Symmetric Tilt Grain Research Articles

Atomistic sliding mechanisms of the Σ=5 symmetric tilt grain boundary in bcc iron

Atomistic computer simulations were performed to investigate the mechanisms of grain-boundary sliding in bcc Fe using molecular statics and molecular dynamics with embedded-atom method interatomic potentials. For this study we have chosen the Σ = 5, (310)[001] symmetrical tilt boundary with tilt angle θ = 36.9°. Sliding was determined to be governed by grain-boundary dislocation activity with Burgers vectors belonging to the displacement shift complete lattice. The sliding process was found to occur through the nucleation and glide of partial grain-boundary dislocations, with a secondary grain-boundary structure playing an important role in the sliding process. Interstitial impurities and vacancies were introduced into the grain boundary to study their role as nucleation sites for the grain-boundary dislocations. While vacancies and H interstitials act as preferred nucleation sites, C interstitials to not.

Comparative studies of microstructure and impedance of small-angle symmetrical and asymmetrical grain boundaries in SrTiO 3

Several low-angle symmetrical [0 0 1]-tilt grain boundaries and an asymmetrical grain boundary with both tilt and twist components were examined by high-resolution transmission electron microscopy, conventional transmission electron microscopy, and impedance spectroscopy. The symmetrical tilt grain boundaries consist of isolated dislocation cores and the Burgers vectors are translation vectors of the crystal. Strain analysis shows that the strain fields around the dislocation cores overlap with increasing misorientation angle. The a.c. impedance response of the low-angle grain boundaries reveals a marked blocking effect for charge transport across the low-angle symmetrical grain boundaries, which increases with increasing misorientation angle. In the case of the mixed asymmetrical grain boundary, however, the blocking effect is low despite the large misorientation. The resistance and electrical potential of this grain boundary were calculated and compared with those obtained from the symmetrical grain boundaries. A relationship between microstructure and macroscopic electrical property can approximately be arrived by considering anion vacancies to be preferentially situated in highly distorted regions such as dislocation cores.

Energy calculation for symmetrical tilt grain boundaries in iron

Abstract An atomic study of [0 0 1] symmetrical tilt grain boundary (STGB) in iron has been made with modified analytical embedded atom method (MAEAM). The energies of two rigid-body crystals joined together directly are unrealistically high due to very short distance between atoms near grain boundary (GB) plane in either crystal. For each of 27 (h k 0) GB planes, a relative slide between grains could result in a decrease in GB energy and a minimum value could be obtained at specific translation distance Lmin/L(h k 0). Three lowest minimum-energies are corresponding to (3 1 0), (5 3 0) and (5 1 0) boundary successively, from minimization of GB energy, these boundaries should be preferable in (h k 0) boundaries. In addition, the minimum energy increases with increasing ∑, but decreases with increasing interplanar spacing.

Grain boundary sliding and migration in copper: Vacancy effect

We investigated the interaction between the vacancy and $\ensuremath{\Sigma}5$ (210)[001] symmetric tilt grain boundary during the sliding by taking copper as a model material. The geometry optimization was done by simulating an annealing process at elevated temperature. For interatomic interaction we used an empirical many-body potential of the embedded atom method. The obtained atomic formations were used as input to ab initio calculation. The results confirmed that the sliding process invokes the interface migration in such a way that the vacancy effectively migrates to a more convenient position and reduces the GB energy.

Atomistic simulations of the effects of segregated elements on grain-boundary fracture in body-centered-cubic Fe

