Outstanding Energy Storage Performance in High-Hardness (Bi[subscript 0.5]K[subscript 0.5])TiO[subsc
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Chen, Liang↗
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Why Firn Quakes
Snow dampens sounds, but anecdotal reports concisely describe audible propagating collapse events—firnquakes—in Antarctic and Arctic snowfields. We propose combining granular and continuum mechanics to form a testable theory for conditioning, triggering, and propagation of firnquakes consistent with scarce data. A central condition for collapse events is unconsolidated firn at depth. As firn grains compact, stresses are transmitted along force chains which carry the overburden and transition into a continuous medium by pressure sintering. This granular legacy creates solid-like supports of denser layers that keep the material below unconsolidated. Dynamic amplification triggers local brittle failure of the supports, which induces a cascade of collapse propagation. Using bulk density from ice cores as proxy for stiffness, we find the flexural wave speed by collapsing supports matches the recorded firnquake velocities on the order of 100 m/s. Our theory is to be tested in firn sheets and other compacting granular materials.
Voigtländer, A. [Lawrence Berkeley National Labora↗
Fracturing in Wet Granular Media Illuminated by Photoporomechanics
Here, we study fluid-induced deformation and fracture of granular media and apply photoporomechanics to uncover the underpinning grain-scale mechanics. We fabricate spherical photoelastic particles of 2-mm diameter to form a monolayer granular pack in a circular Hele-Shaw cell that is initially filled with a viscous fluid. The key distinct feature of our system is that, with spherical particles, the granular pack has a connected pore space, thus allowing for pore-pressure diffusion and the study of effective stress in coupled poromechanical processes. We inject air into the fluid-filled photoelastic granular pack, varying the initial packing density and confining weight. With our recently developed experimental technique, photoporomechanics, we find two different modes of fluid invasion: fracturing in fluid-filled elastic media (with strong photoelastic response) and viscous fingering in frictional fluids (with weak or negligible photoelastic response). We directly visualize the evolving effective stress field and discover an effective stress shadow behind the propagating fracture tips, where the granular pack exhibits undrained behavior. We conceptualize the behavior of the system by means of a mechanistic model for a wedge of the granular pack bounded by two growing fractures. The model captures the pore-pressure build-up inside the stress shadow region and the grain compaction in the annular region outside. Our model reveals that a jamming transition determines the distinct rheological behavior of the wet granular pack, from a friction-dominated to an elasticity-dominated response.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Analysis of time-dependent strain heterogeneity in shales using X-ray microscopy and digital volume correlation
In this paper, we report the results of a 4-dimensional (3 spatial dimensions plus time) in-situ creep experiment on a milli-core shale plug from Barnett formation in Texas. An outstanding challenge in shale mechanics is connecting observable characteristics to predictable mechanical and hydraulic behavior. We employ novel imaging and analysis techniques to statistically link sample mineralogy and structure to observed deformation. In particular, we focus on mechanisms of porosity reduction during transient response to step changes in stress, analogous to the aseismic deformation that occurs after an episode of fracturing. Our main goal in this study is to take the first steps to visualize and capture the small-scale deformation mechanisms involved in creep of shales, using imaging techniques. To do so, we conducted a uniaxial creep experiment inside an Xradia Versa 520 micro-CT system for 12 h at room temperature under a constant uniaxial stress of 25 MPa. We employed a Digital Volume Correlation (DVC) method to measure micro-scale deforspmation of the sample by comparing the resulting volumetric images with a high-resolution scan of the sample obtained prior to the creep experiment. The results indicate that the time-dependent deformation in the compliant clay plus kerogen matrix constituents facilitates rigid grain rotation and compaction of intergranular porosity at the boundary between rigid grains and matrix.
