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DOE OSTI2016

Diffusion of biomass pyrolysis products in H-ZSM-5 by molecular dynamics simulations

Diffusion of biomass pyrolysis vapors and their upgraded products is an essential catalytic property of zeolites during catalytic fast pyrolysis and likely plays a critical role in the selectivity of these catalysts. Characterizing the diffusivities of representative biofuel molecules is critical to understand shape selectivity and interpret product distribution. Yet, experimental measurements on the diffusivities of oxygenated biofuel molecules at pyrolysis temperatures are very limited in the literature. As an alternative approach, we conducted MD simulations to measure the diffusion coefficients of several selected molecules that are representative of biomass pyrolysis vapors, namely water, methanol, glycolaldehyde, and toluene in H-ZSM-5 zeolite. The results show the diffusion coefficients calculated via MD simulations are consistent with available NMR measurements at room temperature. The effect of molecular weight and molecular critical diameter on the diffusivity among the chosen model compounds is also examined. Furthermore, we have characterized the diffusivities of representative biofuel molecules, namely xylene isomers, in H-ZSM-5. Our calculations determined that the ratio of the diffusion coefficients for xylene isomers is p -xylene: o -xylene: m -xylene ≈ 83:3:1 at 700 K. Furthermore, our results also demonstrate the different diffusivity between p-xylene and toluene is due to the molecular orientations when the molecules diffuse along the channels in H-ZSM-5 and provide deep insight into the effect of molecular orientation on its diffusivity.

09 BIOMASS FUELS↗

DOE OSTI2016

Self-diffusion of protons in H{sub 2}O ice VII at high pressures: Anomaly around 10 GPa

The self-diffusion of ice VII in the pressure range of 5.5–17 GPa and temperature range of 400–425 K was studied using micro Raman spectroscopy and a diamond anvil cell. The diffusion was monitored by observing the distribution of isotope tracers: D{sub 2}O and H{sub 2}{sup 18}O. The diffusion coefficient of hydrogen reached a maximum value around 10 GPa. It was two orders of magnitude greater at 10 GPa than at 6 GPa. Hydrogen diffusion was much faster than oxygen diffusion, which indicates that protonic diffusion is the dominant mechanism for the diffusion of hydrogen in ice VII. This mechanism is in remarkable contrast to the self-diffusion in ice I{sub h} that is dominated by an interstitial mechanism for the whole water molecule. An anomaly around 10 GPa in ice VII indicates that the rate-determining process for the proton diffusion changes from the diffusion of ionic defects to the diffusion of rotational defects, which was suggested by proton conductivity measurements and molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

On the Diffusivity of Moist Static Energy and Implications for the Polar Amplification Response to Climate Warming

Energy balance models (EBMs) have been widely used in a range of climate problems, but the assumption of constant diffusivity in the parameterization of the moist static energy (MSE) flux can be hardly justified. We demonstrate in this study that the diffusive MSE flux can be derived from the basic energy balance equation with a few tolerable assumptions. The estimated diffusivity is both spatially and seasonally dependent, and its midlatitude average is then tested against several scaling theories for the midlatitude eddy diffusivity. The result supports the diffusivity theory of Held and Larichev (1996) modified for the moist atmosphere, affording a dynamics-based parameterization of MSE diffusivity. The implementation of the parameterization in an EBM leads to an interactive MSE diffusivity that accounts for the midlatitude eddy response to climate forcing perturbations. Under a uniform radiative forcing, the EBM with a diffusivity so parameterized produces a weakening of the midlatitude diffusivity and a modestly polar-amplified surface temperature response as an inevitable outcome under the dual constraints of the nonlinear Clausius-Clapeyron relation and the temperature gradient-dependent diffusivity, even in the absence of any poleward amplifying radiative feedbacks. As the consequence of more isothermal temperature and reduced diffusivity, the variance of the midlatitude surface temperature also decreases with warming.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Effects of Moisture on Diffusion in Unmodified Wood Cell Walls: A Phenomenological Polymer Science Approach

