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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Investigation of the feasibility of developing low permeability polymeric films

The feasibility of reducing the gas permeability rate of Mylar and Kapton films without drastically effecting their flexibility characteristics at cryogenic temperatures was considered. This feasibility was established using a concept of diffusion bonding two layers of metallized films together forming a film-metal-film sandwich laminate. The permeability of kapton film to gaseous helium was reduced from a nominal ten = to the minus 9 power cc-mm/sq cm sec. cm Hg to ten to the minus 13 power cc-mm/ sq cm - sec. cm Hg with some values as low as ten to the minus 15 power cc - mm/sq cm m-sec - cm Hg being obtained. Similar reductions occurred in the liquid hydrogen permeability at -252 C. In the course of the program the permeability, flexibility and bond strength of plain, metalized and diffusion bond film were determined at +25 C, -195 C and -252 C. The cryogenic flexibility of Kapton film was reduced slightly due to the metallization process but no additional loss in flexibility resulted from the diffusion bonding process.

Hoggatt, J. T.↗
DOE OSTI2026

Achieving high rate performance in hybrid pristine-recycled cathodes using model-informed electrode designs

Direct recycling lithium-ion battery cathodes, a process that retains the engineered oxide structures from end-of-life materials, presents a cost-effective and energy-efficient alternative to other battery recycling methods. However, while direct-recycled cathodes have demonstrated performance comparable to that of pristine materials at low cycling rates, their high-rate performance remains uncertain. Morphology changes in cathode particles, a main mode of degradation, directly impact rate performance by limiting surface kinetics and solid-phase diffusion. If direct recycling processes do not sufficiently restore pristine-like morphologies, the recycled materials may retain structural defects that hinder high-rate performance. The present work uses a physics-based pseudo-2D model to simulate hybrid electrodes with pristine and artificially “aged/recycled” NMC materials to investigate potential impacts of incorporating performance-limited aged cathode materials into cells. The study highlights how differences in transport and kinetic properties can influence rate capabilities in mixed electrodes — particularly in high-loading cells in high-demand applications. However, model results also reveal a possible mitigation strategy via dual-layer electrode architectures with lower-performing materials positioned near the current collector. Simulations of 4.0 mAh cm −2 cells cycled at 4C using a dual-layer architecture provided approximately 5%–30% more capacity in constant-current protocols compared to homogeneously blended electrode architectures with the same loadings and mixed-material compositions. These findings highlight the importance of strategic electrode design in minimizing potential performance losses and facilitating the integration of recycled materials into high-performance batteries, advancing sustainable and cost-effective battery manufacturing.

25 ENERGY STORAGE↗
DOE OSTI2024

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1992

Space Station Freedom combustion research

Extended operations in microgravity, on board spacecraft like Space Station Freedom, provide both unusual opportunities and unusual challenges for combustion science. On the one hand, eliminating the intrusion of buoyancy provides a valuable new perspective for fundamental studies of combustion phenomena. On the other hand, however, the absence of buoyancy creates new hazards of fires and explosions that must be understood to assure safe manned space activities. These considerations - and the relevance of combustion science to problems of pollutants, energy utilization, waste incineration, power and propulsion systems, and fire and explosion hazards, among others - provide strong motivation for microgravity combustion research. The intrusion of buoyancy is a greater impediment to fundamental combustion studies than to most other areas of science. Combustion intrinsically heats gases with the resulting buoyant motion at normal gravity either preventing or vastly complicating measurements. Perversely, this limitation is most evident for fundamental laboratory experiments; few practical combustion phenomena are significantly affected by buoyancy. Thus, we have never observed the most fundamental combustion phenomena - laminar premixed and diffusion flames, heterogeneous flames of particles and surfaces, low-speed turbulent flames, etc. - without substantial buoyant disturbances. This precludes rational merging of theory, where buoyancy is of little interest, and experiments, that always are contaminated by buoyancy, which is the traditional path for developing most areas of science. The current microgravity combustion program seeks to rectify this deficiency using both ground-based and space-based facilities, with experiments involving space-based facilities including: laminar premixed flames, soot processes in laminar jet diffusion flames, structure of laminar and turbulent jet diffusion flames, solid surface combustion, one-dimensional smoldering, ignition and flame spread of liquids, drop combustion, and quenching of panicle-air flames. Unfortunately, the same features that make microgravity attractive for fundamental combustion experiments, introduce new fire and explosion hazards that have no counterpart on earth. For example, microgravity can cause broader flammability limits, novel regimes of flame spread, enhanced effects of flame radiation, slower fire detector response, and enhanced combustion upon injecting fire extinguishing agents, among others. On the other hand, spacecraft provide an opportunity to use 'fire-safe' atmospheres due to their controlled environment. Investigation of these problems is just beginning, with specific fire safety experiments supplementing the space based fundamental experiments listed earlier; thus, much remains to be done to develop an adequate technology base for fire and explosion safety considerations for spacecraft.

