) framework to capture the etch pit formation process. This capability, integrated into the DSMC code SPARTA (Stochastic Parallel Rarefied-gas Time-accurate Analyzer), models material removal in the presence of active sites, leading to the formation of etch pits. The current work focuses on studying the effects of these etch pits on the material properties of FiberForm, a widely used base material in thermal protection systems (TPS). The microstructure of virgin FiberForm, obtained via X-ray microtomography, is imported into SPARTA to generate the ablated geometries with etch pits. These modified microstructures are then analyzed using the Porous Microstructure Analysis (PuMA) software to compute various material properties, including elasticity, thermal conductivity, and permeability. We investigate the variation of these properties due to the complex surface topology changes caused by etch pit formation. Additionally, we compare the effects of pitting with the conventional model of shrinking fibers, traditionally used to simulate the ablation of carbon structures. Significant differences emerge between the two approaches. Consequently, this physically realistic model of material removal through etch pit formation offers improved accuracy in predicting the degradation of carbon-based TPS during oxidation. It also provides insights into other mechanisms, such as spallation, where chunks of material are removed into the flow due to etch pit growth. Ultimately, this model enhances our understanding of failure modes in these materials during ablation.

PuMA↗
NASA NTRS1991

An overview of self-consistent methods for fiber-reinforced composites

The Walker et al. (1989) self-consistent method to predict both the elastic and the inelastic effective material properties of composites is examined and compared with the results of other self-consistent and elastically based solutions. The elastic part of their method is shown to be identical to other self-consistent methods for non-dilute reinforced composite materials; they are the Hill (1965), Budiansky (1965), and Nemat-Nasser et al. (1982) derivations. A simplified form of the non-dilute self-consistent method is also derived. The predicted, elastic, effective material properties for fiber reinforced material using the Walker method was found to deviate from the elasticity solution for the v sub 31, K sub 12, and mu sub 31 material properties (fiber is in the 3 direction) especially at the larger volume fractions. Also, the prediction for the transverse shear modulus, mu sub 12, exceeds one of the accepted Hashin bounds. Only the longitudinal elastic modulus E sub 33 agrees with the elasticity solution. The differences between the Walker and the elasticity solutions are primarily due to the assumption used in the derivation of the self-consistent method, i.e., the strain fields in the inclusions and the matrix are assumed to remain constant, which is not a correct assumption for a high concentration of inclusions.

Gramoll, Kurt C.↗
DOE OSTI2024

Demonstrating resonant ultrasound spectroscopy as a viable technique to characterize thermally conditioned high explosive materials

We present results of resonant ultrasound spectroscopy (RUS) measurements applied to granular high explosive materials at different bulk pressing densities and degree of thermal conditioning. The material chosen in this study is a ubiquitously used explosive material known as pentaerythritol tetranitrate (PETN), which is used commercially in civil and defense applications both as a binderized plastic bonded explosive material and an unbinderized neat material. However, changes in granular PETN bulk elastic properties due to thermal conditioning, which could have implications for better understanding environmental aging-related effects, have not been well studied even though it is believed that elasticity may play an important role in explosive material initiation mechanisms. Furthermore, monitoring elastic property changes in granular explosive pressings has not yet been demonstrated using RUS, which is an appealing non-destructive characterization tool that requires only dry point contact with the explosive material. To this end, we report the first study using RUS to quantify the elastic properties of binderized and neat PETN pressings as well as to quantify changes in elastic properties as a function of both thermal conditioning and bulk pressing density. Elastic stiffness coefficients, sometimes more commonly referred to as elastic constants, calculated from the RUS measurements on the different PETN-based materials show a significant increase for the post-conditioned samples compared to the pre-conditioned samples. This trend of increasing elastic properties with thermal conditioning was consistent for different density pressings, different thermal exposure conditions, and even different neat PETN pressings of differing average crystal sizes and/or specific surface areas.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Benchmarking Microscale Ductility Measurements (Final Report of the Project DE-NE0008799)

