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

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Structural evolution of liquid silicates under conditions in Super-Earth interiors

Molten silicates at depth are crucial for planetary evolution, yet their local structure and physical properties under extreme conditions remain elusive due to experimental challenges. In this study, we utilize in situ X-ray diffraction (XRD) at the Matter in Extreme Conditions (MEC) end-station of the Linear Coherent Linac Source (LCLS) at SLAC National Accelerator Laboratory to investigate liquid silicates. Using an ultrabright X-ray source and a high-power optical laser, we probed the local atomic arrangement of shock-compressed liquid (Mg,Fe)SiO 3 with varying Fe content, at pressures from 81(9) to 385(40) GPa. We compared these findings to ab initio molecular dynamics simulations under similar conditions. Results indicate continuous densification of theO-O and Mg-Si networks beyond Earth’s interior pressure range, potentially altering melt properties at extreme conditions. This could have significant implications for early planetary evolution, leading to notable differences in differentiation processes between smaller rocky planets, such as Earth and Venus, and super-Earths, which are exoplanets withmasses nearly three times that of Earth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Dense hydrogen layers for high performance MagLIF

We report that Magnetized Liner Inertial Fusion (MagLIF) experiments driven by the Z machine produce >10 13 deuterium-deuterium fusion reactions. Simulations indicate high yields and gains (1000) with increased current and deuterium-tritium layers for burn propagation. Such a coating also isolates the metal liner from the gaseous fuel, which should reduce mixing of liner material into the fuel. However, the vapor density at the triple point is only 0.3 kg/m3, which is not high enough for MagLIF operation. We present two solutions to this problem. First, a fuel wetted low-density plastic foam can be used to form a layer on the inside of the liner. The desired vapor density can be obtained by controlling the temperature. This does however introduce carbon into the layer which will enhance radiation losses. Simulations indicate that this wetted foam layer can significantly contribute to the fusion yield when the foam density is less than 35 kg/m 3 . Second, we show that a pure frozen fuel layer can first be formed on the inside of the liner and then low temperature gaseous fuel can be introduced just before the implosion without melting a significant amount of the ice layer. This approach is the most promising for MagLIF to produce high yield and gain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Spatiotemporally Registered In-Situ and Ex-Situ Datasets for Laser-based Blown Powder Directed Energy Deposition

This dataset is comprised of in situ sensing data collected during laser-based, blown powder directed energy deposition (DED) of Inconel 718 representing eight different printing conditions: (1) nominal, (2) +15% scan speed, (3) +12% laser power, (4) +42% powder feed rate, (5) +100% jerk limit, (6) +10% layer height, (7) +20% hatch spacing, (8) +20% carrier gas flow. All eight DED builds constructed an identical test coupon geometry consisting of geometric features representative of industrial print requirements (e.g., bulk deposition, thin walls, overhangs). In situ data consists of xyz-coordinates (100 Hz) and on-axis melt pool camera video (60 Hz), both of which have been temporally synchronized to spatially map the melt pool camera data. In addition, post-build X-ray computed tomography (XCT) data for each of the eight test geometries have been spatially registered to the recorded xyz-coordinates, allowing for comparisons between melt pool camera data and flaws identified in the XCT data.

additive manufacturing↗
DOE OSTI2025

Derivation of physical equations for high-speed laser welding using large language models

It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.

