Grain Boundary Coupling Research Articles

Magnetic exchange coupling and effect of grain and grain boundaries on conduction mechanism of (MgFe2O4)100-x /(BaFe12O19)x nanocomposites

(MgFe2O4)100-x/(BaFe12O19)x, soft/hard nanocomposites (NCs) having different hard ferrite ratio i.e. x = 0, 25, 50, 75 and 100 have been synthesized via in-situ auto-combustion sol-gel method. XRD patterns ensured the co-existence of both hexaferrite and spinel ferrite phases without any impure phase and no significant difference in average crystallite size was observed. The FTIR and Raman spectra confirmed the fabrication of desired material without any impurity. The absence of blocking peak in the ZFC measurements revealed that the blocking temperature of these NCs lie above room temperature. The M-H loops taken at different temperatures resulted into single smooth curve indicating strong interphase exchange-coupling among hard-soft ferrite phases. The occurrence of shoulder peak in dM/dH versus H curve for molar ratio x = 50 is indication of weak exchange coupling between the two phases. From modified Block's law fitting, the Block's constant (B) exponentially declined with the addition of hard phase that revealed higher value of exchange-coupling constant J. The complex impedance analysis (Nyquist/Cole-Cole plots) and its simulation using an equivalent model circuit revealed the major contribution of both grains and grin-boundaries toward the total conduction mechanism of the NCs. These findings indicate that the higher value of impedance makes these NCs favorable candidates for numerous technological areas like electromagnetic shielding and high band-pass filters.

Shear-coupling of graphene grain boundaries: Elementary mechanisms, effects of topology, and role of buckling

Engineering grain boundary structure is a promising method for rational control of the microstructure and mechanical properties of two-dimensional materials. In bulk materials, shear stresses can drive grain boundary migration through the dislocations in grain boundaries. However, while shear coupling of grain boundaries has been studied in bulk materials like nanocrystalline copper, its translation to two-dimensional materials where out-of-plane deformation can relieve in-plane shear is not yet established. We investigate how the low flexural rigidity of graphene effects shear coupled grain boundary motion using atomic scale simulations of flat and buckled grain boundaries. We define the coupling shear strain as the strain at which a grain boundary has advanced by one Burgers vector and is at equilibrium and the critical shear strain as the strain at which migration of the first dislocation in the grain boundary becomes thermodynamically favorable. We show that the out-of-plane deformation does not influence the coupling shear strain and is governed only by the grain boundary topology. While the critical shear strain is altered somewhat by the low flexural rigidity due to buckling induced softening, it is also still dominated by the grain boundary topology. Our atomic scale results are synthesized into two models that predict the coupling and critical shears.

Established Model on Polycrystalline Graphene Oxide and Analysis of Mechanical Characteristic

It may cause more novel physical effects that the combination with in-plane defects induced by grain boundaries (GBs) and quasi three-dimensional system induced by oxidation functional group. Different from those in blocks, these new physical effects play a significant role in the mechanical properties and transport behavior. Based on the configuration design, we investigate the in-plane and out-plane geometric deformation caused by the coupling of GBs and oxygen-containing functional groups and establish a mechanical model for the optimal design of the target spatial structure. The results show that the strain rate remarkably affect the tensile properties of polycrystalline graphene oxide (PGO). Under high oxygen content (R = 50%), with the increasing strain rate, the PGO is much closer to ductile fracture, and the ultimate strain and stress will correspondingly grow. The growth of temperature reduces the ultimate stress of PGO, but the ultimate strain remains constant. When the functional groups are distributed at the edge of the GBs, the overall strength decreases the most, followed by the distribution on the GBs. Meanwhile, the strength of PGO reaches the greatest value when the functional groups are distributed away from the GBs.

A New Formulation of Coupling and Sliding Motions of Grain Boundaries Based on Dislocation Structure

A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consuming calculation of the long-range elastic interaction. In this model, the long-range elastic interaction is replaced by a constraint of Frank's formula. The constrained evolution problem in our new continuum model is further solved by using the projection method. Effects of the coupling and sliding motions in our new continuum model and relationship with the classical motion by curvature model are discussed. The continuum model is validated by comparisons with discrete dislocation dynamics model and the early continuum model [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178] in which the long-range dislocation interaction is explicitly calculated.