Despite the importance of cell wall diffusion to nearly all aspects of wood utilization, diffusion mechanisms and the detailed effects of moisture remain poorly understood. In this perspective, we introduce and employ approaches established in polymer science to develop a phenomenological framework for understanding the effects of moisture on diffusion in unmodified wood cell walls. The premise for applying this polymer-science-based approach to wood is that wood polymers (cellulose, hemicelluloses, and lignin) behave like typical solid polymers. Therefore, the movement of chemicals through wood cell walls is a diffusion process through a solid polymer, which is in contrast to previous assertions that transport of some chemicals occurs via aqueous pathways in the cell wall layers. Diffusion in polymers depends on the interrelations between free volume in the polymer matrix, molecular motions of the polymer, diffusant dimensions, and solubility of the diffusant in the polymer matrix. Because diffusion strongly depends on whether a polymer is in a rigid glassy state or soft rubbery state, it is important to understand glass transitions in the amorphous wood polymers. Through a review and analysis of available literature, we conclude that in wood both lignin and the amorphous polysaccharides very likely have glass transitions. After developing and presenting this polymer-science-based perspective of diffusion through unmodified wood cell walls, suggested directions for future research are discussed. A key consideration is that a large difference between diffusion through wood polymers and typical polymers is the high swelling pressures that can develop in unmodified wood cell walls. This pressure likely arises from the hierarchical structure of wood and should be taken into consideration in the development of predictive models for diffusion in unmodified wood cell walls.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

GALACTIC WINDS DRIVEN BY ISOTROPIC AND ANISOTROPIC COSMIC-RAY DIFFUSION IN DISK GALAXIES

The physics of cosmic rays (CRs) is a promising candidate for explaining the driving of galactic winds and outflows. Recent galaxy formation simulations have demonstrated the need for active CR transport either in the form of diffusion or streaming to successfully launch winds in galaxies. However, due to computational limitations, most previous simulations have modeled CR transport isotropically. Here, we discuss high-resolution simulations of isolated disk galaxies in a 10{sup 11} M {sub ⊙} halo with the moving-mesh code Arepo that include injection of CRs from supernovae, advective transport, CR cooling, and CR transport through isotropic or anisotropic diffusion. We show that either mode of diffusion leads to the formation of strong bipolar outflows. However, they develop significantly later in the simulation with anisotropic diffusion compared to the simulation with isotropic diffusion. Moreover, we find that isotropic diffusion allows most of the CRs to quickly diffuse out of the disk, while in the simulation with anisotropic diffusion, most CRs remain in the disk once the magnetic field becomes dominated by its azimuthal component, which occurs after ∼300 Myr. This has important consequences for the gas dynamics in the disk. In particular, we show that isotropic diffusion strongly suppresses the amplification of the magnetic field in the disk compared to anisotropic or no diffusion models. We therefore conclude that reliable simulations which include CR transport inevitably need to account for anisotropic diffusion.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Influence of strong Coulomb coupling on diffusion in atmospheric pressure plasmas

Ion diffusion in atmospheric pressure plasmas is examined and particular attention is paid to the fact that ion–ion interactions can be influenced by strong Coulomb coupling. Three regimes are identified. At low ionization fractions (x i ≲ 10 —6 ), standard weakly correlated ion-neutral interactions set the diffusion rate. At moderate ionization fractions (10 —6 ≲ x i ≲ 10 —2 ) there is a transition from ion-neutral to ion–ion collisions setting the diffusion rate. In this regime, the effect of strong Coulomb coupling in ion–ion collisions is accounted for by applying the mean force kinetic theory. Since both ion-neutral and ion–ion interactions contribute a comparable amount to the total diffusion rate, models (such as particle-in-cell or fluid) must account for both contributions. At high ionization fractions (x i ≳ 10 —2 ), strongly correlated ion–ion collisions dominate and the plasma is heated substantially by a disorder-induced heating (DIH) process associated with strong correlations. The temperature increase due to DIH strongly influences the ion diffusion rate. This effect becomes even more important, and occurs at lower ionization fractions, as the pressure increases above atmospheric pressure. In addition to ion diffusion, DIH affects the neutral gas temperature, therefore influencing the neutral diffusion rate. Model predictions are tested using molecular dynamics simulations, which included a Monte Carlo collision routine to simulate the effect of ion-neutral collisions at the lowest ionization fractions. The model and simulations show good agreement over a broad range of ionization fractions. Importantly, the results provide a model for ion diffusion, on a wide range of ionization fractions and pressures, solely considering the elastic contribution to the diffusion coefficient—as an illustration of how strong Coulomb coupling influences diffusion processes in general.

