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DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid–governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. As a result, more sophisticated materials than fluids (e.g., elastic–plastic materials) have been considered as well.

42 ENGINEERING↗

DOE OSTI2020

Ion redistributions at interfaces facilitate nucleation and growth of branched Ag 3 PO 4 polypods

Branched structures are of spectacular interest due to their improved light-harvesting, direct carrier transportation pathway, high surface area, and controllable electronic structures. Understanding their growth mechanisms and controlling factors enables the design of materials with improved functions. Interfaces of liquid-solid and air-liquid are known to change the chemical and physical properties of the liquid solution. However, their role in crystal growth, especially of branched structures, is seldom investigated. In this work we synthesized branched silver phosphate polypods in a thin layer of aqueous solution at room temperature taking advantage of the unique properties near the interfaces. The branched crystals nucleate and grow with a liquid thickness of 810 µm or below requiring the presence of both the gas-liquid and liquid-solid interfaces. The hydrophilicity of the solid substrate also facilitates nucleation and growth. Our results indicate that the synergism of long-range electric fields (ion distributions) at the interfaces promotes not only the nucleation and growth of silver phosphate but also the formation of branched structures. This work can be a reference for facilitating crystal nucleation and growth and controlling structures with specific morphologies, such as branched ones, by understanding and mimicking the properties at the interfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2026

All‐Solid‐State Batteries With Mechanically Stable Interfaces Consisting of a Zero‐Strain Cation‐Disordered Rocksalt Cathode

Interface stabilization is critical to the development of working all‐solid‐state batteries. Rigid cathode/solid electrolyte interfaces often disintegrate due to anisotropic volume change of cathode‐active materials, resulting in irreversible capacity loss. Herein, we demonstrate that Li 1.211 Mo 0.467 Cr 0.3 O 2 (LMCO), a pioneering cation‐disordered rocksalt oxide (DRX) cathode that has intrinsically small volume change upon lithium intercalation, can be integrated with a thiophosphate‐based solid electrolyte for all‐solid‐state batteries. Interface stability of the all‐solid LMCO cell was investigated by electrochemical impedance spectroscopy, X‐ray micro‐computed tomography, and electron microscopy. Since LMCO was initially synthesized as a layered phase exhibiting a large volume change, interface disintegration can be observable in the early cycles. As layered LMCO phase‐transformed into DRX LMCO in subsequent cycles, reintegration of the interfaces occurs within a pressurized cell as a result of its zero‐stain behavior. Consequently, the DRX LMCO cathode maintains interface integrity, and thus electrical wiring, over an extended number of cycles, leading to improved capacity retention with small internal cell resistance.

DRX↗

DOE OSTI2022

A Many-Body Perturbation Theory Approach to Energy Band Alignment at the Crystalline Tetracene–Silicon Interface

Hybrid inorganic–organic semiconductor (HIOS) interfaces are of interest for new photovoltaic devices operating above the Shockley–Queisser limit. Predicting energy band alignment at the interfaces is crucial for their design, but represents a challenging problem due to the large scales of the system, the energy precision required and a wide range of physical phenomena that occur at the interface. To tackle this problem, many-body perturbation theory in the non-self-consistent GW approximation, orbital relaxation corrections for organic semiconductors, and line-up potential method for inorganic semiconductors which allows for tractable and accurate computing of energy band alignment in crystalline van-der-Waals hybrid inorganic–organic semiconductor interfaces are used. In this work, crystalline tetracene physisorbed on the clean hydrogen-passivated 1 × 2 reconstructed (100) silicon surface is studied. Using this computational approach, it is found that the energy band alignment is determined by an interplay of the mutual dynamic dielectric screening of two materials and the formation of a dipole layer due to a weak hybridization of atomic/molecular orbitals at the interface. The significant role of the exchange-correlation effects in predicting band offsets for the hybrid inorganic–organic semiconductor interfaces is also emphasized.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2016

An implementation and evaluation of the MPI 3.0 one-sided communication interface

