Grain Boundary Diffusion Research Articles

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 α-U phase, which has a highly anisotropic crystal structure and physical properties, is present in U-Zr fuel. The character and behavior of α-U grain boundaries will strongly impact fuel thermophysical performance under irradiation. We study the interaction of point defects with grain boundaries, diffusion along grain boundaries, and the predicted diffusional creep behavior of α-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 α-U at prototypical metallic fuel operation conditions is extremely high and could help explain observed metallic fuel swelling behaviors.

Enhanced reliability of Cu-Sn bonding through the microstructure evolution of nanotwinned copper

Kirkendall voids are detrimental to the Cu-Sn bonding interface, causing the failure of the high-density package. Herein, the perpendicularly aligned nanotwinned Cu (p-ntCu) and the horizontally aligned nanotwinned Cu (h-ntCu) are prepared by controlling the electrodeposition procedure. The p-ntCu shows advantages both in fast-bonding process and in void suppression through the in-situ microstructure evolution. Compared with h-ntCu, the abundant perpendicularly aligned twin boundaries in p-ntCu provide fast interdiffusion paths to build a bonding interface. In the bonding process, p-ntCu grows to ultra-large-grained Cu with an average grain size of 6.68 μm. The reduced density of normal grain boundaries in p-ntCu lowers the Cu diffusion rate and contributes to more balanced interdiffusion at the bonding interface, which is confirmed by molecular dynamics simulation and kinetic calculations of intermetallic compound (IMC) growth. In addition, the low impurity content in p-ntCu further reduces the diffusion flux imbalance and limits the nucleation of Kirkendall vacancies. Consequently, the p-ntCu/Sn interface keeps void-free during 150 °C long-term thermal aging due to the synergistic effect of reduced grain-boundary diffusion and lower impurity content, which will be beneficial for achieving high-reliability Cu-Sn bonding.

Simulated hydrogen diffusion in diamond grain boundaries

To evaluate hydrogen diffusion within diamond, a series of molecular dynamics simulations have been carried out in which diffusion coefficients and activation energies were determined. Diamond grown via chemical vapour deposition (CVD) contains a high hydrogen concentration within grain boundaries, because of this, common tilt grain boundaries were recreated from transmission electron microscopy images taken from literature. Diffusion coefficients of hydrogen placed within the grain boundary were estimated and compared to the bulk diffusion. Unlike many crystalline structures, some grain boundaries presented limited diffusion when compared to the bulk. Diffusion characteristics of grain boundaries are thought to be a result of channelling effects combined with the formation of sp3C-H bonds with sp2 carbon present within some grain boundaries - increasing and decreasing diffusion rates respectively. Potential wells were observed across some but not all the grain boundaries resulting in hydrogen trapping and anisotropic diffusion.

The grain-scale signature of isotopic diffusion in ice

Abstract. Diffusion limits the survival of climate signals on the water stable isotopes in ice sheets. Diffusive smoothing acts not only on annual signals near the surface, but also on long-timescale signals at depth as they shorten to decimetres or centimetres. Short-circuiting of the slow diffusion in crystal grains by fast diffusion along liquid veins can explain the “excess diffusion” found on some ice-core isotopic records. But experimental evidence is lacking as to whether this mechanism operates as theorised; theories of the short-circuiting also under-explore the role of diffusion along grain boundaries. The non-uniform patterns of isotopic deviation δ across crystal grains induced by short-circuiting offer a testable prediction of these theories. Here, we extend the modelling for grain boundaries (and veins) and calculate these patterns for different grain-boundary diffusivities and thicknesses, temperatures, and vein-water flow velocities. Two isotopic patterns are shown to prevail in ice of millimetre grain size: (i) an axisymmetric “pole” pattern with excursions in δ centred on triple junctions, in the case of thin, low-diffusivity grain boundaries, and (ii) a “spoke” pattern with excursions around triple junctions showing the impression of grain boundaries, when these are thick and highly diffusive. The excursions have widths ∼ 10 %–50 % of the grain radius and variations in δ ∼ 10−2 to 10−1 times the bulk isotopic signal for oxygen and deuterium, which set the minimum measurement capability needed to detect the patterns. We examine how the predicted patterns vary with depth through a signal wavelength to suggest an experimental procedure, based on laser ablation mapping, of testing ice-core samples for these signatures of isotopic short-circuiting. Because our model accounts for veins and grain boundaries, its predicted enhancement factor (quantifying the level of excess diffusion) characterises the bulk-ice isotopic diffusivity more comprehensively than past studies.