Faeth, G. M.↗
DOE OSTI2020

A Comparison of RESRAD and GoldSim Models for Assessing Radiological Dose for a RCRA Landfill - 20418

US Ecology Idaho (USEI) operates a Resource Conservation and Recovery Act (RCRA) Subtitle C, Hazardous Waste Treatment, Storage, and Disposal (TSD) Facility on a 640-acre property in Owyhee County, Idaho. USEI accepts a wide variety of RCRA-exempt low activity radioactive wastes, including naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (USEI 2009). The performance of the landfill with regard to radiological operating permit requirements was previously assessed using a model constructed with the residual radioactivity (RESRAD) computer program, developed by Argonne National Laboratory for the U.S. Department of Energy (DOE). RESRAD supports the evaluation of several environmental transport pathways related to a radionuclide-contaminated soil source term, but it was not conceived as a model for the evaluation of landfill radiological performance. A more comprehensive and realistic model is desired in order to better support submissions to both the State of Idaho's Department of Environmental Quality as well as the U.S. Nuclear Regulatory Commission. A Performance Assessment (PA) computer model was developed using GoldSim software for the USEI RCRA Subtitle C landfill. The RESRAD computer model was specifically developed for calculating soil cleanup criteria and radiological dose and cancer risk from residual radioactive material in soil. To evaluate site-specific conditions, users may select from among a number of available environmental transport and exposure pathways and modify 'default' parameter values. In GoldSim, a user must construct the model 'from scratch.' However, this modeling is facilitated by a number of specialized elements available in GoldSim to support a radiological mass transport model. These include elements for defining radiological decay and ingrowth, container failure and radiological release, advective and diffusive transport, and other processes. Advantages afforded by the use of RESRAD for modeling radiological dose for a RCRA Subtitle C landfill include ease of use and reasonable flexibility in specifying site-specific conditions. GoldSim allows for considerably more flexibility and site-specificity than RESRAD, including evaluation of potentially relevant environmental transport processes not supported in RESRAD. The probabilistic modeling capabilities of GoldSim also far exceed those of RESRAD. The pros and cons of RESRAD and GoldSim for this modeling problem are explored with a focus on identifying approaches and critical factors in identifying the appropriate platform. The capabilities of RESRAD and GoldSim for mathematically modeling the disposal system will be contrasted and compared. For example, the existing RESRAD radiological safety assessment evaluated potentially complete exposure pathways related to infiltration to groundwater and upwards diffusion of radon. Additional transport pathways identified in the USEI Idaho facility Conceptual Site Model include deposition of radon decay products in cover material, root uptake of radionuclides in disposed wastes by native plants, and mixing of cover material by burrowing animals. Results of the two models and how the different transport and dose pathways affect results will be discussed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Simultaneous numerical representation of soil microsite production and consumption of carbon dioxide, methane, and nitrous oxide using probability distribution functions

