Intersections Of Grain Boundaries Research Articles

A Conservative and Efficient Model for Grain Boundaries of Solid Electrolytes in a Continuum Model for Solid-State Batteries

Abstract A formulation is presented to model ionic conduction efficiently inside, i.e., across and along grain boundaries. Efficiency and accuracy are achieved by reducing it to a two-dimensional manifold while guaranteeing the conservation of mass and charge at the intersection of multiple grain boundaries. The formulation treats the electric field and the electric current as independent solution variables. We elaborate on the numerical challenges this formulation implies and compare the computed solution with results from an analytical solution by quantifying the convergence towards the exact solution. Towards the end of this work, the model is first applied to setups with extreme values of crucial parameters of grain boundaries to study the influence of the ionic conduction in the grain boundary on the overall battery cell voltage and, secondly, to a realistic microstructure to show the capabilities of the formulation.

Grain boundaries-dominated migration failure of copper interconnect under multiphysics field: Insight from theoretical modeling and finite element analysis

As the feature size of Cu interconnects in microelectronic devices are miniaturized into micro- and even nano-scale, the effects of grain boundaries (GBs) on the electromigration (EM) failure become more and more obvious. It is of fundamentally importance to investigate the grain boundaries dominated failure mechanism and lifetime of Cu interconnects. In this work, the interconnection models containing different grain boundaries were constructed by using finite element simulations. The simulation results indicate that the current density at Cu grain boundaries is lower, but the current will be increased locally, when it is almost perpendicular to grain boundaries. However, the temperature is higher locally at grain boundaries. In the early stage of atomic diffusion, thermal migration and stress migration also occur near grain boundaries, resulting in significant atomic segregation near grain boundaries, particularly at the intersection of grain boundaries and near the inclined grain boundaries with small angles to the current direction. The atomic diffusion is considerably accelerated as the density of grain boundaries is increased, but is slowed down by poorly connected columnar grain boundaries.

Effect of Silicon Dioxide Nanoparticles on the Sintering Properties of Beta-Tricalcium Phosphate Composites.

Composite sintered bodies comprising silicon dioxide (SiO2) nanoparticles dispersed in β-tricalcium phosphate (β-TCP) were prepared. The addition of nano-sized colloidal SiO2 to the β-TCP produced well-dispersed secondary phase nanoparticles that promoted densification by suppressing grain growth and increasing linear shrinkage of the sintered bodies. The SiO2 was found not to react with the β-TCP at 1120 °C and the substitution of silicon for phosphorous to produce a solid solution did not occur. This lack of a reaction is ascribed to the absence of available calcium ions to compensate for the increase in charge associated with this substitution. The SiO2 nanoparticles were found to be present near the intersections of grain boundaries in the β-TCP. β-TCP composite sintered body containing 2.0 and 4.0 wt% SiO2 exhibited a bending strength comparable to that of cortical bone and hence could potentially be used as a bone filling material.

Dynamic mechanical properties and failure mechanism of magnesium aluminum spinel based on experiments and peridynamic simulations

Experiments and peridynamic simulations of the split-Hopkinson pressure bar (SHPB) have been conducted to investigate the dynamic mechanical behaviors of magnesium aluminate (Mg-Al) spinel. The high-speed camera and scanning electron microscopy were used to observe the failure process and the fracture surface. In our modified model, the crystal orientation and grain boundary strength were explicitly quantified, accompanied by the dual-horizon peridynamic technique, resulting in high calculation accuracy and efficiency. Then effects of the stress state and strain rate on the failure mechanism of spinel have been investigated with the damage evolution process. Micro-pores tend to be generated at the intersection of grain boundaries, while cracks will propagate along these micro-pores, leading to trans-granular and inter-granular failures. Finally, the microstructure effects on the mechanical properties of spinel have been systemically investigated. The strength and distribution of grain boundaries were found to significantly affect the strength and crack propagation of Mg-Al spinel.