fast neutral gas heating↗

DOE OSTI2020

Measurement of moisture-dependent ion diffusion constants in wood cell wall layers using time-lapse micro X-ray fluorescence microscopy

Our future bioeconomy depends on increased utilization of renewable lignocellulosic biomass. Controlling the diffusion of chemicals, such as inorganic ions, within secondary plant cell walls is central to many biomass applications. However, insufficient understanding of intra-cell-wall diffusion within secondary plant cell walls is hindering the advancement of many lignocellulosic biomass applications. In this work, X-ray fluorescence microscopy was used to measure diffusion constants of K + , Cu 2+ , and Cl - diffusing through loblolly pine (Pinus taeda) cell wall layers under 70%, 75%, or 80% relative humidity (RH). Results revealed that diffusion constants increased with RH, the larger Cu 2+ diffused more slowly than the K + , and the Cl - diffusion constant was the same as that for the counter cation, indicating cations and anions diffused together to maintain charge neutrality. Comparison with electrical conductivity measurements showed that conductivity is being controlled by ion mobility over these RH. The results further support that intra-cell-wall diffusion of inorganic ions is a Fickian diffusion process occurring through rubbery amorphous polysaccharides, which contradicts previous assertions that intra-cell-wall diffusion is an aqueous process occurring through water pathways. Researchers can now utilize polymer science approaches to engineer the molecular architecture of lignocellulosic biomass to optimize properties for specific end uses.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

Diffusion and mobility of atomic particles in a liquid

The diffusion coefficient of a test atom or molecule in a liquid is determined for the mechanism where the displacement of the test molecule results from the vibrations and motion of liquid molecules surrounding the test molecule and of the test particle itself. This leads to a random change in the coordinate of the test molecule, which eventually results in the diffusion motion of the test particle in space. Two models parameters of interaction of a particle and a liquid are used to find the activation energy of the diffusion process under consideration: the gas-kinetic cross section for scattering of test molecules in the parent gas and the Wigner–Seitz radius for test molecules. In the context of this approach, we have calculated the diffusion coefficient of atoms and molecules in water, where based on experimental data, we have constructed the dependence of the activation energy for the diffusion of test molecules in water on the interaction parameter and the temperature dependence for diffusion coefficient of atoms or molecules in water within the models considered. The statistically averaged difference of the activation energies for the diffusion coefficients of different test molecules in water that we have calculated based on each of the presented models does not exceed 10% of the diffusion coefficient itself. We have considered the diffusion of clusters in water and present the dependence of the diffusion coefficient on the cluster size. The accuracy of the presented formulas for the diffusion coefficient of atomic particles in water is estimated to be 50%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Resolving and Measuring Diffusion in Complex Interfaces: Exploring New Capabilities