Influence of stabilized zirconium dioxide and high hydrostatic pressure on the kinetics of sintering nanopowders of metastable aluminum oxide

The paper presents an analysis of the effect of processing powders with high hydrostatic pressure (HHP) (300, 500, 700 MPa) and stabilized zirconium dioxide (ZrO2 + 3 mol.% Y2O3, (YSZ)) doping on the compaction of metastable nanopowders mixture with γ+θ-Al2O3 + n% YSZ (n = 0, 1, 5, 10, 15 wt%) composition during sintering. The behavior of nanopowders at the initial stage of sintering was studied by dilatometry at a constant heating rate of 5 °C/min, in temperature range from 20 °C to 1500 °C. It has been determined that sintering of compacts occurs in two stages: compaction of γ + θ-Al2O3 (Ⅰ-st stage metastable phases), compaction of the stable α-Al2O3 (ⅠⅠ-nd stage), accompanied by inhibition between them. An “effect of mutual protection against crystallization” of powder mixtures was determined using the X-ray diffraction method. This is characteristic of systems obtained by co-precipitation. A connection between the above mentioned inhibition and an increase in the YSZ additive was found. That, also, correlates to the effect of “mutual protection against crystallization” of Al2O3 – YSZ powder mixtures. A study of the mechanisms and activation energies of γ+θ-Al2O3 + n% YSZ systems’ (n = 0, 1, 5, 10, 15 wt%) sintering depending on the YSZ additive amount and the HHP value showed that a dopant and pressure increase leads to activation energy decrease of the initial sintering stage, and the prevailing sintering mechanism is volumetric diffusion in corundum grains. Also, the work shows that for γ+θ-Al2O3 + ≥5 wt% YSZ systems, the optimal compaction pressure is HHP ≥500 MPa, which corresponds to the transition of the sintering mechanism from grain-boundary diffusion to volumetric diffusion.

Role of vacuum diffusing temperature and time on improving hysteresis characteristics of grain boundary diffused NdFeB permanent magnets by Dy-metal vapor sorption

This study investigates the impact of vacuum grain boundary diffusion (GBD) conditions on sintered NdFeB permanent magnets using Dy-vapor sorption. The study analyzed variables such as vacuum diffusing treatment temperature (T), time (t), and diffusion depth (d). In a 4.5 mm-thick cube-shaped magnet, Dy diffusion increased intrinsic coercivity from 13.13 kOe to 20.56 kOe (56.6 %) with only a 1.5 % reduction in remanence for a modified two-stage grain boundary diffused magnet (940 °C/8 h + 950 °C/0.5 h), achieving commercial G52SH grade. This enhancement exceeds previous GBD studies on non-rare earth compounds or alloys. FE-EPMA analysis attributed the increased coercivity to a continuous Dy-rich region within Nd2Fe14B grains and a thicker core-shell structure forming the (Nd,Dy)2Fe14B phase, which suppresses reversed domain formation. Glow discharge optical emission spectrometer (GDOES) analysis revealed a 2.57 times increase in peak Dy content and a 1.9 times increase in deeper Dy content at 10 μm from the magnet surface compared to the original process. These findings indicate that Dy vapor sorption, combined with a modified two-stage vacuum heat treatment, enhances both the concentration and depth of Dy grain boundary diffusion. Furthermore, the resulting magnet has a clean surface without additional cleaning, beneficial for producing low-cost, high-performance NdFeB magnets.