Transgranular amorphous shear band formation in polycrystalline boron carbide

Intragranular failure plays an important role in the failure process of superhard nanocrystalline ceramics. But the atomistic deformation mechanisms leading to intragranular failure have not been well established. Here we performed large-scale reactive force field (ReaxFF) reactive molecular dynamics (RMD) simulations on the finite shear deformation of nanocrystalline boron carbide (n-B4C) with a grain size of 9.74 nm. We find that intragranular amorphization initiates from grain boundaries (GBs) and propagates along the rhombohedral (011)<21¯1¯> slip system. To illustrate the atomic mechanism of amorphous shear band formation along this slip system, we combined density functional theory (DFT) and RMD simulations on the shear deformation of single crystal B4C. These simulations displayed that the dislocation nucleation occurs along this slip system, accompanied with bond breaking of intraicosahedral bonds within B11C cage. This leads to the amorphous shear band formation under the applied shear deformation. Our simulations suggest that the coupling of dislocation nucleation and GB sliding leads to the intragranular amorphous shear band formation and may leads to the intragranular failure in n-B4C.

Effects of H segregation on shear-coupled motion of 〈110〉 grain boundaries in α-fe

By using large-scale molecular dynamics (MD) simulations, the influence of solute hydrogen (H) segregation into several typical [11¯0] symmetric tilt grain boundaries (STGBs) on the shear response and coupled grain boundary (GB) migration of bicrystals in α-Fe is systematically examined. Depending on our geometric model of coupling for [11¯0] STGBs in body-centred cubic (BCC) metals, two different coupling branches (〈100〉 and 〈111〉) are predicted and further validated by the MD results. Our atomistic simulations show that solute H atoms impede coupled GB motion irrespective of the GB structure, which mainly stems from the fact that H considerably modifies the local atomic structures of the GBs. At high H concentrations, the response of GBs to shear deformation changes from GB coupling to pure GB sliding. In addition, it is found that H can facilitate the vacancy generation via enhancing the interaction of GB dislocations within the framework of the H-enhanced localized plasticity (HELP) mechanism. Although H-vacancy clusters are formed by solute H combining with nucleated vacancies, they cannot grow larger owing to the migration of GBs with extensive dislocation plasticity. This directly prevents the occurrence of H embrittlement (HE). These findings deepen our overall understanding of the role of solute H in GB-mediated plasticity process (GB migration) of metallic materials and provide a possible path to designing new materials with high resistance to HE.

Design of crystalline-amorphous nanolaminates using deformation mechanism maps

The deformation behavior of crystalline-amorphous nanolaminates is controlled by a confluence of mechanisms involving dislocation and grain boundary (GB) plasticity in the crystalline phase, shear transformation zone (STZ) plasticity and its localization into shear bands in the amorphous phase, and their coupling across the amorphous-crystalline interface. Leveraging molecular dynamics simulations, the influence of microstructural length scales on the mechanical behavior is quantified using deformation mechanism maps, which provide mechanistic insights into the scaling of mechanical properties with layer thickness ratio and grain size. We find that flow stress primarily scales with the relative phase fraction as deformation shifts toward STZ dominated plasticity with increasing amorphous layer thickness while the onset of plasticity is also influenced by grain size due to the role of GB plasticity in yielding. Toughness limiting mechanisms involve void formation at GBs and shear localization in the amorphous layer, where the former is attributed to dislocation-GB interactions during mixed mode deformation and the latter to dislocation slip bands biasing the process of shear localization. An Ashby plot representation combining flow stress with void and shear band localization factors demonstrates that configurations with microstructural length scales promoting cooperative strain accommodation through the coupling of dislocation, GB, and STZ plasticity exhibited limited strain localization while retaining a high flow stress, thus providing a mechanistic basis for microstructural design of crystalline-amorphous nanolaminates.