Effect of a Long-Range Dislocation Pileup on the Atomic-Scale Hydrogen Diffusion near a Grain Boundary in Plastically Deformed bcc Iron

In this paper, we present concurrent atomistic-continuum (CAC) simulations of the hydrogen (H) diffusion along a grain boundary (GB), nearby which a large population of dislocations are piled up, in a plastically deformed bi-crystalline bcc iron sample. With the microscale dislocation slip and the atomic structure evolution at the GB being simultaneously retained, our main findings are: (i) the accumulation of tens of dislocations near the H-charged GB can induce a local internal stress as high as 3 GPa; (ii) the more dislocations piled up at the GB, the slower the H diffusion ahead of the slip–GB intersection; and (iii) H atoms diffuse fast behind the pileup tip, get trapped within the GB, and diffuse slowly ahead of the pileup tip. The CAC simulation-predicted local H diffusivity, Dpileup−tip, and local stresses, σ, are correlated with each other. We then consolidate such correlations into a mechanics model by considering the dislocation pileup as an Eshelby inclusion. These findings will provide researchers with opportunities to: (a) characterize the interplay between plasticity, H diffusion, and crack initiation underlying H-induced cracking (HIC); (b) develop mechanism-based constitutive rules to be used in diffusion–plasticity coupling models for understanding the interplay between mechanical and mass transport in materials at the continuum level; and (c) connect the atomistic deformation physics of polycrystalline materials with their performance in aqueous environments, which is currently difficult to achieve in experiments.

Effect of element segregation on deformation mechanisms of nano/ultrafine-grained 304 stainless steel

The effect of Cr and Ni element segregation on austenite stability and deformation mechanisms of nano/ultrafine-grained 304 stainless steel obtained by cryogenic rolling plus annealing treatment was systematically studied. The results showed that the nano/ultrafine-grained steel had a good combination of strength and ductility (yield strength ∼896 MPa, tensile strength ∼977 MPa, and elongation ∼39.6%). According to the findings, the formation of Cr segregation in the body-centered cubic structure at the intersection of austenite grain boundaries and localised austenite grains with low Ni content reduced the austenite stability of the nano/ultrafine-grained steel and promoted the generation of strain-induced martensite during plastic deformation, resulting in the deformation mechanism dominated by the transformation-induced plasticity effect.

The effect of Mn containing dispersoids on the distribution of slip and fracture mode in Al-Mg-Si-Mn alloys

Improvements in the fracture performance of Al-Mg-Si extrusions are required to meet the demands of the automotive market. The fracture mode and the associated ductility results from competition between transgranular and intergranular fracture paths where intersection of slip bands and grain boundaries plays a significant role. In this study, the distribution of plastic strain within grains for microstructures with different spacings of Mn dispersoids was quantified using high resolution digital image correlation. It was observed that plastic strain was organized into slip bands where the magnitude of local shear strain decreased with reduced inter particle spacing of the dispersoids. It is proposed that this leads to a lower stress concentration on the grain boundary, decreasing the propensity for intergranular fracture. This was consistent with the findings that intergranular fracture was dominant in the dispersoid free material whereas low and high densities of dispersoids gave rise to a transgranular fracture mode.

Twin-boundary-spacing-dependent strength in gradient nano-grained copper

Twin boundaries acting as efficient barriers for dislocation propagation can significantly improve the strength of conventional polycrystalline materials, which peaks at a critical value. Whether such a critical value also exists in heterostructured materials is poorly understood. In this study, molecular dynamics simulations are performed to reveal the underlying deformation mechanisms of gradient nano-grained materials with different-sized twins. The results indicate that the critical twin boundary spacing where the strength begins to soften decreases and the maximum strength of the material increases with the declining of the gradient. The plastic deformation mechanism below the critical value is dominated by the nucleation and emission of twinning partial dislocations parallel to the twin boundary at the intersections of twin and grain boundaries. The high-density twin boundary spacing destabilizes the grain boundary architecture, resulting in a decline in strength.

