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DOE OSTI2023

Diffuse Reflectance Spectroscopy and Principal Component Analysis to Retrospectively Determine Production History of Plutonium Dioxide

Diffuse reflectance spectroscopy measurements in the shortwave infrared (930–1600 nm) spectral region were acquired for Pu 2 (C 2 O 4 ) 3 •9H 2 O and its thermal decomposition product, PuO 2 . We analyzed a total of eight PuO 2 samples that were produced at different calcination temperatures (300, 350, 450, 525, 600, 675, 750, and 900 °C). Our goal was to identify spectroscopic fingerprints that could be used to gain retrospective information regarding the production parameters of these important nuclear compounds. The diffuse reflectance spectrum of Pu 2 (C 2 O 4 ) 3 •9H 2 O features several broad bands that currently preclude detailed analysis. However, all PuO 2 samples produced relatively sharp spectral features that got sharper and more intense for samples that were produced at higher calcination temperatures. The electronic band observed at 1433 nm in the diffuse reflectance spectra of PuO 2 was found to be a sensitive indicator of crystallinity; a result that is corroborated by ancillary Raman spectroscopy measurements. Principal component analysis of diffuse reflectance spectra was able to clearly rank and categorize PuO 2 samples based on the calcination temperature that was employed during their production. Thus, we show herein that important retrospective information pertaining to the process history of PuO 2 can be gained through the relatively simplistic combination of diffuse reflectance spectroscopy and principal component analysis. This discovery presents a new method for determining the provenance and process history of PuO 2 and should have an impact in the fields of nuclear forensics and nuclear nonproliferation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

DRIFT: Diffusivity Regulation of Isotopes by nanoconFinementT

Spontaneous isotope fractionation has been reported under nanoconfinement conditions in naturally occurring systems, but the origin of this phenomena is currently unknown. Two existing hypotheses have been proposed, one based on changes in the solvation environment of the isotopes that reduces the non-mass dependent hydrodynamics contribution to diffusion. The other is that isotopes have mass-dependent surface adsorption, varying their total diffusion through nanoconfined channels. To investigate these hypotheses, benchtop experiments, nuclear magnetic resonance (NMR) spectroscopy, and molecule scale modeling were applied. Classical molecular dynamics simulations identified that the Na + and Cl - hydration shells across the three different salt solutions ( 22 Na 35 Cl, 23 Na 35 Cl, 24 Na 35 Cl) did not vary as a function of the Na + isotope, but that there was a significant pore size effect, with larger hydration shells at larger pore sizes. Additionally, while total adsorption times did not vary as a function of the Na + isotope or pore size, the free ion concentration, or those adsorbed on the surface for <5% of the simulation time did exhibit isotope dependence. Experimentally, challenges occurred developing a repeatable experiment, but NMR characterization of water diffusion rates through ordered alumina membranes was able to identify the existence of two distinct water environments associated with water inside and outside the pore. Further NMR studies could be used to confirm variation in hydration shells and diffusion rates of dissolved ions in water. Ultimately, mass-dependence adsorption is a primary driver of variations in isotope diffusion rates, rather than variation in hydration shells that occur under nanoconfinement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Model Parameter Development for Complex Materials: Species-Specific Diffusion Barriers in 316 Stainless Steel from Systematic DFT Calculations

Vacancy-mediated diffusion barriers in 316 stainless steel have been systematically calculated using density functional theory to provide essential parameters for mesoscale microstructure evolution models. A statistical sampling approach employing 210 nudged elastic band calculations across multiple special quasi-random structures captures the effects of local chemical environments in this concentrated alloy. The computational methodology addresses challenges specific to chemically disordered systems, including proper magnetic treatment throughout multi-step calculations and validation against experimental structural properties. The calculated activation barriers reveal clear species-dependent diffusion behavior with the hierarchy Ni >> Fe ˜ Cr >> Mo. Nickel exhibits the highest barriers (0.74–1.31 eV, mean 1.045 eV), confirming its role as the slowest-diffusing major component. Iron and chromium show similar moderate barriers averaging 0.587 eV and 0.522 eV, respectively. Remarkably, molybdenum demonstrates exceptionally low barriers (0.12–0.28 eV, mean 0.194 eV), suggesting much higher mobility than previously recognized and potentially significant implications for precipitation kinetics and microstructure evolution. The barrier ranges remain consistent across different 316 SS compositions, supporting parameter transferability for modeling applications. The overall mean barrier of 0.64 eV provides a practical approximation for phase field simulations, while species-specific values enable detailed treatments of diffusion-controlled processes. This systematic approach establishes a validated framework for generating diffusion parameters in other concentrated alloys where experimental data are limited, while providing the first systematic set of species-specific barriers for predictive modeling of 316 stainless steel microstructure evolution.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Atomic Diffusivities of Yttrium, Titanium and Oxygen Calculated by Ab Initio Molecular Dynamics in Molten 316L Oxide-Dispersion-Strengthened Steel Fabricated via Additive Manufacturing