58 GEOSCIENCES↗
Concurrent measurement of strain and chemical reaction rates in a calcite grain pack undergoing pressure solution: Evidence for surface-reaction controlled dissolution
Pressure solution is inferred to be a significant contributor to sediment compaction and lithification, especially in carbonate sediments. For a sediment deforming primarily by pressure solution, the compaction rate should be directly related to the rate of calcite dissolution, transport along grain contacts, and calcite reprecipitation. Previous experimental work has shown that there is evidence that deformation in wet calcite grain packs is consistent with control by pressure solution, but considerable ambiguity remains regarding the rate limiting mechanism. We present the results of laboratory compaction experiments designed to directly measure calcite dissolution and precipitation rates (recrystallization rates) concurrently with strain rate to test whether measured rates are consistent with predicted rates both in absolute magnitude and time evolution. Recrystallization rates are measured using trace element chemistry (Sr/Ca, Mg/Ca) and isotopes (87Sr/86Sr) of fluids flowing slowly through a compacting grain pack as it is being triaxially compressed. Imaging techniques are used to characterize the grain contacts and strain effects in the post-experiment grain pack. Our data show that calcite recrystallization rates calculated from all three geochemical parameters are in approximate agreement and that the rates closely track strain rate. The geochemically inferred rates are close to predicted rates in absolute magnitude. Uncertainty in grain contact dimensions makes distinguishing between surface reaction control and diffusion control difficult. Measured reaction rates decrease faster than predicted from standard pressure solution creep flow laws. This inconsistency may indicate that calcite dissolution rates at grain contacts are more complex, and more time-dependent, than suggested by geometric models designed to predict grain contact stresses.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A soft departure from jamming: the compaction of deformable granular matter under high pressures
Here, the high-pressure compaction of three-dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follows the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.
36 MATERIALS SCIENCE↗
KOMPASS-II: Compaction of Crushed salt for Safe Containment – Phase 2
Long-term stable sealing elements are a basic component in the safety concept for a possible repository for heat-emitting radioactive waste in rock salt. The sealing elements will be part of the closure concept for drifts and shafts. They will be made from a welldefinied crushed salt in employ a specific manufacturing process. The use of crushed salt as geotechnical barrier as required by the German Site Selection Act from 2017 /STA 17/ represents a paradigm change in the safety function of crushed salt, since this material was formerly only considered as stabilizing backfill for the host rock. The demonstration of the long-term stability and impermeability of crushed salt is crucial for its use as a geotechnical barrier. The KOMPASS-II project, is a follow-up of the KOMPASS-I project and continues the work with focus on improving the understanding of the thermal-hydraulic-mechanical (THM) coupled processes in crushed salt compaction with the objective to enhance the scientific competence for using crushed salt for the long-term isolation of high-level nuclear waste within rock salt repositories. The project strives for an adequate characterization of the compaction process and the essential influencing parameters, as well as a robust and reliable long-term prognosis using validated constitutive models. For this purpose, experimental studies on long-term compaction tests are combined with microstructural investigations and numerical modeling. The long-term compaction tests in this project focused on the effect of mean stress, deviatoric stress and temperature on the compaction behavior of crushed salt. A laboratory benchmark was performed identifying a variability in compaction behavior. Microstructural investigations were executed with the objective to characterize the influence of pre-compaction procedure, humidity content and grain size/grain size distribution on the overall compaction process of crushed salt with respect to the deformation mechanisms. The created database was used for benchmark calculations aiming for improvement and optimization of a large number of constitutive models available for crushed salt. The models were calibrated, and the improvement process was made visible applying the virtual demonstrator.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Templated Growth and Passivation of Vertically Oriented Antimony Selenide Thin Films for High-Efficiency Solar Cells in Substrate Configuration
Antimony selenide (Sb 2 Se 3 ) is a promising low-cost photovoltaic material with a 1D crystal structure. The grain orientation and defect passivation play a critical role in determining the performance of polycrystalline Sb 2 Se 3 thin-film solar cells. In this work, a seed layer is introduced on a molybdenum (Mo) substrate to template the growth of a vertically oriented, columnar Sb 2 Se 3 absorber layer by closed space sublimation. By controlling the grain orientation and compactness of the Sb 2 Se 3 seeds, obtain high-quality Sb 2 Se 3 absorber layers with passive Sb 2 Se 3 /Mo interfaces is obtained, which in turn improve the transport of photoexcited charge carriers through the absorber layer and its interfaces. Post-deposition annealing of absorber layers in ambient air is further utilized to passivate the defects in Sb 2 Se 3 and enhance the quality of the front heterojunction. As a result of systematic processing optimization, Sb 2 Se 3 planar heterojunction solar cells are fabricated in substrate configuration with a champion power conversion efficiency of 8.5%.
