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DOE OSTI2026

Seismic Event Characterization Using Full Moment Tensors on the Hypersphere

Moment tensor solutions provide insights into the deformation that has occurred in the source region of a seismic event and are therefore of great value in identifying different types of seismic sources, such as when monitoring for underground nuclear tests. Despite this utility, inversion of waveforms recorded by seismometers for their full seismic moment tensor is not yet routine, and development of robust methods to classify events based on this information is in its infancy. Here, we assemble an inventory of 1405 full moment tensor solutions that include explosive, earthquake, and collapse events, and investigate the use of anisotropic probability distribution functions on the 5D hypersphere to discriminate between these sources. Using a Bayesian classifier, we obtain optimal success rates of 98.4% across all events and demonstrate that modification of the prior probabilities provides a natural way to alter the balance between not missing desirable events (such as explosions) versus misclassifying large numbers of undesired events (such as earthquakes). The approach is specifically designed to progress from traditional, bipolar event screening metrics to more generalized event identification across multiple types of seismic sources. Despite current databases containing insufficient numbers of events to definitively demonstrate at present, we also find intriguing evidence of subgroupings within individual source populations on the hypersphere, for example, between chemical and nuclear explosions, raising the potential possibility of discriminating between these event types in the future.

Geosciences↗

DOE OSTI2024

Predicting Fracture Porosity Evolution in Sandstone (Final Report)

To better understand porosity, strength, chemical reactivity, and patterns of fractures, we developed methods using mineral deposits to unravel how fracture growth and diagenesis interact to create and destroy fracture porosity. Quartz and dolomite cement textures and associated fluid inclusion assemblage sequences and thermal histories provided data to infer the duration and rates at which fractures open. We developed and tested a model that accounts for how fracture porosity and rock properties change as a function of thermal exposure and how fracture size and arrangement evolve. Effects of cement deposits on growth were investigated with new geomechanical models and new methods to quantify fracture spatial arrangement. We tested these concepts in a wide range of rock types using outcrop and core-based datasets. We documented opening histories of fractures and fracture arrays in contrasting tectonic and thermal regimes. Our methods set a new standard for fracture characterization and our diagenetic-geomechanical model accurately predicts fluid flow characteristics of fractured rocks based on coupled effects of diagenesis and deformation. Results represent a significant advance in fundamental understanding of fractures in the Earth and have application to improving subsurface engineering operations in a wide range of contexts including geothermal and sequestration applications. The breakthrough of successfully reconstructing the timing and opening rates of parts of single fractures and portions of fracture arrays to document the growth and linkage of fracture arrays was an accomplishment of this grant that is being followed up in our current BES grant DE-SC0022968, ‘Reconstructing and Predicting Fracture Pattern Evolution‘

58 GEOSCIENCES↗

DOE OSTI2024

Landscape of nuclear deformation softness with spherical quasiparticle random-phase approximation

We investigate the stability and softness of nuclei against quadrupole, octupole, and hexadecapole deformation. By applying the spherical Skyrme-force Hartree-Fock Bardeen-Cooper-Schrieffer quasiparticle random phase approximation, we diagnose ground-state deformation when imaginary solutions are obtained, i.e., the spherical ground state collapses. We also calculate the multipole polarizability in spherical nuclei with no collapse, as a measure of softness. This numerically light and theoretically sound method is found able to capture deformation patterns across the nuclide chart. As a result, the connection between the intrinsic shape of nuclei and the dynamics of their low-lying collective states is established and the role of shell structure is discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

High Thermoelectric Performance and Defect Energetics of Multipocketed Full Heusler Compounds