Oxide-dispersion-strengthened (ODS) steels have long been viewed as a prime solution for harsh environments. However, conventional manufacturing of ODS steels limits the final product geometry, is difficult to scale up to large components, and is expensive due to multiple highly involved, solid-state processing steps required. Additive manufacturing (AM) can directly incorporate dispersion elements (e.g., Y, Ti and O) during component fabrication, thus bypassing the need for an ODS steel supply chain, the scale-up challenges of powder processing routes, the buoyancy challenges associated with casting ODS steels, and the joining issues for net-shape component fabrication. In the AM process, the diffusion of the dispersion elements in the molten steel plays a key role in the precipitation of the oxide particles, thereby influencing the microstructure, thermal stability and high-temperature mechanical properties of the resulting ODS steels. In this work, the atomic diffusivities of Y, Ti, and O in molten 316L stainless steel (SS) as functions of temperature are determined by ab initio molecular dynamics simulations. The latest Vienna Ab initio Simulation Package (VASP) package that incorporates an on-the-fly machine learning force field for accelerated computation is used. At a constant temperature, the time-dependent coordinates of the target atoms in the molten 316L SS were analyzed in the form of mean square displacement in order to obtain diffusivity. The values of the diffusivity at multiple temperatures are then fitted to the Arrhenius form to determine the activation energy and the pre-exponential factor. Given the challenges in experimental measurement of atomic diffusivity at such high temperatures and correspondingly the lack of experimental data, this study provides important physical parameters for future modeling of the oxide precipitation kinetics during AM process.

Chemistry↗

DOE OSTI2020

Diffusion coefficients in the envelopes of white dwarfs

The diffusion of elements is a key process in understanding the unusual surface composition of white dwarfs and their spectral evolution. The diffusion coefficients of Paquette et al. have been widely used to model diffusion in white dwarfs. In this work, we perform new calculations of the coefficients of interdiffusion and ionic thermal diffusion with (1) a more advanced model that uses a recent modification of the calculation of the collision integrals that is more suitable for the partially ionized, partially degenerate, and moderately coupled plasma and (2) classical molecular dynamics. The coefficients are evaluated for silicon and calcium in white dwarf envelopes of hydrogen and helium. A comparison of our results with Paquette et al. shows that the latter systematically underestimates the coefficient of interdiffusion yet provides reliable estimates for the relatively weakly coupled plasmas found in nearly all types of stars, as well as in white dwarfs with hydrogen envelopes. In white dwarfs with cool helium envelopes (${T}_{\mathrm{eff}}$ < 15,000 K), the difference grows to more than a factor of two. We also explored the effect of the ionization model used to determine the charges of the ions and found that it can be a substantial source of discrepancy between different calculations. Finally, we consider the relative diffusion timescales of Si and Ca in the context of the pollution of white dwarf photospheres by accreted planetesimals and find factor of ≳3 differences between calculations based on Paquette et al. and our model.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series

Abstract. Improving the quantification of soil thermal and physical properties is key to achieving a better understanding and prediction of soil hydro-biogeochemical processes and their responses to changes in atmospheric forcing. Obtaining such information at numerous locations and/or over time with conventional soil sampling is challenging. The increasing availability of low-cost, vertically resolved temperature sensor arrays offers promise for improving the estimation of soil thermal properties from temperature time series, and the possible indirect estimation of physical properties. Still, the reliability and limitations of such an approach need to be assessed. In the present study, we develop a parameter estimation approach based on a combination of thermal modeling, sliding time windows, Bayesian inference, and Markov chain Monte Carlo simulation to estimate thermal diffusivity and its uncertainty over time, at numerous locations and at an unprecedented vertical spatial resolution (i.e., down to 5 to 10 cm vertical resolution) from soil temperature time series. We provide the necessary framework to assess under which environmental conditions (soil temperature gradient, fluctuations, and trend), temperature sensor characteristics (bias and level of noise), and deployment geometries (sensor number and position) soil thermal diffusivity can be reliably inferred. We validate the method with synthetic experiments and field studies. The synthetic experiments show that in the presence of median diurnal fluctuations ≥ 1.5 ∘C at 5 cm below the ground surface, temperature gradients > 2 ∘C m−1, and a sliding time window of at least 4 d the proposed method provides reliable depth-resolved thermal diffusivity estimates with percentage errors ≤ 10 % and posterior relative standard deviations ≤ 5 % up to 1 m depth. Reliable thermal diffusivity under such environmental conditions also requires temperature sensors to be spaced precisely (with accuracy to a few millimeters), with a level of noise ≤ 0.02 ∘C, and with a bias defined by a standard deviation ≤ 0.01 ∘C. Finally, the application of the developed approach to field data indicates significant repeatability in results and similarity with independent measurements, as well as promise in using a sliding time window to estimate temporal changes in soil thermal diffusivity, as needed to potentially capture changes in bulk density or water content.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series: Supporting Data