Effects of titanium addition on the microstructure and mechanical properties of quaternary CoCrFeNi high entropy alloy

The effects of minor Ti addition on the microstructure and mechanical properties of the as-cast quaternary equiatomic CoCrFeNi high entropy alloy were studied experimentally and supported by thermodynamic modeling. The phase evolution, microstructure, and shear properties were investigated using X-ray diffraction, optical and scanning electron microscopy, and the shear punch test. It was shown that during the solidification process, the interdendritic segregation of Ti resulted in discontinuous precipitation of the R-phase and serrated grain boundaries. The mechanism of grain refinement was attributed to some additional constitutional undercooling and intersection of tortuous grain boundaries; this, in turn, led to the formation of a bimodal grain structure. The shear elongation and shear strength of 1 and 2 at.% Ti-containing samples simultaneously increased, in comparison with the base alloy. This interesting improvement of the mechanical properties was related to the simultaneous grain refinement, precipitation of the R-phase, and the formation of tortuous grain boundaries.

Study on non-equilibrium solidification microstructure of Al–Cu3–Si–Mg alloy by MMDF

Al–Cu3–Si–Mg wheel hubs were prepared by molten metals die forging (MMDF). The as-cast microstructure morphology of the alloy formed under pressure was observed by optical microscope and scanning electron microscope. The granular phases θ (Al2Cu) were distributed in the α–Al grains, and the cross phases β (Mg2Si) grew near the grain boundary in the α–Al grains. Polygonal compounds φ (AlxTi9La2Ce6Cu) and irregular eutectic structures mainly formed by (α + Al2Cu) eutectic formed under non-equilibrium solidification were found at the grain boundaries. Q (Al5Cu2Mg8Si6) phases were found at the intersection of grain boundaries. With the increase of pressure, the proportion of irregular eutectic structures (α + Al2Cu) decreased from 7.3% to 5.2%. Combined with microstructure analysis and thermodynamic software analysis, the non-equilibrium solidification path was determined as follows: L → L + φ → L + α + φ → L + (α + e) + α + φ → (α + e) + Q + α + φ → (α + e) + Q + [α + θ] + φ → (α + e) + Q + [α + θ + β] + φ

Twinning behavior and hydrogen embrittlement of a pre-strained twinning-induced plasticity (TWIP) steel

The twinning behavior and hydrogen embrittlement (HE) of a twinning-induced plasticity (TWIP) steel were investigated for different pre-strains at different strain rates. The lower pre-strain rate led to thinner twins and higher twin volume fraction. The influence of the twin characteristics on HE sensitivity was analyzed from statistical data on the evolution of surface crack characteristics during secondary straining period after cathodic hydrogen charging. Based on the ratio of crack initiation sites caused by the intersection of twins and grain boundaries, it was found that thinner twins in twin bundles of similar thickness promoted the generation of hydrogen-induced cracks (HICs).

In-situ revealing the degradation mechanisms of Pt film over 1000 °C

• The high temperature degradation behaviors of passivated Pt film was studied by in-situ STEM. • The voids formed preferentially at intersections of grain boundaries with Pt-SiN x interface at 1020–1040 °C. • At temperatures above 1040 °C, the voids formed at both the grain boundaries and inside Pt grains. • The growth of voids inside the grains was accelerated by electromigration at high temperature. Degradation of a metallic film under harsh thermal-mechanical-electrical coupling field conditions determines its service temperature and lifetime. In this work, the self-heating degradation behaviors of Pt thin films above 1000 °C were studied in situ by TEM at the nanoscale. The Pt films degraded mainly through void nucleation and growth on the Pt-SiN x interface. Voids preferentially formed at the grain boundary and triple junction intersections with the interface. At temperatures above 1040 °C, the voids nucleated at both the grain boundaries and inside the Pt grains. A stress simulation of the suspended membrane suggests the existence of local tensile stress in the Pt film, which promotes the nucleation of voids at the Pt-SiN x interface. The grain-boundary-dominated mass transportation renders the voids grow preferentially at GBs and triple junctions in a Pt film. Additionally, under the influence of an applied current, the voids that nucleated inside Pt grains grew to a large size and accelerated the degradation of the Pt film.