14 SOLAR ENERGY↗
Characterizing the uppermost 100 m structure of the San Jacinto fault zone southeast of Anza, California, through joint analysis of geological, topographic, seismic and resistivity data
We present results from complementary geological, topographic, seismic and electrical resistivity surveys at the Sagebrush Flat (SGB) site along the Clark fault (CF) strand of the San Jacinto fault zone trifurcation area southeast of Anza, California. Joint interpretation of these data sets, each with unique spatiotemporal sensitivities, allow us to better characterize the shallow (<100 m) fault zone at this structurally complex site. Geological mapping at the surface shows the CF has three main subparallel strands within a <100 m zone with varying degrees of rock damage. These strands intersect units of banded gneiss and tonalite, and various sedimentary units. Near the surface, the weathered but more intact tonalite and gneiss to the southwest have relatively high VP. The low-lying flat sedimentary basins around the two southwestern-most CF strands and elevated damaged gneiss to the northeast have lowest VP <500 m s–1. The high relief of the northeast gneiss unit may in part be explained by its extensive damage and inferred increased relative rock uplift. Resistivity imaging shows the unconsolidated dry basin sediments (maximum >1300 Ohm.m) contrasted against the compacted fine-grained (potentially wet) materials within the CF core and the Bautista Formation (minimum <40 Ohm.m), which is slightly elevated above the flat basins. The inverse relationship between VP (increases) and resistivity (decreases) in the uppermost ~15 m can be characterized as log–log linear with slopes of –2.6 to –4. At depths >30 m, the velocity heterogeneity near the surface merges into larger-scale structures that are generally slower on the northeast side of the CF core compared to the southwest side (as much as ~40 per cent reduction in average VP). A previous study revealed a 20–37 per cent variability in peak ground velocities across the SGB site from local earthquakes. The upper end of that range is associated with the near-surface unconsolidated sedimentary basins and northeast damaged gneiss unit. Preliminary analysis of time-dependent topography mostly shows effects of changing vegetation and anthropogenic activity.
Geochemistry & Geophysics↗
Arbitrarily accurate, nonparametric coarse graining with Markov renewal processes and the Mori–Zwanzig formulation
Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging due to the high dimension in which simulations are carried out and, consequently, due to the very large amount of data that are typically generated. Coarse graining is a popular technique for addressing this problem by providing compact and expressive representations. Coarse graining, however, potentially comes at the cost of accuracy, as dynamical information is, in general, lost when projecting the problem in a lower-dimensional space. This article shows how to eliminate coarse-graining error using two key ideas. First, we represent coarse-grained dynamics as a Markov renewal process. Second, we outline a data-driven, non-parametric Mori–Zwanzig approach for computing jump times of the renewal process. Numerical tests on a small protein illustrate the method.
