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At least 163 records · Page 9

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationally greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simulation of Spent Nuclear Fuel loading into a Final Waste Repository

Previous work towards studying repository loading have used: - spent nuclear fuel (SNF) with an average burnup composition; - a lumped capacitance thermal model for calculating temperature in a Cyclus repository model. The goal of this work is to improve on the repository models and use U.S. historical SNF inventory data in simulations to more accurately study the loading of a waste repository. These goals will be achieved by: - using UNF-ST-and-DARDS Unified Database (UDB) that has historic assembly-specific data (e.g, isotopic composition, heat) in Cyclus simulations; - implementing a more accurate thermal model within a Cyclus repository model. Objectives: - Create a Cyclus spent fuel conditioning model that packages spent fuel bundles into packages which have user-defined properties. - Create a Cyclus medium-fidelity repository model that gives accurate time and spatial dependent temperature values and loads the repository based on a user-selected loading strategy. Cyclus is an agent-based extensible framework for modeling flow of material through user-defined nuclear fuel cycles. In Cyclus, each facility in the fuel cycle is modeled individually and the facilities interact with one another as independent agents. The spent fuel conditioning model accepts spent fuel bundles and puts them into a cylindrical waste package. In the spent fuel conditioning model, the user can define variables: For each layer, radius, thermal conductivity, thermal diffusivity; For each package, Number of spent fuel bundles, Radius and height. The waste repository model accepts waste packages and emplaces them into available positions within the waste repository based on a thermal criteria. The thermal criteria is a temperature limit at the interface between the waste package surface and the host geology, that is set based on the repository's host geology. In the waste repository model, the user can define the variables: Capacity, Distance between waste packages, Distance between drifts, Repository host geology, Loading Strategy. After the addition of new waste packages at each time step, the waste repository model recalculates the temperature at each location in the repository. If the addition of this new package causes its temperature to exceed the thermal limit, it will be placed back into the buffer. A thermal model that relies on a transient 'outside' model and quasi-steady-state 'inside' model is used to accurately determine the temperature in the repository. The 'outside' model assumes a homogenous medium with the Engineered Barrier System (EBS) replaced by the geologic medium. Temperature solutions for the central waste package, adjacent point and line sources are superimposed to calculate the temperature at specific points in the repository. The central drift consists of one finite line source which represents the central waste package. The central drift also consists of point sources that represent neighboring waste packages in the central drift. The neighboring drifts are represented by infinite line sources. The 'inside' model is considered to be at a quasi-steady-state condition because EBS has a relatively low thermal mass compared to the infinite geologic medium. The steady state calculation is performed at each time step with the heat source and interface temperature as boundary conditions. Future Work: Run Cyclus simulations with U.S. historical SNF inventory data, the spent fuel conditioning and repository models to study how waste package acceptance strategies impact repository loading.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Kinetics study of the evolution of oxygen-related defects in mono-crystalline silicon subjected to electron-irradiation and thermal treatment

The diffusion and dissociation mechanisms governing the evolution of oxygen and vacancy-oxygen defects in Czochralski-grown Si samples have been studied. The samples were irradiated at (i) room temperature or (ii) elevated temperature (350 °C) by MeV electrons and then isothermally annealed at 8 different temperatures in the range of 300 °C to 500 °C. The evolution of the concentrations of oxygen complexes (O{sub n}, n ≤ 3) and mono-vacancy-oxygen defects (VO{sub n}, n ≤ 4) have been followed by infrared absorption measurements of local vibrational modes originating from the individual defects. The experimental kinetics data have been compared with simulation results based on the theory for diffusion limited reactions, assuming a model where sequential build-up of the VO{sub n} defects is a key ingredient. A close quantitative agreement is obtained for both sets of samples despite quite different initial conditions prior to the annealing, which adds evidence to the validity of the model. Values for the diffusivity and dissociation rates of VO{sub n} (n ≤ 4) and O{sub n} (n ≤ 3) have been deduced and in general, the mobility and stability of VO{sub n} decrease and increase with n, respectively. For all the defects, partial dissociation appears as a prevailing process during diffusion, while full dissociation of VO{sub n} is limited by an energy barrier identical to that of interstitial oxygen (O{sub i}) diffusion (∼2.55 eV). The oxygen dimer and trimer are fast diffusers but slower than substitutional oxygen, i.e., VO; VO is found to be the most mobile species, whilst O{sub i} is the slowest one with a difference in diffusivity of up to 7 orders of magnitude in the studied temperature range.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization

Nonlocal models naturally handle a range of physics of interest to SNL, but discretization of their underlying integral operators poses mathematical challenges to realize the accuracy and robustness commonplace in discretization of local counterparts. This project focuses on the concept of asymptotic compatibility, namely preservation of the limit of the discrete nonlocal model to a corresponding well-understood local solution. We address challenges that have traditionally troubled nonlocal mechanics models primarily related to consistency guarantees and boundary conditions. For simple problems such as diffusion and linear elasticity we have developed complete error analysis theory providing consistency guarantees. We then take these foundational tools to develop new state-of-the-art capabilities for: lithiation-induced failure in batteries, ductile failure of problems driven by contact, blast-on-structure induced failure, brittle/ductile failure of thin structures. We also summarize ongoing efforts using these frameworks in data-driven modeling contexts. This report provides a high-level summary of all publications which followed from these efforts.

97 MATHEMATICS AND COMPUTING↗

Numerical Study of PAHs and Soot Emissions from Gasoline–Methanol, Gasoline–Ethanol, and Gasoline– n -Butanol Blend Surrogates

Soot formation is an intricate phenomenon, and soot propensity of a fuel is interwoven with the fuel composition, physical and chemical properties, and combustion environment. Here, the present study examines the hypothesis that in addition to the chemical composition of the fuel, the sooting nature of the fuel is closely coupled with its chemical property known as octane sensitivity (S). With this motivation, the present study numerically investigates the effects of gasoline surrogate composition and its property, octane sensitivity (S), on polycyclic aromatic hydrocarbons (PAHs) and soot emissions. Four-component toluene primary reference fuel (TPRF)–alcohol blends, comprising iso-octane, n-heptane, toluene, and one of the three different alcohols- methanol, ethanol, and n-butanol, are used as gasoline surrogates. A total of 320 TPRF–alcohol mixtures, with S in the range of 1–10, are examined under laminar counterflow diffusion flame conditions. A detailed chemical mechanism coupled with a comprehensive soot model, which includes reactions for soot inception, surface growth, PAH condensation, and oxidation, is adopted. The analysis indicates that the toluene content in the fuel mixture has a prominent effect, while the alcohol content and octane sensitivity of the fuel have a weak correlation with the PAHs and soot. Thus, it is not clear if any of these three variables, namely, toluene content in the fuel, alcohol content in the fuel, and S, are individually sufficient to characterize the PAHs and soot across various blends. For this reason, a new variable (X CHO ) based on the elemental composition of the fuel mixture is identified and it is shown that X CHO along with S of the fuel characterize soot emissions satisfactorily. Further, a reaction path analysis indicates that the efficacy of alcohols in reducing soot emissions follows the order: methanol > ethanol > n-butanol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural constraint integration in a generative model for the discovery of quantum materials

Billions of organic molecules have been computationally generated, yet functional inorganic materials remain scarce due to limited data and structural complexity. Here, in this work, we introduce Structural Constraint Integration in a GENerative model (SCIGEN), a framework that enforces geometric constraints, such as honeycomb and kagome lattices, within diffusion-based generative models to discover stable quantum materials candidates. SCIGEN enables conditional sampling from the original distribution, preserving output validity while guiding structural motifs. This approach generates ten million inorganic compounds with Archimedean and Lieb lattices, over 10% of which pass multistage stability screening. High-throughput density functional theory calculations on 26,000 candidates shows over 95% convergence and 53% structural stability. A graph neural network classifier detects magnetic ordering in 41% of relaxed structures. Furthermore, we synthesize and characterize two predicted materials, TiPd 0.22 Bi 0.88 and Ti 0.5 Pd 1.5 Sb, which display paramagnetic and diamagnetic behaviour, respectively. Our results indicate that SCIGEN provides a scalable path for generating quantum materials guided by lattice geometry.

36 MATERIALS SCIENCE↗

Decomposition of methane diluted with inert gas in an RF discharge cell

Decomposition of methane using non-thermal plasmas is an attractive route for producing hydrogen-rich gases and valuable carbon nanomaterials. Understanding how plasma discharge modes influence methane decomposition in optimizing plasma-assisted chemical conversion remains unexplored. This study explores the coupling between the discharge structure and product selectivity in RF capacitively coupled discharges operating in methane/inert gas mixtures in the pressure range of 2–3 torr. Under our experimental conditions the discharge exhibits mode transitions from uniform to striated in Ar and Kr and from diffuse to contracted in Ar and Kr with <5% CH 4 . The discharges in He and Ne remained uniform under our operating conditions, and their mixtures with CH 4 remained diffuse. A 0-d model for Ar/CH 4 discharge established a threshold for contraction while also asserting the importance of Ar$^{*}_{\textrm{m}}$ in the dissociation and ionization processes. The highest degree of methane decomposition, >99.7% with the main products of acetylene and graphitized solid carbon was achieved in the contracted discharge mode for both Kr or Ar with ⩽5% CH 4 . We demonstrate that contraction can play a crucial role in the effective decomposition of methane with value-added products and that both the electronic and thermal properties of plasma gas are responsible for this effect.