Hot Deformation Behaviors of the Mg-3Sn-2Al-1Zn Alloy: Investigation on its Constitutive Equation, Processing Map, and Microstructure

In this work, the Mg-3Sn-2Al-1Zn (TAZ321, wt. %) alloy with excellent high temperature resistance was compressed using a Gleeble-3500 thermo-mechanical simulator at a wide temperature and the strain rate range. The kinetics analyses showed that the dominant deformation mechanism was likely caused by the cross slipping of dislocations. A constitutive equation which expressed the relationship between the flow stress, deformation temperature, and strain rate was established, and the average activation energy Q was calculated to be 172.1 kJ/mol. In order to delineate the stability and instability working domains, as well as obtain the optimum hot working parameters of the alloy, the hot processing maps in accordance with Prassad’s criterion are constructed at the true strain of 0.2, 0.4, 0.6, and 0.8, respectively. Based on the hot processing map and microstructure observation, the optimum hot working parameter was determined to be 350 °C/1 s−1. The continuous fine dynamic recrystallization (CDRX) grains occurred in the optimum deformation zone. The predicted instability domains was identified as T = 200–300 °C, = 10−2–1 s−1, which corresponded to the microstructure of deformation twinning and micro cracks at the intersection of grain boundaries.

Unveiling annealing texture formation and static recrystallization kinetics of hot-rolled Mg-Al-Zn-Mn-Ca alloy

The development of Mg-Al-Zn-Mn-Ca series alloys provides a potential prospect to achieve high strength and formability at room temperature (RT). The formation of elliptical annular texture is treated as a crucial factor for the enhanced RT formability. However, the origin of such an elliptical annular texture formation has been rarely reported. Herein, we unveiled the formation and evolution of elliptical annular texture in the hot-rolled Mg-1.6Al-0.8Zn-0.4Mn-0.5Ca (AZMX1100, wt.%) alloy after annealing at different temperatures for 1 h, and its static recrystallization (SRX) kinetics in given annealing temperature for different time. The results revealed that the formation of elliptical annular texture in the hot-rolled AZMX1100 alloy after annealing was derived from nucleation-oriented SRX mechanism, which took place in 200−300 °C, induced by cracked chain-shaped Al2Ca phases, contraction twins, intersections of double twins, intersections of double twins and grain boundaries and non-basal slips. On further annealing from 300−450 °C, the grains with 45°–70° transverse direction (TD) preferentially grew, which made elliptical annular texture extended along the TD. Based on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model, Avrami exponent n value was estimated to be 0.68–1.02, attributed to non-random SRX nucleation, giving rise to the lower activation energy QR of nucleation of ∼74.24 kJ/mol. Since the co-segregation of Al, Zn and Ca atoms in grain boundaries created a strong interaction of solutes and grain boundaries, the hot-rolled AZMX1100 alloy exhibited the higher activation energy Qg (∼115.48 kJ/mol) of grain growth.