We report a first-principles density-functional study of electron-phonon interactions in and thermoelectric transport properties of the full Heusler compounds Sr 2 BiAu and Sr 2 SbAu. Our results show that ultrahigh intrinsic bulk thermoelectric performance across a wide range of temperatures is physically possible and point to the presence of multiply degenerate and highly dispersive carrier pockets as the key factor for achieving this. Sr 2 BiAu, which features ten energy-aligned low-effective-mass pockets (six along Γ-X and four at L), is predicted to deliver n-type zT=0.4-4.9 at T=100-700 K. Comparison with the previously investigated compound Ba 2 BiAu shows that the additional L pockets in Sr 2 BiAu significantly increase its low-temperature power factor to a maximum value of 12 mW m -1 K -2 near T=300 K. However, at high temperatures the power factor of Sr 2 BiAu drops below that of Ba 2 BiAu because the L states are heavier and subject to strong scattering by phonon deformation, as opposed to the lighter Γ-X states, which are limited by polar-optical scattering. Sr2SbAu is predicted to deliver a lower n-type zT=3.4 at T=750 K due to appreciable misalignment between the L and Γ-X carrier pockets, generally heavier scattering, and a slightly higher lattice thermal conductivity. Soft acoustic modes, which are responsible for the low lattice thermal conductivity, also increase the vibrational entropy and high-temperature stability of these Heusler compounds, suggesting that their experimental synthesis may be feasible. The dominant intrinsic defects are found to be Au vacancies, which drive the Fermi level towards the conduction band and work in favor of n-doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Measurement of the azimuthal anisotropy of charged particles in sNN=5.36TeV O16+O16 and Ne20+Ne20 collisions with the ATLAS detector

This paper presents the first measurements of the azimuthal anisotropy coefficients , which quantify the -order Fourier modulation of charged-particle azimuthal distributions, for in and collisions recorded with the ATLAS detector at the CERN Large Hadron Collider in 2025. The coefficients are measured as a function of transverse momentum ( ), collision centrality, and event multiplicity. They are extracted using two complementary methods: two-particle correlations with a template-fit subtraction of short-range nonflow contributions, and four-particle subevent cumulants, which intrinsically suppress nonflow effects and provide sensitivity to flow fluctuations. The results show a clear hierarchy and a nonmonotonic dependence on , reaching a maximum around , consistent with trends observed in heavy-ion collisions. Detailed comparisons between the two collision systems reveal an enhanced in central collisions, consistent with theory expectations based on the predicted prolate deformation of neon nuclei, in contrast to the slightly tetrahedral structure predicted for oxygen. The four-particle cumulant results highlight strong event-by-event fluctuations and provide the greatest sensitivity to nuclear shape effects. These measurements can place new constraints on the initial geometry and the hydrodynamic response in light-ion collisions, offering valuable input for models of nuclear structure.

Aad, G↗

DOE OSTI2016

Single-energy computed tomography-based pulmonary perfusion imaging: Proof-of-principle in a canine model

Purpose: Radiotherapy (RT) that selectively avoids irradiating highly functional lung regions may reduce pulmonary toxicity, which is substantial in lung cancer RT. Single-energy computed tomography (CT) pulmonary perfusion imaging has several advantages (e.g., higher resolution) over other modalities and has great potential for widespread clinical implementation, particularly in RT. The purpose of this study was to establish proof-of-principle for single-energy CT perfusion imaging. Methods: Single-energy CT perfusion imaging is based on the following: (1) acquisition of end-inspiratory breath-hold CT scans before and after intravenous injection of iodinated contrast agents, (2) deformable image registration (DIR) for spatial mapping of those two CT image data sets, and (3) subtraction of the precontrast image data set from the postcontrast image data set, yielding a map of regional Hounsfield unit (HU) enhancement, a surrogate for regional perfusion. In a protocol approved by the institutional animal care and use committee, the authors acquired CT scans in the prone position for a total of 14 anesthetized canines (seven canines with normal lungs and seven canines with diseased lungs). The elastix algorithm was used for DIR. The accuracy of DIR was evaluated based on the target registration error (TRE) of 50 anatomic pulmonary landmarks per subject for 10 randomly selected subjects as well as on singularities (i.e., regions where the displacement vector field is not bijective). Prior to perfusion computation, HUs of the precontrast end-inspiratory image were corrected for variation in the lung inflation level between the precontrast and postcontrast end-inspiratory CT scans, using a model built from two additional precontrast CT scans at end-expiration and midinspiration. The authors also assessed spatial heterogeneity and gravitationally directed gradients of regional perfusion for normal lung subjects and diseased lung subjects using a two-sample two-tailed t-test. Results: The mean TRE (and standard deviation) was 0.6 ± 0.7 mm (smaller than the voxel dimension) for DIR between pre contrast and postcontrast end-inspiratory CT image data sets. No singularities were observed in the displacement vector fields. The mean HU enhancement (and standard deviation) was 37.3 ± 10.5 HU for normal lung subjects and 30.7 ± 13.5 HU for diseased lung subjects. Spatial heterogeneity of regional perfusion was found to be higher for diseased lung subjects than for normal lung subjects, i.e., a mean coefficient of variation of 2.06 vs 1.59 (p = 0.07). The average gravitationally directed gradient was strong and significant (R{sup 2} = 0.99, p < 0.01) for normal lung dogs, whereas it was moderate and nonsignificant (R{sup 2} = 0.61, p = 0.12) for diseased lung dogs. Conclusions: This canine study demonstrated the accuracy of DIR with subvoxel TREs on average, higher spatial heterogeneity of regional perfusion for diseased lung subjects than for normal lung subjects, and a strong gravitationally directed gradient for normal lung subjects, providing proof-of-principle for single-energy CT pulmonary perfusion imaging. Further studies such as comparison with other perfusion imaging modalities will be necessary to validate the physiological significance.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2013