The Q1 Message Passing Interface (MPI) 3.0 standard includes a significant revision to MPI’s remote memory access (RMA) interface, which provides support for one-sided communication. MPI-3 RMA is expected to greatly enhance the usability and performance ofMPI RMA.We present the first complete implementation of MPI-3 RMA and document implementation techniques and performance optimization opportunities enabled by the new interface. Our implementation targets messaging-based networks and is publicly available in the latest release of the MPICH MPI implementation. Here using this implementation, we explore the performance impact of new MPI-3 functionality and semantics. Results indicate that the MPI-3 RMA interface provides significant advantages over the MPI-2 interface by enabling increased communication concurrency through relaxed semantics in the interface and additional routines that provide new window types, synchronization modes, and atomic operations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Propagation of Spin Waves Through an Interface Between Ferromagnetic and Antiferromagnetic Materials

Boundary conditions for order parameters at an interface between ferromagnetic (FM) and two-sublattice antiferromagnetic (AFM) materials are obtained in the continuous medium approximation similarly to the approach which allows one to take into account the finite thickness of the FM/FM interface, which is much less than spin wavelength. Three order parameters are considered inside an interface of finite thickness with the magnetization M of FM, magnetizations of both sublattices M{sub 1} and M{sub 2} of AFM. The uniform and non-uniform exchange between all order parameters are taken into account to the interface energy. Using these boundary conditions, the excitation of a surface evanescent spin wave is considered in AFM when the spin wave in FM falls onto this interface. The coefficients and the phases of transmission and reflection of spin wave through the FM/AFM interface are derived.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Geophysical methods reveal the soil architecture and subsurface stratigraphic heterogeneities across land-lake interfaces along Lake Erie

Abstract Purpose The land-lake interface is a unique zone where terrestrial and aquatic ecosystems meet, forming part of the Earth’s most geochemically and biologically active zones. The unique characteristics of this interface are yet to be properly understood due to the inherently high spatiotemporal variability of subsurface properties, which are difficult to capture with the traditional soil sampling methods. Geophysical methods offer non-invasive techniques to capture variabilities in soil properties at a high resolution across various spatiotemporal scales. Methods We combined electromagnetic induction (EMI), electrical resistivity tomography (ERT), and ground penetrating radar (GPR) with data from soil cores and in situ sensors to investigate hydrostratigraphic heterogeneities across land-lake interfaces along the western basin of Lake Erie. Results EMI revealed high spatial heterogeneities in ECa distribution across the land-lake interfaces, with higher values in the wetland and transition zones compared to the upland zone. Soil ECa maps matched soil maps from a public database with the hydric soil units delineated as high conductivity zones (ECa > 40 mS/m). ERT and GPR showed vertical variation in soil properties with clear stratigraphic boundaries, and correlation of ERT profiles with lithologs from piezometers revealed the stratigraphic units of silt–clay and till sequence down to 3.5 m depth which are consistent with the surficial geology of the study area. Conclusions These results validate the use of multiple geophysical methods for extrapolating soil properties and mapping stratigraphic structures at land-lake interfaces, thereby providing the missing information required to improve the earth system model (ESM) of coastal interfaces.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

Irradiation-induced formation of a spinel phase at the FeCr/MgO interface

Oxide dispersion strengthened ferritic/martensitic alloys have attracted significant attention for their potential uses in future nuclear reactors and storage vessels, as the metal/oxide interfaces act as stable high-strength sinks for point defects while also dispersing helium. Here, in order to unravel the evolution and interplay of interface structure and chemistry upon irradiation in these types of materials, an atomically sharp FeCr/MgO interface was synthesized at 500 °C and separately annealed and irradiated with Ni 3+ ions at 500 °C. After annealing, a slight enrichment of Cr atoms was observed at the interface, but no other structural changes were found. However, under irradiation, sufficient Cr diffuses across the interface into the MgO to form a Cr-enriched transition layer that contains spinel precipitates. First-principles calculations indicate that it is energetically favorable to incorporate Cr, but not Fe, substitutionally into MgO. Furthermore, our results indicate that irradiation can be used to form new phases and complexions at interfaces, which may have different radiation tolerance than the pristine structures.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Effects of three-dimensional Cu/Nb interfaces on strengthening and shear banding in nanoscale metallic multilayers