Failure analysis of a furnace roller in continuous annealing line after long-term service at high temperatures

The rollers used to convey steel strips in a continuous-annealing furnace were deformed after about 12 years of service, resulting in an unevenness of the rolled strips. In this study, failure causes of the furnace rollers were investigated in terms of degradation of microstructure and mechanical properties of the roller material. After a long period of high temperature service, the microstructure of the material has changed significantly. A large number of network-like carbides precipitated at the grain boundaries, and these carbides have been greatly coarsened. It was also found that a great number of σ-phase have formed on the coarsened carbides, and that the volume fraction of the σ-phase on the grain boundaries has exceeded 50%. In addition, creep cavities have been found in the grain boundaries. Especially in regions with dense grain boundaries, the cavities formed at the intersection of grain boundaries have been linked into chains, which tend to develop into cracks. The grain boundaries of the furnace roller material after service has been severely embrittled. Both tensile and impact fracture surfaces show brittle intergranular fracture characteristics. Compared to the unused material, the tensile strength and impact toughness of the failed roller decreased significantly due to the deterioration of the microstructure. Because of the degraded mechanical properties, the rollers are prone to deformation under the service loads, thus cannot guarantee the normal production of strip steels. The results of this study provide a reference for evaluating the remaining life of furnace rollers after long-term service at elevated temperatures.

Deformation behavior of BCC tantalum nanolayered composites with modulated layer thicknesses

The metallic nanolayered composite composed of alternating nanocrystalline and coarse-grain layers of the same element features stronger bonding interlaminar interfaces than that consisting of different elements; therefore, it is less vulnerable to brittle interfacial fracture. Despite numerous studies on face-centered-cubic (FCC) metallic nanolayered composites, the structure-mechanical property relationships of body-centered-cubic (BCC) metallic nanolayered composites have yet to be elucidated. Using molecular dynamics simulations, we investigated the deformation and fracture mechanism of BCC tantalum (Ta) nanolayered composites, composed of alternating nanocrystalline and single-crystalline layers. Our findings reveal that unlike FCC nanolayered composites, whose main deformation mechanism is twin nucleation, BCC nanolayered composites favor twin thickening, which rotates the whole single-crystalline layer to the twin orientation and finally eliminates all twin boundaries in the single-crystalline layer. Such preference for twin thickening is attributed to its much smaller energy barrier than that for twin and dislocation nucleation. The fracture of Ta nanolayered composites is caused by intergranular cleavage cracks, originated from the intersection of twin boundaries and grain boundaries. In the range of strain rates used by MD simulations (107/s~109/s), rising strain rates leaves less time for crack coalescence and propagation at each load increment, thus enhancing the fracture strength and strain of BCC nanolayered composites.

3D X-ray tomography characterization of creep cavities in small-punch tested 316 stainless steels

Small-punch (SP) test has become an effective approach to evaluate creep properties of critical structural components in fusion and power plants for recent years. To explore the SP test technique, here we report quantitative analysis of creep cavities in the SP creep tested 316 stainless steel specimen at 600 °C and 500 N using a three dimensional X-ray tomography system. The results show that creep cavities nucleated preferentially at four kinds of places: high angle grain boundaries, intersection of twins and grain boundaries, triple junctions and intersections of first order and second order twins. The cavity morphology shows that both of the average size and the density of the cavities close to the fracture are the largest. The distribution of the local stress evaluated by the distribution of the cavities provides more details for an understanding of creep damage evolution in the 316 stainless steel at high temperature.

Static recrystallization behavior of hot-rolled Mg-Zn-Ce magnesium alloy sheet

Static recrystallization behavior of Mg-1.5Zn-0.2Ce (wt%) alloy rolled at 480 °C was investigated at different annealing stages using quasi-in-situ electron backscattered diffraction (EBSD) analyses, which were carried out repeatedly in the same region to trace microstructural evolution. In the as-rolled condition, double twins exhibit the highest fraction compared with tensile and compression twins. Double twins mostly exist in deformed grains with basal orientations, and statically recrystallized grains mainly nucleate at the intersections of double twins and pre-existing grain boundaries. Statically recrystallized grains tend to exhibit TD-tilted orientations and grow along double twins to consume adjacent basal-oriented grains. This is the main reason for inducing the change from a RD-split texture to a well-weakened TD-split texture during annealing. The residual unrecrystallized grains with TD-tilted orientations and the growth advantage of TD-tilted grains also enhance the formation of TD-split texture.