RF plasma↗

Diffusive confinement of free radical intermediates in the OH radical oxidation of semisolid aerosols

Multiphase chemical reactions (gas + solid/liquid) involve a complex interplay between bulk and interface chemistry, diffusion, evaporation, and condensation. Reactions of atmospheric aerosols are an important example of this type of chemistry: the rich array of particle phase states and multiphase transformation pathways produce diverse but poorly understood interactions between chemistry and transport. Their chemistry is of intrinsic interest because of their role in controlling climate. Their characteristics also make them useful models for the study of principles of reactivity of condensed materials under confined conditions. Previously, we have reported a computational study of the oxidation chemistry of a liquid aliphatic aerosol. In this study, we extend the calculations to investigate nearly the same reactions at a semisolid gas-aerosol interface. A reaction-diffusion model for heterogeneous oxidation of triacontane by hydroxyl radicals (OH) is described, and its predictions are compared to measurements of aerosol size and composition, which evolve continuously during oxidation. Our results are also explicitly compared to those obtained for the corresponding liquid system, squalane, to pinpoint salient elements controlling reactivity. The diffusive confinement of the free radical intermediates at the interface results in enhanced importance of a few specific chemical processes such as the involvement of aldehydes in fragmentation and evaporation, and a significant role of radical-radical reactions in product formation. The simulations show that under typical laboratory conditions semisolid aerosols have highly oxidized nanometer-scale interfaces that encapsulate an unreacted core and may confer distinct optical properties and enhanced hygroscopicity. This highly oxidized layer dynamically evolves with reaction, which we propose to result in plasticization. The validated model is used to predict chemistry under atmospheric conditions, where the OH radical concentration is much lower. The oxidation reactions are more strongly influenced by diffusion in the particle, resulting in a more liquid-like character.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Application of Scalar Filtered Density Function to Turbulent Flows Under Supercritical Condition

Abstract The scalar filtered density function (FDF) methodology is extended and employed for large eddy simulation (LES) of turbulent flows under supercritical condition. To describe real fluid behavior, the extended methodology incorporates the generalized heat and mass diffusion models along with real fluid thermodynamic relations which are derived using the cubic Peng–Robinson equation of state. These models are implemented within the stochastic differential equations comprising the scalar FDF transport. Simulations are conducted of a temporally developing mixing layer under supercritical condition and the results are assessed by comparing with data generated by direct numerical simulation (DNS) of the same layer. The consistency of the proposed FDF methodology is assessed. The LES-FDF predictions are shown to agree favorably with the DNS data and exhibit several key features pertaining to supercritical turbulent flows.

Energy & Fuels↗

The Method of Finite Averages: A rigorous upscaling methodology for heterogeneous porous media

Rigorous upscaling techniques offer accurate and computationally-efficient strategies for modeling the average behaviors of multi-physical, multiscale phenomena in geological porous media. However, such techniques often rely on a variety of methodological assumptions that prohibit their rigorous application to practical systems (e.g., systems involving heterogeneous porous media, system-scale boundary conditions, and fine-scale dynamics that are not diffusion-dominant). In this work, we aim to formulate an upscaling methodology with few methodological assumptions to provide high levels of model generality and foster the utilization of rigorously-derived upscaled models in practice. In particular, we introduce the Method of Finite Averages (MoFA), a novel upscaling methodology for rigorously modeling heterogeneous porous media and system-scale boundary conditions. We then detail MoFA’s implementation for the advective–diffusive transport of a single species and compare the methodology with classic numerical techniques, as well as other rigorous upscaling techniques, to highlight MoFA’s unique combination of rigor and generality. We then validate the derived model while demonstrating its benefits in three numerical experiments. The results suggest that (1.) the applicability and a priori error guarantees of MoFA models do not directly depend on system geometry, (2.) a model’s applicability and error guarantees can be can arbitrarily expanded and reduced, respectively, with further computational expense, and (3.) downscaling with MoFA provides an efficient strategy for generating accurate pore-scale solutions from upscaled results. Ultimately, the results evidence that upscaled models can be rigorously derived for heterogeneous porous media systems and resolved in a fraction of the time it takes to perform the equivalent pore-scale simulations.

