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Coupled chemo-mechanical modeling of point-defect diffusion in a crystal plasticity fast Fourier transform framework
Below the yield strength and at moderate-to-high homologous temperatures, the inelastic deformation of metals is mostly governed/rate-controlled by vacancy diffusion-mediated processes. As a function of grain size, stress, temperature and dislocation content, vacancies (or atoms) can adopt preferential diffusion paths across grain interiors, along grain boundaries, or towards and along dislocations, resulting in climb and self-climb. In the steady state and under constant load, grain boundary and grain bulk vacancy diffusion-mediated plasticity have been described in seminal works by Coble and by Nabarro and Herring, respectively. Yet, the interplay between all aforementioned potential diffusion pathways has not been comprehensively mapped. This work presents a thermodynamically-consistent full-field model integrated within a voxel-based elasto-viscoplastic fast Fourier transform framework, which considers the coupling between the diffusion-mediated plasticity mechanisms. In the proposed approach, the kinetics and kinematics of plastic deformation due to vacancy diffusion along grain boundaries and grain bulk, as well as the exchange between grain boundaries and bulk are described explicitly. A homogenization approach at the voxel level is further introduced to simultaneously consider bulk and grain boundary diffusion in a numerically efficient fashion. The new formulation predicts the expected strain rate dependencies and the scaling of the steady-state creep rate with respect to grain size, temperature, and stress. Finally, the model predicts the transition from grain bulk to grain boundary-dominated diffusion with reduction in grain size, a significant step towards capturing transitions in deformation behavior without any phenomenological or ad-hoc adjustments.
Origin of fast oxide ion diffusion along grain boundaries in Sr-doped LaMnO 3
Enhanced oxide ion diffusion by 3 to 5 orders of magnitude along grain boundary core in Sr-doped LaMnO 3 .
Atomic Diffusion, Segregation, and Grain Boundary Migration in Nickel-Based Alloys from Molecular Dynamics Simulations
Grain boundary diffusion and metal mobility in alloys control material performance in many applications and yet remain poorly understood at a mechanistic level. With advances in accessible time and length scales for computational molecular simulations, and recent force field developments, we now possess tools to help unravel those mechanisms. Using large-scale molecular dynamics simulations, here we examined vacancy-mediated diffusion processes in Ni-5Cr alloy with low and high-energy grain boundaries. We show that atomic diffusion inside the grain boundary plane is about four times higher than bulk diffusion, at any temperature, and exhibits a typical Arrhenius behavior with a very small energy barrier (0~.8 eV for Cr and 0.7 eV for Ni within 1300-1600 K). Additionally, the fastest diffusing species inverts; Cr diffusion was faster than Ni in the bulk but slower in the grain boundaries. This is attributed to the creation of high cohesive energy clusters of Cr at the grain boundary. Grain boundary migration was also observed to be temperature dependent and appears to be two times higher in the 5% Cr alloy than in pure Ni, highlighting the important role of the alloying element on grain boundary motion.
Phase-field model for diffusion-induced grain boundary migration: An application to battery electrodes
Diffusion-induced grain boundary migration is a phenomenon in which a grain boundary moves in response to the driving forces generated by diffusing solute species. For example, diffusing solute species change the atomic volume in the host material, either by filling a vacancy with a misfitting solute atom or by expanding host lattices through interstitial diffusion. These volume changes are inhomogeneous and are stored as elastic energy in the material that drives grain boundaries. In this paper, we introduce our previously developed Cahn-Hilliard–phase-field-crystal model (CH-PFC) as a computational tool to investigate diffusion-induced grain boundary migration in crystalline materials. This multiscale phase-field model couples the composition field of a diffusing species with the crystallographic texture of a host material. We apply the CH-PFC model to battery electrodes and investigate whether interstitial solute diffusion induces grain growth in FePO 4 /LiFePO 4 electrodes. To this end, we compute grain growth in 60 FePO 4 electrodes by conducting two parallel trials: In the first trial, we cycle the electrode and calculate diffusion-induced grain growth. In the second trial, we do not cycle the electrode and calculate curvature-driven grain growth. We find a statistically significant grain growth in the cycled electrodes and negligible grain growth in the noncycled electrodes. Altogether, we show that the CH-PFC model not only predicts electrode microstructures as a function of the Li composition, but also predicts the crystallographic features of an electrode during battery operation.