Manipulation of the atomic-scale structure of two-dimensional (2D) interfaces have been shown to provide nanocomposites with enhanced strength, deformability, and radiation damage resistance. In comparison with 2D interfaces, here we investigate the mechanical response of nanocomposites containing three-dimensional (3D) Cu/Nb interfaces consisting of a chemical/structural gradient separating pure Cu and Nb layers, through which the lattice mismatch between face-centered cubic Cu and body-centered cubic Nb is accommodated over a distance of several nanometers. Furthermore, it is demonstrated that 3D interfaces increase the yield and flow strength by 50% and 22%, respectively, over composites containing 2D interfaces at similar layer thicknesses. After 14% compressive strain, the onset of shear banding results in co-deformation of both Cu and Nb phases within and outside of the shear band. We conclude with a discussion of the role of interface structure in shear band formation and growth in 3D Cu/Nb.

3-dimensional interface↗

DOE OSTI2022

Characterization of the atomic-level structure of γ-alumina and (111) Pt/γ-alumina interfaces

The atomic-level structure of platinum/γ-alumina interfaces is characterized in a model system of dense γ-alumina embedded with faceted Pt NPs produced by implantation of platinum ions into sapphire followed by thermal annealing in air at 800 °C. Aberration-corrected scanning transmission electron microscopy (STEM) was used to collect atomic-resolution images, which are compared to STEM image simulations of two experimentally-based bulk models of γ-alumina by Smrčok et al. and Zhou and Snyder. A density functional theory (DFT) based model of (111) interfaces with different chemical terminations (O, Al 1 , Al 2 ) of the γ-alumina developed by Oware Sarfo et al. is also compared to experimental STEM data from Pt/γ-alumina interfaces. Further, the Smrčok γ-alumina model provides a better fit than the Zhou structure to the bulk of the γ-alumina. The oxygen-terminated Oware Sarfo model best fits the experimental data and is a very good model close to the interface. However, the fit of the interface model to the experimental data is poorer beyond the third atomic layer in the γ-alumina. This is attributed to compromises required in the design of the model to limit the cell size and computational time for DFT calculations. Understanding the accuracy and limits of the structural models of γ-alumina and Pt/γ-alumina interfaces is important to further the understanding of the structure/property relationships in this system.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Multi-material hydrodynamics with algebraic sharp interface capturing

A finite volume method for Eulerian multi-material hydrodynamics with sharp interface capturing is presented here. The pressure-temperature non-equilibrium multi-material system with finite-rate pressure relaxation in mixed-cells is considered here. This pressure closure facilitates material-property-dependent pressure relaxation, rather than instantaneous pressure equilibration, which in turn allows the use of unsplit high-order time-integrators. A modified tangent of hyperbola for interface capturing (THINC) method is used to reconstruct multi-material (> 2) interfaces, on three-dimensional unstructured meshes. A simple modification which extends the THINC reconstruction to interfaces between more than two materials is proposed. It is demonstrated that the modified THINC can capture multi-material interfaces within 2–4 tetrahedral cells. Since no geometric reconstructions are required by the THINC method, the presented multi-material method is algorithmically simple, and computationally efficient. Consistent reconstructions of conserved quantities at material interfaces ensure that conservation and closure laws are satisfied at the discrete level. Through a suite of test problems solved on unstructured meshes, it is demonstrated that the presented method is a promising candidate for accurate and efficient multi-material hydrodynamics computations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Influence of processing on secondary phase formation and microstructural evolution at U-10Mo alloy and Zr interlayer interfaces

