A molecular dynamics survey of grain boundary energy in uranium dioxide and cerium dioxide

Uranium dioxide (UO₂) is the primary fuel material that is used in current nuclear reactors. As one of the most fundamental material parameters, grain boundary (GB) energy strongly influences many fuel properties, and the influences depend on the characters and properties of individual GBs. Using molecular dynamics simulations, a high throughput survey of GB energy in UO₂ was carried out for the purpose of elucidating the roles of GB geometry such as misorientation and inclination, as well as the bonding nature of UO₂, in affecting GB energy. GB energies in CeO₂ were calculated as well for comparison with UO₂ to investigate the generality of GB energy anisotropy in fluorite phase oxides. The results show significant GB energy anisotropy in both UO₂ and CeO₂ that is associated with the cubic symmetry of the fluorite structure. More interestingly, the GB anisotropy is found to be dependent not only on the crystal structure but also the ionic bonding. As such, the GB energy anisotropy in fluorite oxides has significant differences compared with that in fcc metals. The data obtained and the increased knowledge on GB anisotropy will facilitate GB engineering for nuclear fuels with improved properties.     

Reduced grain boundary energies in rare-earth doped MgAl2O4 spinel and consequent grain growth inhibition

Grain growth inhibition in MgAl₂O₄ spinel nanostructure was achieved by grain boundary (GB) segregation of rare-earth dopants. Microcalorimetric measurements showed that dense spinel compacts doped with 3 mol% of R₂O₃ (R = Y, Gd, and La) had decreased GB energies as compared to the undoped spinel, representing reduction in the driving force for grain growth. Segregation energies of the three dopants to the Σ3 (111) GB were calculated by atomistic simulation. The dopants with higher ionic radius tend to segregate more strongly to GBs. The GB energies were calculated from atomistic simulation and, consistent with experiments, a systematic reduction in GB energy with dopant ionic size was found. High temperature grain growth experiments revealed a significant reduction of grain growth in the doped nanostructures as compared to the undoped one, which was attributed to increased metastability or possibly also a GB dragging originated from the dopant segregation.     

Highly porous Sr-doped TiO2 ceramics maintain compressive strength after grain boundary corrosion

Maintaining sufficient mechanical support during bone healing is an essential property for ceramic bone scaffolds. However, grain boundary (GB) dissolution may compromise the mechanical strength of polycrystalline ceramics in the physiological environment. Therefore, we investigated the GB formation and its impact on the compressive strength and corrosion behavior in TiO₂ scaffolds doped with calcium and strontium. To alter the GB composition and densification process, sintering conditions were altered. Prolonged sintering times and increased sintering temperature led to improved densification and increased strength in Ca-doped scaffolds. However, dissolution of the resulting amorphous GBs caused a significant loss of compressive strength when exposed to an acidic environment. In contrast, a crystalline SrTiO₃ GB phase present in Sr-doped scaffolds, for which increased sintering temperature combined with rapid cooling led to a significantly improved compressive strength. Formation of SrTiO₃ crystals in the GBs maintained the strength for over 4 weeks in an acidic environment.     

First-principles study of impurity segregation in zirconia,hafnia, and yttria-stabilized-zirconia grain boundaries

The impurity segregation behavior in symmetric tilt Σ5 (310)/[001] grain boundaries (GBs) of cubic ZrO₂, HfO₂, and yttria-stabilized ZrO₂ (YSZ) were studied using first-principles calculations. The substitutional impurities, including divalent (Mg, Ca), trivalent (Al, Y), and tetravalent (Si, Ti) elements, were considered. It is found that divalent and trivalent impurities tend to segregate to a narrow region within 4 Å of the GB plane, while the tetravalent impurities have a much more scattered segregation profile extending 8–15 Å from the GB plane. For ZrO₂ GB, the calculated grain boundary impurity enrichment factor for yttrium dopant is about 1.7, which is in good agreement with the experimental value of 1.9. For YSZ GB, there exist a strong GB segregation tendency for Mg, Ca, and Si, and a very weak segregation tendency for Ti in the YSZ GB, which is consistent with experimental findings.     