Production and consumption of nitrous oxide (N 2 O), methane (CH 4 ), and carbon dioxide (CO 2 ) are affected by complex interactions of temperature, moisture, and substrate supply, which are further complicated by spatial heterogeneity of the soil matrix. This microsite heterogeneity is often invoked to explain non-normal distributions of greenhouse gas (GHG) fluxes, also known as hot spots and hot moments. To advance numerical simulation of these belowground processes, we expanded the Dual Arrhenius and Michaelis-Menten (DAMM) model, to apply it consistently for all three GHGs with respect to the biophysical processes of production, consumption, and diffusion within the soil, including the contrasting effects of oxygen (O 2 ) as substrate or inhibitor for each process. High-frequency chamber-based measurements of all three GHGs at the Howland Forest (ME, USA) were used to parameterize the model using a multiple constraint approach. The area under a soil chamber is partitioned according to a bivariate lognormal probability distribution function (PDF) of carbon (C) and water content across a range of microsites, which leads to a PDF of heterotrophic respiration and O 2 consumption among microsites. Linking microsite consumption of O 2 with a diffusion model generates a broad range of microsite concentrations of O 2 , which then determines the PDF of microsites that produce or consume CH 4 and N 2 O, such that a range of microsites occurs with both positive and negative signs for net CH 4 and N 2 O flux. Results demonstrate that it is numerically feasible for microsites of N 2 O reduction and CH 4 oxidation to co-occur under a single chamber, thus explaining occasional measurement of simultaneous uptake of both gases. Simultaneous simulation of all three GHGs in a parsimonious modeling framework is challenging, however it increases confidence that agreement between simulations and measurements is based on skillful numerical representation of processes across a heterogeneous environment.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Establishment of a Vertically Integrated Domestic Manufacturing Process for Production of Substrates Needed for Manufacture of Gas Diffusion Layers

In this project, AvCarb, LLC evaluated the baseline performance metrics of commercial carbon veils and their corresponding Gas Diffusion Layers (GDLs) with the goal of establishing an optimized, vertically integrated production system for wet-laid nonwoven substrates used in gas diffusion media for electrochemical energy storage and conversion devices. Mechanical testing and microstructural characterization were conducted and used to develop a multiscale computational model capable of simulating and predicting the performance of GDLs in fuel cells. Although the project successfully generated foundational transport and modeling data, it was terminated prior to identifying the critical GDL design parameters necessary for full optimization. The program aimed to improve carbon veil fabrication through enhanced fiber dispersion, fiber-fiber adhesion control, and improved web formation, enabling the production of high-quality, uniform substrates. Simulations were intended to guide mixing and solution delivery system design and process conditions, followed by production-scale trials to evaluate fiber dispersion, web uniformity, and mechanical robustness. At full deployment, the proposed production line would have been capable of producing approximately 650,000 m² of carbon veil annually. This capability remains strategically important, as the United States currently lacks a domestic source of wet-laid nonwoven carbon substrates that satisfy the stringent quality requirements for fuel-cell GDLs and electrolyzers representing an ongoing supply-chain vulnerability. Beyond supply-chain benefits, the project established a robust benchmarking dataset for existing commercial carbon veils while advancing next-generation material concepts targeting improved performance and manufacturing consistency.

Olson, Cynthia Lemay↗
NASA NTRS1983

Evolutionary effects of helium diffusion in population II stars

Evolutionary calculations continuing until well past turnoff are presented for models of low-mass Population II stars which take into account the effects of the diffusion of helium relative to hydrogen. Evolutionary tracks, cluster isochrones and hydrogen distributions were obtained for stellar masses in the range 0.75 to 1.01 solar masses, both in the presence and absence of diffusion. It is found that for a star of a given mass, diffusion speeds up the evolutionary process on the main sequence, although after turnoff evolution is slowed with respect to the case without diffusion. As the stars ascend the red giant branch, their outer regions are remixed so that evidence of helium diffusion is erased, and the evolutionary tracks of the models with and without diffusion converge. Thus, if the age of a globular cluster is determined from the absolute magnitude at turnoff or from fitting isochrones, diffusion results in a 25% reduction in the derived age at a turnoff magnitude of 4.23, and a 14% reduction at a turnoff magnitude of 3.45.

