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DOE OSTI2022

Understanding Heterogeneities in Quantum Materials

Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. Finally, the understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Emerging contact force heterogeneity in ordered soft granular media

Under external perturbations, inter-particle forces in disordered granular media are well known to form a heterogeneous distribution with filamentary patterns. Better understanding these forces and the distribution is important for predicting the collective behavior of granular media, the media second only to water as the most manipulated material in global industry. However, studies in this regard so far have been largely confined to granular media exhibiting only geometric heterogeneity, leaving the dimension of mechanical heterogeneity a rather uncharted area. In this work, through a FEM contact mechanics model, we show that a heterogeneous inter-particle force distribution can also emerge from the dimension of mechanical heterogeneity alone. Specifically, we numerically study inter-particle forces in packing of mechanically heterogeneous disks arranged over either a square or a hexagonal lattice and under quasi-static isotropic compression. Our results show that, at the system scale, a hexagonal packing exhibit a more heterogeneous inter-particle force distribution than a square packing does; At the particle scale, for both packing lattices, preliminary analysis shows the consistent coexistence of outliers (i.e., softer disks sustaining larger forces while stiffer disks sustaining smaller forces) in comparison to their homogeneous counterparts, which implies the existence of nonlocal effect. Further analysis on the portion of outliers and on spatial contact force correlations suggest that the hexagonal packing shows more pronounced nonlocal effect over the square packing under small mechanical heterogeneity. However, such trend is reversed when assemblies becomes more mechanically heterogeneous. Lastly, we confirm that, in the absence of particle reorganization events, contact friction merely plays the role of packing stabilization while its variation has little effect on inter-particle forces and their distribution.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Inferring transmission heterogeneity using virus genealogies: estimation and targeted prevention

Spread of HIV typically involves uneven transmission patterns where some individuals spread to a large number of individuals while others to only a few or none. Such transmission heterogeneity can impact how fast and how much an epidemic spreads. Further, more efficient interventions may be achieved by taking such transmission heterogeneity into account. To address these issues, we developed two phylogenetic methods based on virus sequence data: 1) to generally detect if significant transmission heterogeneity is present, and 2) to pinpoint where in a phylogeny high-level spread is occurring. We derive inference procedures to estimate model parameters, including the amount of transmission heterogeneity, in a sampled epidemic. We show that it is possible to detect transmission heterogeneity under a wide range of simulated situations, including incomplete sampling, varying levels of heterogeneity, and including within-host genetic diversity. When evaluating real HIV-1 data from different epidemic scenarios, we found a lower level of transmission heterogeneity in slowly spreading situations and a higher level of heterogeneity in data that included a rapid outbreak, while R0 and Sackin’s index (overall tree shape statistic) were similar in the two scenarios, suggesting that our new method is able to detect transmission heterogeneity in real data. We then show by simulations that targeted prevention, where we pinpoint high-level spread using a coalescence measurement, is efficient when sequence data are collected in an ongoing surveillance system. Such phylogeny-guided prevention is efficient under both single-step contact tracing as well as iterative contact tracing as compared to random intervention.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Heterogeneities at multiple length scales in 2D layered materials: From localized defects and dopants to mesoscopic heterostructures

Two-dimensional (2D) materials hold great promise for applications in optoelectronics, quantum information science, and energy conversion due to their remarkable properties imbued by their physical characteristics. Although heterogeneities in their intrinsic structure are the major challenges limiting their synthesis and predictable properties, they also provide a pathway to controllably tune the properties and broaden the potential of 2D materials. Heterogeneities that can be tailored, including defects, dopants, strain, edges, and layer stackings offer transformative opportunities in heterogeneous 2D materials through the introduction of novel properties for technological applications. This article provides a review of recent progress in studying heterogeneities in 2D materials. The review uses examples from our work to develop a strategy to understand the heterogeneities across multiple length scales to link the effect of heterogeneity at the nanoscale with the macroscale properties of 2D materials. We describe specific types of heterogeneities and explore novel synthesis and processing methods for their controlled production with example of the potential impact and applications enabled by their intriguing properties. Finally, we provide a perspective on how to extend the range of tunable properties through further engineering the heterogeneities in 2D materials.