36 MATERIALS SCIENCE↗
DOE OSTI2025

High Energy Density Physics of Inertial Confinement Fusion Ablator Materials (Final Technical Report)

The goal of this project was to conduct dynamic compression experiments and predictive simulations to reveal the fundamental high-energy-density (HED) physics of amorphous carbon. These results are essential for assessing amorphous carbon as a potential ablator material for next generation of inertial confinement fusion (ICF) capsules. We made significant progress in exploring the HED properties of amorphous carbon through experiments at Omega EP Laser and the European XFEL, in addition to billion-atom, quantum-accurate molecular dynamics (MD) simulations. Through our joint experimental and simulation program, we mapped the phase diagram of amorphous carbon, uncovering its range of metastability and identifying phase transitions to diamond and liquid carbon along the Hugoniot and at higher pressures using double shock compression pathways. Our findings indicate that amorphous carbon melts at significantly lower shock pressures than high-density carbon (diamond). However, nanocrystalline diamond nucleates across a broad range of pressures and temperatures. This emergence of the nanocrystalline microstructure during compression can negatively impact the planarity of the shock front and potentially trigger ablator/fuel mixing during Inertial Fusion Energy (IFE) applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Fundamentals of Polymer Crystallization in Laser Powder Bed Fusion for New Material Screening

Although laser powder bed fusion (PBF/LB) was one of the first industrially viable additive manufacturing (AM) methods for end-use part production, polyamides remain grossly dominant at both the commercial- and researchscale. The research community continues to develop and refine “rapid screening” methods for evaluating the suitability of a new polymer for PBF/LB. The so-called “SLS Process Window,” which is the difference between melting and crystallization temperature measured at 10 K min-1 as originally outlined in the patent literature, is perhaps the most often reported screening method. Although perhaps appropriate as part of a larger study, the simplistic guidelines put forth by the “SLS Process Window” are not sufficiently scientifically rigorous to understand how crystallization kinetics affects successful 3D printing. The common understanding of the SLS Process Window omits details from published theories of polymer crystallization. as evidenced by published assumptions and methods in PBF/LB process modeling papers. The authors explain polymer crystallization in the PBF/LB process context and propose replacing the “process window” with crystallization halftime and physical gelation for new material screening. These measurements better represent behavior critical for ensuring a lengthy coexistence of solid powder and molten polymer affecting warp-free parts.

CHATHAM, CAMDEN A.↗
DOE OSTI2024

The right conditions for high-precision dynamic temperature and heat capacity measurement via pyrometry and conductivity

The pursuit of accurate bulk temperature T under extreme conditions has been a long-standing goal of the high pressure science community, complicated by a lack of data to inform models. To reach these extremely high-pressure, high-temperature (high P − T) conditions, a combination of dynamic and heated static experiments (e.g., diamond or gem anvil cel experiments) are used. For example, in a diamond anvil cell (DAC) experiment, a sample placed in the DAC is first pressurized. Following pressurization, the sample T is increased either by heating the entire DAC (usually using resistive heating, and limited to ∼1000K) or by applying intense laser power to the sample surfaces. In a dynamic experiment, the process of pressurizing the sample also heats it. In the case of shock physics experiments, such heating is substantial, easily reaching thousands of Kelvin; in our work we have seen T ∼17000K. Most methods of measuring temperature at ambient are not compatible with experiments under these high-pressure, high-temperature conditions: thermocouples break, melt, or have conductivity properties that differ from ambient where they are calibrated; thermometers would melt; both are too slow. As a result most methods are based on non-contact techniques such as x-ray diffraction broadening, neutron scattering, or optical methods. Of these, optical methods using the visible and near-infrared region of the spectrum are the most commonly used as the sources and detectors are readily available. In the case of optical methods the optical depth, and therefore the measurement location, is limited to the surface. When a window or anvil material is used, heat flows from the sample into the window/anvil. Likewise, if the sample undergoes a change in thermodynamic state, such as expansion upon release, different T may be expected. As a result, the surface or apparent temperature T app measurement will differ from the bulk or interior temperature that is desired. This surface measurement must be related to the bulk measurement using thermal transport models and material models. While it is tempting to conclude that one should just use x-ray methods that directly probe the interior, even these methods have been shown to depend on thermal transport and material models. Regardless of the method used to create the high P − T condition, therefore, we must understand the role of thermal transport and material models upon our interpretation of the T measurement, as well as the errors and uncertainties associated with the choice of models used in the analysis. This is a substantial area of research and this paper is by no means a complete survey of the relevant sources of uncertainty. For example, we have yet to begin to address alternate transport models in a detailed manner (e.g., Tan-Ahrens), or the many models that use additional layers to approximate melting, turbulence, or epitaxial phenomena). Likewise, we have not explored the impact upon uncertainty of thermal models that use temperature-dependent thermal transport coefficients, or the wide range of material models that can be applied. Instead, this paper focuses on using one simple model, the Urtiew-Grover model, to understand the sources of error in T measurement so that we may identify how best to focus future research efforts to return the best improvements and avoid working on over-optimizing a single type of measurement. To this end, we work through some of the best and worst case scenarios for T measurement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