Stringfellow, G. S.↗
NASA NTRS1972

Enhanced diffusion welding of TD-NiCr sheet.

A method termed 'enhanced diffusion welding' has been developed to produce solid-state welds in TD-NiCr (Ni-20Cr-2ThO2) alloy sheet with weld strengths of 100% of the parent metal strength. Diffusion welded joints were made in specially processed TD-NiCr that equaled the tensile-shear and creep-rupture shear strengths of the parent material at 1090 deg C. The following observations have been made: specially processed TD-NiCr is preferred over commercial TD-NiCr for diffusion welding; the weld line can be eliminated when joining specially processed TD-NiCr by 600-grit sanding and electropolishing the faying surfaces prior to welding; and, a two-step weld cycle is preferred for diffusion welding of this alloy.

Holko, K. H.↗
NASA NTRS2003

Laminar Soot Processes (LSP) Experiment: Findings From Space Flight Measurements

The present experimental study of soot processes in hydrocarbon-fueled laminar nonbuoyant and nonpremixed (diffusion) flames at microgravity within a spacecraft was motivated by the relevance of soot to the performance of power and propulsion systems, to the hazards of unwanted fires, and to the emission of combustion-generated pollutants. Soot processes in turbulent flames are of greatest practical interest, however, direct study of turbulent flames is not tractable because the unsteadiness and distortion of turbulent flames limit available residence times and spatial resolution within regions where soot processes are important. Thus, laminar diffusion flames are generally used to provide more tractable model flame systems to study processes relevant to turbulent diffusion flames, justified by the known similarities of gas-phase processes in laminar and turbulent diffusion flames, based on the widely-accepted laminar flamelet concept of turbulent flames. Unfortunately, laminar diffusion flames at normal gravity are affected by buoyancy due to their relatively small flow velocities and, as discussed next, they do not have the same utility for simulating the soot processes as they do for simulating the gas phase processes of turbulent flames.

Sunderland, P. B.↗
DOE OSTI2023

Diffusion, atomic transport, and ordering in Al-Zr alloys: FCC and liquid phases

Additive manufacturing of materials with controlled microstructure demands knowledge of atomic scale properties near the solid-liquid transition state. Many of these properties are not affordable by experimental techniques and computer modeling is the possible solution to the problem. In this paper, we present the results of an extended atomistic study of intrinsic atomic transport due to vacancy diffusion in FCC and L12 solid phases and diffusion in the liquid phase of Al-Zr alloys. A deceleration of the overall self-diffusion was observed when Zr was added to Al. The effect was stronger in the solid and weaker in the liquid. Additionally, the effect was strongly temperature dependent in the solid phases, but not in the liquid. Atomic transport was chemically biased: transport of Zr atoms was significantly slower than that of Al atoms, and this bias effect was stronger in the solid phases. The overall diffusion and chemical ordering processes in the liquid state were five to six orders in magnitude faster than in the solid. Chemical short-range order parameters in the liquid saturated at values close to those in the ordered L12 structure of Al3Zr. Chemical and structural ordering in the solid phases was negligible over the modeled microsecond time scale. Here, the results are discussed in view of optimizing additive manufacturing parameters for the controlled formation of metastable L1 2 precipitates.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The Sluggish Diffusion of Cations in CeO 2 Probed through Molecular Dynamics and Metadynamics Simulations

Cation diffusion in fluorite‐structured CeO 2 , though far slower than anion diffusion, is an important, high‐temperature process because it governs diverse fabrication and degradation phenomena. Herein, cation diffusion is studied by means of classical molecular dynamics and metadynamics simulations. Three different mechanisms are examined: migration involving an isolated cerium vacancy, migration involving a cerium vacancy in a defect associate with an oxygen vacancy, and migration involving a cation divacancy. For each mechanism, defect diffusion coefficients are calculated as a function of temperature, from which the respective activation enthalpy of defect migration is obtained. Through comparisons with experimental cation diffusion data (specifically, of the absolute magnitude of the cation diffusivity as well as its activation enthalpy), it is concluded that cation diffusion takes place predominantly neither by isolated vacancies nor by cation vacancy–oxygen vacancy associates but by cation divacancies.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Role of Wadsley Defects and Cation Disorder to Enhance MoNb 12 O 33 Diffusion