2D materials↗

DOE OSTI2023

HetArch: Heterogeneous Microarchitectures for Superconducting Quantum Systems

Noisy Intermediate-Scale Quantum Computing (NISQ) has dominated headlines in recent years, with the longer-term vision of Fault-Tolerant Quantum Computation (FTQC) offering significant potential but at currently intractable resource costs and quantum error correction (QEC) overheads. For problems of interest, FTQC will require millions of physical qubits with long coherence times, high-fidelity gates, and compact sizes to surpass classical systems. Just as heterogeneous specialization has offered scaling benefits in classical computing, it is likewise gaining interest in FTQC. However, systematic use of heterogeneity in either hardware or software elements of FTQC systems remains a serious challenge due to the vast design space and the variable physical constraints. This paper meets the challenge of making heterogeneous FTQC design practical by introducing HetArch, a toolbox for designing heterogeneous quantum systems, and using it to explore heterogeneous design scenarios. Using a hierarchical approach, we successively break quantum algorithms into smaller operations (akin to classical application kernels), thus greatly simplifying the design space and resulting tradeoffs. Specializing to superconducting systems, we then design optimized heterogeneous hardware composed of varied superconducting devices, abstracting physical constraints into design rules that enable devices to be assembled into standard cells optimized for specific operations, which, in turn, form heterogeneous modules optimized for quantum subroutines. Finally, we provide a heterogeneous design space exploration framework which reduces the simulation burden by a factor of 10^4 or more and allows us to characterize optimal design points. We use these techniques to design superconducting quantum modules for entanglement distillation, error correction, and code teleportation, reducing error rates by 2.6×, 10.7×, and 3.4× compared to homogeneous systems.

Quantum Computing, Quantum Physics, Computer Archi↗

DOE OSTI2022

Chapter 3: Nanostructured Iron Oxide Hybrid Composites as Heterogeneous Fenton-Like Catalyst for Remediation of Persistent Organic Pollutants

In water purification research and technologies, heterogeneous Fenton catalysts are evolving as an excellent material recently. A summary of present research on heterogeneous Fenton/Fenton-like processes is essential for developing novel and high-efficiency organic wastewater treatment methods. In this chapter, we discussed the basics of Fenton reactions taking the example of iron oxides and their different composites, such as bimetallic composites, composites with carbon compounds, and Fe metal-organic frameworks (MOFs). The important operating parameters (solution pH, H 2 O 2 dosage, amount of catalyst used, and reaction temperature) in heterogeneous Fenton-like reactions are discussed. Strategies to increase the rate and activities of heterogeneous Fenton catalysts by using energy sources are presented. The mechanistic aspects of heterogeneous Fenton processes and reusability of catalysts along with their application in real wastewater plants are summarized and discussed. Finally, we concluded with the scope and future prospects of heterogeneous Fenton catalysis research to motivate the readers to construct novel and efficient heterogeneous Fenton/Fenton-like systems for industrial applications.

carbon composites↗

DOE OSTI2025

Informing field-scale CO 2 storage simulations with sandbox experiments: The effect of small-scale heterogeneities

Small-scale heterogeneities can significantly affect the fate of the CO 2 plume and trapping during CO 2 migration. We conducted geologic carbon storage field-scale simulations to investigate the impact of small-scale heterogeneities on plume dynamics and trapping performance. Small-scale heterogeneities have been shown to increase the amount of trapped CO 2 during buoyancy-driven flow. The trapped CO 2 saturation is validated by previous sandbox experimental work during buoyancy-driven flow in realistic heterogeneous domains and is implemented through the critical CO 2 saturation parameter (i.e., the first non-zero value in the drainage CO 2 relative permeability curve). Depending on the type and degree of heterogeneity, various critical CO 2 saturation values are exhibited. Furthermore, we investigated the effect of small-scale heterogeneities when multiple capillary pressure models are employed. This study demonstrates that an increase in critical CO 2 saturation reduces the CO 2 plume size and lateral extent, accompanying an increase in residual trapping and a decrease in solubility trapping. Lastly, we show that independent of the capillary pressure model used, an increase in critical saturation leads to similar CO 2 plume dynamics distribution and trapping performance. These results emphasize the importance of quantifying the effect of small-scale heterogeneity as they affect the large-scale behavior of the CO 2 plume.

