Grain Boundary Energy Research Articles

Effect of grain boundary misorientation angle on diffusion behavior in molybdenum-tungsten systems

Grain boundary (GB) diffusion plays a key role in the long-term service processes of engineering materials at elevated temperatures. GB diffusion processes are strongly relying on the misorientation angle of the two adjacent grains. However, the orientation dependence of GB diffusion is not well understood. In this work, two types of tungsten coating were deposited onto a substrate consisting of a single molybdenum crystal to forming diffusion couples. The diffusion profiles of isolated GBs have been measured by electron backscatter diffraction and energy dispersive X-ray spectroscopy. The effect of the tungsten GB misorientation angle (θ) on the diffusivity of molybdenum was investigated. GB structures with different misorientation angles were resolved using high-resolution transmission electron microscopy. As θ increased from 5° to 18°, the spacing between the dislocations composing the GBs decreased from greater than 10 to 3 atomic spaces. Furthermore, when θ was greater than 18° a 0.53 nm wide ordered structure was formed, and this structural change increased the GB energy. Consequently, the GB diffusion coefficient increased by 3- and 7- orders of magnitude fold as compared to the volume diffusion coefficient for low- and high-angle GBs, respectively. The GB energies were approximately 1.1 and 2.1 J m−2 in low- and high-angle GBs, respectively. This is the first time that tungsten GB energies were determined through experimental method.

Combined effect of surface polarization and ZnO addition on antibacterial and cellular response of Hydroxyapatite-ZnO composites.

Bacterial infection is among the serious concerns in orthopaedic during/after surgery. Here, we demonstrate a novel technique to induce the antibacterial response in biomaterial substrates via surface polarization. In the present work, hydroxyapatite, HA-xZnO (x = 3.0, 4.5 and 7.5 wt. %) composites were processed by solid state sintering route at 1250 °C for 2 h. After phase evolution analyses, the detailed dielectric and electrical measurements were performed over a wide range of temperature (30-500 °C) and frequency (1 Hz-1 MHz). The impedance spectroscopic analyses suggest the activation energies for grains and grain boundaries for HA and HA-3 wt.% ZnO are (1.36, 1.44 eV), and (1.18, 1.98 eV), respectively. The sintered samples were polarized under polarizing temperature and voltage of 500 °C and 20 kV, respectively. The viability of Escherichia Coli (E. Coli) and Staphylococcus Aureus (S. Aureus) bacteria is observed to reduce significantly for polarized HA-x ZnO (x = 4.5 and 7.5 wt. %) composites as compared to their respective counterparts. On the other hand, polarization supports the proliferation of SaOS2 cells. Overall, the combination of surface polarization and optimal ZnO addition in HA has been demonstrated to significantly improve the antibacterial as well as osteoblast-like SaOS2 cellular response.

Solute effects on the Σ3 [formula omitted] tilt grain boundary in BCC Fe: Grain boundary segregation, stability, and embrittlement

Solute segregation can profoundly affect the thermodynamic stability and cohesive properties of the grain boundaries (GBs) in Fe-based alloys. In the present work, first-principles calculations based on density functional theory (DFT) are performed to understand the atomistic mechanisms of the solute-GB interactions under the dilute limit condition. The segregation effects of six transition metal elements (Cr, Ni, Cu, Zr, Ta, and W) on the Σ3 111[11-0] tilt boundary in BCC Fe are systematically studied by examining GB energy, solute segregation energy, and GB cohesion. The solute segregation energy is verified to be composed of a combination of the strain and electronic contributions rather than either of them alone, even for the solute elements with large atomic volume. The potential effects of the FCC/BCC polymorphic phase transformations on the solute segregation behaviors are also discussed. The dynamic change in atomic and electronic structures with straining are investigated to provide physical insights into the effects of solute segregation on the properties of the GB cohesion.