Wadsley-Roth (WR) niobates have emerged as high-rate anode materials that can combine rapid ionic diffusion with good electronic conductivity. WR compounds have been defect-enhanced by limited annealing, however, such materials often contain multiple types of defects. In particular, both Wadsley defects (variable block size) and transition metal disorder have the potential to modify transport rates, however the corresponding effects are not well understood mechanistically. Here, MoNb 12 O 33 (MNO) was calcined at two different temperatures to compare a defect-rich condition (MNO-800) with a proximal order-rich condition (MNO-900) as assessed through XRD, XANES, EXAFS, and STEM characterizations. Galvanostatically cycled lithium half cells of MNO-800 exhibited additional capacity (307 mAhg −1 at 0.1C, 4.66% higher) and improved high-rate capacity of 200 mAhg −1 at 10C. ICI-based overpotential analysis identified solid state diffusion as the dominant rate limiting process where MNO-800 correspondingly exhibited ∼3X faster capacity-weighted diffusivity. A machine-learning interatomic potential was trained to density functional theory and then applied with molecular dynamics (MLIP-MD) to examine the possible roles of Wadsley defects and transition metal disorder. For both defect-types, Li was found to populate and activate fast diffusion paths from window sites at lower extents of lithiation as compared to the order-rich model.

defect↗
NASA NTRS1986

Modulation of galactic cosmic rays in the heliosphere

Observations of the intensity of galactic cosmic rays and anomalous components near earth and in the outer heliosphere are providing important tests for theories of solar modulation. The most recent observations show effects that seem to require that models for modulation include gradient and curvature drifts as well as the conventional processes of convection, adiabatic deceleration, and diffusion. New observations are required to define the interplay of these processes in the three-dimensional heliosphere.

Mckibben, R. B.↗
DOE OSTI2022

Direct and Sensitive Electrochemical Evaluation of Pramipexole Using Graphitic Carbon Nitride (gCN) Sensor

Pramipexole (PMXL) belongs to the benzothiazole class of aromatic compounds and is used in treating Parkinson’s disease; however, overdosage leads to some abnormal effects that could trigger severe side effects. Therefore, it demands a sensitive analytical tool for trace level detection. In this work, we successfully developed an electrochemical sensor for the trace level detection of PMXL, using the voltammetric method. For the analysis, graphitic carbon nitride (gCN) was opted and synthesized by using a high-temperature thermal condensation method. The synthesized nanoparticles were employed for surface characterization, using transmission electron microscopy (TEM), X-ray diffraction (XRD), and atomic force microscopy (AFM) techniques. The electrochemical characterization of the material was evaluated by using the electrochemical impedance spectroscopy (EIS) technique to evaluate the solution–electrode interface property. The cyclic voltammetry (CV) behavior of PMXL displayed an anodic peak in the forward scan, indicating that PMXL underwent electrooxidation, and an enhanced detection peak with lower detection potential was achieved for gCN-modified carbon paste electrode (gCN·CPE). The influence of different parameters on the electrochemical behavior was analyzed, revealing the diffusion governing the electrode process with an equal number of hydronium ions and electron involvement. For the fabricated gCN·CPE, good linearity range was noticed from 0.05 to 500 µM, and a lower detection limit (L D ) of 0.012 µM was achieved for the selected concentration range (0.5 to 30 µM). Selectivity of the electrode in PMXL detection was investigated by conducting an interference study, while the tablet sample analysis demonstrates the sensitive and real-time application of the electrode. The good recovery values for the analysis illustrate the efficiency of the electrode for PMXL analysis.