Essential work of fracture evaluation of fracture behavior of glass bead filled linear low‐density polyethylene

The effect of the glass bead (GB) size and bead content on the fracture behavior of GB‐filled linear low‐density polyethylene (LLDPE) composites was evaluated by means of the essential work of fracture (EWF). The results indicated the specific EWF (w_e) is lower for the composites than that of pure LLDPE and the obtained w_e values do not show significant differences for the filled samples with different GB diameters. The non‐EWF or plastic work (βw_p) also decreased with the addition of GBs, indicating that less energy is absorbed during the fracture process for the composites filled with different diameter GBs. For the composites filled with GBs of different contents, the w_e decreased with increasing GB contents and the βw_p that was higher than that of pure LLDPE at relatively low contents also decreased with the content of GBs. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1781–1787, 2006     

Ge4+ doped CaCu2.95Zn0.05Ti4O12 ceramics: Two-step reduction of loss tangent

CaCu₃Ti₄O₁₂ ceramics have been extensively studied for their potential applications as capacitors in recent years; however, these materials exhibit very large dielectric losses. A novel approach to reducing the dielectric loss tangent in two steps, while increasing the dielectric permittivity, is presented herein. Doping CaCu₃Ti₄O₁₂ with a Zn dopant reduces the loss tangent of the ceramic material from 0.227 to 0.074, which is due to the increase in grain boundary (GB) resistance by an order of magnitude (from 6.3× 10³ to 3.93 × 10⁴ Ω cm). Zn-doping slightly changes the microstructure and dielectric permittivity of the CaCu₃Ti₄O₁₂ ceramic, which reveals that the primary role of the Zn dopant is to tune the intrinsic properties of the GBs. Surprisingly, the addition of the Ge⁴⁺ dopant into the Zn²⁺-doped CaCu₃Ti₄O₁₂ ceramic sample led to a further decrease in the loss tangent from 0.074 to 0.014, due to enhanced GB resistance (3.1 × 10⁵ Ω cm). The grain size increased remarkably from 2–3 μm to 85–90 μm, corresponding to a significant increase in the dielectric permittivity (~1–4 × 10⁴). The large increase in GB resistance is due to the intrinsic potential barrier height at the GBs and the segregation of the Cu-rich phase in the GB region. First-principles calculations revealed that Zn and Ge are preferentially located at the Cu sites in the CaCu₃Ti₄O₁₂ structure. The substitution of the Ge dopant does not hinder the role of the Zn dopant in terms of improving the electrical properties at the GBs. These phenomena are effectively explained by the internal barrier layer capacitor model. This study provides a way of improving the dielectric properties of ceramics for their practical use as capacitors.     

Distribution of Σ3 misorientations in polycrystalline strontium titanate

SrTiO₃ is a potential electrolyte material for solid-oxide fuel cells due to its high ion conductivity. Grain boundaries (GBs) play an important role in bulk ion conductivity. It has been reported that the resistance of Σ3 GBs is much lower than the general GB in SrTiO₃. In order to clarify the conflicting reports on the prevalence of Σ3 GBs in SrTiO₃, grain size and GB misorientations in Nb-doped and undoped SrTiO₃ have been investigated as a function of annealing time. The observations suggest that the prevalence of both low-angle GBs and Σ3 GBs is strongly correlated to both abnormal grain growth and annealing time. In particular, the Σ3 GB population approaches that predicted by the Mackenzie random distribution when abnormal grain growth dominates.     

Atomistic analyses of the effect of temperature and morphology on mechanical strength of Si–C–N and Si–C–O nanocomposites

3-D molecular dynamics (MD) analyses of SiC–Si₃N₄ nanocomposite deformation and SiCO nanocomposite deformation are performed at 300 K, 900 K, and 1500 K. In SiC–Si₃N₄ nanocomposites, distribution of second phase SiC particles, volume fraction of atoms in GBs, and GB thickness play an important role in temperature dependent mechanical behavior. The deformation mechanism is a trade-off between the stress concentration caused by SiC particles and Si₃N₄–Si₃N₄ GB sliding. The temperature increase tends to work in favor of GB sliding leading to softening of structures. However, microstructural strength increases with increase in temperature when GBs are absent. In the case of SiCO nanocomposites, findings indicate that temperature change dependent amorphization of nanodomains, the nanodomain wall placement, the nanodomain wall thickness, and nanodomain size are important factors that directly affect the extent of crystallinity and the strength against mechanical deformation.     