AMVOS: Additive Manufacturing Video Object Segmentation Dataset

This dataset provides labeled video frames from four additive manufacturing (AM) processes for video object segmentation (VOS) tasks. It contains 90 video segments comprising 900 individually annotated frames across five AM datasets: laser hot-wire directed energy deposition (LHW-DED), tungsten inert gas wire arc additive manufacturing (TIG-WAAM), plasma arc welding (PAW), visible-light polymer extrusion (visPolymer), and near-infrared polymer extrusion (irPolymer). Each video segment consists of 10 contiguous frames with corresponding pixel-level object instance annotations. Depending on the process, two of four object classes are labeled per frame: Melt Pool, Feed Wire, Nozzle, or Material. Raw frames are provided as .jpg files and annotations as palettized .png files. The dataset follows the directory structure of established VOS benchmarks (DAVIS, YouTube-VOS, MOSE), enabling direct integration into VOS model training and evaluation pipelines for foundation model fine-tuning, domain adaptation, or zero-shot performance benchmarking. Data was collected at Oak Ridge National Laboratory's Manufacturing Demonstration Facility.

Wetzel, Jon [ORNL]↗
DOE OSTI2022

Stabilization of the Polar Structure and Giant Second-Order Nonlinear Response of Single Crystal γ-NaAs 0.95 Sb 0.05 Se 2

The dearth of suitable materials significantly restricts the practical development of infrared (IR) laser systems with highly efficient and broadband tuning. Recently, γ-NaAsSe 2 is reported, and it exhibits a large nonlinear second-harmonic generation (SHG) coefficient of 590 pm V —1 at 2 µm. However, the crystal growth of γ-NaAsSe 2 is challenging because it undergoes a phase transition to centrosymmetric δ-NaAsSe 2 . Herein, the stabilization of non-centrosymmetric γ-NaAsSe 2 by doping the As site with Sb, which results in γ-NaAs 0.95 Sb 0.05 Se 2 is reported. The congruent melting behavior is confirmed by differential thermal analysis with a melting temperature of 450 °C and crystallization temperature of 415 °C. Single crystals with dimensions of 3 mm × 2 mm are successfully obtained via zone refining and the Bridgman method. The purification of the material plays a significant role in crystal growth and results in a bandgap of 1.78 eV and thermal conductivity of 0.79 Wm —1 K —1 . The single-crystal SHG coefficient of γ-NaAs 0.95 Sb 0.05 Se 2 exhibits an enormous value of |d 11 | = 648 ± 74 pm V —1 , which is comparable to that of γ-NaAsSe 2 and ≈20× larger than that of AgGaSe 2 . Importantly, the bandgap of γ-NaAs 0.95 Sb 0.05 Se 2 (1.78 eV) is similar to that of AgGaSe 2 , thus rendering it highly attractive as a high-performing nonlinear optical material.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Decoding the Atomic Structure of Ga 2 Te 5 Pulsed Laser Deposition Films for Memory Applications Using Diffraction and First-Principles Simulations