This exploratory LDRD targeted the use of a new high resolution spectroscopic diffusion capabilities developed at Sandia to resolve transport processes at interfaces in heterogeneous polymer materials. In particular, the combination of high resolution magic angle spinning (HRMAS) nuclear magnetic resonance (NMR) spectroscopy with pulsed field gradient (PFG) diffusion experiments were used to directly explore interface diffusion within heterogeneous polymer composites, including measuring diffusion for individual chemical species in multi-component mixtures. Several different types of heterogeneous polymer systems were studied using these HRMAS NMR diffusion capabilities to probe the resolution limitations, determine the spatial length scales involved, and explore the general applicability to specific heterogeneous systems. The investigations pursued included a) the direct measurement of the diffusion for poly(dimethyl siloxane) polymer (PDMS) on nano-porous materials, b) measurement of penetrant diffusion in additive manufactures (3D printed) processed PDMS composites, and c) the measurement of diffusion in swollen polymers/penetrant mixtures within nano-confined aluminum oxide membranes. The NMR diffusion results obtained were encouraging and allowed for an improved understanding of diffusion and transport processes at the molecular level, while at the same time demonstrating that the spatial heterogeneity that can be resolved using HRMAS NMR PFG diffusion experiment must be larger than ~μm length scales, expect for polymer transport within nanoporous carbons where additional chemical resolution improves the resolvable heterogeneous length scale to hundreds of nm.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Preparation of Diffusion Couples for Irradiation and High Temperature Testing of Representative TRISO PyC/SiC

Understanding the release of fission products from intact tristructural-isotropic (TRISO) coated particle fuel during normal and off-normal service is necessary to ensuring safe and efficient reactor operation. Planar diffusion couples have been fabricated to determine the diffusion kinetics of select fission product species (Ag, Ag+Pd, Eu, and Sr) in pyrocarbon (PyC) and silicon carbide (SiC) materials which are representative of TRISO fuel. Obtaining accurate diffusion coefficients for these systems in representative materials will allow for higher fidelity inputs for fuel performance models. Three different diffusion couple variants have been produced which include a Baseline, PyC, and SiC variant. The Baseline variant serves as an example of representative PyC and SiC layers as the layer properties mimic those found in TRISO fuel from the second Advanced Gas Reactor Fuel Qualification and Development Program. The PyC and SiC variants include variation in the respective layer properties to understand the impact of PyC density and SiC grain size on fission product diffusion. The diffusion couples were designed to allow for exploration of neutron irradiation on diffusion reflecting in reactor behavior as well as high temperature thermal diffusion reflecting diffusive transport during off-normal conditions. The methodology for selecting the diffusion couple design, refinement of the individual variant layer properties, and the complete process for diffusion couple construction are summarized in this report.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Tritium Diffusion in Fe-Al Aluminide Coating Bulk Phases

The theoretical investigations of interstitial tritium diffusion pathways in various Al-rich (>60% at. Al) iron aluminide coating phases found that in FeNiAl 5 tritium prefers to diffuse in between layers, while in Fe 4 Al 13 , tritium prefers to diffuse across layers. In the case of Fe 2 Al x phases, the simulations show that the variable Al content in the channels affects the diffusion behavior of tritium in the channels. For 100% of vacancy, tritium prefers to diffuse at the center of the channel, while for 0% Al vacancy, tritium prefers to diffuse along the channel’s wall. In the case where 50% Al vacancy are present in the channels, tritium can diffuse in a mixed way, with positions oscillating between the channel’s center and wall. However, the large energy barrier involved in this case suggests that tritium diffusion could be correlated with Al diffusion in the channels. While we found that at 600 K interstitial tritium diffuses faster in Fe 2 Al x phases (D Τ ≤10 -11 m 2 .s -1 ), then in Fe 4 Al 13 (D Τ ≈10 -12 m 2 .s -1 ), and finally in FeNiAl 5 (D Τ ≈10 -13 m 2 .s -1 ), we also find that interstitial tritium generally diffuses faster in Fe-Al coating phases than in γ-LiAlO 2 pellets (D Τ ≈10 -14 m 2 .s -1 ).