Nanoindentation responses near single grain boundaries in oxide ceramics

Local mechanical responses near single grain boundaries (GBs) of 9.8 mol% Y₂O₃-stabilized ZrO₂ bicrystals, SrTiO₃ bicrystal, and Al₂O₃ polycrystal were investigated by nanoindentation at room temperature to reveal single GB contributions to the mechanical properties. Contrary to the concept of the Hall–Petch strengthening, the hardness showed negligible variations among grain interiors, GB vicinities, and just on GBs in the samples. Importantly, the hardness may be underestimated owing to GB grooving in thermally etched samples. Despite the negligible change in intrinsic hardness, the transmission electron microscopy observation of the ZrO₂ specimen under impressions revealed dislocation pileups at GBs. These results suggest that single GBs of oxide ceramics prevented dislocation movement but with limited strengthening contributions. This should correspond to the macroscopic Hall–Petch behaviors in oxide ceramics, where the Hall–Petch coefficients normalized by friction stress are significantly smaller than those in metals.     

Molecular Dynamics Simulation of Oxygen Ion Diffusion in Yttria Stabilized Zirconia Single Crystals and Bicrystals

Molecular dynamics simulation studies have been performed to study the oxygen ion diffusion in yttria stabilized zirconia single crystals and bicrystals separated by tilt grain boundaries (GBs). Two types of GBs which are Σ 5 (3 1 0) and Σ 13 (5 1 0) are studied at temperatures between 1,000 K and 2,000 K. The effect of grain size, which is the distance between two GBs, and the effect of GB orientations are systematically investigated in this study. The oxygen diffusion in the bicrystals is found to be blocked by the GB, and the blocking effect increases with decreasing grain size and is affected by different grain orientations. In addition, the oxygen diffusion along the GB plane is most hindered.     

Structure and shear response of <001> tilt grain boundary in titanium nitride

The equilibrated structures and shear responses of <001> titanium nitride (TiN) symmetric tilt grain boundaries (GBs) are investigated using molecular dynamics simulation. The equilibrated GBs are only composed of the kite-shaped structures connected with edge dislocation cores. From the shear response analysis of TiN GBs, we find that there exist two major deformation modes, i.e., GB sliding and shear deformation coupled with GB motion (shear-coupling). GB sliding may finally lead to the GB fracture and the shuffling of GB atoms. The shear-coupling could be further divided into the ideal and non-ideal ones. For the ideal shear-coupling, the shear deformation coupling with GB motion can be exactly described by a factor solely dependent on the GB tilt angle. However, it is not if the additional shear deformations caused by GB sliding or vacancy emission occur during the shear-coupling. Based on the geometrical analysis of atomic deformation mechanism in GB, we propose two theoretical coupling factors to describe the shear-coupling with the additional GB shear deformations. In addition, the deformation mode of GBs could be changed by elevating the temperatures and adding vacancies into GBs.     

Direct measurement of interface energies of magnesium aluminate spinel and a brief sintering analysis

Surface and grain boundary energies are key parameters for understanding and controlling microstructural evolution. However, reliable thermodynamic data on interfaces of ceramics are relatively scarce, limiting the realization of their relevance in processes such as sintering and grain growth. In this work, the heat of sintering itself was used to quantify both surface and grain boundary energies in MgAl₂O₄ spinel. Nanoparticles were compacted and heated inside a Differential Scanning Calorimeter (DSC) when densification and grain growth were observed. The evolved heat signal was quantitatively attributed to the respective microstructural evolution in terms of interfacial area change, allowing determination of average surface and grain boundary energies for MgAl₂O₄ as 1.49 J m⁻² and 0.57 J m⁻², respectively. The data was then used to interpret the thermodynamics involved in density and grain growth during isothermal sintering of MgAl₂O₄.     