36 MATERIALS SCIENCE↗
NASA NTRS1987

Comparative radiation resistance, temperature dependence and performance of diffused junction indium phosphide solar cells

Indium phosphide solar cells whose p-n junctions were processed by the open tube capped diffusion and by the closed tube uncapped diffusion of sulfur into Czochralski-grown p-type substrates are compared. Differences found in radiation resistance were attributed to the effects of increased base dopant concentration. Both sets of cells showed superior radiation resistance to that of gallium arsenide cells, in agreement with previous results. No correlation was, however, found between the open-circuit voltage and the temperature dependence of the maximum power.

Weinberg, I.↗
NASA NTRS2022

Diffusion in Melts and Magmas

Diffusion results from random motion of particles and entities. Diffusion in melts and magmas is due to thermally excited random motion of atoms, ions, and clusters, and plays a critical role in magmatic and volcanic processes. In melts and magmas, diffusion is one of the two mechanisms of mass transfer; the other being bulk flow (referred to as convection or advection). When both are present, diffusion refers to the dispersive motion relative to the mean bulk flow in a given reference frame (Richter et al. 1998). Diffusion plays critical roles in controlling magma mixing (Watson 1982; Koyaguchi 1985, 1989; Lesher 1994; Huber et al. 2009; Guo and Zhang 2020), mineral growth and dissolution rates in magmas (e.g., Watson 1982; Harrison and Watson 1983; Zhang et al. 1989; Newcombe et al. 2014; Macris et al. 2018), bubble growth and dissolution rate in magmas (Sparks 1978; Proussevitch and Sahagian 1998; Liu and Zhang 2000; Zhang 2013), and elemental and isotope fractionation during mineral 2 growth and dissolution (Jambon 1980; Richter et al. 1999, 2003; Watson and Muller 2009; Chopra et al. 2012; Watkins et al. 2014, 2017; Holycross et al. 2016, 2018). As a result, diffusion also plays an essential role in explosive volcanic eruptions and magma crystallization. Furthermore, diffusion has important applications in geospeedometry (Lasaga 1983, 1998; Zhang 1994, 2008; Trail et al. 2016; Zhang and Xu 2016). Experimental investigation of diffusion in geologically relevant silicate melts began to flourish in the 1970’s when micro-analytical measurements of diffusion profiles became available. In addition to the vast number of papers published since then, numerous books and reviews are available for diffusion in silicate melts. Hofmann et al. (1974) edited a book titled “Geochemical Transport and Kinetics” published by Carnegie Institution of Washington. This was the first landmark book summarizing the field. Lasaga and Kirkpatrick (1981) edited a book “Kinetics of Geochemical Processes” as volume 8 of the Reviews in Mineralogy (later becoming Reviews in Mineralogy and Geochemistry) series. Zhang and Cherniak (2010) edited “Diffusion in Minerals and Melts” as volume 72 of Reviews of Mineralogy and Geochemistry series, in which one chapter focused on diffusion theory, five chapters on diffusion in silicate melts (Behrens 2010; Lesher 2010; Liang 2010; Zhang and Ni 2010; Zhang et al. 2010), and other chapters were on experimental, analytical, and computational methods, and diffusion in minerals. Several textbooks covered the principles and applications of diffusion theories (Kirkaldy and Young 1987; Shewmon 1989; Cussler 1997; Lasaga 1998; Zhang 2008; Vrentas and Vrentas 2016), and two classic books covered the mathematics of diffusion (Carslaw and Jaeger 1959; Crank 1975). In preparing for this review chapter, we thought carefully about what to cover for this vast field, and decided to briefly go through the fundamentals of diffusion (more complete review can be found in Chakraborty 1995; Zhang 2008, 2010) and solutions to often-encountered 3 diffusion problems, and then focus on post-2010 diffusion studies on silicate melts and magmas. Here, melts refer to (mostly natural) silicate liquid, and magmas refer to crystal-bearing and/or bubble-bearing melts in which the continuous phase is the melt. There is a large body of work on diffusion in glasses, especially in the materials science literature, which is not covered in this review.

Youxue Zhang↗