Enhanced diffusion of phosphorus at grain boundaries
Enhanced diffusion of phosphorus at grain boundaries in cast polycrystalline photovoltaic materials (Wacker, HEM, and Semix) was studied. It was found that the enhancements for the three materials were the same, indicating that the properties of boundaries are similar, even though they were grown by different techniques. In addition, it was observed that grain boundaries capable of enhancing the diffusion always have strong recombination activities. Both phenomena could be related to dangling bonds existing at the boundaries. The present study gives the first evidence that incoherent second order twins of 111/115-plane type are diffusion-active.
A model for the compositions of non-stoichiometric intermediate phases formed by diffusion reactions, and its application to Nb 3 Sn superconductors
In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb 3 Sn superconductors. In the first part, the governing equations for the bulk diffusion and interphase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that “frozen” bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Lastly, we apply this model to the Nb 3 Sn superconductors and propose approaches to control their compositions.
Understanding of Void Formation in Cu/Sn-Sn/Cu System During Transient Liquid Phase Bonding Process Through Diffusion Modeling
Transient Liquid Phase (TPL) bounding of Sn foil sandwiched between two Cu foils involves, in the temperature range above the melting point of Sn (232 °C) and below 350 °C, the formation and the growth of two intermetallic compounds (IMCs) Cu{sub 6}Sn{sub 5} and Cu{sub 3}Sn and mostly unintended micro-pores. The present study aims to analyze the mechanism of void development during the soldering process through an experimental and modeling approach of diffusion-controlled IMC transformation. This modeling couples the diffusion process and the interface motion with the volume shrinkage induced by the difference of partial molar volumes of atoms between each phase. We also consider two types of inter-diffusion transports: (i) inter-diffusion based on the exchange of Cu and Sn atoms and (ii) inter-diffusion of Sn atoms with vacancies allowing Kirkendall void formation. The simulations of IMC growth performed correspond to a sequence of planar phase layers, where the distinctive scallop morphology of the Cu{sub 6}Sn{sub 5} layer is described through an analytical function allowing to quantify the grain boundary diffusion pathway. We take into account of the volume diffusion mechanism for Cu{sub 3}Sn intermetallic. For Cu{sub 6}Sn{sub 5} intermetallic two mechanisms are considered, volume diffusion and grain boundary diffusion, limited by grain growth. The simulations of IMC growth kinetics, for different transport scenarios, are compared to the experimental evolving morphologies to determine the most likely mechanism of micro-void formation.
Lattice and grain boundary self-diffusion in
Lattice and grain boundary self-diffusion coefficients of radioactive nickel 63 into high purity nickel measured over temperature range 650-475 degrees C
Demonstrate Improved Ag Diffusion and Describe the Basis for Pd Penetration Modeling in SiC
In past work, an effective diffusivity coefficient was determined for Ag transport through the silicon carbide layer of a tristructural isotropic fuel particle. The effective diffusivity coefficient accounts for the microstructure of the silicon carbide and includes both bulk diffusion and grain boundary diffusion of Ag. In this report, the model has been improved by accounting for the enhanced concentration of vacancies in the bulk due to irradiation, which substantially influence bulk diffusivity at low temperatures. To improve the BISON model and make it fission rate dependent, effective diffusivity calculations have been performed that incorporate the radiation modified bulk diffusivity. The microstructure and irradiation-dependent effective diffusivity has also been implemented into BISON, and its predictions for Ag release from tristructural isotropic fuel have been successfully compared to AGR-1 post irradiation measurements. Moreover, a new feature has been developed in the Multiphysics Object-Oriented Simulation Environment (MOOSE) to account for different grain boundary types. The Ag diffusivity in 5 (210)/[001] grain boundaries has been computed and was found to be greater than in random high-angle grain boundaries. The presence of the fission product Pd can also have an important effect on the properties of the silicon carbide layer in tristructural isotropic particles. The penetration of Pd into the silicon carbide layer causes a corrosion reaction that can lead to the failure of the silicon carbide layer; however, this corrosion reaction is not well understood. To enable an improved understanding of the mechanism, ab-initio molecular dynamics simulations of Pd interaction with bulk silicon carbide have been performed. The improved understanding of the reaction will form a basis for future improvements to the BISON’s Pd penetration failure model
Type IV failure in weldment of creep resistant ferritic alloys: II. Creep fracture and lifetime prediction
The creep rupture behavior (Type IV failure) for weldments of creep strength enhanced ferritic steel is numerically analyzed, using an integrated microstructure- and micromechanics-based finite element model. To account for the large microstructure gradients across weldments, a two-dimensional digital microstructure is constructed based on the actual observed microstructure of ferritic steel weldment by using the Voronoi-tessellation method. According to the fracture mechanism studies and literature experimental observations, the Type IV failure is identified as an intergranular creep fracture in the fine-grained or intercritical heated affected zone (FGHAZ or ICHAZ). In the present study, the following micromechanics model is employed to determine the micromechanical and microstructural origins for the failure process above, accounting for the underlying physical fracture mechanisms at different length scales, including nucleation of grain boundary cavities, their growth by competition of grain boundary diffusion and grain interior creep, viscous grain boundary sliding, and the emergence of microcracks by coalescence and their evolution to the ultimate failure. The methodology demonstrates the capabilities in modeling the Type IV failure and providing quantitative creep rupture lifetime prediction which shows an excellent agreement with long-term creep experimental data for creep strength enhanced ferritic steels and their weldments. In particular, the drop-off in time to rupture at high temperatures and low stress levels in the creep rupture curves is quantitatively predicted, and the transition of failure mechanisms from creep-controlled to diffusion-controlled creep fracture mechanism is illustrated.