An atomic scale characterization of coupled grain boundary motion in silicon bicrystals

The mechanical response of symmetric tilt grain boundaries (GBs) in silicon bicrystals under shear loading are characterized using molecular dynamics simulations. It is seen that under shear, high-angle GBs namely Σ5 and Σ13 having a rotation axis [0 0 1] demonstrate coupled GB motion, such that the displacement of grains parallel to the GB interface is accompanied by normal GB motion. An atomic-scale characterization revealed that concerted rotations of silicon tetrahedra within the GB are the primary mechanisms leading to the coupled GB motion. Interestingly, so far, this phenomenon has only been examined in detail for metallic systems. A distinguishing feature of the coupled GB motion observed for the silicon symmetric tilt bicrystals as compared to metallic bicrystals is the fact that in the absence of shear, spontaneous coupled motion is not observed at high temperatures.

Trapped Flux and Levitation Properties of Multiseeded YBCO Bulks for HTS Magnetic Device Applications—Part I: Grain and Current Features

The strongly connected or coupled grain boundaries (GBs) between adjacent grains and their macroembodiment as flowing intergrain supercurrents crossing the GBs inside multi- seeded bulk high-temperature superconductors were elucidated by trapped-flux evaluation. Trapped-fleld measurements, after cutting and polishing two multiseeded YBCO bulk samples, were conducted to present the existence of coupled GBs and their distribution along the c-axis growth. The intensive trapped-flux density observed near the GB areas inside the whole sample is direct evidence of a strongly connected or coupled GB. The relatively strong trapped flux near the GB areas and the significant improvement of the total trapped flux compared with the isolated single-grain bulks were ascribed to the intergrain supercurrent flowing across the GBs in large macroscopic loops with coordination of the intragrain supercurrent circulating in each grain of the multiseeded bulk. Based on the experimental results, a simplified simulation model that incorporates two forms of the intra- and inter supercurrents flowing inside the multiseeded bulk is introduced to reproduce the trapped-flux density features, and qualitative agreement is obtained by comparison with the experimental ones.

Influence of grain boundary connectivity on the trapped magnetic flux of multi-seeded bulk superconductors

The top-seeded melt-growth process with multi-seeding technique provides a promising way to fabricate large-sized bulk superconductors in an economical way. To understand the essential characteristics of the multi-seeded bulks, the paper reports the influence of the grain boundary (GB) coupling or connectivity on the total trapped magnetic flux. The coupling ratio, the lowest trapped flux density in the GB area to the averaged top value of the two neighboring peak trapped fields, is introduced to reflect the coupling quality of GBs inside a multi-seeded bulk. By the trapped flux density measurement of four different performance multi-seeded YBCO bulk samples as representatives, it was found that the GB coupling plays an important role for the improvement of the total trapped magnetic flux; moreover, somewhat more significant than the widely used parameter of the peak trapped fields to evaluate the physical performance of bulk samples. This characteristic is different with the case of the well-grown single-grain bulks.

Shear response of theΣ9⟨110⟩{221}symmetric tilt grain boundary in fcc metals studied by atomistic simulation methods

The shear response of the Sigma 9 {221} symmetric tilt grain boundary (GB) in three fcc metals Cu, Al, and Ni has been studied by atomistic simulation methods with the embedded atom method for interatomic potentials and with a bicrystal model. By applying an energy minimization procedure, it was found that there are two optimized structures of this particular GB at zero temperature for all the three metals studied. Shear of bicrystals at room temperature has been studied by the molecular-dynamics simulation method. Various kinds of structure evolution behavior have been found for this GB depending on the shear direction: (1) pure GB sliding; (2) GB atomic shuffling accompanied by lattice dislocation emission from the GB; and (3) GB migration coupled with GB sliding, namely, GB coupling motion. The GB coupling motions can differ in the direction and distance of the GB migration depending on the shear direction. An analysis with the aid of the coincidence site lattice theory indicates that the structure evolution behavior can be attributed to several elementary structure transformations inherent to this particular GB. A pair parameter (lambda, kappa) is proposed to describe the GB coupling motions.