A new approach for phase field modeling of grain boundaries with strongly nonconvex energy

Grain boundaries (GBs) are key players in determining macroscopic material behavior and driving the creation of microstructure in nanocrystalline materials. Microstructure typically features irregular features and morphology such as microfaceting, due to the strong nonconvexity of GB energy with respect to boundary plane orientation. Mesoscale simulation of microstructure evolution can be done effectively using the multiphase field (MPF) method. However, strongly nonconvex boundary energies present numerical challenges in MPF simulations. The lack of convexity in GB energy causes the minimal GB energy problem to be mathematically ill-defined. Numerically, this causes mesh dependency and instability. In this work we present an additively decoupled regularization scheme utilizing a K23 second order curvature regularization to penalize regions of sharp curvature induced by nonconvex GB energy. Physically, the K23 regularization corresponds to corner or triple junction dislocations, and does not adversely affect the diffuse properties of the GB or the GB energy. It is shown that the additively decoupled K23 regularization term admits a numerically convenient variational derivative, when evolved in the eigenbasis of the Hessian curvature tensor. This enables K23 to be determined in terms of derivatives in the natural coordinate system, which is advantageous for implementations on a regular grid. The faceting behavior in GBs is demonstrated using a parallel adaptive mesh refinement code. It is shown that faceting is stable even if the GB energy exhibits cusps and the regularization parameter effectively controls the faceting length scale. Evolution of an inclusion is studied for smooth and non-smooth GB energies and results are compared against analytic Wulff shapes. The proposed scheme leverages Lagrange multipliers to use a modified fourth order Allen–Cahn system in lieu of a sixth order Cahn–Hilliard system for numerical efficiency.

Mesoscale Modeling of High Burn-Up Structure Formation and Evolution in UO2

A phase-field model was developed to simulate the high burn-up structure formation and evolution in UO2. The model takes into account the interfacial energies of grain boundaries and bubble surfaces, the strain energy associated with dislocations, and the chemical energy of gas atoms. This enables the model to simulate the formation and growth of sub-grains and bubbles in a self-consistent manner. The model results demonstrate strong effects of dislocation density (its magnitude and distribution), grain boundary energy, and bubble radius and number density on the formation of the sub-grains. For polycrystalline UO2, the model predicts the average size of the recrystallized grains to lie within the range of 0.3–0.5 µm corresponding to a dislocation density range of $$ \rho = (2.5 \times 10^{15} - 2.65 \times 10^{15} ) \;{\text{m}}^{ - 2} $$ or equivalent to 70–75 GWd/tHM burn-up. These predictions agree reasonably well with data reported in the literature.

Twinning from Triple Lines in Nanocrystalline Copper by Molecular Dynamics Simulation

As the intersecting line of three grain boundaries (GBs), triple line possesses large stress concentration and extra energy, which makes it the optimal nucleation site for twin embryos. In present work, molecular dynamics (MD) simulation on nanocrystalline Cu indicated that 27 out of 28 twins were emitted from triple lines. Stress relaxation and energy reduction were considered to be the driving force for twinning from triple lines. This could be proved by changes of dihedral angles, relative GB energy sum, average atomic von Mises shear stress and average atomic energy.

Effect of grain boundary angle on the thermal conductivity of nanostructured bicrystal ZnO based on the molecular dynamics simulation method

ZnO is a widely used semiconductor material due to its excellent physical and mechanical properties. The thermal transport behavior across a single grain boundary (GB) of bicrystal ZnO with varying tilt angles from 5.45° to 67.38° was investigated using a nonequilibrium molecular dynamics simulation. The GB energy and Kapitza resistance as a function of tilt angle were determined and parameters of the extended Read-Shockley model were calculated. The Kapitza resistance varied monotonically with a GB angle <36° and was nearly constant when the angle was >36°. Furthermore, effective thermal conductivity and Kapitza resistance were found to depend strongly on the sample length and temperature. Finally, we compared the phonon density of states of the two types of GBs and found a mismatch in the low frequency that might explain the effect of the GBs structures on heat conduction.