EDS V26 Containment Vessel Explosive Qualification Test Report

The objective of the test was to qualify the vessel for its intended use by subjecting it to a 1.25 times overtest. The criteria for success are that the measured strains do not exceed the calculated strains from the vessel analysis, there is no significant additional plastic strain on subsequent tests at the rated design load (shakedown), and there is no significant damage to the vessel and attached hardware that affect form, fit, or function. Testing of the V25 Vessel in 2011 established a precedent for testing V26 [2]. As with V25, two tests were performed to satisfy this objective. The first test used 9 pounds of Composition C-4 (11.25 lbs. TNT-equivalent), which is 125 percent of the design basis load. The second test used 7.2 pounds of Composition C-4 (9 lbs. TNT-equivalent) which is 100 percent of the design basis load. The first test provided the required overtest while the second test served to demonstrate shakedown and the absence of additional plastic deformation. Unlike the V25 vessel, which was mounted in a shipping cradle during testing, the V26 vessel was mounted on the EDS P2U3 trailer prior to testing. Visual inspections of the EDS vessel, surroundings, and diagnostics were completed before and after each test event. This visual inspection included analyzing the seals, fittings, and interior surfaces of the EDS vessel and documenting any abnormalities or damages. Photographs were used to visually document vessel conditions and findings before and after each test event.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Synchrotron high energy X-ray diffraction study of microstructure evolution of severely cold drawn NiTi wire during annealing

Microstructure evolution of a cold-drawn NiTi shape memory alloy wire was investigated by means of in-situ synchrotron high-energy X-ray diffraction during continuous heating. The cold-drawn wire contained amorphous regions and nano-crystalline domains in its microstructure. Pair distribution function analysis revealed that the amorphous regions underwent structural relaxation via atomic rearrangement when heated above 100 °C. The nano-crystalline domains were found to exhibit a strong cold work induced lattice strain anisotropy having a preferential <111> fiber orientation along the wire axial direction. The lattice strain anisotropy systematically decreased upon heating above 200 °C, implying a structural recovery. A broad conical texture was formed in the wire specimen after crystallization similar in detail to the initial <111> texture axial orientation of the nano-crystalline domains produced by the severe cold wire drawing deformation.

crystallization↗

DOE OSTI2019

Solute-dislocation interaction in Mg from first-principles: and twinning dislocations with flexible boundary conditions

We relax the cores of $\langle c+a \rangle$ edge and screw dislocations, and $(10\overline{1}2)$ and $(10\overline{1}1)$ twinning dislocations in Mg using first-principles calculations with flexible boundary conditions (FBC). FBC couple highly distorted cores to a harmonic lattice through lattice Green functions (LGF), allowing dislocations to relax as isolated defects. Unlike previous FBC calculations using bulk LGFs, we use LGFs specifically for dislocated geometries. The optimized geometries provide sites for computing solute-dislocation interactions via direct substitution, as well as local strain and slip for input to computationally efficient geometric solute interaction models. The interactions are inputs for solid-solution strengthening models. We compute interactions between Al, Ca, Mn, Sn, and Zn and the dislocations, and predict corresponding changes in stress for dislocation motion. We compare the strengthening of each of these non-basal deformation modes to basal strengthening and examine implications for ductility in Mg alloys. Funding from DOE-USAMP Cooperative Agreement Number DE-EE0007756.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Experimental study of compaction localization in carbonate rock and constitutive modeling of mechanical anisotropy

