Atomic Structure and Properties of the (310) Symmetrical Tilt Grain Boundary (STGB) in SrTiO3. Part I: Atomistic Simulations

The relaxed structure and energy of the (310) symmetrical tilt grain boundary (STGB) in SrTiO₃ have been calculated using static lattice energy minimization methods. In principle, the (310) GB plane can either be a cation-rich, positively charged SrTiO plane or a negatively charged oxygen plane, and both scenarios have been considered in this report. The effect of point-defect reconstruction at the GB core region, manifested either as completely missing columns or as half-filled columns of ions as suggested by experiments, has been analyzed. The results indicate that while Schottky defects are very strongly preferred energetically at the GB core, there is not significant gain in energy by having half-filled columns, as opposed to fully-dense and fully-empty columns, at the GB core. The simulation results have been analyzed in the context of Pauling's rules of crystal chemistry and bicrystallography. The results form the basis for an objective comparison with experimental studies in Part II of the paper.     

Atomistic Modeling of Point Defects and Diffusion in Copper Grain Boundaries

The atomic structure of several symmetrical tilt grain boundaries (GBs) in Cu and their interaction with vacancies and interstitials as well as self-diffusion are studied by molecular statics, molecular dynamics, kinetic Monte Carlo (KMC), and other atomistic simulation methods. Point defect formation energy in the GBs is on average lower than in the lattice but variations from site to site within the GB core are very significant. The formation energies of vacancies and interstitials are close to one another, which makes the defects equally important for GB diffusion. Vacancies show interesting effects such as delocalization and instability at certain GB sites. They move in GBs by simple vacancy-atom exchanges or by long jumps involving several atoms. Interstitial atoms can occupy relatively open positions between atoms, form split dumbbell configurations, or form highly delocalized displacement zones. They diffuse by direct jumps or by the indirect mechanism involving a collective displacement of several atoms. Diffusion coefficients in the GBs have been calculated by KMC simulations using defect jump rates determined within the transition state theory. GB diffusion can be dominated by vacancies or interstitials, depending on the GB structure. The diffusion anisotropy also depends on the GB structure, with diffusion along the tilt axis being either faster or slower than diffusion normal to the tilt axis. In agreement with Borisov's correlation, the activation energy of GB diffusion tends to decrease with the GB energy.     

HRTEM Studies of the Structures and the Defects of Exact and Near ∑ = 11 {332} Tilt Grain Boundaries in Ni

A = 11 {332} Ni bicrystal was grown by solidification. The Grain Boundary (GB) atomic structure studied by high resolution electron microscopy (HREM) has been shown to depend upon the position in the bicrystal of the extracted sample. Strongly correlated to the atomic structure, (GB) defects (GBD) have been characterized: all their Burgers vectors belong to the Displacement Shift Complete (DSC) lattice and the height of the step associated with each GBD varies up to a few nanometers. In the symmetrical and almost symmetrical GBs, at the head of the bicrystal, the dislocation cores can be well localized, whereas in the asymmetrical GBs, at the end of the bicrystal, their cores are much more difficult to localize on the HREM image. The influence on the GB structures of the impurity content which varies along the bicrystal is also discussed.     

The Electronic Structure of Pristine and Doped (100) Tilt Grain Boundaries in SrTiO3

To understand the electronic properties of doped grain boundaries, we reviewed the atomic scale techniques currently available to study the electronic structure at pristine SrTiO₃ grain boundaries. The knowledge gained from the pristine boundaries is used to interpret experimental and theoretical results from a Mn doped 5 SrTiO₃ grain boundaries. Mn atoms are shown to preferentially substitute at specific Ti sites at the grain boundary core. Furthermore, the formal oxidation state of the Mn atoms at the grain boundary core was found to be reduced compared to the Mn atoms substituting for Ti in the bulk. This change of valence did not, however, significantly affect the atomic structure of the grain boundary, as determined by Z-contrast imaging and electron energy-loss spectroscopy, which revealed similar fine-structure features at both the doped and pristine grain boundary. We conclude, therefore, that composition and atomic structure have different effects on the local electronic structure and should be treated separately in any segregation and electrical conductivity models for grain boundaries.     