Diffusion mechanisms in chemical vapor-deposited iridium coated on chemical vapor-deposited rhenium
Radiation-cooled rocket thruster chambers have been developed which use CVD Re coated with CVD Ir on the interior surface that is exposed to hot combustion gases. The Ir serves as an oxidation barrier which protects the structural integrity-maintaining Re at elevated temperatures. The diffusion kinetics of CVD materials at elevated temperatures is presently studied with a view to the prediction and extension of these thrusters' performance limits. Line scans for Ir and Re were fit on the basis of a diffusion model, in order to extract relevant diffusion constants; the fastest diffusion process is grain-boundary diffusion, where Re diffuses down grain boundaries in the Ir overlayer.
Grain boundary self-diffusion and point defect interactions in α -U via molecular dynamics
Though metallic U-Zr fuel has been used in nuclear reactors since the 1960s, many of its fundamental and thermodynamic properties are still unknown. The a-U phase, which has a highly anisotropic crystal structure and physical properties, is present in U-Zr fuel. The character and behavior of a-U grain boundaries will strongly impact fuel thermophysical performance under irradiation. Here, we study the interaction of point defects with grain boundaries, diffusion along grain boundaries, and the predicted diffusional creep behavior of a-U via molecular dynamics. We calculate the segregation energy of vacancies and interstitials to grain boundaries and quantify the biased sink strength of the grain boundaries, and observe that this sink strength is not strongly dependent on the grain boundary orientation. We also find that grain boundary diffusivity is strongly dependent on the grain boundary energy and grain boundary orientation. The presence of point defects within the grain boundary can induce diffusion in grain boundaries with low formation energies and can enhance diffusion in high-energy grain boundaries. We also find that diffusional creep of a-U at prototypical metallic fuel operation conditions is extremely high and could help explain observed metallic fuel swelling behaviors.
Grain growth and pore coarsening in dense nano-crystalline UO 2+ x fuel pellets
Dense nano-sized UO 2+x pellets are synthesized by spark plasma sintering with controlled stoichiometries (UO 2.03 and UO 2.11 ) and grain sizes (~100 nm), and subsequently isothermally annealed to study their effects on grain growth kinetics and microstructure stability. The grain growth kinetics is determined and analyzed focusing on the interaction between grain boundary migration, pore growth and coalescence. Grains grow much bigger in nano-sized UO 2.11 than UO 2.03 upon thermal annealing, consistent with the fact that hyper-stoichiometric UO 2+x is beneficial for sintering due to enhanced U ion diffusion from excessive O ion interstitials. The activation energies of the grain growth for UO 2.03 and UO 2.11 are determined as ~1.0 and 1.3~2.0 eV, respectively. As compared with the micron-sized UO 2 in which volumetric diffusion dominates the grain coarsening with an activation energy of ~3.0 eV, the enhanced grain growth kinetics in nano-sized UO 2+x suggests that grain boundary diffusion controls grain growth. Lastly, the higher activation energy of more hyper-stoichiometric nano-sized UO 2.11 may be attributed to the excessive O interstitials pinning grain boundary migration.