Grain size effect on the electrical properties of nanocrystalline Gd2Zr2O7 ceramics

A detailed study on the effect of grain size of nanocrystalline Gd2Zr2O7 (GZO) ceramics on its electrical properties, particularly the ionic conductivity, is reported. The nanocrystalline GZO was prepared by chemical co-precipitation method. The GZO ceramic with different grain sizes from 5 to 55 nm was fabricated by sintering them at different temperatures varying from 800 to 1400 °C. Structural studies were performed by X-ray diffraction and Raman spectroscopy and found the cubic pyrochlore phase of GZO in all cases. Their crystallite size has been increased from 5 to 55 nm as well as the structural ordering has been increased with the increase in sintering temperature. The ac electrical impedance analysis showed a dramatic increase in ionic conductivity with increasing grain size. The ionic conductivity measured at 700 °C was 8.7 × 10−6, 12.5 × 10−6, 20.4 × 10−6 and 45.4 × 10−6 S cm−1 for respective grain sizes 5, 12, 25, and 55 nm of GZO ceramics. Increase in conductivity was correlated to the increase in grain size. The activation energy for grain conductivity was found to be 1.42 ± 0.01 eV for all GZO ceramics irrespective of their grain size. However, the activation energy of grain boundary and total conductivity had decreased with increasing grain size. The activation energy for total conductivity was obtained to be 1.5, 1.48, 1.46 and 1.42 eV for 5, 12, 25, and 55 nm GZO ceramics respectively. Further, the ac conductivity was found to obey the universal Jonscher's power law and the power exponent s was found to increase with the increase in temperature. It was also showed that the non-overlapping small polaron tunneling (NSPT) has been the best suited theoretical model to explain the conduction mechanism occurred in GZO ceramics. In addition, increase in co-operative dynamics of mobile ions with increase in grain size was found to favor the enhancement of conductivity.

Role of grain boundaries on ductility in Mg-Y alloys

The impact of the grain size and the chemical composition of an alloying element on mechanical properties in ductility was investigated using wrought processed various Mg-Xat%Y binary alloys (where, X = 0.1, 0.3, 1.0 and 2.0). The average grain sizes of these Mg-Y alloys after a subsequent annealing process varied from around 5 µm to over 100 µm. The elongation-to-failure in tension was influenced by the grain size, irrespective of the yttrium content. The Mg-Y alloys consisting of meso‑grained structures (average grain size of ∼20–30 µm) exhibited good elongation-to-failure of ∼25–30%; however, “further” grain refinement led to a decrease in the properties of ductility. This tendency was confirmed to have no relation to the yttrium content. Deformed microstructural observations revealed that grain boundaries were the source of non-basal dislocation slips, but became crack-propagation sites. Although grain refinement from coarse- to meso‑sizes (up to around ∼20–10 µm) was effective, fine-grained alloys were unlikely to show a large elongation-to-failure due to grain boundary embrittlement. Not only the critical resolved shear stress but also the segregation energy of grain boundary is a considerable characteristic for alloying elements to improve ductility in magnesium alloys. Furthermore, in the case of fine-grained Mg-rare earth alloys, it is necessary to take into consideration that grain boundaries become not only the source of non-basal dislocation slips but also the route for crack-propagation.

A Compact Model for 2-D Poly-MoS2 FETs With Resistive Switching in Postsynaptic Simulation

The analog resistive switching (RS) characteristics in 2-D polycrystalline (poly-) molybdenum disulfide (MoS2) field-effect transistors (FETs) enable new electronic devices capable of emulating biological synaptic behaviors. In 2-D poly-materials, grain boundary (GB)-induced trap states are of major significance to RS behaviors. However, there is still a lack of appropriate compact models that capture accurate physical mechanisms. Therefore, we developed a surface potential-based compact model, based on the theories of the GB energy barrier and space charge limited current (SCLC). By calibrating to experimental data of MoS2, the physical parameters are extracted, and the model explains the scaling behaviors of channel lengths and grain sizes. Due to the electric-field-induced defect redistribution, the energy barrier modulation at a single-GB (e.g., intersecting GB) quantitatively matches the reported experiments. Moreover, the possible SCLC-based RS behavior is also investigated. Furthermore, we have optimized the set/reset process and simulated the postsynaptic current (PSC) with a tunable potentiation (or depression) process, and then the gate voltage dependence and statistical effects on RS and PSC have been investigated. Thus, this model provides important devices physics insights of 2-D poly-materials and it guides device design, fabrication, and material engineering, to meet the requirements of the future neuromorphic computing application.