58 GEOSCIENCES↗

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomain $\Omega^{hs}$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $\Omega^{hs}$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $\Omega^{hs}$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.

Barajas-Solano, David A.↗

Short- and Intermediate-Range Structure and Dynamics of Fe-Ni-C Liquid Under Compression

Properties of liquid Fe alloys under high-pressure conditions are crucial for understanding the composition, thermal state, and dynamics of Earth’s core. Experiments on such liquids, however, are often performed under pressures far below those of the outer core, necessitating long extrapolations of experimental results to core conditions. Such estimates can be complicated by light elements possibly forming pressure-dependent molecular clusters that can significantly affect the physical properties of liquids as core conditions are approached. First-principles molecular dynamics simulations were employed to compute the properties of an Fe-Ni-C liquid with a composition of Fe 3.7 Ni 0.37 C at 1673 K and pressures from 0 to 67 GPa to benchmark computational methods on pressure effects on the structure and properties of the liquid relative to low pressure experimental results. The short-range structure is manifested by the coordination number (CN) of Fe/Ni-Fe/Ni being around 12, indicative of a nearly close-packed structure in the pressure range, and the CN of C-Fe/Ni gradual increasing from 6.5 to 8.5, indicative of an approximately octahedral to cubic transition as pressure increases. The Fe/Ni-Fe/Ni bond distance, however, is found to be 10 times more compressible than the C-Fe/Ni distance. The intermediate-range structure of Fe/Ni-Fe/Ni and C-Fe/Ni subsystems, described by a partial configurationally decomposed distribution function, undergoes substantial changes, characterized by a significant increase of the number of polyhedra that share 3 atoms with each other. Such dense configurations are related to an increased bulk modulus, decreased diffusion coefficient, decreased activation volume for diffusion, and increased shear viscosity. Reproducing the experimental observations at low pressures provides important support for modeling the liquid under the conditions relevant to the outer core.

58 GEOSCIENCES↗

Simplified calculation of the area specific impedance for solid-state battery design

Simplified algebraic area specific impedance (ASI) correlations have been developed for solid-state composite battery electrodes made of a single ion conducting electrolyte, conductive additive, and intercalation active material. Two ASI expressions were developed, one for short times ( i.e. , pulsed power operation) and another for the pseudo steady state operation (i.e., sustained discharge for energy estimation). A full electrochemical model based on porous electrode theory was developed to examine the accuracy of the simplified ASI expressions. The simplified expressions agree favorably with full model results over a wide range of parameters (i.e. , electrode thicknesses, electrolyte conductivities, solid-state diffusion coefficients, specific surface areas, etc.) and conditions (i.e. , C-rates, states of charge, and pulse times). Under most conditions, the error between the full model and the correlations is well below 7 %. Higher errors were observed for the pseudo steady state expression at high/ low states of charge where the assumption of uniform reaction distributions loses validity. Here, the short time ASI has higher error at low states of charge due to the nonlinearity of the open circuit voltage equation, which is assumed linear in the formulation of the simplified algebraic expression.

25 ENERGY STORAGE↗

A computational investigation of high-flux, plate-and-frame membrane modules for industrial carbon capture

In this work, we study the application of membrane-based separation systems for carbon capture, considering plate-and-frame membrane modules. The successful deployment of membrane CO 2 capture system relies on high-performing membranes as well as effective membrane modules that can fully exploit the developed membranes. A plate-and-frame membrane module is especially attractive for CO 2 capture from industrial flue gas due to its lower pressure drop compared to its counterparts such as spiral wound modules and hollow fiber modules. To design better plate-and-frame modules, we investigate their basic unit - a single membrane stack through a combination of computational modeling and experimental investigations. The modeling approach is based on Computational Fluid Dynamics (CFD) to represent a multiphysics problem, including the fluid flow and diffusion processes within a membrane module. We use experimental data collected under different operating conditions to validate the CFD model. Numerical results suggest a good agreement between experiments and model outputs for the CO 2 recovery, CO 2 mole fraction in the retentate and permeate, and stage-cut. The CFD model is able to predict accurately the flow behavior, providing valuable insights on the effects of fluid dynamics on mass transfer of CO 2 . We also carry out a sensitivity analysis to identify the effect of key parameters on the CO 2 recovery and the CO 2 purity of the outlet streams.