We studied the detailed fracture behavior of a Σ=5 symmetrical-tilt grain boundary at low temperatures in Fe, using empirical interatomic potentials. For loadings just above the Griffith value, the crack propagates along the boundary for a distance of about 5 nm and then deflects toward the grains. When the boundary is loaded well above the Griffith criterion in pure bcc Fe, the crack deflects and propagates in an intragranular manner. Lattice trapping effects were observed in the initial stages, as the crack propagates along the grain boundary in a brittle manner with a periodicity given by the structural unit of the grain boundary. The effects of impurities on crack propagation along the grain boundary were simulated with various amounts of substitutional (Cr and Ni) and interstitial (H and C) impurities. The H impurities result in a strong embrittlement of the grain boundary, and no deflection of the fracture to the inside of the grains is observed. The element C has the opposite effect, inducing the deflection of the fracture to the interior of the grains from the beginning of the simulation. For the substitutional Ni and Cr impurities, the effects on grain-boundary fracture behavior are less dramatic, with Cr decreasing the resistance to grain-boundary fracture, if present in high concentrations. These effects agree with expectations based on the relative energies of segregation of the impurities to the grain boundary and free surface.

Numerical analysis of solute segregation atΣ5(310)∕[001]symmetric tilt grain boundaries inY2O3-dopedZrO2

Atomistic mechanisms that determine atomic coordination and local concentration of dopants at $\ensuremath{\Sigma}5$ $(310)∕[001]$ symmetric tilt grain boundaries in ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$-doped ${\mathrm{ZrO}}_{2}$ are analyzed using atomistic simulation techniques. Segregation mechanisms are found to be different from those in metals or metalloids, with local strain relief controlled by short-range interactions, which act as the driving force for segregation, while long-range Coulombic interactions between the grain boundary region and the dopants resist segregation. It is found that ${\mathrm{Y}}^{3+}$ ions segregate to a region within around 0.6 nm either side of the grain boundary plane. The equilibrium local concentration of dopants in the vicinity of the grain boundary, which is determined by the balance between repulsive forces between dopants and the grain boundary and attractive forces associated with local strain relief, is calculated to be 16.7 mol % for 10.3 mol % ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$-doped ${\mathrm{ZrO}}_{2}$. Cosegregation of an ${\mathrm{O}}^{2\ensuremath{-}}$ vacancy is necessary to accommodate a ${\mathrm{Y}}^{3+}$ ion at the $\ensuremath{\Sigma}5$ grain boundary; ${\mathrm{O}}^{2\ensuremath{-}}$ vacancies play important roles in reducing repulsion between dopants and the grain boundary and relieving local strain further. These conclusions are supported by Monte Carlo simulations using an unrestricted model. Segregation-induced modifications to the grain boundary structure observed in the simulations are used to interpret experimental HREM and $Z$-contrast images.

Atomistic simulation of grain boundary energetics – Effects of dopants

Many enhancements in properties of nanocrystalline materials due to the ultra-fine grain size are lost if grain growth occurs during application. As a preliminary study, molecular statics (MS) and molecular dynamics (MD) simulations are used to study the energy of a two-dimensional coincident site lattice Σ7 symmetric tilt grain boundary in a Cu bicrystal. Impurity atom(s) of various characteristics and concentration were added to the near vicinity of the grain boundary to determine the structural and energetic affect. The dopant atoms are capable of altering the grain boundary energy even if several atomic spacings separate the two. Also, it is shown that the grain boundary energy can be reduced to zero, which has been theoretically proposed as necessary for achieving a metastable state for nanocrystals. The results of this investigation will aid further computational and experimental work aimed at stabilizing the microstructure of nanocrystalline material.

Atomic and electronic structure of [0001]/( $$\bar{1}\bar{2}30$$ ) Σ7 symmetric tilt grain boundary in ZnO bicrystal with linear current-voltage characteristic

The atomic and electronic structures of [0001]/(\(\bar{1}\bar{2}30\)) Σ 7 symmetric tilt grain boundary in an undoped ZnO bicrystal were investigated by high-resolution transmission electron microscopy (HRTEM) and first-principles calculations. HRTEM imaging and atomistic calculations revealed that the grain boundary was composed of at least two types of structural units. It was also found that one of the structural units has two threefold-coordinated atoms per a unit and the other has two fivefold-coordinated atoms. First-principles calculations indicated that these atoms with various coordination numbers do not form deep unoccupied electronic states in the band gap of ZnO, which is in consistency with a linear current-voltage characteristic observed for the bicrystal with the Σ 7 boundary.