This dataset consists of soil temperature time series that were used to estimate soil thermal diffusivity and its uncertainty trough the probabilistic modelling approach developed and presented in the article named "Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series" and published in Earth Surface Dynamics. There are two compressed (.zip) files that contains synthetic (Synthetic_soiltemp_Teller.zip) and field (Field_soiltemp_Teller.zip) data. There is one MATLAB file that requires MATLAB to execute but any text editor can open it. The Synthetic_soiltemp_Teller.zip file includes 5 comma-delimited data files (.csv) each of which contains soil temperature time series generated through forward modeling (i.e., heat-conduction process in a heterogeneous medium using an explicit finite difference method) to mimic various types of temperature gradients, trend and fluctuations. These synthetic soil temperatures were used to investigate the impact of different environmental conditions on the uncertainty of thermal diffusivity estimates. The Field_soiltemp_Teller.zip file contains 28 comma-delimited data files (.csv) out of which (a) 27 files includes soil temperature time series recorded from 27 temperature probes located in a site along Teller Road about 40 km northwest of Nome, Alaska (64.72°N, 165.94°W), (b) one includes the name and coordinates of the 27 probes. These field soil temperatures were used to infer soil thermal diffusivity at numerous locations and depths in a discontinuous permafrost environment, and to evaluate the links between the estimated soil thermal diffusivity values and soil physical properties. The comma-delimited data files (.csv) of the synthetic and field soil temperature time series includes date and time (UTC) in the first column and soil temperature from 5 cm below the ground surface to 1.05 m depth (with 5 or 10 cm spacing between sensors) in the other columns. The measurements were acquired every 15 minutes. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Dopant diffused Si surface passivation by H 2 S gas reaction and quinhydrone-methanol treatment

Phosphorus (n + ) and boron (p + ) diffused n-type textured Cz Si wafers are passivated by two different methods: gas phase H 2 S reaction and quinhydrone-methanol (QH-MeOH) solution. The dopant diffused surface passivation quality, quantified by saturation current density (J 0 ), strongly depends on the diffusion type and the passivation method. H 2 S reaction at 550ºC passivates n + diffused surface as good as state-of-the-art Si oxide/silicon nitride stack (SiO 2 /SiN X ), while QH-MeOH passivates p + diffused surface to the same level as state-of-the-art atomic layer deposited aluminum oxide / silicon nitride stack (Al 2 O 3 /SiN X ).

Das, Ujjwal↗

DOE OSTI2022

Tritium diffusion and formation in the bulk and defective surface of γ-LiAlO2 pellets: First-principles investigation

In tritium-producing burnable absorber rods (TPBAR), γ-LiAlO2 is used in the form of an annular ceramic pellet enriched with the 6Li isotope. When irradiated in a pressurized water reactor (PWR), the 6Li pellets absorb neutrons and produce tritium (3H) through 6Li + n 3H + α. The 3H chemically reacts with the metal getter where it is captured and leads to formation of a metal hydride. For TPBARs to enable effective tritium production in PWRs, we investigated the 3H diffusion pathways in the bulk and surface of γ-LiAlO2 with different concentrations of lithium defects. The calculated results for bulk and low-index surfaces, thermal conductivity, 3H activation energy barriers, and the 3H diffusion coefficients in γ-LiAlO2 are in good agreement with the available experimental values. In the bulk, our results show that the smallest activation energy barrier is 0.63 eV for substitutional 3H diffusion with a diffusion coefficient of 3.25x10-12 m2/s. After 3H diffused from bulk to the surface, it could form different species (such as 3H2, 3H2O, C3H4) depending on the surface structure, vacancy types and the impurity carbon. Our results indicate that the 3H2 is the main product from γ-LiAlO2 pellets. As the number of VLi vacancies and 3H atoms increases under irradiation (3H-rich condition), 3H2O release could increase from the surface of γ-LiAlO2 pellets.