36 MATERIALS SCIENCE↗

DOE OSTI2024

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. Further, the calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Model-based analysis of the impact of diffuse radiation on CO 2 exchange in a temperate deciduous forest

Clouds and aerosols increase the fraction of global solar irradiance that is diffuse light. This phenomenon is known to increase the photosynthetic light use efficiency (LUE) of closed-canopy vegetation by redistributing photosynthetic photon flux density (400–700 nm) from saturated, sunlit leaves at the top of the canopy, to shaded leaves deeper in the canopy. We combined a process-based carbon cycle model with 10 years of eddy covariance carbon flux measurements and other ancillary data sets to assess 1) how this LUE enhancement influences interannual variation in carbon uptake, and 2) how errors in modeling diffuse fraction affect predictions of carbon uptake. Modeled annual gross primary productivity (GPP) increased by ≈0.94% when observed levels of diffuse fraction were increased by 0.01 (holding total irradiance constant). The sensitivity of GPP to increases in diffuse fraction was highest when the diffuse fraction was low to begin with, and lowest when the diffuse fraction was already high. Diffuse fraction also explained significantly more of the interannual variability of modeled net ecosystem exchange (NEE), than did total irradiance. Two tested radiation partitioning models yielded over- and underestimates of diffuse fraction at our site, which propagated to over- and underestimates of annual NEE, respectively. Our findings highlight the importance of incorporating LUE enhancement under diffuse light into models of global primary production, and improving models of diffuse fraction.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Non-monotonic behavior of the lateral diffusivity in an adsorbate as a function of the surface coverage

Diffusion dynamics of adsorbate particles confined on a surface strongly depends on the adsorbate surface coverage. Our molecular dynamics simulation reveals that the average lateral diffusivity of the Lennard-Jones adsorbate on a flat substrate varies non-monotonically with the surface coverage. Given that the adsorbate becomes stratified into distinct layers, we propose a novel approach to analyze the lateral diffusion of the adsorbate particles in different layers, via dividing the total lateral diffusion into consecutive lateral diffusion processes, separated by the layer boundary crossing events. A new definition of the lateral diffusivity in the specific layer has been introduced, and it is revealed that the total lateral diffusivity is equal to the sum of lateral diffusivities in different layers. Furthermore, the non-monotonic behavior of the average lateral diffusivity with the surface coverage is found to result from the difference in behavior of the lateral diffusivity between the first and other layers.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Analyzing the co-evolution of green technology diffusion and consumers’ pro-environmental attitudes: An agent-based model

Massive diffusion of green technologies is significant for building a cleaner world. However, the process of technology diffusion is usually slow and complex. An in-depth understanding of the mechanism regarding green technology diffusion is an essential precondition for effectively stimulating this process. Green technology diffusion heavily involves both social and technological changes. Although existing studies have provided rich knowledge about identifying critical drivers and barriers affecting green technology diffusion, research that considers consumers’ pro-environmental attitudes and green technology diffusion as an evolving system is still sparse. Aiming at exploring the co-evolution of consumers’ pro-environmental attitudes and green technology diffusion, this paper builds an agent-based model that integrates the relative agreement model with technology diffusion theories to conduct a sequence of controlled numerical experiments, which progressively unveil how attitudinal and technological factors impact green technology diffusion. The main findings include that (1) improving consumers’ pro-environmental attitudes is prominently beneficial to green technology diffusion and maturation; (2) technology maturity has very limited impact on consumers’ first-time purchases but significantly affects consumers’ satisfaction, which would further impact consumers’ repeat purchases; (3) consumers that do not support green technologies frequently emerge during the evolution of attitudes (despite the high technology maturity), which corresponds to the emergence of the anti-environmental groups observed in the real world; (4) active interactions between non-adopters enable their attitudes to converge, which results in the polarization of consumers’ attitudes.