Thermodynamic Stability of Nano-grained Alloys Against Grain Coarsening and Precipitation of Macroscopic Phases

Thermodynamic conditions are derived here for binary alloys to have their grain boundary (GB) energies negative, ensuring the stability of some nano-grained (NG) alloys. All binary alloys are found to belong to one of the following three types. Type 1 is the unstable NG alloy both against grain coarsening and precipitation of a macro-phase. Type 2 is the partly stable NG alloy, stable against coarsening but not against precipitation. Type 3 is the fully stable NG alloy, both against coarsening and precipitation. Alloys type 1 have negative, or low-positive interaction energies between the components. Alloys type 2 have medium-positive interaction energies, while alloys type 3 have high-positive interaction energies. Equations are derived for critical interaction energies separating alloys type 1 from type 2 and those from type 3, being functions of the molar excess GB energy of the solute, temperature (T) and composition of the alloy. The criterion to form a stable NG alloy is formulated through a new dimensionless number (Ng), defined as the ratio of the interaction energy to the excess molar GB energy of the solute, both taken at zero Kelvin. Systems with Ng number below 0.6 belong to alloy type 1, systems with Ng number between 0.6 and 1 belong to alloy type 2, while systems with Ng number above 1 belong to alloy type 3, at least at T = 0 K. The larger is the Ng number, the higher is the maximum T of stability of the NG alloy. By gradually increasing temperature alloys type 3 convert first into type 2 and further into type 1. The Ng number is used here to evaluate 16 binary tungsten-based (W-B) alloys. At T = 0 K type 3 NG alloys are formed with B = Cu, Ag, Mn, Ce, Y, Sc, Cr; type 2 is formed in the W-Ti system, while type 1 alloys are formed with B = Al, Ni, Co, Fe, Zr, Nb, Mo and Ta. For the W-Ag system the region of stability of the NG alloys is shown on a calculated phase diagram, indicating also the stable grain size.

Interactions of plasticity and phase transformation under shock in iron bicrystals

The interaction of plasticity and martensitic transformation in iron bicrystals under shock has been investigated via nonequilibrium molecular-dynamic simulations with our modified analytic embedded-atom model potential. Our results show that grain boundaries (GBs) can change the kinetics of α → ɛ martensitic transformations. The condition that GBs trigger strain induced transformation (SIT) is revealed, that is, the local structure of GBs can be converted to a hexagonal close packing (HCP) lattice with a lower potential barrier than the BCC → HCP transformation (stress assist transformation, SAT) because the driving energy of transition can be partly provided by the energy of GBs. It can explain why the threshold of the phase transition can be greatly reduced in samples containing some types of GBs. The threshold of SIT is lower than that of SAT, which agrees well with experimental results. Then, the nucleation kinetics of phase transition induced by dislocations are described. The propagation of dislocation provides the driving force for the nucleation of the phase transition. The dislocations can be directly emitted from the GBs under shock, which provides a new view that the phase transition is not always preceded by dislocations near GBs. In addition, dislocations can be induced by pre-existing dislocations under shock, which makes it understandable that GBs can emit dislocations. Our findings have an important significance for experimental studies and macroscopic and mesoscopic scale simulations regarding iron martensitic transformation.

Nucleation and growth of helium bubble at (110) twist grain boundaries in tungsten studied by molecular dynamics**Project supported by the National Natural Science Foundation of China (Grant Nos. 11305136, 11675230, 11375242, and U1832112).

Migration of He atoms and growth of He bubbles in high angle twist grain boundaries (HAGBs) in tungsten (W) are investigated by atomic simulation method. The energy and free volume (FV) of grain boundary (GB) are affected by the density and structure of dislocation patterns in GB. The migration energy of the He atom between the neighboring trapping sites depends on free volume along the migration path at grain boundary. The region of grain boundary around the He bubble forms an ordered crystal structure when He bubble grows at certain grain boundaries. The He atoms aggregate on the grain boundary plane to form a plate-shape configuration. Furthermore, high grain boundary energy (GBE) results in a large volume of He bubble. Thus, the nucleation and growth of He bubbles in twist grain boundaries depend on the energy of grain boundary, the dislocation patterns and the free volume related migration path on the grain boundary plane.