Conventional macroscale experimentation is generally considered to be straightforward with few limitations. Conversely, micro/nanoscale experimentation presents numerous challenges in loading device design, sample preparation and handling, as well as accurate understanding of grain size and local texture effects on recorded measurements. Despite these challenges, nanopillar compression, MEMs based micro-tension, and nanoindentation approaches have been able to provide fundamental contributions to the understanding of material behavior at small lengthscales. However, the overarching shortcoming of these micro/nanoscale experimentation approaches, is the inability to directly translate measurements evaluated at the nm and µm length scales (e.g., hardness) to macroscale tensile material behavior (i.e., elastic modulus, yield strength, and ductility). The objectives of the proposed study are, 1) to establish best practices for obtaining tensile microscale ductility measurements, and 2) to validate methodologies to for comparing microscale ductility measurements to macroscale ductility measurements. In order to achieve these objectives, a multi-lengthscale, multi-temperature testing protocol and simulation framework are executed first on copper as a model material to validate the following approach, and second on reactor grade Zircaloy-2. Experiments are conducted on specimens extracted from the same test piece to ensure nominally identical grain size and texture from specimens to specimen. Motivated by the need to isolate the contribution of size-effects on obtained mechanical property measurements, specimens are manufactured with thicknesses at the micro- (1-10 µm), meso- (10-100's µm), and macroscales (sub-sized ASTM E8). In-situ full-field deformation techniques (scanning electron microscopy (SEM) grid methods and optical DIC) are incorporated into testing at each specimen length-scale to capture plasticity localization and evolution. Experimental testing for all specimens is conducted at both room temperature and elevated temperatures to probe the role of thermal activation on plastic deformation accommodation processes. Simulation efforts focus on examining the mechanical behavior of microscale specimens using a finite element approach with explicitly resolved grain morphologies, and an embedded crystal plasticity model. The cost-efficient implementation method allows for the modeling of a statistically significant number of both real (i.e., digital twin) and generated microstructures to obtain an understanding of the interrelationships between specimen microstructure and geometric variables (grain size, texture, specimen geometry, etc.) on microscale mechanical behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Recent Advances in Thermoplastic Puncture-Healing Polymers

Self-healing materials provide a route for enhanced damage tolerance in materials for aerospace applications. In particular, puncture-healing upon impact has the potential to mitigate significant damage caused by high velocity micrometeoroid impacts. This type of material also has the potential to improve damage tolerance in load bearing structures to enhance vehicle health and aircraft durability. The materials being studied are those capable of instantaneous puncture healing, providing a mechanism for mechanical property retention in lightweight structures. These systems have demonstrated healing capability following penetration of fast moving projectiles -- velocities that range from 9 mm bullets shot from a gun (approx.330 m/sec) to close to micrometeoroid debris velocities of 4800 m/sec. In this presentation, we report on a suite of polymeric materials possessing this characteristic. Figure 1 illustrates the puncture healing concept. Puncture healing in these materials is dependent upon how the combination of a polymer's viscoelastic properties responds to the energy input resulting from the puncture event. Projectile penetration increases the temperature in the vicinity of the impact. Self-healing behavior occurs following puncture, whereby energy must be transferred to the material during impact both elastically and inelastically, thus establishing two requirements for puncture healing to occur: a.) The need for the puncture event to produce a local melt state in the polymer material and b.) The molten material has to have sufficient melt elasticity to snap back and close the hole. 1,2 Previous ballistic testing studies revealed that Surlyn materials warmed up to a temperature approx.98 C during projectile puncture (3 C higher than it s melting temperature). 1,2 The temperature increase produces a localized flow state and the melt elasticity to snap back thus sealing the hole. Table 1 lists the commercially polymers studied here, together with their physical properties. The polymers were selected based on chemical structure, tensile strengths, tensile moduli, glass transition temperature, melting temperatures, and impact strength. The thermal properties of the polymers were characterized by Differential Scanning Calorimetry (DSC) and Dynamic Mechanical Analysis (DMA). Mechanical properties were assessed by a Sintech 2W instron according to ASTM D1708 or D638 at crosshead speeds of 5.08 cm/min. 7.6 cm x 7.6 cm panels of the different materials were prepared and ballistic testing was performed at various temperatures. The panels were shot with a .223 caliber semiautomatic rifle from a distance of 23 meters at various temperatures. Chronographs were used to measure initial and final bullet velocity. Temperatures at the site of impact were measured using a FLIR ThermaCAM S60 thermal camera. A Vision Research model Phantom 9 high speed video camera was used to capture high speed video footage of ballistics testing.