Coupling of grain boundary sliding and migration within the range of boundary specialness

Stress-induced behavior of high-angle near-coincidence symmetric tilt boundaries has been examined in bicrystal specimens of zinc. Parameters of coupling between boundary sliding and migration were determined. The angular deviation from the coincidence misorientation within the range of boundary specialness has a noticeable effect on the sliding-to-migration ratio, called “coupling factor”. Mechanisms of coupled boundary sliding and migration based on the motion of edge-type extrinsic and intrinsic grain boundary dislocations are discussed. It has been demonstrated that the observed alteration of the coupling factor with the change in boundary misorientation is due to the change of the parameters of extrinsic secondary grain boundary dislocations. The obtained results have also shown the limitation of the coincidence site lattice/displacement shift complete lattice model for the quantitative description of the structure of near-coincidence boundaries.

Evaluation of the Effect of Area Factors on the Grain Connectivity of Ex-Situ${\rm MgB}_{2}$ Cores

The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> performance of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> tape is thought to depend on the grain-boundary coupling between the grains of an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> core and between particles within a grain. This work investigates the influence of these area-dependent factors on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> performance and the measured grain connectivity of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> cores. While the influence of area factors on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> - B performance of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> tapes is small, the effect on measured grain connectivity is larger. Therefore, the relationship between the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> - B performance of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> tape and grain connectivity should carefully take this phenomenon into account. Moreover, this study reveals that different ways to evaluate the grain connectivity have advantages and disadvantages for detecting the influence of the area factors. We propose an evaluation guideline for the grain connectivity of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> cores in order to analyse the reasons for area-dependent changes. We believe that this work will improve our understanding of grain connectivity and allow it to be used as feedback in investigations of the fabrication of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-situ</i> MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> tape with high <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> - B performance.

Strain-driven grain boundary motion in nanocrystalline materials

We report fully three-dimensional atomistic molecular dynamics studies of strain-induced grain boundary mobility in nanocrystalline Ni at room temperature. The position of a statistically significant number of grain boundaries was monitored as a function of the strain level for a strain rate of 3.3 × 10 8 s −1 for two different interatomic potentials. The results show the grain boundaries migrating with velocities of 2–3 m/s, depending on the interatomic potential used. Detailed analysis of the process shows that grain boundary migration is accompanied by grain rotation and in many cases dislocation emission. The results suggest that grain rotation, grain boundary sliding, and grain boundary migration occur simultaneously in nanocrystalline metals as part of the intergranular plasticity mechanism. The effects of free surfaces present in the sample on these related mechanisms of plasticity were investigated in detail and it was found that the presence of free surfaces lowers the flow stress observed for the samples and increases the amount of grain boundary sliding, while actually decreasing the average velocity of grain boundary migration parallel to itself. Finally, we report observations of grain coalescence in the samples with a free surface. The results are discussed in terms of the coupling of grain boundary sliding and migration.

Isothermal stress relaxation in electroplated Cu films. I. Mass transport measurements

Recent studies on Cu interconnects have shown that interface diffusion between Cu and the cap layer dominates mass transport for electromigration. The kinetics of mass transport by interface diffusion strongly depends on the material and processing of the cap layer. In this series of two papers, we report in Part I the interface and grain-boundary mass transport measured from isothermal stress relaxation in electroplated Cu thin films with and without a passivation layer and in Part II a kinetic model developed to analyze the stress relaxation based on the coupling of grain boundary and interface diffusion. We show that a set of isothermal stress relaxation experiments together with appropriate modeling analysis can be used to evaluate the kinetics of interface and grain-boundary diffusion that correlate to electromigration reliability of Cu interconnects. Thermal stresses in electroplated Cu films with and without passivation, subjected to thermal cycling and isothermal annealing at selected temperatures, were measured using a bending-beam technique. Thermal cycling experiments showed the effect of passivation and provided information to select the initial stresses and temperatures for isothermal stress measurements. Isothermal experiments at moderate temperatures showed a significant transient behavior of stress relaxation. Based on the kinetic model developed in Part II, grain boundary and interface diffusivities were deduced. While the deduced grain boundary diffusivity reasonably agrees with other studies, the diffusivity at the Cu∕SiN cap layer interface was found to be generally lower than the grain-boundary diffusivity at the temperature range of the present study.