Über den Zusammenhang zwischen der relativen Reaktionsrate der polyfunktionalen Esterkondensation und der Viskosität

The Relation between the Relative Reaction Rate of Polyfunctional Ester Condensation and the Viscosity By representing the three dimensional ester condensation in alkyds with the parameters Ψ K and K' the critical space of the polycondensation, in which all the formulations have a gelation point, can be demarcated. The solubility parameter δ_γ2 is used to determine the optimum solution mixture. The derived relation K_rel. is put in relation to viscosity, so that one obtains the viscosity development valid for all the formulations, irrespective of the condensation limit.     

Synergic grain boundary segregation and precipitation in W- and W-Mo-containing high-entropy borides

The structures of W- and W-Mo-containing high-entropy borides (HEBs) are systematically studied by combining atomic-resolution transmission electron microscopy imaging, electron diffraction, and chemical analysis. We reveal that W or W-Mo addition in HEBs leads to segregation of these elements to the grain boundaries (GBs). In the meantime, W- or W-Mo-rich precipitates also form along the GBs. Crystallographic analysis and atomic-scale imaging show that the GB precipitates in both W- and W-Mo-containing HEBs have a cube-on-cube orientation relationship with the matrix. With further strain analysis, the coherency of the precipitate/matrix interface is validated. Nanoindentation tests show that the simultaneous GB segregation and coherent precipitation, as a supplement to the grain hardening, provide additional hardening of the HEBs. Our work provides an in-depth understanding of the GB segregation and precipitation behaviors of HEBs. It suggests that GB engineering could be potentially used for optimizing the performance of high-entropy ceramics.     

Giant dielectric behavior of monovalent cation/anion (Li+, F−) co-doped CaCu3Ti4O12 ceramics

Giant dielectric behavior and electrical properties of monovalent cation/anion (Li⁺, F⁻) co-doped CaCu₃Ti₄O₁₂ ceramics prepared by a solid-state reaction route were systematically investigated. Substitution of Li⁺ and F⁻ led to a significantly enlarged mean grain size. A reduced loss tangent (tanδ ~0.06) with the retainment of an ultra-high dielectric permittivity (ε′ ~7.7-8.8 × 10⁴) was achieved in the co-doped ceramics, while the breakdown electric field and nonlinear coefficient of CaCu₃Ti₄O₁₂ ceramics were increased by co-doping with (Li⁺, F⁻). The variations in nonlinear electrical properties and giant dielectric response, as well as the dielectric relaxation, were well explained by the Maxwell-Wagner polarization model for an electrically heterogeneous microstructure, in which a Schottky barrier height at the grain boundaries (GBs) was formed. ε′ was closely correlated to the GB capacitance. Significantly decreased tanδ value and enhanced nonlinear properties were related to a significant increase in the GB resistance, which was attributed to the significantly increased potential barrier height and conduction activation energy at the GBs. The semiconducting nature of the grains was also studied using X-ray photoelectron spectroscopy and found to originate from the presence of Cu⁺ and Ti³⁺ ions.     

Effects of the glass bead content and the surface treatment on the mechanical properties of polypropylene composites

Polypropylene composites filled with glass beads (GBs) were prepared by means of a twin‐screw extruder. The tensile properties and impact‐fracture strength of the composites were measured at room temperature to identify the effects of the GB content and surface treatment on the mechanical properties. The results show that the relative elastic modulus increased nonlinearly, whereas the tensile strength decreased with increasing GB volume fraction (?_f). The notched impact strength increased with increasing ?_f when ?_f was less than 11%, and then, it decreased; this might have been related to the GB aggregation in the case of higher concentration. The mechanical properties of the composite systems in which the GB surface was treated with silane coupling agent were better than those of the composite systems filled with the untreated GBs under the same conditions. Furthermore, the impact‐fractured surfaces were observed with a scanning electron microscope to understand the interfacial morphology between the inclusion and the matrix and to examine the toughening mechanisms. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Oxygen permeation mechanism in polycrystalline mullite at high temperatures