The effect of space-charge formation on the grain-boundary energy of an ionic solid.

Taking the model system of an oxide containing acceptor dopant cations and charge-compensating oxygen vacancies, we calculate at the continuum level the change in the excess grain-boundary energy of an ionic solid upon space-charge formation. Two different cases are considered for the space-charge layers: (i) only vacancies attain electrochemical equilibrium and (ii) both dopants and vacancies attain electrochemical equilibrium. The changes calculated for a specific set of grain boundaries indicate that, depending on dopant concentration, space-charge formation can decrease the excess free energy by up to 15% in the first case and by up to 45% in the second case. The possibility of the excess grain-boundary energy going to zero and the possible effects of an external electric field on the excess grain-boundary energy are also discussed. This article is part of a discussion meeting issue 'Energy materials for a low carbon future'.

Key factors in radiation tolerance of BCC metals under steady state

Different materials would exhibit discrepant behaviors of radiation tolerance under energetic particle irradiation, due to the effect of intrinsic features (like defect migration energy and sink strength of grain boundaries) and extrinsic conditions (like irradiation rate and temperature) on defect accumulation. We wonder what the general rules of radiation tolerance are in body-centered cube (BCC) transition metals. Based on the steady state chemical rate theory, the influence of these intrinsic features and extrinsic conditions on vacancy accumulation is thus investigated in typical BCC metals including V, Cr, Fe, Nb, Mo, Ta and W. It shows that V, Cr, Fe and Nb exhibit obvious advantage in radiation resistance than that of Ta, Mo and W under typical service conditions, due to their higher vacancy diffusivities. In addition, the smaller grain size and lower irradiation rate, the higher anti-irradiation ability of BCC metals. Therefore, we propose that, under practical irradiation rates and temperatures, BCC metals with low vacancy migration energy and small grain size should be recommended in the selection of new nuclear materials, at least in the view of steady state.

Phonon-Grain-Boundary-Interaction-Mediated Thermal Transport in Two-Dimensional Polycrystalline MoS2.

Although dislocations and grain boundaries (GBs) are ubiquitous in large-scale MoS2 samples, their interaction with phonons, which plays an important role in determining the lattice thermal conductivity of polycrystalline MoS2, remains elusive. Here, we perform a systematic study of the heat transport in two-dimensional polycrystalline MoS2 by both molecular dynamics simulation and atomic Green's function method. Our results indicate that the thermal boundary conductance of GBs of MoS2 is in the range from 6.4 × 108 to 35.3 × 108 W m-2 K-1, which is closely correlated with the overlap between the vibrational density of states of GBs and those of the pristine lattice, as well as the GB energy. It is found that the GBs strongly scatter the phonons with frequency larger than 2 THz, accompanied by a pronounced phonon localization effect and significantly reduced phonon group velocities. Furthermore, by comparing the results from realistic polycrystalline MoS2 to those from different theoretical models, we observe that the Casimir model is broken down and detailed phonon dynamics at a specific GB should be taken into account to accurately describe the phonon transport in polycrystalline materials. Our findings will provide useful guidelines for designing efficient thermoelectric and thermal management materials based on phonon-GB interaction.