CFD simulation↗

CFD modeling of high-flux plate-and-frame membrane modules for industrial carbon capture

In this work, we study the application of membrane-based separation systems for carbon capture, considering plate-and-frame membrane modules. The successful deployment of membrane CO2 capture system relies on high-performing membranes as well as effective membrane modules that can fully exploit the developed membranes. A plate-and-frame membrane module is especially attractive for CO2 capture from industrial flue gas due to its lower pressure drop compared to its counterparts such as spiral wound modules and hollow fiber modules. To design better plate-and-frame modules, we investigate their basic unit - a single membrane stack through a combination of computational modeling and experimental investigations. The modeling approach is based on Computational Fluid Dynamics (CFD) to represent a multiphysics problem, including the fluid flow and diffusion processes within a membrane module. We use experimental data collected under different operating conditions to validate the CFD model. Numerical results suggest a good agreement between experiments and model outputs for the CO2 recovery, CO2 mole fraction in the retentate and permeate, and stage-cut. The CFD model is able to predict accurately the flow behavior, providing valuable insights on the effects of fluid dynamics on mass transfer of CO2. We also carry out a sensitivity analysis to identify the effect of key parameters on the CO2 recovery and the CO2 purity of the outlet streams.

Dosso, Cheick↗

GALACTIC COSMIC-RAY INTENSITY MODULATION BY COROTATING INTERACTION REGION STREAM INTERFACES AT 1 au

We present a new model that couples galactic cosmic-ray (GCR) propagation with magnetic turbulence transport and the MHD background evolution in the heliosphere. The model is applied to the problem of the formation of corotating interaction regions (CIRs) during the last solar minimum from the period between 2007 and 2009. The numerical model simultaneously calculates the large-scale supersonic solar wind properties and its small-scale turbulent content from 0.3 au to the termination shock. Cosmic rays are then transported through the background, and thus computed, with diffusion coefficients derived from the solar wind turbulent properties, using a stochastic Parker approach. Our results demonstrate that GCR variations depend on the ratio of diffusion coefficients in the fast and slow solar winds. Stream interfaces inside the CIRs always lead to depressions of the GCR intensity. On the other hand, heliospheric current sheet (HCS) crossings do not appreciably affect GCR intensities in the model, which is consistent with the two observations under quiet solar wind conditions. Therefore, variations in diffusion coefficients associated with CIR stream interfaces are more important for GCR propagation than the drift effects of the HCS during a negative solar minimum.

79 ASTRONOMY AND ASTROPHYSICS↗

Adsorption and Capillary Condensation-Induced Imbibition in Nanoporous Media

Multiphase flow phenomena in nanoporous media are encountered in many science and engineering applications. Shales, for example, possessing complex nanopore networks, have considerable importance as source rocks for unconventional oil and gas production and as low-permeability seals for geologic carbon sequestration or nuclear waste disposal. This work presents a theoretical investigation of the processes controlling adsorption, capillary condensation, and imbibition in such nanoporous media, with a particular focus on understanding the effects of fluid-fluid and fluid-pore wall interaction forces in the interconnected nanopore space. Building on a new theoretical framework, we developed a numerical model for the multiphase nanoporous flow and tested it against water vapor uptake measurements conducted on a shale core sample. The model, which is based on the density functional approach, explicitly includes the relevant interaction forces among fluids and solids while allowing for a continuum representation of the porous medium. The experimental data include gravimetrically measured mass changes in an initially dry core sample exposed to varying levels of relative humidity, starting with a low relative humidity (rh = 0.31) followed by a period of a higher relative humidity (rh = 0.81). During this process, water vapor uptake in the dry core is recorded as a function of time. Our model suggests that, under low rh conditions, the flow within the shale sample is controlled by adsorption- and diffusion-type processes. After increasing the rh to 0.81, the uptake of water vapor becomes more significant, and according to our model, this can be explained by capillary condensation followed by immiscible displacement in the core sample. It appears that strong fluid-pore wall attractive forces cause condensation near the inlet, which then induces water imbibition further into sample.

58 GEOSCIENCES↗

Understanding copper diffusion in CuInSe 2 with first-principles based atomistic and continuum models

We investigate the diffusion of copper in CuInSe 2 using thermodynamic and kinetic models based on density functional theory calculations, attempting to reconcile large differences in reported experimental diffusivities. We find that observations of rapid chemical diffusion can be explained by large thermodynamic factors, which we calculate using a compositionally constrained model of intrinsic point defect formation. We further characterize how copper diffusion coefficients depend on material synthesis conditions and exhibit their variation across the CuInSe 2 secondary phase diagram. In doing so, we identify stable off-stoichiometries that are dominated by either vacancy- or interstitial-mediated diffusion mechanisms. These results are employed in the development of a continuum reaction–diffusion model, which we use to simulate experimental depth profiles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