Gordon, K. L.↗
NASA NTRS2009

Self-Assembling, Flexible, Pre-Ceramic Composite Preforms

In this innovation, light weight, high temperature, compact aerospace structures with increased design options are made possible by using self-assembling, flexible, pre-ceramic composite materials. These materials are comprised of either ceramic or carbon fiber performs, which are infiltrated with polymer precursors that convert to ceramics upon thermal exposure. The preform architecture can vary from chopped fibers formed into blankets or felt, to continuous fibers formed into a variety of 2D or 3D weaves or braids. The matrix material can also vary considerably. For demonstration purposes, a 2D carbon weave was infiltrated with a SiC polymer precursor. The green or unfired material is fabricated into its final shape while it is still pliable. It is then folded or rolled into a much more compact shape, which will occupy a smaller space. With this approach, the part remains as one continuous piece, rather than being fabricated as multiple sections, which would require numerous seals for eventual component use. The infiltrated preform can then be deployed in-situ. The component can be assembled into its final shape by taking advantage of the elasticity of the material, which permits the structure to unfold and spring into its final form under its own stored energy. The pre-ceramic composites are converted to ceramics and rigidized immediately after deployment. The final ceramic composite yields a high-temperature, high-strength material suitable for a variety of aerospace structures. The flexibility of the material, combined with its high-temperature structural capacity after rigidization, leads to a less complex component design with an increased temperature range. The collapsibility of these structures allows for larger components to be designed and used, and also offers the potential for increased vehicle performance. For the case of collapsible nozzle extensions, a larger nozzle, and thus a larger nozzle exit plane, is possible because interference with surrounding structures can be avoided in the collapsed state. The larger exit plane leads to an increase in expansion area ratio, which has the potential to increase thrust and overall rocket performance. In general, the use of advanced ceramic materials can lead to improved engine and vehicle performance. The ceramics can run hotter, so less cooling is required. Fuel to coolant ratios can be balanced more readily to reduce weight. Engine efficiency can also be increased with hotter combustion and exhaust temperatures. In addition, the ceramic composites themselves can reduce the component weight by as much as 50 percent, which can translate into greater payload for the vehicle

Jaskowiak, Martha H.↗
DOE OSTI2026

Effect of stress and temperature on zero group velocity Lamb modes

Zero group velocity (ZGV) Lamb wave resonances are highly localized and sensitive to changes in material properties, making them a viable option for probing residual stresses and elastic nonlinearity through acoustoelastic effects. Temperature changes also influence ZGV modes and need to be accounted for, particularly when measuring the small frequency shifts associated with acoustoelastic effects. We use a laser-based ultrasonic system to measure the third-order elastic constants of several materials. A temperature compensation scheme is devised to remove the effects of temperature fluctuations from the measurements. Furthermore, the measured third-order elastic constants are used to predict the temperature dependence of the ZGV resonances using thermo-acoustoelasticity theory, and these predictions are compared to experimental measurements. We find that thermo-acoustoelasticity theory was unable to reliably predict the shift in ZGV resonances with temperature. These results could have important implications in understanding the limitations of thermo-acoustoelasticity theory and in developing precision ZGV resonance-based systems to detect and quantify residual stress in parts, a particularly relevant problem in additive manufacturing techniques including powder bed fusion and directed energy deposition.

Engineering↗
DOE OSTI2023

A parametric finite element study for determining burst strength of thin and thick-walled pressure vessels

To accurately predict the burst strength of both thin and thick-walled pressure vessels (PVs), a parametric study of PV burst strength was performed for a wide range of vessel geometries and materials using elastic-plastic finite element analysis (FEA). A valid FEA model was established through a detailed study of 2D versus 3D FEA models, the critical stress failure criterion versus the limit load criteria, and the thick-wall effect on the FEA simulations. Here, the results show that the stresses and strains at the mean diameter, rather than outside diameter, determines a more accurate burst strength for both thin and thick-walled PVs. On this basis, a parametrized FEA script using the ABAQUS Python application programming interface (API) was used to create a large database of PV burst strengths for a variety of vessel geometries and materials, demonstrating that Python scripting is a powerful technique for performing parametric studies or generating large databases. From the FEA results, using the regression method, a new burst pressure model was developed as a function of the vessel geometry (D/t ratio) and material properties (UTS and n). As validated by a large number of full-scale burst test data, the proposed burst model can very accurately predict the burst strength for both thin and thick-walled PVs.

