Symmetric Tilt Grain Research Articles

Asymmetric tilt grain boundary structure and energy in copper and aluminium

Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Σ5 and Σ13 systems with a boundary plane rotated about the ⟨ 100 ⟩ misorientation axis, and the Σ9 and Σ11 systems rotated about the ⟨ 110 ⟩ misorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Σ5 and Σ13 systems in the ⟨ 100 ⟩ system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Σ9 and Σ11 systems in the ⟨ 110 ⟩ system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Σ9 (221) and Σ11 (332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index {111} and {110} planes bounding the interface region.

Structures and energies of Σ 3 asymmetric tilt grain boundaries in copper and aluminium

The objective of this research is to use atomistic simulations to investigate the energy and structure of symmetric and asymmetric Σ3 ⟨110⟩ tilt grain boundaries. A nonlinear conjugate gradient algorithm was employed along with an embedded atom method potential for Cu and Al to generate the equilibrium 0 K grain boundary structures. A total of 25 ⟨110⟩ grain boundary structures were explored to identify the various equilibrium and metastable structures. Simulation results show that the Σ3 asymmetric tilt grain boundaries in the ⟨110⟩ system are composed of only structural units of the two Σ3 symmetric tilt grain boundaries. The energies for the Σ3 grain boundaries are similar to previous experimental and calculated grain boundary energies. A structural unit and faceting model for Σ3 asymmetric tilt grain boundaries fits all of the calculated asymmetric grain boundary structures. The significance of these results is that the structural unit and facet description of all Σ3 asymmetric tilt grain boundaries may be predicted from the structural units of the Σ3 coherent twin and incoherent twin boundaries for both Cu and Al.

Decohesion of iron grain boundaries by sulfur or phosphorous segregation: First-principles calculations

We performed first-principles calculations to simulate the grain boundary decohesion in ferromagnetic bcc iron (Fe) $\ensuremath{\Sigma}3(111)$ symmetrical tilt grain boundaries by progressively adding solute atoms [sulfur (S) or phosphorous (P)] to the boundaries. We show that there are two mechanisms of decohesion: (i) fracture surface stabilization with reference to the grain boundary by the segregated solute atoms without interaction between them, and (ii) grain boundary destabilization by a repulsive interaction among the segregated and neighboring solute atoms. It is found that the dominant mechanism for the S-induced decohesion is the former (i), while that for P is the latter (ii). This difference makes P a much weaker embrittling element comparing with S because the mechanism (ii) simultaneously brings about the reduction of the grain boundary segregation energy.

Mechanism of Effects of Rare Earths on Microstructure and Properties at Elevated Temperatures of AZ91 Magnesium Alloy

By using real-space recursion method, the energetics of the undoped and A1 and/or RE atoms doped Σ(1450) <0001> symmetric tilt grain boundaries (GBs) in AZ91 alloys were investigated. Similar calculations were performed on undoped and doped bulk α Mg for comparison. The results showed that A1 atoms segregated at GBs in AZ91 alloys. When RE atoms were added, they also segregated at GBs, and their segregation is stronger than A1 atoms'. Therefore, RE atoms retard the segregation of A1 atoms. Calculations of interaction energy indicated that A1 atoms repelled each other, and could form ordered phase with host Mg atoms. On the contrary to the case of A1, RE atoms attracted each other, they could not form ordered phase with Mg, but could form clusters. Between RE and A1, there existed attractive interaction, and this attractive interaction was the origin of Al 11 RE 3 precipitation. Precipitation of A1 11 RE 3 particles with high melting point and high thermal stability along GB improves high temperature properties of AZ91 alloys.

Structure and free volume of 〈1 1 0〉 symmetric tilt grain boundaries with the E structural unit

Atomistic simulations are used to investigate the structure and interfacial free volume of 〈1 1 0〉 symmetric tilt grain boundaries in copper containing the E structural unit from the Σ9(2 2 1) θ = 141.1° grain boundary. In this work, a stereologically-based methodology is used to calculate the grain boundary free volume along with the spacing and connectivity of free volume. After generating the minimum energy equilibrium grain boundary, we examine (i) the grain boundary structure, (ii) a measure of free volume associated with the grain boundary, (iii) spatial correlation functions of the distribution of free volume, and (iv) images of grain boundary free volume distribution. Using the results from these calculations, the influence of free volume spatial distribution and grain boundary structure on dislocation dissociation and nucleation is briefly discussed for boundaries with the E structural unit subjected to tensile loading normal to the interface along with the potential implications of free volume connectivity.

Bond-order potential for simulations of extended defects in tungsten

We present a bond-order potential BOP for the bcc transition metal tungsten. The bond-order potentials are a real-space semiempirical scheme for the description of interatomic interactions based on the tight-binding approximation. In the hierarchy of atomic-scale-modeling methods the BOPs thus provide a direct bridge between electronic-structure and atomistic techniques. Two variants of the BOP were constructed and extensively tested against accurate first-principles methods in order to assess the potentials’ reliability and applicability. A comparison of the BOP with a central-force potential is used to demonstrate that a correct description of directional mixed covalent and metallic bonds is crucial for a successful and fully transferable model. The potentials are applied in studies of low-index surfaces, symmetrical tilt grain boundaries, and dislocations.