Static and Dynamic Electron Holography of Electrically Active Grain Boundaries in SrTiO3

The dynamics of electrostatic potential barriers at grain boundaries (GBs) in Nb-doped SrTiO₃ bicrystals is investigated using a unique combination of bulk and in-situ TEM electrical measurements across isolated GBs, coupled with electron holography under in-situ applied bias. The Nb bulk-doped bicrystals exhibit a positive GB potential that suppresses reversibly under applied bias greater than the nonlinearity threshold in the current-voltage curve. This suppression is interpreted as break-down of the potential barrier to current transport.The results on Nb bulk-doped bicrystals have been compared to those in which Mn has been added as a grain boundary specific dopant. This acceptor doping of the grain boundary causes an appreciable increase in the grain boundary resistance and extension of the nonlinear regime. A preliminary account of static electron holography shows a relatively flat potential profile across the GB, indicating probable compensation of donor states at the GB core with Mn-acceptors. Interestingly, the phase profile under applied bias in this case exhibits a reversible dip at the GB which is interpreted as an activation of GB trap states due to Mn-acceptor dopants trapping extra electrons (the majority charge carriers) at the GB core, inducing a negative GB potential, and diminishing current transport until the threshold bias is exceeded.The synergistic combination of nanoscale TEM measurements coupled with traditional macroscopic electrical measurements is emphasized.     

Grain Boundary Channel Formation During Interdiffusion in Alloys

We present results of an experimental study of a new phenomenon accompanying grain boundary (GB) interdiffusion: the hole channel formation along GBs. The objects for study were plates of a homogeneous Cu-5 at.% Sn alloy, which were annealed at 800°C in purified hydrogen. Porous zones were found with GB hole channels perpendicular to the surface and practically equidistant from one another. The porous zone propagation and the average pore size growth at early stages of annealing obey a parabolic law. The observed processes are caused by nucleation and growth of the Cu₃Sn phase at the free surface. The new phase works as diffusion pump pumping out Sn atoms from the alloy towards the growing compound layer. The GB channel formation has been described as a relaxation process accompanying GB interdiffusion of Sn and Cu atoms with unequal partial diffusion coefficients (D _Sn>D _Cu). Excessive vacancies appearing at the GBs due to the inequality between D _Sn and D _Cu are absorbed by bulk and GB sinks, and tensile stresses appear near the GBs stimulating hole channels or groove formation.     

Interaction of Point Defects with Grain Boundaries in fcc Metals

Structures of several symmetrical tilt grain boundaries (GBs) with different tilt axes in Cu and Al and their interaction with vacancies and interstitials are studied using atomistic computer simulations with embedded-atom potentials. The lowest defect formation energy in a GB is found to correlate with the GB energy in both Cu and Al. Importantly, vacancies and self-interstitials in GBs have comparable formation energies, suggesting that both defects are equally important for GB diffusion and other properties. Vacancies in GBs can be either localized at certain sites or be delocalized over several sites. Some GB sites do not support a stable vacancy at all. Self-interstitial atoms can occupy relatively open interatomic positions, form split dumbbell configurations, or give rise to highly delocalized displacement zones. These structural forms of point defects have been observed across the whole set of twelve GBs in Cu and six GBs in Al studied in this paper as well as in our previous work [Interface Science 11, 131–148 (2003)]. It is suggested that these structural forms are general to all GBs in fcc metals. They can be explained by the existence of internal stresses and alternating tension and compression regions in the GB core.     

Direct method for determining the segregation in silver-copper solid solutions not prone to brittle breakage of grain boundaries

A new method is proposed for measuring the chemical composition of grain boundaries (GBs) in copper-based alloys not prone to embrittlement of boundaries. This method is based on embrittlement of copper GBs by bismuth penetrating from the gas phase of bismuth telluride (Bi₂Te₃). Chemical analysis of the GB surface is performed via Auger-electron spectroscopy. The GB composition is measured in a solid solution of silver (its volume concentration is 1.4 at %) and copper. The segregation annealing temperature is 570°C. The silver concentration across the broken surface of the GB (its thickness is five to ten atomic layers) is 4.7 at %. Therefore, the ratio between silver concentrations within the GB and the grain volume (the enrichment coefficient) is approximately 3.5.     

Progress in the Investigations of Grain Boundary Relaxation

Internal friction (or damping) is a measure of energy dissipation during mechanical vibration. The internal friction peak induced by grain boundary (GB) relaxation was discovered by Kê in polycrystals in 1947. The GB internal friction and related anelastic effects have been successfully interpreted by Zener's anelastic theory and viscous sliding model. Since then, the GB internal friction peak has been widely used to study the dynamic process of GBs, impurity segregation at GBs and relevant processes in materials science.

Previously, the GB internal friction was mostly studied with polycrystalline materials, in which mixed contributions of different types of GBs are involved. Since the microstructures and behaviors for different types of GBs are different, the detailed mechanism of the GB peak in polycryatals has not been clearly clarified.

From the beginning of the 21th century, the internal friction in bicrystals (each has a single boundary) with different misorientations and rotation axes has been systematically investigated. The results indicate that the internal friction can be used to distinguish the individual behavior of different types of GBs and applied to the practice of “GB engineering.”