Structural and phase transformations in Fe-Pd-Ag layered thin films by grain boundary diffusion

The influence of the stacking order and of an additional Ag layer on the formation of ordered phases in thin (< 50 nm) layered Fe/Pd and Fe/Ag/Pd films was investigated at 460 °C. The samples were prepared by magnetron sputtering at room temperature on Si/SiO2 substrate and were post-annealed in vacuum. Composition depth profiling and x-ray diffraction were used to characterize the processes. It has been shown, that the stacking order strongly influences the formation of ordered phases both in Fe/Pd bilayered and Fe/Ag/Pd trilayered films. In bilayered Fe/Pd films for both stacking orders the FePd3 phase appeared and it also showed L12 ordering for one stacking order. Addition of Ag layer between the Fe and Pd layers found to promote the formation of FePd phase which showed L10 ordering or A1 disordered structure depending on stacking order. Based on the analysis of the chemical depth profiles and XRD patterns the transformations were interpreted by grainboundary diffusion mechanisms including grainboundary diffusion induced grainboundary migration and solid state reaction.

Integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids - Part I: Theoretical framework

This study proposes an integrated model for simulating Coble creep deformation and void nucleation/growth in a 3D polycrystalline solid. Part I of the paper provides a theoretical framework for the proposed model. A representative volume element approach is employed to predict the effects of 3D polycrystalline morphology. The model comprises two distinct but interconnected stages: deformation and void nucleation/growth. The deformation stage of the proposed model comprises two sub-models: grain boundary (GB) migration and GB diffusion. The void nucleation/growth stage is composed of three consecutive calculations: void nucleation, void growth, and postprocessing. The process simulated in the void nucleation/growth stage is driven by relative GB velocity of the respective GBFs and diffusional fluxes between adjacent GBFs, which are provided from the deformation stage. The void nucleation rate is quantified using the relative GB velocity, and the initial void size is determined based on the stability condition for void existence derived from Helmholtz free energy. The void growth rate is evaluated by the atomic diffusion on the GBF and the surface of each void.

Analysis of mechanism for effectively coercivity increment in (Nd, Ce)-Fe-B diffusion magnets

In this work, we explore how Ce in (Nd, Ce)-Fe-B magnet optimizes the microstructure of the base magnet, and enhances Grain Boundary Diffusion (GBD) of Dy. As Ce/total rare earth (TRE) content increases from 0 wt% to 16.95 wt%，the coercivity of the base magnets decreased by 24.93 %. However, lower-melting-point Ce element tended to distribute in the grain boundaries (GBs), and the thickness of the GBs layer increased from 2.46 nm to 5.54 nm. This provided more pathways for the subsequent GBD. Importantly, the diffusion depth of Dy element increased, and more core-shell structure formed as Ce increased. It led to a higher coercivity increment. Compared to GBD magnets without Ce, the coercivity increment of GBD magnets with Ce/TRE = 16.95 wt% increased by 39.54 %.

Reviving Fatigue Surface for Solid-State Upcycling of Highly Degraded Polycrystalline LiNi1-x-yCoxMnyO2 Cathodes.

The ongoing tide of spent lithium-ion batteries (LIBs) urgently calls for high-value output in efficient recycling. Recently, direct regeneration has emerged as a novel recycling strategy but fails to repair the irreversible morphology and structure damage of the highly degraded polycrystalline layered oxide materials. Here, this work carries out a solid-state upcycling study for the severely cracked LiNi1-x-yCoxMnyO2 cathodes. The specific single-crystallization process during calcination is investigated and the surface rock salt phase is recognized as the intrinsic obstacle to the crystal growth of the degraded cathodes due to sluggish diffusion in the heterogeneous grain boundary. Accordingly, this work revives the fatigue rock salt phase by restoring a layered surface and successfully reshapes severely broken cathodes into the high-performance single-crystalline particles. Benefiting from morphological and structural integrity, the upcycled single-crystalline cathode materials exhibit an enhanced capacity retention rate of 93.5% after 150 cycles at 1C compared with 61.7% of the regenerated polycrystalline materials. The performance is also beyond that of the commercial cathodes even under a high cut-off voltage (4.5V) or high operating temperature (45°C). This work provides scientific insights for the upcycling of the highly degraded cathodes in spent LIBs.