Dynamics of atomic species involved in shear-induced displacements at sliding symmetricalgrain boundaries: a numerical study

Molecular dynamics methods have been used to study the mechanical response under shearof two Cu systems containing symmetrical tilt and twist grain boundaries, respectively. Theinvestigation focuses on the mechanism of localized atomic displacements during plasticdeformation. It is shown that grain boundary sliding generates a perturbed layer of atomicspecies, with thickness increasing approximately with the square root of time. Thedynamics of the atomic displacement processes, even though apparently stochastic, isintimately connected with the local density experienced by atoms under shear.

Prediction of Energies of Tilt Boundaries in Al-Pb Alloy

ABSTRACTEnergies for symmetric tilt grain boundaries in pure Al and in Al with substitutional Pb defects at coincident sites along the grain boundaries were calculated using a modified embedded atom method potential and density functional theory. The agreement between the analytic potential, the first principles calculations and experiment is reasonably good for the pure system. For the Al-Pb system both the analytic potential and first principles calculations predict that Pb segregation to the interface is energetically preferred compared to the dilute solution. The application of a disclination structural unit model to calculating grain boundary energies over the entire range of tilt angles is also explained.

Computer simulation of symmetrical tilt grain boundaries in noble metals with MAEAM

This paper reports that an atomic scale study of [10] symmetrical tilt grain boundary (STGB) has been made with modified analytical embedded atom method (MAEAM) for 44 planes in three noble metals Au, Ag and Cu. For each metal, the energies of two crystals ideally joined together are unrealistically high due to very short distance between atoms near the grain boundary (GB) plane. A relative slide between grains in the GB plane results in a significant decrease in GB energy and a minimum value is obtained at specific translation distance. The minimum energy of Cu is much higher than that of Ag and Au, while the minimum energy of Ag is slightly higher than that of Au. For all the three metals, the three lowest energies correspond to identical (111), (113) and (331) boundary successively for two translations considered; from minimization of GB energy, these boundaries should be preferable in [10] STGB for noble metals. This is consistent with the experimental results. In addition, the minimum energy increases with increasing reciprocal planar coincidence density Σ, but decreases with increasing relative interplanar distance d/a.

Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper

First principles calculations of the Sigma 5 (310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However numerical results show a striking equivalence between the alkali metal Na and the semi metal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unravelled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the nett reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.

Low-energy sputtering events at free surfaces near anti-phase and grain boundaries in Ni3Al

Atomic recoil events on free surfaces orthogonal to two different anti-phase boundaries (APBs) and two grain boundaries (GBs) in Ni3Al are simulated using molecular dynamics methods. The threshold energy for sputtering, E sp, and adatom creation, E ad, are determined as a function of recoil direction. The study is relevant to FEG STEM (a scanning transmission electron microscope fitted with a field emission gun) experiments on preferential Al sputtering and/or enhancement of the Ni–Al ratio near boundaries. Surfaces intersected by {110} and {111} APBs have minimum E sp of 6.5 eV for an Al atom on the Ni–Al mixed (M) surface, which is close to the value of 6.0 eV for a perfect M surface. High values of E sp of an Al atom generally occur at a large angle to the surface normal and depend strongly on the detailed atomic configuration of the surface. The mean E sp, averaged over all recoil directions, reveals that APBs have a small effect on the threshold sputtering. However, the results for E ad imply that an electron beam could create more Al adatoms on surfaces intersected by APBs than on those without. The equilibrium, minimum energy structures for a (001) surface intersected by either Σ5[001](210) or Σ25[001](340) symmetric tilt grain boundaries are computed. E sp for surface Al atoms near these GBs increases monotonically with increasing recoil angle to the surface normal, with a minimum value, which is only about 1 eV different from that obtained for a perfect surface. Temperature up to 300 K has no effect on this result. It is concluded that the experimental observations of preferential sputtering are due to effects beyond those for E sp studied here. Possible reasons for this are discussed.

Oxygen Diffusion along Symmetric [0001] Tilt Grain Boundaries in α-Alumina

Grain boundary diffusion coefficients of oxygen (δDgb) at 1793K in high purity α-alumina bicrystals with Σ7{2 _ ,310}/[0001] and Σ31{7 _ ,1140}/[0001] symmetric tilt grain boundaries were measured by means of the isotopic exchange and diffusion depth profiling using SIMS. δDgb of both grain boundaries were determined to be 7.1x10-24 [m3/sec] for Σ7 grain boundary and 5.3 x10-24 [m3/sec] for Σ31 grain boundary, respectively. These results indicate that Σ values do not directly relate to grain boundary diffusion properties.

Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum

A traction–displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics (MD) simulations. An MD model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat Σ99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element—an atomistic analog to a continuum cohesive zone model element—the results from the MD simulation are recast to obtain an average continuum traction–displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion.