Neuromorphic computing, reconfigurable optical metamaterials that are operational over a wide spectral range, holographic and nonvolatile displays of extremely high resolution, integrated smart photonics, and many other applications need next-generation phase-change materials (PCMs) with better energy efficiency and wider temperature and spectral ranges to increase reliability compared to current flagship PCMs, such as Ge 2 Sb 2 Te 5 or doped Sb 2 Te. Gallium tellurides are favorable compounds to achieve the necessary requirements because of their higher melting and crystallization temperatures, combined with low switching power and fast switching rate. Ga 2 Te 3 and non-stoichiometric alloys appear to be atypical PCMs; they are characterized by regular tetrahedral structures and the absence of metavalent bonding. The sp 3 gallium hybridization in cubic and amorphous Ga 2 Te 3 is also different from conventional p-bonding in flagship PCMs, raising questions about its phase-change mechanism. Furthermore, gallium tellurides exhibit a number of unexpected and highly unusual phenomena, such as nanotectonic compression and viscosity anomalies just above their melting points. Using high-energy X-ray diffraction, supported by first-principles simulations, we will elucidate the atomic structure of amorphous Ga 2 Te 5 PLD films, compare it with the crystal structure of tetragonal gallium pentatelluride, and investigate the electrical, optical, and thermal properties of these two materials to assess their potential for memory applications, among others.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Laser powder bed fusion parameter estimation with k-NN

Abstract Laser powder bed fusion (L-PBF) is a technique within additive manufacturing that uses a high power density laser to build parts from fused powdered metal alloy. This technology is well equipped to produce complex parts with otherwise impossible features, such as hidden voids or lattice structures. Alongside capability, reliability and quality are key characteristics considered when choosing a manufacturing method, and these are gaining attention as this method becomes more prevalent in industry. One main indicator of a stable L-PBF process is consistent melt pool geometry, and the properties of which are likely to determine the quality of the part produced. As computing power and sensing technologies become more advanced, this melt pool geometry could be studied in real time. This work addresses the challenge by leveraging a k-nearest neighbor (k-NN) model to identify key features within melt pool imagery and predict the energy density. The k-NN model was trained on data provided by the National Institute of Standards and Technology (NIST). Data preprocessing was performed on the images to extract features that were used in the k-NN model. This approach was used to accurately infer the energy density of unseen layers within the same part. The algorithm was subsequently tested with unique scan strategies and found to reasonably estimate the energy density of different parts. A fivefold cross validation found the algorithm to be consistently predicting the class of 91.4% of the in situ melt pool images.

Jung, Patrick (ORCID:0000000267890859)↗
DOE OSTI2022

Predicting defects in laser powder bed fusion using in-situ thermal imaging data and machine learning

Variation in the local thermal history during the Laser Powder Bed Fusion (LPBF) process in Additive Manufacturing (AM) can cause micropore defects, which add to the uncertainty of the mechanical properties (e.g., fatigue life, tensile strength) of the built materials. In-situ sensing has been proposed for monitoring the AM process to minimize defects, but successful minimization requires establishing a quantitative relationship between the sensing data and the porosity, which is particularly challenging with a large number of variables (e.g., laser speed, power, scan path, powder property). Physics-based modeling can simulate such an in-situ sensing-porosity relationship, but it is computationally costly. In this work, we develop Machine Learning (ML) models that can use in-situ thermographic data to predict the micropore of LPBF stainless steel materials. This work considers two identified key features from the thermal histories: the time above the apparent melting threshold ($\tau$) and the maximum radiance ( T max ). These features are computed, stored for each voxel in the built material, and then used as inputs. The binary state of each voxel, either defective or normal, is the output. Different ML models are trained and tested for the binary classification task. In addition to using the thermal features of each voxel to predict its own state, the thermal features of neighboring voxels are also included as inputs. This is shown to improve the prediction accuracy, which is consistent with thermal transport physics around each voxel contributing to its final state. Among the models trained, the F1 scores on test sets reach above 0.96 for Random Forests. Feature importance analysis based on the ML models shows that T max is more important to the voxel state than $\tau$ . The analysis also finds that the thermal history of the voxels above the present voxel is more influential than those beneath it. Our study significantly extends the capability of using in-situ thermographic data to predict porosity in LPBF materials. Finally, since ML models are fast, they may play integral roles in the optimization and control of such AM technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Elevated temperature ductility dip in an additively manufactured Al-Cu-Ce alloy