36 MATERIALS SCIENCE↗
Microstructure, Transport, and Mechanics of Compacted Clay Simulated at the 0.1 μm Scale (1400 Smectite Clay Particles) Using a Coarse-Grained Model with Explicit Counterions
Clay-rich geomaterials play a critical role in many subsurface systems. The macroscale properties of these materials (low permeability, high ionic conductivity, high swelling pressure, etc.) are sensitive to molecular-level adsorption and hydration interactions at clay−water interfaces. Efforts to develop multiscale simulation approaches to predict these properties reveal a scale gap between atomistic simulations (typically limited to systems smaller than 10 nm) and continuum-scale models (which use computational grid elements with dimensions ≳ 10 μm). In this study, we present a coarse-grained (CG) framework that partly bridges this gap by simulating compacted smectite clay assemblages with dimensions of 0.1 μm containing 1,400 clay particles across a range of dry densities (1,050 to 1,850 kg·m −3 ) and Na/Ca counterion compositions (Na fraction ranging from 0.2 to 1). The simulated systems, along with their reconstructed binary three-dimensional pore networks, are used to evaluate the microstructure, pore size distribution, tortuosity, ion diffusivity, and swelling pressure of compacted smectite clay. Results show that our approach captures important features of the mesoscale heterogeneity of compacted clays, including tactoid formation, hierarchical porosity, and anisotropic pore networks. Results also reveal how compaction and counterion composition govern emergent behaviors, including dominant pore sizes, directional transport, and electrochemical response. This work highlights the potential of CG simulations to bridge molecular and continuum scales and to advance geotechnical and environmental applications involving clay-rich materials as well as related nanoporous media such as geopolymers and calcium-silicate-hydrate. However, the results also suggest that accurate prediction of certain microstructural and mechanical properties (e.g., swelling pressure) may require even larger-scale systems on the order of 1 μm.
02 PETROLEUM↗
Coarse-grained fixed-point tensor networks and holographic reflected entropy in 3D gravity
We use the framework of fixed-point BCFT tensor networks to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS 3 /CFT 2 , for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-c limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-c limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data.
AdS-CFT correspondence↗
Shock compaction heating and collisional processes in the production of type 3 ordinary chondrites: Lessons from the (nearly) unique L3 chondrite melt breccia Northwest Africa 8709
Abstract Northwest Africa (NWA) 8709 is a rare example of a type 3 ordinary chondrite melt breccia and provides critical information for the shock compaction histories of chondrites. An L3 protolith for NWA 8709 is inferred on the basis of oxygen isotope composition, elemental composition, diverse mineral chemistry, and overall texture. NWA 8709 is among the most strongly shocked type 3 chondrites known, and experienced complete melting of the matrix and partial melting of chondrules. Unmelted phases underwent FeO reduction and partial homogenization, with reduction possibly occurring by reaction of olivine and low‐Ca pyroxene with an S‐bearing gas that was produced by vaporization. Chondrules and metal grains became foliated by uniaxial compaction, and during compression, chondrules and fragments became attached to form larger clumps. This process, and possibly also melt incorporation into chondrules to cause “inflation,” may have contributed to anomalously large chondrule sizes in NWA 8709. The melt breccia character is attributed to strong shock affecting a porous precursor. Data‐model comparisons suggest that a precursor with 23% porosity that was impacted by a 3 km/s projectile could have produced the meteorite. The rarity of other type 3 ordinary chondrite melt breccias implies that the immediate precursors to such chondrites were lower in porosity than the NWA 8709 precursor, or experienced weaker shocks. Altogether, the data imply a predominantly “quiet” dynamical environment to form most type 3 ordinary chondrites, with compaction occurring in a series of relatively weak shock events.