Low-angle grain boundary structures and size effects of nickel nanolaminated structures

Recent experiments have demonstrated the fabrication of nickel nanolaminated structures with low-angle grain boundaries and that these nanolaminated structures exhibit an ultrahigh hardness of 6.4 GPa and excellent thermal stability. However, the detailed microstructure of the low-angle grain boundary in these nanolaminated structures and plastic deformation mechanisms underlying their ultrahigh hardness have remained elusive to date. Thus, we performed a series of large-scale atomistic simulations to explore the microstructures, thermal stability and energies of the low-angle grain boundary in nanolaminated nickel and to further mimic the plastic deformation of nanolaminated nanopillars. First, we examined the thermal stability of low-angle grain boundaries in nanolaminated structures with three typical textures observed in previous experiments, and we found that the {111}<110>-textured nanolaminated structure is the most stable and has a critical temperature of approximately 750 K for stability. The low-angle grain boundary in such nanolaminated structures consists of a periodic arrangement of three types of dislocations with Burgers vectors of 1/2[101], 1/3[11¯1] and 1/6[14¯1]. Our simulations also showed that the grain boundary energy of the low-angle grain boundary with misorientation of 5° is approximately 0.70 J/m2 and that the interaction energy between two low-angle grain boundaries follows a power law as the lamellar thickness, with an exponent of −1.14. We further simulated the uniaxial compression and tension of nanolaminated nanopillars with a texture of {111}<110> and different lamellar thicknesses. The simulation results showed that as the lamellar thickness decreases, both compressive and tensile yield stresses significantly decrease, while their flow stresses slightly increase. The size effect on yield stress is attributed to dislocation escape from the low-angle grain boundary due to some typical reactions of constituent dislocations, while the size effect on flow stress is related to a complex reaction and interaction of high-density dislocations. Our study provides a fundamental understanding of the grain boundary structure and plastic deformation in textured nanolaminated metals, which offers insights for the design of stronger nanolaminated structures.

Grain boundary curvatures in polycrystalline SrTiO3: Dependence on grain size, topology, and crystallography

AbstractBy mapping grain orientations on parallel serial sections of a SrTiO3 ceramic, it was possible to reconstruct three‐dimensional orientation maps containing more than 3000 grains. The grain boundaries were approximated by a continuous mesh of triangles and mean curvatures were determined for each triangle. The integral mean curvatures of grain faces were determined for all grains. Small grains with fewer than 16 neighbors mostly have positive mean curvatures while larger grains with more than 16 neighbors mostly have negative mean curvatures. It is also possible to correlate the mean curvature of individual triangles with the crystallographic characteristics of the grain boundary. The mean curvature is lowest for grain boundaries with (100) orientations and highest for grain boundaries with (111) orientations. This trend is inversely correlated to the relative areas of grain boundaries and directly correlated to the relative grain boundary energy. The direct correlation between the energy and curvature is consistent with the expected behavior of grain boundaries made up of singular orientations. Furthermore, because both the relative energy and curvature of grain boundaries with (100) orientations are minima in the distributions, these boundaries also have the lowest driving force for migration.

Nanoscale mapping of the electron density at Al grain boundaries and correlation with grain-boundary energy

Grain-boundary (GB) structures and energies are often calculated and have revealed correlations between the GB energy and change in electron density at the GB. In this work, the plasmon peak in valence electron energy-loss spectroscopy (VEELS) was used to determine the variation in electron density across four well-characterized GBs in Al, spanning a range of known GB energies. The results show that the plasmon energy is lower at the GB than in the adjacent grains due to a decrease in electron density, and the GB energy increases proportional to the density decrease. The decrease in electron density also extends further into adjacent grains with increasing GB energy, extending beyond the geometric changes, or physical width, revealed by electron microscopy. Plasmon damping also increases with increasing GB energy, indicative of increasing disruption of the electron density with increasing GB energy. These results demonstrate that VEELS can be a valuable tool for detecting small electron density changes at GBs, and this change clearly influences, and is correlated to, the GB energy.

Discontinuous model combined with an atomic mechanism simulates the precipitated η′ phase effect in intergranular cracking of 7-series aluminum alloys

A first-principles calculation reveals that the phase that is precipitated in a grain boundary weakens the cohesiveness of the grain boundary. The hydrogen atom is likely to be trapped in the Al/MgZn2 boundary when it diffuses through the grain boundaries, which further reduces the cohesive energy of grain boundaries including Al-H-MgZn2. A discontinuous peridynamic model is proposed to compensate for a deficiency of the finite element method. The peridynamic simulation results show that the cracks grow obviously along the grain boundaries containing Al-H-MgZn2.