Thermo-mechanical processing of uranium-10 wt. % molybdenum (U-10Mo) fuel plates leads to microstructure changes at the U-10Mo/Zr interfaces. Secondary phases formed at this interface are particularly important to interfacial bond strength, process optimization, and maintaining structural integrity of the U-10Mo fuel plates during irradiation. In this work, we determined the phases and phase transformation products occurring at the interface of the U-10Mo fuel and Zr interlayer when the fuel plate is subjected to short and long hot isostatic pressure times. Interfacial morphology, structure and composition of phases formed, and relative hardness across the U-10Mo/Zr interfaces were studied using a multi-length scale, multi-modal characterization approach involving electron microscopy, atom probe tomography, and atomic force microscopy. Here, results highlight that the extent of phase transformations, secondary phase formation, and hardness variability across interfaces can be controlled by modifying processing parameters. Phase diagram construction and thermodynamic calculations were performed using the Thermocalc software to identify expected phases formed at interfaces during the maximum hold temperature of 560 °C experienced during HIP.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

An axial temperature profile curvature criterion for the engineering of convex crystal growth interfaces in Bridgman systems

A unifying idea is presented for the engineering of convex melt-solid interface shapes in Bridgman crystal growth systems. Previous approaches to interface control are discussed with particular attention paid to the idea of a “booster” heater. Proceeding from the idea that a booster heater promotes a converging heat flux geometry and from the energy conservation equation, we show that a convex interface shape will naturally result when the interface is located in regions of the furnace where the axial thermal profile exhibits negative curvature, i.e., where d 2 T/dz 2 < 0. This criterion is effective in explaining prior literature results on interface control and promising for the evaluation of new furnace designs. Here we posit that the negative curvature criterion may be applicable to the characterization of growth systems via temperature measurements in an empty furnace, providing insight about the potential for achieving a convex interface shape, without growing a crystal or conducting simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Conversion of ethanol to 1,3–butadiene over Ag–ZrO 2 /SiO 2 catalysts: The role of surface interfaces

A series of Ag–ZrO 2 /SiO 2 catalysts with different metal–support interfaces were synthesized in an effort to elucidate the roles of specific interfaces in controlling the ethanol to 1,3–butadiene conversion and selectivity. According to the results of detailed characterizations (e.g. CO/pyridine–DRIFTS, XPS, TEM, NH 3 –TPD, and 1 H MAS NMR), it was found that the Ag–O–Si interfaces significantly enhanced the dehydrogenation of ethanol while the presence of ZrO 2 improved the interaction between Ag and ZrO 2 /SiO 2 , creating more Ag δ+ active sites. In this research, the high dispersion of ZrO 2 on SiO 2 generated abundant Zr–O–Si interfaces with medium and weak Lewis acidity, promoting the condensation of acetaldehyde to crotonaldehyde. These Zr–O–Si interfaces in close interaction with Ag δ+ species played a critical role in the enhanced H transfer during the MPV reduction of crotonaldehyde to crotyl alcohol. The synergies among the interfaces resulted in retarded ethanol dehydration reactivity, balanced ethanol dehydrogenation and condensation reactions, and a subsequent high 1,3–butadiene yield.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

From coherent to incoherent mismatched interfaces. A generalized continuum formulation of surface stresses

The equilibrium of coherent and incoherent mismatched interfaces is reformulated in the context of continuum mechanics based on the Gibbs dividing surface concept. Two surface stresses are introduced: a coherent surface stress and an incoherent surface stress, as well as a transverse excess strain. Additionally, the coherent surface stress and the transverse excess strain represent the thermodynamic driving forces of stretching the interface while the incoherent surface stress represents the driving force of stretching one crystal while holding the other fixed and thereby altering the structure of the interface. These three quantities fully characterize the elastic behavior of coherent and incoherent interfaces as a function of the in-plane strain, the transverse stress and the mismatch strain. The isotropic case is developed in detail and particular attention is paid to the case of interfacial thermo-elasticity. This exercise provides an insight on the physical significance of the interfacial elastic constants introduced in the formulation and illustrates the obvious coupling between the interface structure and its associated thermodynamics quantities. Finally, an example based on atomistic simulations of Cu/Cu 2 O interfaces is given to demonstrate the relevance of the generalized interfacial formulation and to emphasize the dependence of the interfacial thermodynamic quantities on the incoherency strain with an actual material system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