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DOE OSTI2022

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr 3 ) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Onset of kinetic effects on Rayleigh–Taylor instability: Advective–diffusive asymmetry

In nature and engineering applications, the Rayleigh–Taylor instability (RTI) occurs over a wide range of Atwood, Reynolds, Mach, and Knudsen numbers. At low Atwood, Mach, and Knudsen numbers, the classic advective instability causes quasi-symmetric bubble and spike growth on the two sides of the interface. However, recent findings suggest that at high degrees of rarefaction, advective effects are suppressed and molecular diffusion leads to planar growth of the density fronts on either side of the interface. This study aims to investigate the flow physics of the transition from advective to diffusive behavior, focusing on the onset of the kinetic effects. Using the gas kinetic methodology, RTI is simulated over a range of Knudsen and Mach numbers in the transition regime. The simulation results reveal the various stages of transformation from advective instability to diffusive transport. For the first time, the study demonstrates the existence of a Knudsen–Mach parameter regime where the bubble side exhibits advective instability, while the other side shows a planar density front due to molecular diffusion, rather than the canonical advective spike shape. The dominance of different mechanisms on the two sides of the interface leads to the advective–diffusive asymmetry. In conclusion, the findings of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers.

42 ENGINEERING↗

DOE OSTI2022

Evidence for superionic H 2 O and diffusive He–H 2 O at high temperature and high pressure

In this work, we present the evidence of superionic phase formed in H 2 O and, for the first time, diffusive H 2 O–He phase, based on time-resolved x-ray diffraction experiments performed on ramp-laser-heated samples in diamond anvil cells. The diffraction results signify a similar bcc-like structure of superionic H 2 O and diffusive He–H 2 O, while following different transition dynamics. Based on time and temperature evolution of the lattice parameter, the superionic H 2 O phase forms gradually in pure H 2 O over the temperature range of 1350–1400 K at 23 GPa, but the diffusive He–H 2 O phase forms abruptly at 1300 K at 26 GPa. We suggest that the faster dynamics and lower transition temperature in He–H 2 O are due to a larger diffusion coefficient of interstitial-filled He than that of more strongly bound H atoms. This conjecture is then consistent with He disordered diffusive phase predicted at lower temperatures, rather than H-disordered superionic phase in He–H 2 O.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Investigations on a fuzzy process: effect of diffusion on calibration and particle identification in Liquid Argon Time Projection Chambers

Ionization electron diffusion in Liquid Argon Time Projection Chambers (LArTPCs) has typically been considered at the detector design stage, but little attention has been given to its effects on calibration and particle identification. We use a GEANT4-based simulation to study how diffusion impacts these techniques, and give consideration to how this effect is simulated. We find that diffusion can cause a drift-dependent bias to both the median and Most Probable Value (MPV) of dQ/dx distributions. The bias is estimated to be ~2.5% (median) and ~5.0% (MPV) for typical maximum drift times in currently running LArTPCs before adding detector specific considerations such as electric field non-uniformities. This information indicates that these metrics should not be used for calibration without care, contrary to the conventional wisdom. The impact of diffusion on the ability of LArTPCs to separate muons and protons is small, and not expected to pose any problems in future detectors. Diffusion may however be a significant source of systematic uncertainty when separating particles of more similar masses (muons and pions, kaons and protons). Separation of such populations may be improved by implementation of a drift-time dependent particle identification.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2019

Multicomponent mutual diffusion in the warm, dense matter regime

In this work, we present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Furthermore, our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗

DOE OSTI2025

Random Walks With Tweedie: A Unified View of Score-Based Diffusion Models [In the Spotlight]

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals—particularly natural images—and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, in this study, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Matrix Diffusion Controls Mountain Hillslope Groundwater Ages and Inferred Storage Dynamics

Groundwater age distributions provide fundamental insights on coupled water and biogeochemical processes in mountain watersheds. Field-based studies have found mixtures of young and old-aged groundwater in mountain catchments underlain by bedrock; yet, the processes that dictate these groundwater age distributions are poorly understood. In this work, we use the coupled ParFlow-CLM integrated hydrologic and EcoSLIM particle tracking models to simulate groundwater age distributions on a lower montane hillslope in the East River Watershed, Colorado (USA). We develop a convolution-based approach to propagate fracture-matrix diffusion processes to the EcoSLIM advection-dominated age distributions. We compare observed 3 H and 4 He concentrations from two groundwater wells against model predictions that have varying advective transport times and matrix diffusion magnitudes. Based on a Monte Carlo analysis that considers uncertain matrix and fracture parameters, we find that matrix diffusion is needed to jointly predict 3 H and 4 He observations at both wells. The advection-dominated age distributions lack adequate mixing of young and old-aged water to capture the observed co-occurrence of 3 H and 4 He. The model scenario that best matches the 3 H, 4 He, and water level observations when considering both advective flowpath and matrix diffusion mixing processes has a dynamic bedrock groundwater reservoir that is susceptible to considerable storage losses during low-snow periods. This dynamic groundwater system amplifies the need to assimilate deeper bedrock groundwater into watershed hydro-biogeochemical predictions. This work further highlights the importance of considering matrix diffusion when interpreting environmental tracers in bedrock groundwater systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A Study of Ferrocene Diffusion in Toluene/Tween 20/1-Butanol/Water Microemulsions for Redox Flow Battery Applications