Jia, Ting↗

DOE OSTI2022

Photovoltaic structures having multiple absorber layers separated by a diffusion barrier

Photovoltaic structures having multiple absorber layers separated by a diffusion barrier are provided. In one aspect, a method of forming an absorber on a substrate includes: depositing a first layer of light absorbing material on the substrate; depositing a diffusion barrier; depositing a second layer of light absorbing material on the diffusion barrier, wherein the first layer of light absorbing material has a different band gap from the second layer of light absorbing material; and annealing the absorber, wherein the diffusion barrier prevents diffusion of elements between the first layer of light absorbing material and the second layer of light absorbing material during the annealing. A solar cell and method for formation thereof are also provided.

14 SOLAR ENERGY↗

DOE OSTI2020

A comprehensive diffusion mobility database comprising 23 elements for magnesium alloys

We report that reliable experimental diffusion coefficients of 10 key alloying elements in Mg obtained by the present authors together with experimental data in the literature enabled us to perform a systematic test of the reliability of diffusion coefficients obtained from DFT calculations. The computed activation energy values were found to be quite accurate (mostly within 0.2 eV) but the computed pre-factors were less reliable. Such insights allowed us to develop a practical and yet robust strategy to perform diffusion mobility assessments by adopting the computed activation energy while fitting only the pre-factor when available experimental data are limited to a narrow temperature range. The overall good agreement between the DFT data and experimental data also gave us the confidence to employ the computed data for those that were still missing or inaccessible from experimental measurements. A systematic assessment of both the measured and computed diffusion data in hcp Mg was performed using the above holistic approach to yield the most comprehensive open Mg mobility database to date, comprising 23 elements (Mg, Ag, Al, Be, Ca, Cd, Ce, Cu, Fe, Ga, Gd, In, La, Li, Mn, Nd, Ni, Pu, Sb, Sn, U, Y, Zn). This more reliable mobility database will contribute to future development of advanced Mg alloys. The holistic approach developed in this study will be very beneficial to the future establishment of reliable mobility databases for other alloy systems as well.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

The problem of a spatially discontinuous diffusion coefficient (D(x)) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow properties. To date, mass-transfer particle-tracking (MTPT) methods, a family of Lagrangian methods in which diffusion is jointly simulated by random walk and diffusive mass transfers, have been unable to solve this problem. This manuscript presents a new mass-transfer (MT) algorithm that enables MTPT methods to accurately solve the problem of discontinuous D(x). To achieve this, we derive a semi-analytical solution to the discontinuous D(x) problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. Furthermore, this semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a 2 × 2 tiling of 4 subdomains that corresponds to a numerically-generated diffusion field. The solutions generated by this new mass-transfer algorithm closely agree with an analytical 1D solution or, in more complicated cases, trusted numerical results, demonstrating the success of our proposed approach.

42 ENGINEERING↗

DOE OSTI2023

Data-driven methods for diffusivity prediction in nuclear fuels

The growth rate of structural defects in nuclear fuels under irradiation is intrinsically related to the diffusion rates of the defects in the fuel lattice. The generation and growth of atomistic structural defects can significantly alter the performance characteristics of the fuel. This alteration of functionality must be accurately captured to qualify a nuclear fuel for use in reactors. Predicting the diffusion coefficients of defects and how they impact macroscale properties such as swelling, gas release, and creep is therefore of significant importance in both the design of new nuclear fuels and the assessment of current fuel types. In this article, we apply data-driven methods focusing on machine learning (ML) to determine various diffusion properties of two nuclear fuels—uranium oxide and uranium nitride. We show that using ML can increase, often significantly, the accuracy of predicting diffusivity in nuclear fuels in comparison to current analytical models. We also illustrate how ML can be used to quickly develop fuel models with parameter dependencies that are more complex and robust than what is currently available in the literature. In conclusion, these results suggest there is potential for ML to accelerate the design, qualification, and implementation of nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Diffusion and phase formation in the γ-uranium-technetium system

Phase formation in the U-Tc binary system at 800 °C was investigated using a diffusion couple experiment. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) identified four novel potential intermetallic phases - U 7 Tc 3 , U 13 Tc 12 , U 3 Tc 5 , and UTc 4 . Diffusion coefficients were calculated for the intermetallic phases using the Boltzmann-Matano method and were respectively found to be – 120, 38.2, 15.6, and 1.51 × 10 −18 m 2 /s. Tc also exhibits a solid-solution phase with high penetration into the U with a diffusion coefficient of ∼ 10 −14 m 2 /s. Furthermore, these findings expand the number of known U-Tc phases and provide the first diffusion coefficients for the U-Tc system, and contribute valuable data to the broader field of actinide metallurgy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Multiscale, mechanistic modeling of irradiation-enhanced silver diffusion in TRISO particles