ABM↗

DOE OSTI2016

Banded structures in electron pitch angle diffusion coefficients from resonant wave-particle interactions

Electron pitch angle (D{sub αα}) and momentum (D{sub pp}) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies ≤10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = ±1, ±2, … ±5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (α) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D{sub αα} and D{sub pp} coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D{sub pp} diffusion coefficient for ECH waves is one to two orders smaller than D{sub αα} coefficients. For chorus waves, D{sub pp} coefficients are about an order of magnitude smaller than D{sub αα} coefficients for the case n ≠ 0. In case of Landau resonance, the values of D{sub pp} coefficient are generally larger than the values of D{sub αα} coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89° and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10° and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies ≥1 keV, and for whistler mode chorus waves, structures appear for energies >2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Reproducibility of protein x-ray diffuse scattering and potential utility for modeling atomic displacement parameters

Protein structure and dynamics can be probed using x-ray crystallography. Whereas the Bragg peaks are only sensitive to the average unit-cell electron density, the signal between the Bragg peaks—diffuse scattering—is sensitive to spatial correlations in electron-density variations. Although diffuse scattering contains valuable information about protein dynamics, the diffuse signal is more difficult to isolate from the background compared to the Bragg signal, and the reproducibility of diffuse signal is not yet well understood. We present a systematic study of the reproducibility of diffuse scattering from isocyanide hydratase in three different protein forms. Both replicate diffuse datasets and datasets obtained from different mutants were similar in pairwise comparisons (Pearson correlation coefficient ≥0.8). The data were processed in a manner inspired by previously published methods using custom software with modular design, enabling us to perform an analysis of various data processing choices to determine how to obtain the highest quality data as assessed using unbiased measures of symmetry and reproducibility. The diffuse data were then used to characterize atomic mobility using a liquid-like motions (LLM) model. This characterization was able to discriminate between distinct anisotropic atomic displacement parameter (ADP) models arising from different anisotropic scaling choices that agreed comparably with the Bragg data. Our results emphasize the importance of data reproducibility as a model-free measure of diffuse data quality, illustrate the ability of LLM analysis of diffuse scattering to select among alternative ADP models, and offer insights into the design of successful diffuse scattering experiments.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Diffusion of acceptor dopants in monoclinic 𝛽−Ga 2⁢ O 3

𝛽−Ga 2 ⁢O 3 is a promising material for next-generation power electronics because of its ultrawide band gap and high critical breakdown voltage. However, realizing its full potential requires precise control over dopant incorporation and stability. In this work, we use first-principles calculations to systematically assess the diffusion behavior of eight potential deep-level substitutional acceptors (Au, Ca, Co, Cu, Fe, Mg, Mn, and Ni) in 𝛽−Ga 2 ⁢O 3 . We consider two key diffusion mechanisms: (i) interstitial diffusion under nonequilibrium conditions relevant to ion implantation, and (ii) trap-limited diffusion (TLD) under near-equilibrium thermal annealing conditions. Our results reveal a strong diffusion anisotropy along the 𝑏 and 𝑐 axes, with dopant behavior governed by competition between diffusion and incorporation (or dissociation) activation energies. Under interstitial diffusion, Ca$^{2+}_{i}$ and Mg$^{2+}_{i}$ show the most favorable combination of low migration and incorporation barriers, making them promising candidates for efficient doping along the 𝑏 and 𝑐 axes, respectively. In contrast, Au$^{+}_{i}$ diffuses readily, but exhibits an incorporation barrier that exceeds 5 eV, rendering it ineffective as a dopant. From a thermal stability perspective, Co$^{2+}_{i}$ shows poor activation but high diffusion barriers, which may suppress undesirable migration at elevated temperatures. Under trap-limited diffusion, the dissociation of dopant-host complexes controls mobility. Mg$^{2+}_{i}$ again emerges as a leading candidate, exhibiting the lowest dissociation barriers along both axes, whereas Co$^{2+}_{i}$ and Fe$^{2+}_{i}$ display the highest barriers, suggesting improved dopant retention under thermal stress. In conclusion, our findings guide dopant selection by balancing activation and thermal stability, essential for robust semi-insulating substrates.

Defects↗