Ruzicka, Alex M.↗
Compaction of crushed salt for safe containment – a summary of the KOMPASS projects
Abstract. For the underground disposal of high-level nuclear waste in rock salt formations, the safety concept includes the backfilling of open cavities with crushed salt. For the prognosis of the sealing function of the backfill for the safe containment of the radioactive waste, it is crucial to have a comprehensive process understanding of the crushed-salt compaction behavior. The crushed-salt compaction process is influenced by internal properties (e.g., grain size, mineralogy, and moisture content) and boundary conditions (e.g., temperature, stress state, and compaction rate) and, therefore, involves several coupled thermal–hydro–mechanical (THM) processes (Hansen et al., 2014; Kröhn et al., 2017). With the paradigm shift from the limited release of radionuclides to safe containment due to the German Repository Site Selection Act passed in 2017, the importance of crushed salt as geotechnical barrier has increased, with a focus on the evolution of its hydraulic properties. Based on the knowledge gaps in the current process understanding, the “Compaction of crushed salt for safe containment” (KOMPASS) projects were initiated to improve the scientific basis behind using crushed salt for the long-term isolation of high-level nuclear waste within rock salt repositories. The efforts to improve the prediction of crushed-salt compaction begun during the first phase of the KOMPASS projects (Czaikowski et al., 2020) and were followed up in a second phase ending in June 2023. The primary achievements of the projects are as follows (Czaikowski et al., 2020; Friedenberg et al., 2022): specification of the KOMPASS reference material, an easily available and reproducible synthetic crushed-salt material, for generic investigations; development of pre-compaction methods and successful production of samples in the short term and under in situ loading conditions; formulation of an extended laboratory program addressing the isolated investigation of known relevant factors influencing the compaction behavior of crushed salt (Düsterloh et al., 2022); execution of long-term compaction tests addressing isotropic and deviatoric load changes, temperature, and compaction state; construction of a backfill body using the KOMPASS reference material in the Sondershausen mine through collaboration with the SAVER (Entwicklung eines salzgrusbasierten Versatzkonzepts unter der Option Rückholbarkeit) project (Schaarschmidt and Friedenberg, 2022); advancement of the tools for microstructure investigation methods (Svensson and Laurich, 2022); generation (first stages) of a microphysical process list combining literature research with our own findings; benchmarking of long-term compaction test for model development and optimization of various existing models as well as the development of new models; application of a virtual demonstrator (2D model representing a backfilled drift in rock salt) for the visualization of developments and the quantification of the models (Rabbel, 2022). In summary, the KOMPASS projects contributed to the reduction of uncertainties and the strengthening of the safety case for using crushed salt within rock salt repositories.
Friedenberg, Larissa↗
The onset of alloying in Cu-Ni powders under high-shear consolidation
Friction consolidation (FC) is a solid phase processing methodology that densifies a material through high-shear deformation and pressure at elevated temperature. The method has garnered interest in the scientific community because of its ability to produce extremely refined and homogeneous microstructures, off-axis texture development, and improved material properties. This manuscript presents an investigation of Cu and Ni material mixing via evaluation of morphological evolution, grain boundary characterization, and compositional analysis to provide insights on the operational alloying mechanisms occurring under high shear and elevated temperature. Using correlative microscopy techniques, we show alloying progresses via a combination of grain boundary diffusion and interfacial roughening at heterophane boundaries. Evidence supporting Cu infiltration along Ni-Ni grain boundaries along with asymmetric diffusion of Cu into Ni grains is highlighted. The resultant, consolidated microstructure was produced directly from a powder compact in ~30 s and exhibited a submicron, equiaxed grain size.