Stress-induced facet coarsening in a σ $$7\{4\bar{5}10\}$$ symmetrical tilt grain boundary in an alumina bicrystal

Grain boundary sliding and migration often accompany high temperature deformation in alumina, however the studies of the sliding and migration behavior of individual boundaries in bicrystals during deformation are extremely limited.

Transition between low and high angle grain boundaries

The migration of planar, symmetric tilt grain boundaries with different tilt axes was investigated. The driving force for the grain boundary migration was due to an external mechanical stress field. Low as well as high angle grain boundaries can move under this driving force and the activation parameters for the stress induced grain boundary motion are different for low and high angle grain boundaries. The experiments showed a sharp transition from low angle grain boundary to high angle grain boundary behavior. The transition is marked by a clear change in the activation enthalpy for the grain boundary motion without any extended range. We present an overview of the existing experimental results and theoretical considerations of the structure of grain boundaries at the transition. The observation that the transition depends on the rotation axis of the grain boundary and on the grain boundary plane is particularly important, because this will influence the Brandon criterion which is often used in experiments and simulations of grain growth and recrystallization processes.

Direct two-dimensional calculations of grain boundary stiffness

Abstract Lennard-Jones based molecular dynamics simulations of capillarity fluctuations in flat, 2D symmetric tilt grain boundaries show that fluctuation in the high symmetry θ gb = 38.2° − Σ7 boundary is consistent with capillarity wave theory, with a grain boundary stiffness Γ gb = 0.31 ± 0.015 ϵ / r 0 . Low symmetry θ gb = 30° − Σ∞ boundary exhibits peaks at certain modes, indicative of vicinal cusps in the Wulff plot.

アルミナにおける対称傾角粒界の局所ひずみと原子構造

Residual strain and atomic structures in the vicinity of the grain boundaries were investigated for (2310) [0001] Σ21, (4510) [0001]27 and (0112) [2110]R27 symmetrical tilt grain boundaries of Al 2 O 3 bicrystals using convergent beam electron diffraction (CBED) and high-resolution electron microscopy (HRTEM). CBED measurement clearly showed that the R27 grain boundary has a relatively small strain across the boundary. On the other hand, there is strain of about 0.06-0.07% in the area 10 nm from the grain boundaries in both the Z21 and Σ7 grain boundaries. It was found that signs of strain distribution in the vicinity of the grain boundary observed in the Σ21 specimen were opposite to those observed in the Σ7 specimen. The interplanar distances of (2110) a-plane and (0001) c-plane in the Σ21 boundary were confirmed to increase and decrease, respectively, in the vicinity of the grain boundary. In contrast, the respective interplanar distances in the Σ7 boundary decrease and increase, respectively. The difference in the change of interplanar distance observed in the Σ21 and Σ7 boundaries is considered to be closely related to the atomic density at the respective grain boundaries.

マグネシウム［１‐１００］対称傾角粒界の粒界エネルギーとその構造

マグネシウム［１‐１００］対称傾角粒界の粒界エネルギーとその構造

Grain boundary sliding and migration in copper: the effect of vacancies

The atomic structure and mechanism of the interface sliding of the Σ = 5(2 1 0)[0 0 1] symmetric tilt grain boundary (GB) in copper and its interaction with vacancies at an elevated temperature has been studied using a computationally efficient potential based on the Embedding Atom Method in connection with the finite temperature Monte Carlo technique. Grain boundary sliding is performed for pure copper as well as copper containing a vacancy at a selected position. The discontinuous changes of the GB energy at certain sliding distances are associated with GB migrations. Elevated temperature reduces the grain boundary sliding/migration energy by a factor of about 2 but does not increase the rate of migration. Migration of the GB is mediated by the flow of atoms along the interface in coordination with the atoms in bulk. The sliding and migration properties partially depend on the position of the vacancy in the GB core. We found that the grain boundary sliding energy profile in the presence of a vacancy placed at the interface increased the GB energy, but reduces the sliding energy. The sliding process invokes the interface migration in such a way that the vacancy effectively migrates to a more convenient position and reduces the GB energy.