Robust and effective ab initio molecular dynamics simulations on the GPU cloud infrastructure using the Schrödinger Materials Science Suite

Ab initio Born-Oppenheimer molecular dynamics (AIMD) is a valuable method for simulating physico-chemical processes of complex systems, including reactive systems, and for training machine learning models and force fields. Speed and stability issues on traditional hardware preclude routine AIMD simulations for larger systems and longer timescales. We postulate that any practically useful AIMD simulation must generate a trajectory of a minimum 1000 MD steps a day on a moderate cloud resource. In this work, we implement a computing workflow that enables routine calculations at this throughput and demonstrate results for several non-trivial atomistic dynamical systems. In particular, we have employed the GPU implementation of the Quantum ESPRESSO code which we will show increases AIMD productivity compared to the CPU version. In order to take advantage of transient servers (which are more cost and energy effective compared to the stable servers), we have implemented automatic restart/continuation of the AIMD runs within the Schrödinger Materials Science Suite. Finally, to reduce simulation size and thus reduce compute time when modeling surfaces, we have implemented a wall potential constraint. Our benchmarks using several reactive systems (lithium anode surface/solvent interface, hydrogen diffusion in an iron grain boundary) show a significant speed up when running on a GPU-enabled transient server using our updated implementation.

Coercivity and thermal stability enhancement of Nd-Fe-B sintered magnets by grain boundary diffusion with Tb-Al-Cu alloys

The enhancement of the magnetic properties of Nd-Fe-B sintered magnets was investigated using a grain boundary diffusion (GBD) process with serial Tb80Al(20-x)Cux (x = 5–15) (wt.%) alloy diffusion sources to evaluate the influence of non-rare earth metallic elements on the diffusion efficiency. In this study, an optimal Tb diffusion process was achieved at 850 °C for 6 h. The coercivity increments (ΔHcj) of the GBD-treated magnets were found to vary from 9.7 to 10.3 kOe and the highest value was obtained from a magnet diffused with a Tb80Al5Cu15 alloy. The coercivity increments per wt.% Tb usage (ΔHcj/wt.% Tb) of the alloy-GBD magnets were considerably higher than those of pure Tb-GBD magnets, which revealed a 20 % reduction in Tb usage. The improvement in magnetic thermal stability by Tb80(Al-Cu)20-GBD was also confirmed.

Enhancement of coercivity and thermal stability for Nd-Fe-B sintered magnets by diffusing Dy-Co-M (M=Cu, Al) alloys

Commercial N52 sintered NdFeB magnets were processed by grain boundary diffusion (GBD) with Dy-Co-M (M=Cu, Al) alloys. The coercivity of magnets greatly increase to 17.62 and 18.83 kOe respectively when diffusing Dy58Co25Cu17 and Dy58Co25Al17 alloys, which are obviously higher than that of Dy58Co42 GBD-treated magnet with 16.64 kOe. Further thermal stability studies indicate that the thermal stability of Dy58Co25Cu17 and Dy58Co25Al17 GBD-treated magnets is further improved compared to the Dy58Co42 GBD-treated magnet. The results show that the temperature coefficients of remanence (20–120 °C) are reduced from –0.148%/°C to –0.134%/°C and –0.132%/°C by Dy58Co25Cu17 and Dy58Co25Al17 GBD-treatment, respectively. Besides, the irreversible magnetic flux losses (120 °C) for Dy58Co25Cu17 and Dy58Co25Al17 diffusion magnets are 4.76% and 2.79%, respectively. Microstructural analyses demonstrate that the presence of Cu and Al elements reduces the excessive accumulation of Dy and Co on the surface in the diffusion magnets and improves the diffusion depth and utilization of Dy and Co. Furthermore, the flow of Co from the triple junction phase to the thin grain boundary phase is promoted, which contributes to the uniform distribution of Co. In addition, the dynamic evolution of the magnetic domain structure during the temperature rise process was studied. This work provides insight into the preparation of high-performance and high-thermal stability magnets.