Abstract Sedimentary rocks are inherently anisotropic and prone to strain localization. While the influence of rock anisotropy on the brittle/dilative regime has been studied extensively, its influence on the ductile/compactive regime is much less explored. This paper discusses the anisotropic behavior of a high‐porosity carbonate rock from central Europe (the Maastricht Tuffeau). A set of triaxial tests with concurrent x‐ray tomography has been performed at different confining pressures. The anisotropic characteristics of this rock have been investigated by testing samples cored at different inclinations of the bedding, thus revealing non‐negligible effects of the coring direction on yielding and compaction behavior. Specifically, samples cored perpendicular to bedding display higher strength and longer stages of post‐yielding deformation before manifesting re‐hardening. Despite such alterations of the inelastic response, Digital Image Correlation has revealed that the strain localization mode is independent of the coring direction, thus being primarily affected by the confinement level. To capture the observed interaction between material anisotropy and compaction behavior at the continuum‐scale, an elastoplastic constitutive law has been proposed. For this purpose, a set of tensorial bases has been introduced to replicate how the oriented rock fabric modulates the yielding and plastic flow characteristics of the material. The analyses show that the impact of the coring direction on yield function and plastic flow rule is fundamentally different, thus requiring the use of distinct projection strategies (a strategy here defined heterotopic mapping). The performance of the model, studied through parametric analyses and by calibrating the experimental results, illustrates the improved capability of the proposed constitutive approach when applied to strongly anisotropic porous rocks.

Shahin, Ghassan↗

DOE OSTI2019

Calculating the Symmetry Number of Flexible Sphere Clusters

We present a theoretical and computational framework to compute the symmetry number of a flexible sphere cluster in R 3 , using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit. We define the sticky symmetry group of the cluster as the set of permutations and inversions of the spheres which preserve adjacency and can be realized by continuous deformations of the cluster that do not change the set of contacts or cause particles to overlap. The symmetry number is the size of the sticky symmetry group. We introduce a numerical algorithm to compute the sticky symmetry group and symmetry number, and show it works well on several test cases. Furthermore, we show that once the sticky symmetry group has been calculated for indistinguishable spheres, the symmetry group for partially distinguishable spheres (those with nonidentical interactions) can be efficiently obtained without repeating the laborious parts of the computations. Finally, we use our algorithm to calculate the partition functions of every possible connected cluster of six identical sticky spheres, generating data that may be used to design interactions between spheres so they self-assemble into a desired structure.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Bifunctional nanoprecipitates strengthen and ductilize a medium-entropy alloy

Single-phase high- and medium-entropy alloys with face-centred cubic (fcc) structure can exhibit high tensile ductility and excellent toughness, but their room-temperature strengths are low. Dislocation obstacles such as grain boundaries, twin boundaries, solute atoms and precipitates can increase strength. However, with few exceptions, such obstacles tend to decrease ductility. Interestingly, precipitates can also hinder phase transformations. Here, using a model, precipitate-strengthened, Fe–Ni–Al–Ti medium-entropy alloy, we demonstrate a strategy that combines these dual functions in a single alloy. The nanoprecipitates in our alloy, in addition to providing conventional strengthening of the matrix, also modulate its transformation from fcc-austenite to body-centred cubic (bcc) martensite, constraining it to remain as metastable fcc after quenching through the transformation temperature. During subsequent tensile testing, the matrix progressively transforms to bcc-martensite, enabling substantial increases in strength, work hardening and ductility. This use of nanoprecipitates exploits synergies between precipitation strengthening and transformation-induced plasticity, resulting in simultaneous enhancement of tensile strength and uniform elongation. Further, our findings demonstrate how synergistic deformation mechanisms can be deliberately activated, exactly when needed, by altering precipitate characteristics (such as size, spacing, and so on), along with the chemical driving force for phase transformation, to optimize strength and ductility.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Nanocomposites based on thermoplastic elastomers with functional basis of nano titanium dioxide