The interaction of P atoms and radiation defects with grain boundaries in an α-Fe matrix

Classical molecular dynamics simulations have been employed to investigate the influence of P impurity atoms close to grain boundaries in α-Fe. Static calculations have been performed to determine the energetics of P and Fe defects in the grain boundary region for three symmetrical tilt grain boundaries, Σ5(310)[001], Σ41(910)[001] and Σ25(430)[001]. The simulations are carried using two different embedded atom Fe potentials, one of which includes the effect of second nearest neighbours. Both potentials produce quantitatively and qualitatively similar results for the static calculations. It has been shown that P atoms preferrentially segregate to the free volume region in the grain boundary plane. For collision cascade simulations the second nearest-neighbour model is found to predict a higher number of cascade defects in an irradiated perfect Fe matrix.

Structure, energy and solute segregation behaviour of [110] symmetric tilt grain boundaries in yttria-stabilized cubic zirconia

Yttria-stabilized cubic zirconia bicrystals with [110] symmetric tilt grain boundaries are systematically fabricated by the diffusion bonding method. It is revealed that the grain-boundary atomistic structures, excess energies and solute segregation behaviours are strongly dependent on the macroscopic geometries of the boundaries. High-resolution transmission electron microscopy combined with lattice statics calculations suggests that the grain-boundary structures are characterized by the accumulation of coordination-deficient cation sites at their cores, whose densities have a clear correlation with excess energies and amounts of solute segregation. The orientation dependence of grain-boundary properties in cubic zirconia can thus be linked and understood via local grain-boundary atomistic structures with the characteristic miscoordinated cation sites.

Mechanically Controlled, Seeded Formation of a Nanoscale Metastable Phase in Ionic Compounds

Like in epitaxial and hetero-epitaxial growth, the structural order at internal grain boundaries may be used to control the nature of new phases that nucleate at such an interface. We demonstrate this concept via computer simulation. We predict the templated nucleation of a new metastable phase at the (310) symmetric tilt grain boundary in both NaCl and LiCl when subject to an external mechanical constraint. The level of applied stress allows one to control the extent to which this metastable phase grows with nanoscale precision. This interfacial seeding of structural transitions has potential to produce functionally patterned materials for novel logic and sensing devices.

Stress-assisted grain boundary sliding and migration at finite temperature: A molecular dynamics study

The sliding in a Ni symmetrical tilt grain boundary, $\ensuremath{\Sigma}5$ (012) [100], is investigated by modified Parrinello-Rahman molecular dynamics which deals with the thermodynamic ensemble characterized by the number of atoms $N$, temperature $T$, and the shear stress $\mathbf{t}$. It is found that the grain boundary can slide in the direction perpendicular to the tilt axis $[02\overline{1}]$ with the aid of shear stress in that direction. The sliding is coupled to the migration involving a collective motion of the third layer atoms hopping into the hollow site in between the first (GB) and second layers. Here, the critical stress necessary to move the grain boundary damps almost exponentially as the temperature is increased. At temperatures above about $820\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, random walk of GB migration occurs without the assistance of stress. On the other hand, it is only at much higher shear stress that the grain boundary can slide in the direction parallel to the tilt axis [001]. This may be because this sliding mechanism does not involve the coupling to the migration mode.

HRTEM studies of segregated Ga at the Al Σ11 (113) [1ˉ10] symmetrical tilt grain boundary

HRTEM studies of segregated Ga at the Al Σ11 (113) [1ˉ10] symmetrical tilt grain boundary

HTREM Studies of Segregated Ga at the Al Sigma 11 (113)[11―0] Symmetrical Tilt Grain Boundary

Extended abstract of a paper presented at Microscopy and Microanalysis 2004 in Savannah, Georgia, USA, August 1–5, 2004.