Accelerated recrystallization of nanocrystalline films as a manifestation of the inner size effect of the diffusion coefficient

The work is devoted to the study of recrystallization occurring during short-term annealing of 100 nm thick polycrystalline films of copper and silver. It is found that in copper films deposited by the method of thermal evaporation onto a substrate at room temperature, a bimodal crystallite size distribution with maxima at 15 and 35 nm is observed. The bimodal distribution in copper films is preserved during annealing, which leads to a shift of both peaks of the crystallite size distribution histograms to the larger sizes region. In contrast to Cu, even in as-deposited Ag films, besides the nanosized fraction, micron-sized crystallites are present. Apparently, these grains are formed due to the phenomenon of self-annealing and weakly evolve during heating owing to grain growth stagnation. The nanosized fraction in as-deposited Ag films is represented by crystallites with the most probable size of 25 nm, which increases to 50 nm as a result of short-term annealing at the temperature of 250 °C. The grain-boundary diffusion coefficient was determined, which is more than 10−18 m2/s for both films of metals. The obtained value indicates a multiple intensification of self-diffusion processes in films, the thickness of which allows us to refer them to macroscopic sample.

Grain boundary diffusion mechanism in Dy-diffused Nd–Fe–B sintered magnets

Grain boundary diffusion (GBD) is an effective method to enhance the thermal stability of Nd–Fe–B based permanent magnets. When developing a high-performance magnet, it is essential to carry out a study on its mechanisms, in order to reveal the distribution regulation of diffusion solutes and microstructural evolution. In the present work, the phase-field method is applied to investigate the thermodynamic features and the heavy rare-earth Dy migration in a Dy-diffused Nd–Fe–B magnet during the GBD process. In the simulation process, the grain phase transformation and volume diffusion were taken into consideration and the effects of the diffusion mode, initial diffusion source concentration, grain size, and grain boundary (GB) width were explored in a set of magnet models with various grain sizes. An optimized fitting function was introduced to evaluate the solute distribution in grain boundaries and the effective diffusion coefficient. It is shown that the diffusion mode and the GB width have significant impacts on the effective diffusion coefficient. The results provide a theoretical scheme concerning the quantitative evaluation of GBD efficiency based on thermodynamic analysis.

The Effect of TiO2 Addition on Low-temperature Sintering Behaviors in a SnO2-CoO-CuO System

Pure SnO2 has proven very difficult to densify. This poor densification can be useful for the fabrication of SnO2 with a porous microstructure, which is used in electronic devices such as gas sensors. Most electronic devices based on SnO2 have a porous microstructure, with a porosity of &gt; 40%. In pure SnO2, a high sintering temperature of approximately 1300C is required to obtain &gt; 40% porosity. In an attempt to reduce the required sintering temperature, the present study investigated the low-temperature sinterability of a current system. With the addition of TiO2, the compositions of the samples were Sn1-xTixO2-CoO(0.3wt%)-CuO(2wt%) in the range of x ≤ 0.04. Compared to the samples without added TiO2, densification was shown to be improved when the samples were sintered at 950C. The dominant mass transport mechanism appears to be grain-boundary diffusion during heat treatment at 950C.

Identifying multiple synergistic factors on the susceptibility to stress relaxation cracking in variously heat-treated weldments