The deformation and failure mechanisms of Al-9Cu-6Ce (wt%) based alloys fabricated with laser powder bed fusion were investigated from room temperature to 400°C. The yield and ultimate tensile strengths decreased monotonically with increase in temperature, but the tensile elongation dipped unexpectedly at elevated temperatures and exhibited a minimum at 300°C. The dip in tensile elongation occurred with a concomitant dip in strain-rate sensitivity (SRS) of deformation. The as-fabricated alloy microstructure was heterogeneous, and the heat affected zone (HAZ) underneath the melt pool boundary was prone to strain localization. At 300 °C, the reduced SRS promoted the progression of strain localization in the HAZ leading to failure initiation and the dip in tensile elongation. Furthermore, a higher SRS or strain-hardening rate at other temperatures improved the tensile elongation by slowing the progression of strain localization in the HAZ such that failure initiated by other mechanisms elsewhere in the microstructure. Notably, the tensile elongation was limited by the defect structure only in a narrow temperature range (150 - 200 °C) while at other temperatures it was limited by the inherent microstructural features. This investigation exemplifies unexpected deformation and failure mechanisms possible in heterogeneous microstructures that result from additive manufacturing.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Time-Resolved XUV Opacity Measurements of Warm Dense Aluminum

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion research. However, theoretical predictions in the challenging dense plasma regime are conflicting and there is a dearth of accurate experimental data to allow for direct model validation. Here we present time-resolved transmission measurements in solid-density Al heated by an XUV free-electron laser. We use a novel functional optimization approach to extract the temperaturedependent absorption coefficient directly from an oversampled pool of single-shot measurements, and find a pronounced enhancement of the opacity as the plasma is heated to temperatures of order of the Fermi energy. Plasma heating and opacity enhancement are observed on ultrafast timescales, within the duration of the femtosecond XUV pulse. We attribute further rises in the opacity on ps timescales to melt and the formation of warm dense matter

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Multimodal and multiscale strengthening mechanisms in Al-Ni-Zr-Ti-Mn alloy processed by laser powder bed fusion additive manufacturing

The unique thermokinetics of laser-powder bed fusion additive manufacturing (L-PBFAM) has been exploited for development of a novel high-strength Al-Ni-Ti-Zr-Mn alloy. The addition of 0.5 wt% Mn leads to extraordinary improvement in ultimate tensile strength (502 MPa) and work hardening due to the activation of two Mn-induced strengthening mechanisms. First, by a bimodal particle strengthening effect due to Al 31 Mn 6 Ni 12 nano-quasi-crystal particles rejected in inter-dendritic spaces and fibrous Al 3 Ni eutectic dendritic channels, which predominately contributes to the strength improvement, and second by solid solution strengthening from remaining Mn entrapped in Al. These mechanisms supplement the particle strengthening effect imparted by coherent and incoherent Al 3 (Ti,Zr) co-precipitates present at melt pool boundaries, dislocation strengthening due to solidification induced strain, and Hall-Petch and backstress strengthening effect due to heterogenous grain size distribution occurring at various length scales. In conclusion, the solidification dynamics and hierarchical heat distribution that are associated with L-PBFAM resulted in complex spatial variations in these strengthening phenomena and were investigated via a high-throughput multiscale structure–property correlation that involved thermokinetic simulation, X-ray diffraction, high-resolution nanoindentation mapping, and site-specific transmission electron microscopy of the alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Surface roughness and dimensional evaluation of laser powder bed fusion additively manufactured shell and tube heat exchangers