36 MATERIALS SCIENCE↗
Compaction of crushed salt for safe containment – overview of the KOMPASS project
Abstract. In Germany, rock salt formations are possible host rock candidates for a repository for heat-emitting radioactive waste. The safety concept of a repository in salt bases on a multibarrier system consisting mainly of the geological barrier salt and geotechnical seals ensuring safe containment. Crushed salt will be used for backfilling of cavities and sealing measures in drifts and shafts due to its favourable properties and its easy availability (mined-off material). The creep of the rock salt leads to crushed salt compaction with time. Thereby, the crushed salts' porosity is reduced from the initial porosity of 30 %–40 % to a value comparable to the porosity of undisturbed rock salt (≤1 %). In such low porosity ranges, technical impermeability is assumed. The compaction behaviour of crushed salt is rather complex and involves several coupled THM processes (Kröhn et al., 2017; Hansen et al., 2014). It is influenced by internal properties like humidity and grain size distribution, as well as boundary conditions such as temperature, compaction rate or stress state. However, the current process understanding has some important gaps referring to the material behaviour, experimental database and numerical modelling. It needs to be extended and validated, especially in the low porosity range. The objective of the KOMPASS project was development of methods and strategies for the reduction of deficits in the prediction of crushed salt compaction leading to an improvement of the prognosis quality. Key results are as follows (KOMPASS Phase 1, 2020): selection of an easily available and permanently producible synthetic crushed salt mixture, acting as a reference material for generic investigations; development and proof of different techniques for producing pre-compacted samples for further investigations; establishment of a tool of microstructure investigation methods to demonstrate the comparability of grain structures of pre-compacted samples with in-situ compacted material for future investigations; execution of various laboratory experiments using pre-compacted samples, e.g. long-term creep tests which deliver reliable information about time- and stress-dependent compaction behaviour; development of a complex experimental investigation strategy to derive necessary model parameters considering individual functional dependencies. Its technical feasibility was successfully verified; benchmarking with various existing numerical models using datasets from three different triaxial long-term tests. The result was not entirely satisfactory; however, the number of influencing factors is small and further validation work has to be done. Overall, the KOMPASS project has made significant progress in the approaches to solving the outstanding question, building the basis for further investigations.
Friedenberg, Larissa↗
Microscale Mechanical‐Chemical Modeling of Granular Salt: Insights for Creep
Abstract Microscale numerical modeling is potentially an effective approach for understanding salt creep, but it is quite challenging because natural salt grain boundaries can have complex and evolving geometry, and because contacts between these deformable salt mineral grains are dynamic as a result of compaction, chemical reaction, fluid flow, and heat transfer. In this study, we have overcome these challenges and developed a new microscale mechanical‐chemical (MC) model to analyze creep of salt at the microscale, accounting for coupled deformation, dynamic contacts, and chemical reaction in granular systems with realistic geometric representations. The MC model was realized by linking a new microscale mechanical code based on the numerical manifold method (NMM) to a reactive transport code named Crunch. We simulated the processes of reorganization of the salt grains, microfracturing, and pressure solution that contribute to creep at larger scales. Based on this first quantitative microscale model, we found that sharp corners of mineral grains can dominate the contact dynamics, microfracturing, and pressure solution when salt is compacted, thus governing the structural changes and porosity loss of the system. We found that pressure solution, which preferentially dissolves sharp corners and edges, can lead to relatively high porosity loss in the system, thus playing an important role in the creep of salt. Our analysis shows that the dynamic changes of salt granular systems involving grain relocation and pressure solution can occur repeatedly and continuously, thus contributing to longer‐term creep of salt at larger scales.
58 GEOSCIENCES↗
Characterization of γ′/γ″ compact and sandwich type precipitates during long-term high-temperature exposure in Ni-based superalloys
Here, the formation of γ′/γ″ co-precipitates is investigated in Ni-based superalloys with a varying Ti/Al ratio and Ta content and their stability is studied using long-term high-temperature exposure. Transmission electron microscopy and atom probe tomography analyses demonstrate that both higher Ti/Al ratios and increased Ta promote γ″ phase formation, leading to sandwich and compact structures. The compact co-precipitation significantly reduces γ′ precipitate coarsening during 10,000 h exposure at 700°C by restricting elemental diffusion, particularly of aluminum, from the γ matrix to the γ′ phase. For the alloy without a compact structure, and only γʹ precipitates, at the beginning of the exposure, the coarsening rate over 10,000 h was 3.5 times faster than for the alloy with compact γʹ/γʺ precipitates. Evidence of destabilization of the compact morphology was found to occur between 5,000 and 10,000 h exposure and originated from the extensive formation and growth of δ platelets that extended throughout the grains. Thus, the outer layer of the compact, which consists of γʺ, was subjected to the γ″ to δ phase transformation.
gamma double prime↗