Tristructural isotropic (TRISO) particles are under consideration for use in several proposed advanced nuclear reactor concepts. The silicon carbide (SiC) layer in TRISO acts as a barrier to prevent the release of the fission products. However, despite remarkable retention, silver (Ag) release has been observed from intact particles, which requires investigation since the Ag isotope ( 110m Ag) has a long half-life. Previous work focused on developing a multiscale, mechanistic model for Ag diffusion accounting for temperature and microstructure effect and has been successfully validated. In this work, we expand the previous model to account for irradiation-enhanced Ag diffusivity in SiC and improve its accuracy over a wider grain size and temperature ranges relevant for advanced reactor conditions. A temperature, grain size, and flux dependent diffusivity is therefore derived using the mesoscale code MARMOT and implemented in the fuel performance code BISON. The irradiation-enhanced Ag diffusivity in SiC is compared against experimental data and validated using BISON against Ag release measurements from the Advanced Gas Reactor Fuel Development and Qualification Program (AGR-1 and AGR-2). Herein, we quantify the impact of SiC grain size, irradiation, and temperature on Ag release. In agreement with previous studies, we find accounting for SiC grain size improves agreement between BISON predictions and experimental observations for most cases. In conclusion, we also find that accounting for irradiation improves agreement for cases where Ag release was underestimated, but the impact was less significant than accounting for microstructure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Liquid–Solid Boundaries Dominate Activity of CO 2 Reduction on Gas-Diffusion Electrodes

Electrochemical CO 2 electrolysis to produce hydrocarbon fuels or material feedstocks offers a renewable alternative to fossilized carbon sources. Gas-diffusion electrodes (GDEs), composed of solid electrocatalysts on porous supports positioned near the interface of a conducting electrolyte and CO 2 gas, have been able to demonstrate the substantial current densities needed for future commercialization. These higher reaction rates have often been ascribed to the presence of a three-phase interface, where solid, liquid, and gas provide electrons, water, and CO 2 , respectively. Conversely, mechanistic work on electrochemical reactions implicates a fully two-phase reaction interface, where gas molecules reach the electrocatalyst’s surface by dissolution and diffusion through the electrolyte. Because the discrepancy between an atomistic three-phase versus two-phase reaction has substantial implications for the design of catalysts, gas-diffusion layers, and cell architectures, the nuances of nomenclatures and governing phenomena surrounding the three-phase-region require clarification. In this paper we outline the macro, micro, and atomistic phenomena occurring within a gas-diffusion electrode to provide a focused discussion on the architecture of the often-discussed three-phase region for CO 2 electrolysis. From this information, we comment on the outlook for the broader CO 2 electroreduction GDE cell architecture.

CO2 reduction↗

DOE OSTI2023

Effects of diffusion barriers on reaction wave stability in Co/Al reactive multilayers

Bimetallic, reactive multilayers are uniformly structured materials composed of alternating sputter-deposited layers that may be ignited to produce self-propagating mixing and formation reactions. These nanolaminates are most commonly used as rapid-release heat sources. The specific chemical composition at each metal/metal interface determines the rate of mass transport in a mixing and formation reaction. The inclusion of engineered diffusion barriers at each interface will not only inhibit solid-state mixing but also may impede the self-propagating reactions by introducing instabilities to wavefront morphology. Here, this work examines the effect of adding diffusion barriers on the propagation of reaction waves in Co/Al multilayers. The Co/Al system has been shown to exhibit a reaction propagation instability that is dependent on the bilayer thickness, which allows for the occurrence of unstable modes in otherwise stable designs from the inclusion of diffusion barriers. Based on the known stability criteria in the Co/Al multilayer system, the way in which the inclusion of diffusion barriers changes a multilayer's heat of reaction, thermal conductivity, and material mixing mechanisms can be determined. These factors, in aggregate, lead to changes in the wavefront velocity and stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion

The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the nonequilibrium dynamics of a dopant in two-leg 𝑡−𝐽 ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is localized for all investigated nonzero temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models [Phys. Rev. Res. 6, 023325 (2024), SciPost Phys. Core 7, 054 (2024)]. In the presence of spin-exchange processes at rate 𝛼, the dopant diffuses with a diffusion coefficient, 𝐷 ℎ , depending nonmonotonically on 𝛼. It initially increases linearly as 𝐷 ℎ ∝ 𝛼 for 𝛼 ≪ 1 before dropping off as 𝛼 −1 for 𝛼 > 1. Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient 𝐷 ℎ follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.

Anomalous diffusion↗