Nanocomposites based on a thermoplastic elastomer (TPE) (low-density polyethylene (LDPE) and 1,2-polybutadiene in a ratio of 60/40) with functional titanium dioxide nanoparticles of different nature, TiO{sub 2}/TPE, have been prepared and investigated by a complex of methods (X-ray diffraction analysis using X-ray and synchrotron radiation beams, scanning electron microscopy, transmission electron microscopy, and X-ray energy-dispersive spectroscopy). The morphology of the composites is found to be somewhat different, depending on the TiO{sub 2} characteristics. It is revealed that nanocomposites with cellular or porous structures containing nano-TiO{sub 2} aggregates with a large specific surface and large sizes of crystallites and nanoparticles exhibit the best deformation‒strength and fatigue properties and stability to the effect of active media under conditions of ozone and vapor‒air aging.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Mechanism-Resolved PFM of Ferroionic and Ferroelectric Responses in Thickness-Gradient Hf 0.5 Zr 0.5 O 2 Libraries

Resolving growth mechanisms and thickness evolution of functional properties is one of the key tasks in materials discovery and optimization involving thin-film materials, traditionally requiring significant experimental budgets. Here we introduce the combination of thickness-gradient libraries and automated scanning probe microscopy as a systematic pathway to elucidate growth modes and disentangle ferroelectric and electrochemical contributions in ferroelectric thin films. As a model system, we explore the Hf 0.5 Zr 0.5 O 2 (HZO) gradient thin films grown on La x Sr 1-x MnO 3 (LSMO) bottom electrode thin films. Automated piezoresponse force microscopy, spectroscopy, and lithography reveals that irreversible topographic deformation arises from electrochemical activity at the LSMO surface, whereas reversible phase inversion in HZO reflects ferroelectric switching. Automated topography height-map scans are used to further quantify nucleation density, particle-size evolution, and roughness correlations across the thickness-gradient, demonstrating that improved plume stabilization during growth suppresses interfacial reactions and promotes dense, fine-grained HZO conducive to ferroelectric phase formation. This combined materials-engineering and automated-SPM framework establishes a platform for high-throughput, mechanism-resolved characterization of ferroionic and ferroelectric responses in complex oxide films.

FOS: Physical sciences↗

DOE OSTI2026

Can classical DEM simultaneously capture compressibility and flowability of milled biomass?

Accurate prediction of the rheological behavior of biomass is essential for the design and operation of hoppers, feeders, and storage systems in biorefineries. This study examines whether the classical, coarse-grained discrete element method (DEM) formulation can simultaneously reproduce the compressibility and flowability of milled herbaceous biomass, using Miscanthus × giganteus as a representative material. The model represents particles as rigid spheres interacting through Hertz-Mindlin elastic-frictional contacts augmented with an area-dependent cohesion term. Laboratory cyclic compression and wedge-shaped hopper discharge experiments were used as calibration benchmarks. Although the model can independently reproduce each behavior by appropriately tuning particle Young's modulus E and cohesion energy density k, an extensive parametric investigation comprising more than 600 simulations reveals that the optimal parameter regions for compression and hopper flow are distinct and non-overlapping in (E, k) space. Surrogate surface analysis further shows that the corresponding objective-function valleys exhibit similar trends but are approximately parallel and spatially offset, precluding a unified calibration within the explored domain. Sensitivity analysis indicates that compressibility is governed predominantly by stiffness and cohesion, whereas the slope of the mass flow rate-opening relation in hopper discharge is primarily controlled by tangential friction. Extensions incorporating particle size distribution and clumped-sphere representations do not eliminate the incompatibility. These results systematically reveal, for the first time, the structural limitation of simplified DEM formulations in representing biomass rheological behavior, underscoring the necessity for models incorporating additional physical mechanisms, such as particle deformability or enhanced interlocking, to achieve unified predictive capability for biomass handling behavior.