58 GEOSCIENCES↗

DOE OSTI2022

The Effect of Surface Heating Heterogeneity on Boundary Layer Height and Its Dependence on Background Wind Speed

The planetary boundary layer height (PBLH) is a fundamental variable of the planetary boundary layer (PBL). The effect of surface heterogeneity is challenging in the PBL parameterization for numerical weather and climate models. Here we use large eddy simulation data to investigate the impact of surface heating heterogeneity on the PBLH spatial variations and mean values over a domain of typical mesoscale model grid size. It is found that this impact depends on background wind condition. Variance decomposition and Fourier spectra both reveal that for the fully developed sheared convective PBL, surface heterogeneity contributes little to the spatial variation of PBLH, except for the case with heterogeneity scale of 14.4 km. This suggests that surface heterogeneity with length scales less than ~10 km, which is typical for mesoscale modeling, does not induce significant subgrid spatial variation of PBLH. The domain-averaged PBLH is found to generally increase as surface heterogeneity scale decreases, until reaching the scale on the order of PBLH. The findings can be used to inform the parameterization development of PBL processes over heterogeneous surface.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Investigation of Ring-heterogeneous Geometry Approximation for Efficient and Practical SFR Analysis

A novel geometry approximation scheme named ring-heterogeneous approximation for intermediate resolution multiphysics analysis of SFRs is presented. This approach particularly targets neutronics coupled with thermo-mechanics feedback, which dominate the passive safety of SFR designs. The ring-heterogeneous approximation casts an array of pins into volume-preserving bands of materials that constitute the pins. It allows to efficiently simulate SFRs with an unstructured mesh and also to explicitly consider the deformation of each material by retaining their heterogeneity. Verification results with single assembly and core problems of the ABTR benchmark demonstrated that the ring-heterogeneous approximation is a reasonable approximation for SFRs. For a 2D full core problem, the ring-heterogeneous approximation significantly reduced the number of elements by at least a factor of 70 from a fully-heterogeneous mesh while almost exactly preserving the reference fully-heterogeneous solutions with the RMS error of only 0.02% in the ring-wise fission reaction rate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Near‐Surface Hydrology and Soil Properties Drive Heterogeneity in Permafrost Distribution, Vegetation Dynamics, and Carbon Cycling in a Sub‐Arctic Watershed

Abstract Discontinuous permafrost environments exhibit strong spatial heterogeneity at scales too small to be driven by weather forcing or captured by Earth System Models. Here we analyze effects of observed spatial heterogeneity in soil and vegetation properties, hydrology, and thermal dynamics on ecosystem carbon dynamics in a watershed on the Seward Peninsula in Alaska. We apply a Morris global sensitivity analysis to a process‐rich, successfully tested terrestrial ecosystem model (TEM), ecosys , varying soil properties, boundary conditions, and weather forcing. We show that landscape heterogeneity strongly impacts soil temperatures and vegetation composition. Snow depth, O‐horizon thickness, and near‐surface water content, which vary at scales of O(m), control the soil thermal regime more than an air temperature gradient corresponding to a 140 km north–south distance. High shrub productivity is simulated only in talik (perennially unfrozen) soils with high nitrogen availability. Through these effects on plant and permafrost dynamics, landscape heterogeneity impacts ecosystem productivity. Simulations with near‐surface taliks have higher microbial respiration (by 78.0 gC m −2 yr −1 ) and higher net primary productivity (by 104.9 gC m −2 yr −1 ) compared to runs with near‐surface permafrost, and simulations with high shrub productivity have outlying values of net carbon uptake. We explored the prediction uncertainty associated with ignoring observed landscape heterogeneity, and found that watershed net carbon uptake is 60% larger when heterogeneity is accounted for. Our results highlight the complexity inherent in discontinuous permafrost environments and demonstrate that missing representation of subgrid heterogeneity in TEMs could bias predictions of high‐latitude carbon budget.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