Novel Bidecahedral Morphology in Gold Nanoparticles Frozen from Liquid

A bidecahedral morphology in which two truncated decahedral structures share two tetrahedral units, involving two types of symmetric-tilt grain boundaries, is observed as a novel and rare morphology of gold nanoparticles frozen from liquid in free space. This low-symmetry polyhedral morphology with eight multiply twinned domains is intermediate between the icosahedral and decahedral motifs.

Investigation on quenching at a high-angle Cu grain boundary on an atomic scale

We have performed molecular dynamics simulations of structural changes due to quenching the melting interface at a Cu Σ5(310)/[001] symmetrical tilt grain boundary. The simulation results suggest that the grain boundary structures due to quenching are different from those due to heating up to the same temperature. The calculated atom density profiles show that the grain boundary structures can be significantly changed as they are quenched to quite low temperatures.

Studying grain-boundary stresses in copper by the molecular-statics method

Grain-boundary stresses in copper for 60 symmetrical tilt grain boundaries with different orientations of the grain-boundary plane and tilt axis have been calculated by the molecular-statics method with the use of embedded-atom-method potentials of interatomic interaction. It has been established that the grain-boundary stresses are negative for grain boundaries with small excess volumes and increase approximately linearly with a buildup of the excess volume. It has been shown that the increase in grain-boundary stresses is connected with a decrease in the average coordination number of atoms, whereas pairs of closely spaced atoms in the grain-boundary core cause a negative contribution to grain-boundary stresses.

Grain-boundary free energy via thermodynamic integration

In a previous publication by Lusk and Beale [Phys. Rev. E 69, 026117 (2004)], fluctuating cell (FC) theory was used to estimate the free energy of symmetric tilt grain boundaries in an assembly of nearly hard disks. The FC method is much faster than the more traditional thermodynamic integration, but the accuracy of the algorithm has not been assessed in association with persistent defect structures. This motivated the present work wherein the FC free energies are compared directly with the data obtained via thermodynamic integration from an Einstein crystal to an assembly of hard disks. This comparison is made over the range of possible misorientations for symmetric tilt boundaries and indicates that the FC method gives quantitatively accurate estimates for grain-boundary free energy. We also demsonstrate that the FC approximation is quantitatively accurate at determining the free-energy contribution of each particle whether in the bulk or the grain boundary. The FC calculation is about two orders of magnitude faster than a full thermodynamic integration. This approach may offer a numerically efficient means of estimating the free energy of persistent defect structures to greater accuracy than is afforded by the quasiharmonic and local harmonic approximations.

Grain Boundary Structure in ARB Processed Copper

Grain boundary structures in the Accumulative roll-bonding (ARB) processed copper (ARB-Cu) have been studied. The grain boundary structures were observed by high-resolution transmission electron microscopy (HRTEM). In order to clarify the difference between the grain boundaries in ARB-Cu and equilibrium boundaries, calculated atomic structure of symmetric tilt grain boundaries with &lt;110&gt; common axis (&lt;110&gt; symmetric tilt grain boundary; &lt;110&gt; STGB) in Cu were used. The near 14° boundary in the ARB-Cu could be described by the dislocation model, but the dense dislocation region existed near the grain boundary. The high angle boundaries in ARB-Cu could be described by the structural units which were obtained by molecular dynamics (MD) simulation. Furthermore, in the 2 cycles and 6 cycles ARB-Cu (2cARB-Cu and 6cARB-Cu), the deformation twin boundaries could be observed and described by the structural unit. Therefore, it was concluded that the grain boundary structure in the ARB-Cu was not much different from the normal equilibrium grain boundary and explained by conventional dislocation and structural unit models.

Deformation and Recrystallization of Aluminum Bicrystals Having Asymmetric Tilt Grain Boundary

Two types of aluminum bicrystals (Bicrystal 1 and 2) having an asymmetric tilt grain boundary were grown. In Bicrystal I, the orientations of component grains were related to each other by 45° rotation about the normal of the wide surface of the tensile specimen. In Bicrystal 2, although the primary slip planes were symmetric about the grain boundary plane, the component grains were related to each other by 180° rotation about the tensile axis of the specimen. The specimens were deformed to a tensile strain of 0.3 and subsequently annealed. In both bicrystals, deformation bands were not formed symmetrically about the grain boundary. After annealing, no strain induced boundary migration was found. Recrystallization occurred through (111) rotation mechanism. These results were compared with the deformation and recrystallization in aluminum bicrystals having a symmetric tilt grain boundary.

Grain Boundary Decohesion by Sulfur Segregation in Ferromagnetic Iron and Nickel &amp;mdash;A First-Principles Study&amp;mdash;

Using first-principles calculations, we simulate grain boundary decohesion (embrittlement) in ferromagnetic bcc FeΣ3(111)[1\\bar10] and fcc NiΣ5(012)[100] symmetrical tilt grain boundaries by progressively adding sulfur atoms to the boundaries. We calculate the segregation energy of sulfur atom, tensile strength, and cohesive energy of the grain boundaries. We show that a certain amount of sulfur segregation (two atomic layers, 14.4 atom/nm2) is energetically possible to realize considering the calculated segregation energies. At this concentration, the tensile strength and the cohesive energy of the grain boundaries reduce by one order of magnitude comparing with no segregation case.