09 BIOMASS FUELS↗

DOE OSTI2018

Dynamic recrystallization kinetics and microstructure evolution of an AZ91D magnesium alloy during hot compression

Highlights: • DRX kinetic model is developed for the aged AZ91D magnesium alloy. • The DRX behavior in different strained regions was investigated. • Four morphologies of the second phase were proposed during the hot compression tests. • The nucleation mechanisms of the DRX grains were clarified. - Abstract: The flow behavior of as-cast AZ91D magnesium alloy was evaluated by isothermal compression tests within the temperatures of 220 °C, 260 °C, 300 °C, 340 °C, and 380 °C, and the strain rates of 0.001, 0.01, 0.1, 1 and 10s{sup −1}. Based on the stress-strain curve and hyperbolic sine function, the thermal activation energy and the strain rate sensitivity of the material were determined to be 142.2726 kJ·mol{sup −1} and 0.142, respectively. The S type evolution of the dynamic recrystallization with the increasing strain that dynamic recrystallization (DRX) model obtained from stress and strain data. There was a good consistency between the proposed DRX kinetics model and microstructure observation results. Combining isothermal compression specimens with finite element and scanning electron microscopy (SEM) analysis indicated that the sample can be divided into rarely recrystallized region, partially recrystallized region and completely recrystallized region, which falls within the dense deformation zone, free deformation zone and severe deformation zone, respectively. The different forms of the β-Mg{sub 17}Al{sub 12} phase induced by compression tests were confirmed by SEM. Nucleation mechanisms of the DRX were discussed with reference to the transmission electron microscope (TEM) analysis results.

36 MATERIALS SCIENCE↗

DOE OSTI2025

In-situ L-TEM observations of dynamics of nanometric skyrmions and antiskyrmions

Nanometer-scale magnetic skyrmions and antiskyrmions exhibit unique dynamical behaviors in response to external stimuli, which are critical for their applications in low-power-consumption spintronic devices. This review discusses recent advancements in in-situ Lorentz transmission electron microscopy (L-TEM) observations of skyrmion and antiskyrmion dynamics, and demonstrates the manipulation and evolution of these textures in various magnetic materials under electric, magnetic, and thermal stimuli. Specifically, the motion tracking of single skyrmions and their clusters, and the deformation and transformation of skyrmions has been demonstrated in chiral helimagnets FeGe, Co 9 Zn 9 Mn 2 , and Co 10 Zn 10 with precise application of electric currents. Skyrmions can undergo dynamic transitions in current-driven skyrmion motions, from pinned states to linear flows, and even exhibit deformation into elliptical shapes, underscoring their topological robustness and dynamic flexibility. In addition, the manipulation of single antiskyrmions and antiskyrmion-lattice phases in (Fe 0.63 Ni 0.3 Pd 0.07 ) 3 P with S 4 symmetry is discussed, highlighting their high mobility and unique sliding capabilities along stripe domains at room temperature, facilitated by nanosecond pulsed electric currents. Finally, the temperature gradient-driven motion and topological transformation of elliptical skyrmions and antiskyrmions in this same material are investigated. In conclusion, the comprehensive insights gained from the L-TEM imaging technique are pivotal in advancing the design and functionality of next-generation skyrmion/antiskyrmion-based spintronic devices.

(Anti)skyrmion↗

DOE OSTI2025

Evidence for triaxial shape coexistence in 74 Ge

The deformation properties of the low-lying states in 74 Ge have been investigated using multistep Coulomb excitation. The measurements were carried out with the advanced 𝛾-ray tracking array, GRETINA, and the CHICO2 particle detector. A comprehensive set of 𝐸⁢2 transition and diagonal matrix elements was deduced following an analysis with the semiclassical coupled-channels code GOSIA. The data were compared with results of calculations carried out within the framework of the generalized triaxial rotor model as well as with the configuration interaction shell model and the symmetric rotor model. Results from calculations with covariant density functional theory were used to construct a five-dimensional collective Hamiltonian for further comparisons with the data. Collectively, the calculations provide an accurate reproduction of the experimental matrix elements and further support an understanding in terms of the coexistence of two axially asymmetric shapes. In conclusion, this leads to an overall interpretation of the underlying structure of 74 Ge requiring triaxiality, as is also the case in the neighboring even-mass Ge isotopes.

59 ≤ A ≤ 89↗