The 347H austenitic stainless steel has been widely used for pressure vessels and pipeline (PVP) applications due to its excellent creep and corrosion resistance, which fit ideally to the harsh conditions in petrochemical industries, fossil fuel or nuclear power plants, and modern energy storages. However, a failure mode has been commonly observed with cracks emerging at the heat affected zone (HAZ) of weldments during post-weld heat treatment (PWHT) or under intermediate to high temperature service conditions. This phenomenon is termed as Stress Relaxation Cracking (SRC) since the purpose of PWHT is to relieve the welding-induced residual stress fields, or as Stress Age Cracking (SAC) if failure happens during service. A leading literature explanation of this failure suggests that the residual stress relaxation and the precipitation dissolution and/or re-precipitation occur in the same temperature range, which can lead to locally high strains and thus to crack at the grain boundaries. Since in situ spatial measurements of residual stress fields, microstructural evolution, and failure processes are nearly infeasible, this work recourses to a micromechanical finite element framework that models the high temperature failure as the nucleation and growth of grain boundary cavities, whereas various parameters such as thermomechanical loading history and its evolution, the competition of grain-interior dislocation creep and grain-boundary diffusion in failure lifetime, and microstructural heterogeneities (such as the precipitate free zone near grain boundaries) can be quantitatively incorporated. It can be concluded from these microstructure-explicit simulations that an accurate knowledge of residual stress evolution and a carefully calibrated set of material constitutive parameters are the essential prerequisites for lifetime predictions. The understanding of individual governing factors also leads to a mechanistic interpretation of the observed SRC susceptibility C-curves. These results suggest that the criticality of residual stress evolution, but not the precipitation-induced local strains, be the leading factor for SRC.

Wet oxidation of TiZrHfNbTaV high-entropy alloys: Role of grain-boundary and interdendritic diffusion

Refractory high-entropy alloys (RHEAs) are sensitive to thermal oxidation, significantly restricting their service performance and potential applications. However, the wet oxidation behavior of RHEAs has remained poorly understood despite the potential risk of catastrophic oxidation caused by water vapor. In this study, the oxidation mechanism of an equiatomic TiZrHfNbTaV high-entropy alloy (HEA) has been investigated in a wet atmosphere at elevated temperatures. Synchronous oxidation of all elements occurs at temperatures below 800 °C. At temperatures above 800 °C, preferential oxidation of Nb, Ti, and Zr, and internal oxidation of V occur on HEAs, which are thermodynamically less preferred as compared with oxidations of more reactive Hf and Ta. Experimental and theoretical analyses show that the oxide grain boundaries and substrate interdendritic regions of HEAs act as diffusion pathways for V and oxidizing species during preferential and internal oxidation processes. This work provides a fundamental understanding of the oxidation of multicomponent alloys in wet environments, which is helpful in the development of effective oxidation resistance strategies and innovative surface engineering techniques.

Macroscopic demagnetization of the sintered Nd-Fe-B magnets prepared by Tb grain boundary diffusion

Macroscopic demagnetization in sintered Nd-Fe-B magnets by Tb grain boundary diffusion (GBD) is investigated in comparison with non-GBD ones. Demagnetization curves, the coercivity distributions, Tb content, and magnetic fields of the magnets at various external fields (μ0Hext) are analyzed. As μ0Hext approaches coercivity of the GBD magnet, S-N poles form near the center, between and parallel to the original N-S poles, indicating the magnetization reversal near the center of the GBD magnet. This is distinguished from the non-GBD magnets where demagnetization occurs mainly in the pole surfaces. The mechanism for macroscopic demagnetization is discussed.

Impact of grain boundary and surface diffusion on predicted fission gas bubble behavior and release in UO2 fuel

In this work, we quantify the impact of grain boundary (GB) and surface diffusion on fission gas bubble evolution and fission gas release in UO2 nuclear fuel using simulations with a hybrid phase field/cluster dynamics model. We begin with a comprehensive literature review of uranium vacancy and xenon atom diffusivity in UO2 through the bulk, along GBs, and along surfaces. In our model we represent fast GB and surface diffusion using a heterogeneous diffusivity that is a function of the order parameters that represent bubbles and grains. We find that the GB diffusivity directly impacts the rate of gas release via GB transport, and that the GB diffusivity is likely below 104 times the lower value from Olander and van Uffelen (2001). We also find that the surface diffusivity impacts bubble coalescence and mobility, and that the bubble surface diffusivity is likely below 10−4 times the value from Zhou and Olander (1984).