The oxygen permeability of polycrystalline mullite wafers, serving as a model environmental barrier coating layer on SiC fiber‐reinforced SiC matrix composites, was evaluated at temperatures above 1673 h with an oxygen tracer gas (¹⁸O₂). Oxygen permeation occurred by grain‐boundary (GB) diffusion of oxygen from the high oxygen partial pressure (high‐Po ₂) surface to the low‐Po ₂ surface, with simultaneous GB diffusion of aluminum in the opposite direction. This GB interdiffusion of both oxygen and aluminum proceeded without acceleration or retardation, maintaining the Gibbs‐Duhem relationship. Oxygen permeation related to the GB diffusion of silicon was negligibly small compared to that generated by aluminum GB diffusion, resulting in decomposition of the mullite near the low‐Po ₂ surface. The GB diffusion coefficients for oxygen in the vicinity of the high‐Po ₂ surface were determined directly from the SIMS‐¹⁸O line profiles along individual GBs, as assessed from cross sections of the exposed wafer. The coefficients thus obtained were comparable to those determined in the absence of an oxygen potential gradient and those calculated from an oxygen permeation trial under the assumption of nearly ionic conductivity.     

Estimation of the Surface Energy of Polymer Solids

The methods to estimate the surface tension of polymer solids using contact angles have been reviewed in the first part. They are classified into the following three groups depending on the theories or the equations applied: (1) the methods using the Young's equation alone, (2) the methods using the combined equation of Young and Good-Girifalco, and (3) the methods using the equations of work of adhesion. Some notes and comments are given for each method and results are compared with each other. The two-liquids method for rather high energy surface is also introduced.

Next, some new possibilities to evaluate the surface tension of polymer solids are presented by our new contact angle theory in consideration of the friction between a liquid drop and a solid surface. The advancing and receding angles of contact (θ _a and θ _r ) are explained by the frictional tension γ_F and accordingly two kinds of the critical surface tension γ_C (γ_Ca and γ_Cr ) are given.

This work has shown that one of the recommendable ways to evaluate γ_S is either the maximum γ_LV cos θ_a or the maximum γ_C using the advancing contact angle θ_a alone, and another way is the arithmetic or the harmonic mean of the γ_Ca and γ_Cr . A depiction to determine the γ_C such as ln(1 + cos θ₀ ) vs. γ_LV with cos θ₀ = (cos θ₀ + cos θ_r )/2 has also been proposed.     

Electronic transport through ordered and disordered graphene grain boundaries

The evolution of electronic wave packets (WPs) through grain boundaries (GBs) of various structures in graphene was investigated by the numerical solution of the time-dependent Schrödinger equation. WPs were injected from a simulated STM tip placed above one of the grains. Electronic structure of the GBs was calculated by ab-initio and tight-binding methods. Two main factors governing the energy dependence of the transport have been identified: the misorientation angle of the two adjacent graphene grains and the atomic structure of the GB. In case of an ordered GB made of a periodic repetition of pentagon−heptagon pairs, it was found that the transport at high and low energies is mainly determined by the misorientation angle, but the transport around the Fermi energy is correlated with the electronic structure of the GB. A particular line defect with zero misorientation angle Lahiri et al., behaves as a metallic nanowire and shows electron–hole asymmetry for hot electrons or holes. To generate disordered GBs, found experimentally in CVD graphene samples, a Monte-Carlo-like procedure has been developed. Results show a reduced transport for the disordered GBs, primarily attributed to electronic localized states caused by C atoms with only two covalent bonds.     

Oxygen vacancies as a link between the grain growth and grain boundary conductivity anomalies in titanium-rich strontium titanate

Titanium-rich (Sr/Ti?=?0.995) strontium titanate (ST) ceramics, air-sintered in a temperature range of 1400–1625?°C, were reported to possess anomalies in the grain growth and analogous anomalies in the grain boundary (GB) conductivity activation energy. However, these two interface-related phenomena, occurring at GBs, could not be associated with each other using a simple “brick-layer” model. In this work we revise the topic and advocate that the deviation from the model comes from the oxygen vacancies localized at GBs of the rapidly-cooled ST ceramics. To verify this, we annealed the ceramics in oxygen and performed their systematic and comparative analysis using impedance spectroscopy. A levelling-off in the GB conductivity activation energy, which increases for ≤1.24?eV, and a four-fold decrease in the GB permittivity are observed after annealing. Thus, we confirm a key role of oxygen vacancies in relation between the grain growth and GB conductivity anomalies of as-sintered Ti-rich ST ceramics.