IRIS-MEMFLOW: Data Flow-Enabled Portable Memory Orchestration in IRIS Runtime for Diverse Heterogeneity

Task-based programming models and execution paradigms provide a means to decompose a computation by expressing it as a graph in which each node represents a specific computation operating on memory objects and the edges define the dependencies in the execution flow. In this execution model, independent nodes in the graph can be executed concurrently in different computing devices, making it suitable for heterogeneous systems in which computing devices with different architectures coexist. However, careful memory orchestration across heterogeneous devices is needed because copies of the same memory object may reside in multiple devices during execution. Manually ensuring such an orchestration is quite challenging. Not only must an application developer guard against race conditions, but they must also optimize data movement between the host and devices because unnecessary data movement significantly impacts performance. To mitigate these challenges, we enhance the IRIS heterogeneous runtime and introduce IRIS-MEMFLOW–a data flow–enabled portable memory abstraction for seamlessly orchestrating memory in diverse heterogeneous computing environments. By using data-flow analysis, IRIS-MEMFLOW guards against race conditions while multiple heterogeneous devices access memory objects. IRIS-MEMFLOW also optimizes data movement between the host and devices without manual intervention. As a result, IRIS provides improved programming productivity, performance, and portability for multidevice heterogeneous executions in high-performance computing and cloud systems that run diverse architectures from different vendors. The efficacy of IRIS-MEMFLOW is evaluated through experiments that show its capability in terms of programming productivity, multidevice heterogeneity, portability, and low overhead versus the state of the art.

Monil, M. A. H. [ORNL] (ORCID:0000000334194037)↗

DOE OSTI2023

Tiling Framework for Heterogeneous Computing of Matrix based Tiled Algorithms

Tiling matrix operations can improve the load balancing and performance of applications on heterogeneous computing resources. Writing a tile-based algorithm for each operation with a traditional, hand-tuned tiling approach that uses for loops in C/C++ is cumbersome and error prone. Moreover, it must enable and support the heterogeneous memory management of data objects and also explore architecture-supported, native, tiled-data transfer APIs instead of copying the tiled data to continuous memory before the data transfer. The tiling framework provides a tiled data structure for heterogeneous memory mapping and parameterization to a heterogeneous task specification API. We have integrated our tiled framework into MatRIS (Math kernels library using IRIS). IRIS is a heterogeneous run-time framework with a heterogeneous programming model, memory model, and task execution model. Experiments reveal that the tiled framework for BLAS operations has improved the programmability of tiled BLAS and improved performance by ~20% when compared against the traditional method that copies the data to continuous memory locations for heterogeneous computing.

Miniskar, Narasinga Rao↗

DOE OSTI2025

IRIS-MASH: Efficient Multi-device Asynchronous Multi-Stream Heterogeneous Computing

In the rapidly evolving field of high-performance computing (HPC), effectively leveraging heterogeneous devices through asynchronous task programming is paramount. This paper presents a robust asynchronous task programming model tailored for a multi-device, multi-stream execution environment that incorporates a diverse array of heterogeneous computing units, including GPUs from various vendors and other accelerators. Current state-of-the-art task programming models provide methodologies to support asynchronous task executions, but they typically handle homogeneous devices using native programming languages, while support for heterogeneous devices is limited to frameworks like OpenCL. This gap presents significant challenges in abstracting heterogeneous devices to harness their true asynchronous capabilities effectively using their native programming languages. By implementing asynchronous task execution, our model significantly boosts the performance of tiled algorithm task graphs through overlapping data transfers with computation and enabling the simultaneous execution of multiple kernels. We integrate this approach into a heterogeneous Intelligent Runtime System (IRIS) and assess its performance using a suite of tiled algorithm benchmarks from the heterogeneous math kernels library (MatRIS) based on IRIS. Experimental results demonstrate a performance improvement ranging from 1.6 × to 2 × over IRIS without asynchronous support, and a notable 22% performance enhancement compared to established runtime systems such as StarPU and PaRSEC. This approach significantly improves computation efficiency of HPC workflows and provides a solid base for future exploration and development in the area of asynchronous task programming in heterogeneous systems.