42 ENGINEERING↗
DOE OSTI2023

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Abstract This is an update of a previous review (Naumis et al 2017 Rep. Prog. Phys. 80 096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation ( P ) in graphene, (ii) time-dependent strain and its impact on graphene’s electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisation P on hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic ( σ ), electric ( P ) and magnetic ( M ) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI 2 . The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Physics↗
NASA NTRS2009

The Role of Guidance, Navigation, and Control in Hypersonic Vehicle Multidisciplinary Design and Optimization

Airbreathing hypersonic systems offer distinct performance advantages over rocket-based systems for space access vehicles. However, these performance advantages are dependent upon advances in current state-of-the-art technologies in many areas such as ram/scramjet propulsion integration, high temperature materials, aero-elastic structures, thermal protection systems, transition to hypersonics and hypersonic control elements within the framework of complex physics and new design methods. The complex interactions between elements of an airbreathing hypersonic vehicle represent a new paradigm in vehicle design to achieve the optimal performance necessary to meet space access mission objectives. In the past, guidance, navigation, and control (GNC) analysis often follows completion of the vehicle conceptual design process. Individual component groups design subsystems which are then integrated into a vehicle configuration. GNC is presented the task of developing control approaches to meet vehicle performance objectives given that configuration. This approach may be sufficient for vehicles where significant performance margins exist. However, for higher performance vehicles engaging the GNC discipline too late in the design cycle has been costly. For example, the X-29 experimental flight vehicle was built as a technology demonstrator. One of the many technologies to be demonstrated was the use of light-weight material composites for structural components. The use of light-weight materials increased the flexibility of the X- 29 beyond that of conventional metal alloy constructed aircraft. This effect was not considered when the vehicle control system was designed and built. The impact of this is that the control system did not have enough control authority to compensate for the effects of the first fundamental structural mode of the vehicle. As a result, the resulting pitch rate response of the vehicle was below specification and no post-design changes could recover the desired capability.

Ouzts, Peter J.↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. Here this paper introduces a new alternative where the yield envelope is represented by a manifold of which the topology and the geometry are learned from a set of data points in a parametric space (e.g. principal stress space, π-plane). Here, deep geometric learning enables us to reconstruct a highly complex yield envelope by breaking it down into multiple coordinate charts. The global atlas that consists of these coordinate charts in return allows us to represent the yield surface via multiple overlapping patches, each with a specific local parametrization. This setup provides several advantages over the classical implicit function representation approach. For instance, the availability of coordinate charts enables us to introduce an alternative stress integration algorithm where the trial stress may project directly on a local patch and hence circumvent the issues related to non-smoothness and the lack of convexity of yield surfaces. Meanwhile, the local parametric approach also enables us to predict hardening/softening locally in the parametric space, even without complete knowledge of the yield surface. Comparisons between the classical yield function approach on the non-smooth plasticity and anisotropic cam-clay plasticity model are provided to demonstrate the capacity of the models for highly precise yield surface and the feasibility of the implementation of the learned model in the local stress integration algorithm.

42 ENGINEERING↗
DOE OSTI2024

Unified cohesive zone model (UCZM) for fracturing and fragmenting solids

Here, a Unified Cohesive Zone Model (UCZM), which inherits most of the advantages while overcoming the shortcomings of existing Cohesive Zone Models (CZMs), is proposed. Similar to the traditional extrinsic CZM approach, UCZM dynamically inserts the cohesive elements into the system based on local material states (e.g., stress, strain). However, the transition from continua to discontinua is smoothly achieved, thereby eliminating the “time-discontinuous” issue seen in the extrinsic CZM. Moreover, within the novel UCZM framework, the point of transition from continua to discontinua is controllable through the introduction of crack initialization criteria. As a result, the UCZM allows any material models (e.g., elastic, plastic, damage models) for continuum solids and for discrete fracture behavior to work together. In essence, both an enhanced extrinsic cohesive zone model and an intrinsic cohesive zone model can be represented by the proposed unified model. The proposed UCZM has been verified through different numerical examples. The work demonstrates that the UCZM is a highly effective approach for modeling fracture and fragmentation processes in solids.