Moreover, the coupling effect and compensation effect involved in GB relaxation has been recently observed and explained. The coupling effect means a correlated atomic motion occurred in GB relaxation. The compensation effect indicates that the apparent activation enthalpy is linearly related to the activation entropy in GB relaxation. These findings improve the understanding of the mechanism of GB internal friction.

This article attempts to give a comprehensive review to the investigations of GB internal friction in polycrystals, bamboo-crystals, and bicrystals. The microscopic mechanisms and the further applications of GB internal friction are discussed and prospected.     

Coupled structural and magnetic properties of ferric fluoride nanostructures part I: A Metropolis atomistic study

A modified Metropolis atomistic simulation is proposed to model the structure of grain boundaries (GBs) and interfaces in ionic nanostructured systems and is applied to the magnetically interesting case of iron trifluoride (FeF₃). We chose long-range interatomic potentials adjusted on experimental results and adapted a previously established Monte Carlo scheme consisting of various modifications of the simulated annealing/Metropolis algorithm. Atomic structures of twisted and tilted GBs as a function of the relative disorientation of the grains have been achieved yielding close to experimentally measured properties. This approach takes into account the structure of the grains far from the interface in order to constrain the relative orientation of the grains, without any periodic boundary conditions. One concludes that a long-range Coulombic fall off of the interatomic potentials is necessary to obtain GB structures presenting a correct local topology but with a smooth transition from crystalline to amorphous states. The structural features are finally discussed in terms of topological aspects and local magnetic structure.     

Faceting of Σ3 and Σ9 Grain Boundaries in Copper

Faceting is a well documented phenomenon known both for surfaces and interfaces, particularly, grain boundaries (GBs). Faceting can be considered as a phase transition when the original surface or GB dissociates onto flat segments whose energy is less than that of the original surface or GB. For the investigation of GB faceting a cylindrical Cu bicrystal with an island grain was grown by the Bridgman technique. Grain 1 in this bicrystal is completely surrounded by grain 2. The dissociation 9 3 + 3 proceeds during the growth of the bicrystal. The twins appear instead of {111}₁/{115}₂ or (110)_9CSL facet. GB faceting was studied at 1293 K, 1073 K, and 873 K. The profiles of the GB thermal groove were analysed by atomic force microscopy. Wulff-Herring plots and GB phase diagrams have been constructed for the 3, 9 and 9 + 3 GBs. With increasing temperature the facets with low-density CSL-planes disappear in the GB shape. GB roughening phase transition can be responsible for this phenomenon.     

Grain Boundary Diffusion and Linear and Non-Linear Segregation of Ag in Cu

Ag grain boundary (GB) diffusion was measured in the Cu-0.2at%Ag alloy in a wide temperature range from 473 to 970 K. The direct measurements of Ag GB diffusivity D ^alloy _gb under conditions of the Harrison C regime revealed that D ^alloy _gb is almost identical to D ^pure _gb determined earlier for Ag diffusion in high-purity Cu (Divinski, Lohmann, and Herzig, 2001). The penetration profiles determined in the Harrison B regime showed a complex, multi-stage shape. This diffusion behavior can be rationalized assuming that besides GBs significantly covered by segregated Ag atoms, some fraction of GBs remains almost free from Ag atoms in the studied temperature interval. The total amount of pure GBs drastically decreases with decreasing temperature. This hypothesis was proven by measurements of Ag GB diffusion in Cu near 5 bicrystals, which allowed us to analyze in detail the non-linear segregation of Ag in Cu GBs.     

Atomic structure and electronic properties of the ∑37(610) and ∑29(520) [001] tilt grain boundaries in Ge

400 kV high resolution electron microscopy (HREM), deep level transient spectroscopy (DLTS) and steady state electrical measurements have been applied to 37(610) and 29(520) [001] tilt grain boundaries (GBs) in germanium bicrystals. The atomic boundary structures were revealed by experimental HREM images taken under different defocus conditions. Later, structure models were refined by means of a trial-and-error method applying alternatively the image simulation and the molecular static calculation of relaxed structures. The structures were shown to be consistent with the modified structural unit model. Although the structures are different for the two GBs studied, DLTS data and steady state measurements were found to be quite similar for both GBs. Thus, the results point to the extrinsic origin of localized deep states at the GBs. The analysis of DLTS spectra indicates the impurity segregation at the boundary, e.g., the formation of vacancy-type oxygen complexes of a donor-like state at E _c-0.21 eV, which results in the fluctuation of the potential barrier. Defects in the GBs—like facets, atomic steps and secondary grain boundary dislocations—which are characteristic of both boundaries can act as nuclei to the impurity segregation.Presented at the Workshop on High-Voltage and High-Resolution Electron Microscopy, February 21–24, 1994, Stuttgart, Germany.     