Grain Growth During Superplastic Deformation

Significant grain growth occurring during superplastic deformation is related to the micro-mechanism of superplastic flow. Observations performed on the deformed surface of superplastically deformed tensile and shear Pb-62%Sn samples and bi-axially formed AA7475 samples directly indicate that cooperative grain boundary sliding, i.e. sliding of grain groups, is accompanied by cooperative grain boundary migration that can result in an enhanced grain growth. Such a long range correlation in migration of sliding grain boundaries is related to movement of grain boundary dislocations having a step associated with its core. Observed correlation between grain size and strain measured in different regions of a superplastically formed Ti-alloy part and alignment of grain boundaries along shear surfaces support coupling of grain boundary sliding and migration. A model of grain growth considering climb of cellular dislocations, topological defects in a grain array, has been expanded to incorporate gliding and mixed cellular dislocations.

Cooperative Processes in Superplastic Forming Under Different Deformation States

Evidence on cooperative phenomena including sliding and rotation of grain groups and correlated grain boundary migration during superplastic deformation under different strain states is reported. The pattern of macroscopic surfaces at which grain blocks slide as an entity is consistent with that of slip lines predicted by the slip band field theory. Sliding of grains at these shear surfaces occurs in a sequential manner. Increasing strain and applied stress (strain rate) result in decrease in spacing of the shear surfaces. Cooperative grain rotation results in a change in the orientation of the macroscopic shear surfaces and provides accommodation sliding of grain group. Correlated grain boundary migration is due to the coupling of grain boundary sliding and migration caused by characteristics of dislocation movement at grain boundaries.

Electromigration drift velocity in Cu interconnects modeled with the level set method

Electromigration (EM) drift velocity (DV) experiments in polycrystalline pure Cu lines are simulated numerically with the level set method. The simulation is based on a grain boundary (GB) grooving model, incorporating an electric field. The model is distinguished by two key requirements imposed at the triple point where two surfaces and a GB meet: that of GB and surface flux coupling (flux continuity), and that of permanent equilibrium between surface and GB tensions. Surface diffusion exists only at the advancing cathode edge, and is driven both by local curvature gradients and by the local field. Using independent, literature diffusivity values, the simulation yields both the DV prefactor and the EM activation energy in an Arrhenius-type expression. An excellent match is obtained with experimental DV values in the T range of 573–723 K. Some implications regarding the material transport mechanism are discussed.

An investigation on high-angle grain boundaries in melt-textured YBa 2Cu 3O 6+ x superconductors

Six high-angle (range between 17° and 77°) grain boundaries in melt-textured YBa 2Cu 3O 6+ x superconducting materials, namely GB1, GB2, GB3, GB4, GB5 and GB6, have been investigated. Three of them GB1, GB2 and GB3 have high values of critical current, while the other three GB4, GB5 and GB6 possess low values of critical current. From TEM studies, GB1, GB2 and GB6 are found to be related to fully oxygenated CCSL boundary, while GB4 and GB5 are related to oxygen-deficient constraint coincidence site lattice (CCSL) boundary. GB3 is found to be a random grain boundary where its misorientation characteristics do not match any CCSL within the limitation of Σ<100. The analyses of the TEM studies along with the critical current measurements obtained on GB1, GB2, GB4 and GB5 indicate that oxygen distribution at the grain boundary plays an important role in the coupling of grain boundaries in YBa 2Cu 3O 6+ x superconductor. However, the behaviors of GB3 and GB6 suggest that the CCSL theory is not general in predicting the superconducting behavior of high-angle grain boundaries in YBa 2Cu 3O 6+ x superconductors.

Coupling of co-operative grain boundary sliding and co-operative grain boundary migration

Coupling of co-operative grain boundary sliding and co-operative grain boundary migration