Redox flow batteries (RFBs) possess multiple advantages as a flexible energy storage solution. However, RFB researchers are still facing many challenges in finding an appropriate electrolyte. Microemulsions have recently been proposed as a promising alternative RFB electrolyte because of their ability to accommodate organic redox species with fast electron transfer rates that are not soluble in aqueous phase, while still offering the high conductivity of an aqueous salt electrolyte. In this work, we focused on understanding the transport of ferrocene (Fc) in a toluene/Tween 20/1-butanol/water model microemulsion and studied the compositional influence on Fc diffusion. The results show that Fc redistributes among the oil, surfactant, and water microenvironments, and the corresponding diffusion and partition coefficients are quantified. Thus, a tortuous path diffusion model is proposed to describe the mass transport of Fc to an electrode surface. Diffusion coefficients are also obtained by pulsed-field gradient nuclear magnetic resonance (PFG NMR), while the values for Fc diffusion are substantially higher than those from electrochemical measurements, suggesting that they measure samples in different ways. The current contributions from each microenvironment indicate that the Fc permeability is much higher in the oil, even though the electron transfer reaction is likely occurring in the surfactant.

25 ENERGY STORAGE↗

DOE OSTI2025

Ab Initio Insights to Metal Passivation: Diffusion and Defect Formation in Amorphous Zirconia and Alumina

Metal passivation refers to the formation of protective oxide films on metals, which shield them from further corrosion and oxidation, playing a crucial role in maintaining their stability. The mesoscopic Point Defect Model has successfully predicted passivity as a steady state process where oxide growth from oxygen vacancies at the metal/film interface competes with oxide dissolution at the film/environment interface. In this work, informed by the Point Defect Model parameters, we use first-principles calculations to calculate defect formation and atomic diffusion in amorphous materials and correlate these descriptors with the behavior and growth of the oxide film. Focusing on amorphous zirconia and alumina, we demonstrate that defect formation energies exhibit significant variability in amorphous systems. In alumina, vacancies dominate, with cation and anion vacancies occurring at comparable concentrations. Diffusion calculations for stoichiometric amorphous alumina and zirconia, as well as oxygen-deficient zirconia, reveal faster diffusion in the oxygen-deficient case, highlighting the impact of defects on transport. Comparison of calculated self-diffusion coefficients for the dominant defect species with experimentally measured oxide thicknesses shows a clear correlation, suggesting that first-principles-derived diffusivity information can serve as a key descriptor for surface passivation film growth.

Farnell, Mackinzie S. [University of California, B↗

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 OSTI2019

Neptunium(IV) Diffusion through Bentonite Clay

DOE Fellow, Silvina A. Di Pietro, completed a 10-week internship at Lawrence Livermore National Laboratory (LLNL) in Livermore, California. The objective of the study was to determine the diffusion profile of neptunium (Np) in bentonite clay (potential geo-engineered barrier for nuclear waste repositories). Under the mentorship of Drs. Claudia Joseph (Karlsruhe Institute of Technology, Germany) and Mavrik Zavarin, she prepared a series of core abrasion peeling samples. This procedure was a continuation of a Np diffusion experiment conducted by Dr. Joseph during her post-doc residency at LLNL in the year 2016. The second part of the experiment (from now on will be referred as abrasive peeling) focuses on understanding (1) the Np movement through the clay core and (2) the influence of temperature (25°C, 65°C, and 85°C) for the Np transport across the clay core under anaerobic conditions. End of 2016, the diffusion core samples were embedded in epoxy resin to stabilize them for long-term. The abraded core powder samples vary in material (epoxy vs. clay), Np activity and concentration, temperature exposed during the diffusion experiment, and mass, or amount of clay peeled off. Throughout the course of the 10-week internship program at LLNL, the experiments implemented and discussed in this report aimed to answer the questions: (1) How is the Np(IV) diffusion profile through bentonite influenced by the temperature? and (2) Will Np(IV) migrate through the geoengineered barrier of a nuclear waste repository? In addition, Ph.D. candidate Di Pietro received invaluable guidance in experimental design and development that will benefit her ongoing research endeavors.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

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↗