Probing the oxidation kinetics of small permalloy particles
The oxidation of permalloys is important to apply in a wide range. The oxidation and diffusion mechanisms of small permalloy particles with different Fe content are studied by using thermal gravimetric analysis (TGA) and microstructure characterizations. Fe{sub 2}O{sub 3}/(Ni, Fe){sub 3}O{sub 4} plays a key role in the morphology evolution and diffusion mechanisms of small NiFe particles upon oxidation. The activation energies of grain boundary diffusion for the NiFe alloys increase from 141 kJ/mol to 208 kJ/mol as the Fe content increases from 0 to ~50 wt%. We have developed a diffusion process resolved temperature programed oxidation (PR-TPO) analysis method. Three diffusion mechanisms have been recognized by using this method: In addition to the grain boundary diffusion and lattice diffusion, our TGA analysis suggests that the phase conversion from Fe{sub 2}O{sub 3} to (Ni, Fe){sub 3}O{sub 4} induces diffusion change and affects the diffusion process at the intermediate temperature. Relevant oxidation kinetics and diffusion mechanisms are discussed. - Graphical abstract: The oxidation mechanisms of small Permalloy particles with different Fe content is studied by using thermal gravimetric analysis (TGA) and microstructure characterizations. The activation energies of grain boundary diffusion for the NiFe alloys increases from 140 kJ/mol to 208 kJ/mol as the Fe content increases from 0 to 50 wt% as determined by TGA. We have developed a diffusion process resolved temperature programed oxidation (DPR-TPO) analysis method, and three diffusion mechanisms have been recognized by using this method: In addition to the well-known grain boundary diffusion and lattice diffusion, we found that the phase conversion from Fe{sub 2}O{sub 3} to (Ni, Fe){sub 3}O{sub 4} will induce diffusion changes and affect the diffusion process at the intermediate temperature. The diffusion processes can be characterized by the corresponding characteristic peak temperatures in temperature programmed oxidation (TPO) analysis. This work not only give insight knowledge about the oxidation and diffusion processes of small permalloy particles, but also, provides a useful tool for analyzing solid-gas reactions of other materials. - Highlights: • The oxidation kinetics of small NiFe particles were studied by using thermoanalysis. • Grain boundary, lattice, and phase conversion induced diffusions were recognized. • The activation energy of oxidation increases with the Fe content in the alloy. • Each diffusion process corresponds to a characteristic temperature in TPO analysis. • NiFe alloys with ~5–10 wt% Fe content have the lowest oxidation rates.
Diffusion mechanisms in Ir-coated Re for high-temperature, radiation-cooled rocket thrusters
Materials used for radiation-cooled rocket thrusters must be capable of surviving under extreme conditions of high temperatures and oxidizing environments. Thruster chambers were developed using chemical-vapor-deposited (CVD) Re coated with CVD Ir on the inside surface which is exposed to hot combustion gases. Ir serves as an oxidation barrier protecting the Re which maintains structural integrity at high temperatures. In order to predict and extend the performance limits of these Ir-coated Re thrusters, the diffusion kinetics of CVD materials at temperature are studied. Thruster end ring sections were examined using electron microprobe analysis both before and after exposure to high temperature vacuum environments. The resulting elemental maps for Re, Ir, and Mo in the near-surface region allow identification of diffusion mechanisms operating at these temperatures. Line scans for Ir and Re were fit using a diffusion model to extract relevant diffusion constants. The fastest diffusion process is seen to be grain boundary diffusion with Re diffusing down grain boundaries in the Ir overlayer. The measured dependence of the diffusion rate on temperature will allow prediction of operating lifetimes for these thrusters.
Antimony diffusion in CdTe
Group V dopants may be used for next-generation high-voltage cadmium telluride (CdTe) solar photovoltaics, but fundamental defect energetics and kinetics need to be understood. Here, antimony (Sb) diffusion is studied in single-crystal and polycrystalline CdTe under Cd-rich conditions. Diffusion profiles are determined by dynamic secondary ion mass spectroscopy and analyzed with analytical bulk and grain-boundary diffusion models. Slow bulk and fast grain-boundary diffusion are found. Density functional theory is used to understand formation energy and mechanisms. Lastly, the theory and experimental results create new understanding of group V defect kinetics in CdTe.
Phase transformations at interfaces: Observations from atomistic modeling
Here, we review the recent progress in theoretical understanding and atomistic computer simulations of phase transformations in materials interfaces, focusing on grain boundaries (GBs) in metallic systems. Recently developed simulation approaches enable the search and structural characterization of GB phases in single-component metals and binary alloys, calculation of thermodynamic properties of individual GB phases, and modeling of the effect of the GB phase transformations on GB kinetics. Atomistic simulations demonstrate that the GB transformations can be induced by varying the temperature, loading the GB with point defects, or varying the amount of solute segregation. The atomic-level understanding obtained from such simulations can provide input for further development of thermodynamics theories and continuous models of interface phase transformations while simultaneously serving as a testing ground for validation of theories and models. They can also help interpret and guide experimental work in this field.