The growing interest in additively manufactured (AM) heat exchangers drove the need to understand how this construction technique impacts heat exchanger performance. Two primary factors driven by AM that influence heat exchanger performance are surface roughness and geometry. To better understand these parameters, a range of shell and tube heat exchangers constructed using laser powder bed fusion were evaluated. Of those evaluated, the surface roughness throughout a fourteen-tube, zero-baffle heat exchanger was measured using computed tomography. Between the inner and outer tubes, the inner tube surfaces had a greater surface roughness than the outer by 8.07 μm, while the surfaces at the top of the build volume had higher surface roughness values than the bottom. Dimensionally, the inner tube diameters of this heat exchanger were 0.15% different from the design value, while the outer diameters were within a 0.84 % difference. Manual measurements across seven other heat exchangers yielded a maximum 1.15% difference between the design and measured diameters. Across the build volume for all heat exchangers studied, the tube diameters at the top were larger than at the bottom by a maximum of 1.24% difference. Inconsistent melting throughout the individual parts and the build volume, as well as particle splatter and thermal gradient variation were attributed to the surface roughness and dimensional changes seen. These results strengthen the knowledge of dimensional and surface roughness considerations when designing AM heat exchangers.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Photoinduced Melting of V 4 O 7 Correlated State

The compound V 4 O 7 is one of the Magnéli phase (V n O 2n - 1 , n = 3, 4, …, 9) correlated vanadium oxides with distinct intriguing electronic and structural properties. The possibility to manipulate the phase state of V 4 O 7 on an ultrafast time scale by light makes this material promising for potential applications in photonics, optoelectronics, quantum, and neuromorphic circuit design. In this work, the ultrafast spectroscopy of V 4 O 7 reveals the second-order nature of the photoinduced insulator-to-metal transition, emphasizing electronic and lattice contributions. The findings reveal the influence of the laser excitation level and temperature on these dynamics, providing a comprehensive understanding of V 4 O 7 structural changes and response to external stimuli. The phenomenological model based on the Landau–Ginzburg formalism provides a robust framework for explaining the photoinduced transition dynamics, showing a detailed picture of the light interaction with the electronic and lattice subsystems. This integrated approach significantly enhances the understanding of V 4 O 7 complex behavior upon photoexcitation, opening new possibilities for developing new optoelectronic devices and noninvasive optical control of the phase transition pathways in vanadates.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Atypical phase-change alloy Ga 2 Te 3 : atomic structure, incipient nanotectonic nuclei, and multilevel writing

Emerging brain-inspired computing, including artificial optical synapses, photonic tensor cores, neuromorphic networks, etc., needs phase-change materials (PCMs) of the next generation with lower energy consumption and a wider temperature range for reliable long-term operation. Gallium tellurides with higher melting and crystallization temperatures appear to be promising candidates and enable achieving the necessary requirements. Here, using high energy X-ray diffraction and Raman spectroscopy supported by first-principles simulations, we show that vitreous g-Ga 2 Te 3 films essentially have a tetrahedral local structure and sp 3 hybridization, similar to those in the stable fcc Ga 2 Te 3 polymorph and in contrast to a vast majority of typical PCMs. Nevertheless, optical pump–probe laser experiments revealed high-contrast, fast and reversible multilevel SET-RESET transitions raising a question related to the phase change mechanism. A recently observed nanotectonic compression in bulk glassy Ga–Te alloys seems to be responsible for the PCM performance. Incipient nanotectonic nuclei, reminiscent of monoclinic high-pressure HP-Te II and rhombohedral HP-Ga 2 Te 3 , are present as minorities (2–4%) in g-Ga 2 Te 3 but are suggested to grow dramatically with increasing temperature while interacting with appropriate laser pulses. This leads to co-crystallization of HP-polymorphs amplified by a high internal local pressure reaching 4–8 GPa. The metallic HP-forms provide an increasing optical and electrical contrast, favorable for reliable PCM operations, and higher energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