Miniskar, Narasinga Rao [ORNL] (ORCID:000000018259↗

DOE OSTI2025

Shear-Wave Radiation Patterns from Explosive and Earthquake Sources in Scattering, Heterogeneous Media

Distinguishing whether a seismic event is an earthquake or an explosion is a core problem in explosion monitoring. For simplistic models, earthquakes produce a predictable S-wavefield based on their radiation pattern, while an explosion produces no S-wavefield. However, observations from nuclear tests show that explosions can produce significant S-wave energy on both horizontal components. We perform numerical experiments using SPECFEM to constrain when an S-wavefield generated from an explosion might differ from one produced by an earthquake. We generate the S-wavefield for our explosions by placing the source location within a small region consisting of large velocity heterogeneities. For the 2D cases investigated here, a crucial condition is that the size of the region of heterogeneities must be much smaller (approximately 1/12th) than the minimum wavelength of the wavefield for our simulation setups. We investigate both isotropic heterogeneities and anisotropic heterogeneities. Initial results demonstrate that the heterogeneous region lowers the P/S amplitude ratios of an explosion. The presence of strong anisotropic heterogeneities near the source can also produce an S-wavefield with similar amplitudes to the P-wavefield. Lastly, we show that S-wave polarization angles vary as a function of azimuth and distance for explosive sources in the presence of small-scale heterogeneities.

58 GEOSCIENCES↗

DOE OSTI2022

Representing surface heterogeneity in land–atmosphere coupling in E3SMv1 single-column model over ARM SGP during summertime

Abstract. The Earth's land surface features spatial and temporal heterogeneity over a wide range of scales below those resolved by current Earth system models (ESMs). State-of-the-art land and atmosphere models employ parameterizations to represent their subgrid heterogeneity, but the land–atmosphere coupling in ESMs typically operates on the grid scale. Communicating the information on the land surface heterogeneity with the overlying atmospheric boundary layer (ABL) remains a challenge in modeling land–atmosphere interactions. In order to account for the subgrid-scale heterogeneity in land–atmosphere coupling, we implement a new coupling scheme in the Energy Exascale Earth system model version 1 (E3SMv1) that uses adjusted surface variances and covariance of potential temperature and specific water content as the lower boundary condition for the atmosphere model. The new lower boundary condition accounts for both the variability of individual subgrid land surface patches and the inter-patch variability. The E3SMv1 single-column model (SCM) simulations over the Atmospheric Radiation Measurement (ARM) Southern Great Plain (SGP) site were performed to assess the impacts. We find that the new coupling parameterization increases the magnitude and diurnal cycle of the temperature variance and humidity variance in the lower ABL on non-precipitating days. The impacts are primarily attributed to subgrid inter-patch variability rather than the variability of individual patches. These effects extend vertically from the surface to several levels in the lower ABL on clear days. We also find that accounting for surface heterogeneity increases low cloud cover and liquid water path (LWP). These cloud changes are associated with the change in cloud regime indicated by the skewness of the probability density function (PDF) of the subgrid vertical velocity. In precipitating days, the inter-patch variability reduces significantly so that the impact of accounting for surface heterogeneity vanishes. These results highlight the importance of accounting for subgrid heterogeneity in land–atmosphere coupling in next-generation ESMs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Exploring wave propagation in heterogeneous metastructures using the relaxed micromorphic model