Molecular dynamics simulation of effect of grain on mechanical properties of nano-polycrystal -Fe

The nanocrystalline metals are widely investigated due to their unique mechanical properties. Currently, the available studies about deformation mechanisms of metals mainly focus on face-centered cubic metals such as Ni, Cu and Au. However, the body-centered cubic metals are still very limited, despite their industrial importance. Here, we investigate the effects of grain size and temperature on the mechanical behavior of nano-polycrystal -Fe under uniaxial tensile loading by using molecular dynamics (MD) simulation. The models of nanocrystalline -Fe with the grain sizes of 3.95, 6.80, 9.70, 12.50, 15.50, 17.50, 20.70 and 26.00 nm are geometrically created in three dimensions by using Voronoi construction, and these models are relaxed to reach an equilibrium state. Then, each of them has a strain of 0.001 along the Z-direction in each step, keeping zero pressure in the X- and Y-directions until the strain increases up to 0.2. A 1.0 fs time step is used in all of the MD simulations. Based on the data output, the stress-strain curves at different grain sizes are obtained. The results indicate that the peak stresses of nano-polycrystal -Fe decrease with the decrease of grain size, exhibiting a breakdown in the Hall-Petch relation when the grain size is smaller than a critical size. The major deformation mechanism is found to change from dislocation slips and twinning-mediated plasticity in a model with a larger grain size to grain boundary sliding in a model with a smaller grain size. It should be noted that twinning is formed by the emission of 1/6111 partial dislocations along the {112} slip plane. The results show that crack formation during tension is a cause of reducing the flow stress of nano-polycrystal -Fe with a large grain size and that the Young's modulus of nano-polycrystal -Fe decreases with the grain size decreasing. The main reason for the crack nucleation is here that grain boundaries perpendicular to the loading direction bear higher stress and the twin band interacts with grain boundaries at a larger grain size, causing the stress to concentrate at the intersections of grain boundaries. The results also show the detwinning behavior and migration of deformed twins in nano-polycrystal -Fe. The detwinning behavior occurs via the migration of the intersection of grain boundary and twin, and this intersection is incoherent boundary. The migration of deformed twins proceeds by repeating initiation and glide of 1/6111 partial dislocations on adjacent {112} planes. In addition, we find that the nucleation and propagation of dislocation become easier at higher temperature than at lower temperature.

Effects of Different Sintering Temperature on the Microstructure and Piezoelectric Properties of Pb(Nb<sub>2/3</sub>Zn<sub>1/3</sub>)<sub>x</sub>(Zr<sub>52</sub>Ti<sub>48</sub>)<sub>1-X</sub>O<sub>3</sub> Ceramics

In this paper, the effects of different sintering temperature on the microstructure and piezoelectric properties of Pb(Nb2/3Zn1/3)0.03(Zr52Ti48)0.97O3(PNZZT) ceramic samples were investigated. The Pb(Nb2/3Zn1/3)0.03(Zr52Ti48)0.97O3 ceramics materials was prepared by a conventional mixed oxide method. In the period of the experiment, the relationship between crystallographic phase and microstructure were analyzed by X-ray diffraction(XRD) and scanning electron microscopy(SEM) respectively. The XRD patterns shows that all of the ceramic samples are with a tetragonal perovskite structure. Along with sintering temperature increased and the x is 0.03, the grain size gradually become big. Through this experiment, it has been found that when the x is 0.03 and sintered at 1130°C for 2 h, the grains grow well, the grain-boundary intersection of the sample combined well and the porosity of the ceramics decreased, an excellent comprehensive electrical properties of the Pb(Nb2/3Zn1/3)0.03(Zr52Ti48)0.97O3 samples can be obtained. Its best electrical properties are as follows: dielectric constant (ε) is 1105, dielectric loss(tg) is 0.017, electromechanical coupling coefficient (Kp) is 0.287, piezoelectric constant(d33) is 150PC/N