42 ENGINEERING↗
DOE OSTI2020

Localization of deformation in fluid-saturated sandstone

Herein we discuss a laboratory study of inelastic deformation and localization was conducted to evaluate microseismicity and fracture in fluid-saturated rock. Plane strain compression experiments were performed on oil- and water-saturated Berea sandstone under dry, drained, undrained, and quasi-unjacketed conditions. Parameters associated with the elastic and inelastic material response were accurately measured and used in a constitutive model to predict localization of deformation under the drained and undrained conditions. Acoustic emission (AE) activity was recorded and the onset of inelastic response in fluid-saturated rock, similar to dry rock, coincided with an increase in AE rate. Fracture initiation and propagation were successfully monitored by AE locations. Clustering of AE events and the start of inhomogeneous deformation inferred from displacement measurements are shown to be well correlated with the model prediction of the onset of localized deformation under various rock-fluid interaction conditions.

42 ENGINEERING↗
DOE OSTI2022

Study of the interplay between lower-order and higher-order energetic strain-gradient effects in polycrystal plasticity

in this report strain-gradient (SG) plasticity refers to a class of non-local theories in which gradients of plastic slip determine the storage of geometrically necessary dislocations, introducing a length-scale dependence in the mechanical behavior of crystalline materials, which is otherwise lacking in local theories. In this work, we incorporate lower-order (LO) and higher-order energetic (HOE) strain-gradient effects into a crystal plasticity fast Fourier transform (FFT)-based formulation to investigate the interplay of the length scale that each strain-gradient term introduces at the microscale, and the mechanical properties that result at the macroscale. For an applicable range of length scales, we consider two systems: a 1-D two-phase face centered cubic (FCC) laminate and a 3-D FCC polycrystal, and two uniaxial deformation modes: monotonic tension and cyclic tension–compression. We show that increases in the individual LO and HOE length scales increase the hardening rate and strength of the material, respectively. When combined, the strong LO hardening is less pronounced than the effect alone due to the lowering of the gradients due to the HOE microstress. We demonstrate that the LO and HOE hardening manifest as “isotropic” (yield surface expansion) and “kinematic” (yield surface shift) effects, respectively, consistent with their theoretical origins. We show that in cyclic loading, the Bauschinger effect emerges in both local and non-local calculations and link its origins and severity to the behavior in the strain field, slip-system rates, and the HOE microforce.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Atomic-scale imaging of frequency-dependent phonon anisotropy

Directly visualizing vibrational anisotropy in individual phonon modes is essential for understanding a wide range of intriguing optical, thermal and elastic phenomena in materials. Although conventional optical and diffraction techniques have been used to estimate vibrational anisotropies, they fall short in achieving the spatial and energy resolution necessary to provide detailed information. Here, we introduce a new form of momentum-selective electron energy-loss spectroscopy, which enables the element-resolved imaging of frequency- and symmetry-dependent vibrational anisotropies with atomic resolution. Vibrational anisotropies manifest in different norms of orthogonal atomic displacements, known as thermal ellipsoids. Using the centrosymmetric strontium titanate as a model system, we observed two distinct types of oxygen vibrations with contrasting anisotropies: oblate thermal ellipsoids below 60 meV and prolate ones above 60 meV. In non-centrosymmetric barium titanate, our approach can detect subtle distortions of the oxygen octahedra by observing the unexpected modulation of q-selective signals between apical and equatorial oxygen sites near 55 meV, which originates from reduced crystal symmetry and may also be linked to ferroelectric polarization. These observations are quantitatively supported by theoretical modelling, which demonstrates the reliability of our approach. The measured frequency-dependent vibrational anisotropies shed new light on the dielectric and thermal behaviours governed by acoustic and optical phonons. Furthermore, the ability to visualize phonon eigenvectors at specific crystallographic sites with unprecedented spatial and energy resolution opens new avenues for exploring dielectric, optical, thermal and superconducting properties.

Ferroelectrics and multiferroics↗