Metamaterials are artificial structures that can manipulate and control sound waves in ways not possible with conventional materials. While much effort has been undertaken to widen the bandgaps produced by these materials through design of heterogeneities within unit cells, comparatively little work has considered the effect of engineering heterogeneities at the structural scale by combining different types of unit cells. In this paper, we use the relaxed micromorphic model to study wave propagation in heterogeneous metastructures composed of different unit cells. We first establish the efficacy of the relaxed micromorphic model for capturing the salient characteristics of dispersive wave propagation through comparisons with direct numerical simulations for two classes of metamaterial unit cells: namely phononic crystals and locally resonant metamaterials. We then use this model to demonstrate how spatially arranging multiple unit cells into metastructures can lead to tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping. In the case of the broadband wave attenuation application, we show that by building layered metastructures from different metamaterial unit cells, we can slow down or stop wave packets in an enlarged frequency range, while letting other frequencies through. In the case of the rainbow-trapping application, we show that spatial arrangements of different unit cells can be designed to progressively slow down and eventually stop waves with different frequencies at different spatial locations. Finally, in the case of the pulse-shaping application, our results show that heterogeneous metastructures can be designed to tailor the spatial profile of a propagating wave packet. Collectively, these results show the versatility of the relaxed micromorphic model for effectively and accurately simulating wave propagation in heterogeneous metastructures, and how this model can be used to design heterogeneous metastructures with tailored wave propagation functionalities.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2026

Process control-enabled mitigation of microstructural and plastic heterogeneities in additively manufactured Grade 91 steel

Synergizing wire arc-directed energy deposition (WA-DED) additive manufacturing (AM) with particle-strengthened creep strength-enhanced ferritic (CSEF) steels enables fabrication and repair of critical power-plant components. Investigations focused on fusion-welded particle-strengthened CSEF steels, such as Grade 91 steel, have linked microstructurally heterogeneous regions—forming due to heat affected zones (HAZ)—with premature failure during elevated temperature service. Fusion-based AM, including WA-DED, likewise generates microstructurally and plastically heterogeneous regions due to spatiotemporally varying thermokinetics during deposition. However, works investigating such microstructural heterogeneities, their implications for mechanical behavior, and strategies to mitigate their formation remain scarce. This work identifies microstructurally and plastically heterogeneous regions within the WA-DED-processed Grade 91 steel. Spatial microhardness variations in the as-fabricated specimen correlate with the variation in the attributes of grain, martensitic microstructure, and precipitates across the fusion zone and HAZ. Digital image correlation-enabled tensile tests performed at 500 °C revealed pronounced deformation localization and a wave-like strain distribution, with wavelength close to the melt pool depth, indicating susceptibility of the as-fabricated components to premature creep failure. Such heterogeneity in microstructural and mechanical behavior was attributed to recurring solid-state phase transformations. Subsequently, an interlayer temperature control strategy was implemented, wherein maintaining interlayer temperature above the martensitic start temperature mitigated the heterogeneous microstructural and plastic response in the as-fabricated condition. Findings open pathways to achieving deformation-localization- and creep-resistant microstructures in WA-DED fabricated particle-strengthened CSEF steel components, reducing reliance on post-welding heat treatments—conventionally required to enhance creep resistance—and enabling on-demand, short lead-time fabrication of next-generation power-plant components.

Heat affected zones↗

DOE OSTI2022

Probing the Influence of Multiscale Heterogeneity on Effective Properties of Graphite Electrodes

Graphite electrodes in the lithium-ion battery exhibit various particle shapes, including spherical and platelet morphologies, which influence structural and electrochemical characteristics. It is well established that porous structures exhibit spatial heterogeneity, and the particle morphology can influence transport properties. The impact of the particle morphology on the heterogeneity and anisotropy of geometric and transport properties has not been previously studied. Herein, this study characterizes the spatial heterogeneities of 18 graphite electrodes at multiple length scales by calculating and comparing the structural anisotropy, geometric quantities, and transport properties (pore-scale tortuosity and electrical conductivity). We found that the particle morphology and structural anisotropy play an integral role in determining the spatial heterogeneity of directional tortuosity and its dependency on pore-scale heterogeneity. Our analysis reveals that the magnitude of in-plane and through-plane tortuosity difference influences the multiscale heterogeneity in graphite electrodes.

25 ENERGY STORAGE↗