Multi-timescale investigation of radiation damage near TiO2 rutile grain boundaries

To understand the interactions between defects and grain boundaries (GBs) in oxides, two atomistic modeling methods were used to examine the role of GBs in a model system, rutile TiO₂, in modifying radiation-induced defect production and annealing. Molecular dynamics was used to investigate defect production near a symmetric tilt GB at both 300?K and 1000?K. The damage production is found to be sensitive to the initial distance of the primary knock-on atom from the GB. We find three distinct regimes in which GBs have different effects. Similar to GBs in metals, the GB absorbs more interstitials than vacancies at certain distances while this behavior of biased loading of interstitials diminishes at other distances. Further, we obtain the statistics of both interstitial and vacancy clusters produced in collision cascades in terms of their compositions at two temperatures. Perfectly stoichiometric defect clusters represent a small fraction of the total clusters produced. Moreover, a significant reduction in the number of interstitial clusters at 1000?K compared to 300?K is thought to be a consequence of enhanced migration of interstitials towards the GB. Finally, the kinetic properties of certain defect clusters were investigated with temperature accelerated dynamics, without any a priori assumptions of migration mechanisms. Small interstitial clusters become mobile at high temperatures while small vacancy clusters do not. Multiple migration pathways exist and are typically complex and non-intuitive. We use this kinetic information to explain experimental observations and predict their long-time migration behavior near GBs.     

The Effect of Pressure on Indium Diffusion along 〈001〉 Tilt Grain Boundaries in Copper Bicrystals

The effect of pressure on the diffusion of indium along two grain boundaries (GBs) in copper bicrystals has been investigated. The GBs studied were of symmetrical tilt type with a 001 misorientation axis. The tilt angle of one GB was 36.5°, which corresponds to the near 5 coincidence orientation, where is the inverse density of the coincidence sites in the two misoriented crystal lattices. The other GB was a general boundary with a tilt angle of 45°. The diffusion along the 001 tilt axis has taken place at the temperature of 923 K and under argon gas pressures up to 1 GPa. The following activation volumes have been found: 0.94±0.11 _Cu for bulk diffusion,–0.5 ±0.7 _Cu for the diffusivity of the near 5 GB and –0.6±0.3 _Cu for the diffusivity of the 45° 100 GB, where _Cu is the atomic volume of copper. Two interpretations of this result seem plausible. The first interpretation is that the In atoms diffuse along the 001 tilt axis by an instertitialcy mechanism. It is known that for such a diffusion mechanism the activation volume is close to zero. The alternative explanation bases on the observation that the parameter measured is the GB diffusivity, which depends on the product of the GB diffusion coefficient and the segregation factor. An enhancement of the In segregation under pressure would lead to an increase of the GB diffusivity. It seems plausible that both interpretations are true and the fact that the atomic volume of In is a factor of 2.2 larger than that of Cu plays an important role both for the increased segregation of In under pressure and the diffusion mechanism.     

Interfaces in Iron-Rich Ordered Fe-Al Alloys: An Atomic-Scale Simulation Study

The aim of this paper is to investigate the low-temperature structure of interfaces (the (3 1 0) [0 0 1] symmetrical tilt grain boundary (GB) and the (3 1 0) surface) in stoichiometric ordered Fe-Al alloys with B2 and DO₃ structures. In both alloys, (i) the GBs cannot be realistically described by geometrical models, (ii) GBs and surfaces show strong segregation effects. A simple independent-defect model cannot be applied: the interactions between point defects sometimes lead to results opposite to those predicted from the formation energies of isolated point defects. The excess energies and configurations of the most stable interface variants are determined. All interfaces show a tendency to Al segregation except the B2 GB for which the most stable structure is an Fe-rich one. The interface structures are more complex in the DO₃ than in the B2 alloy, with a high multiplicity of DO₃ configurations with close energies. Finally, values of the GB and surface energies are introduced into a Griffith model of brittle fracture, in order to assess the trends of both alloys to intergranular fracture. Comparisons are also drawn with the similar Ni-Al ordered alloys.     

On grain boundary character distribution in materials with cubic structure

From analysis of numerous experimental data on grain boundary (GB) statistics in polycrystals it has been established that certain groups of materials with cubic structure reveal similar GB character distributions (GBCD) (distribution of GBs by reciprocal density of coincidence sites ). It has been shown that GBCD can be described with an empirical low with different parameters for various groups. Several criteria for classification of materials by these groups (the stacking fault energy value, hierarchy of GB energies and mechanism of replacement of high-energy GBs with low-energy ones) have been considered. It has been found that peculiarities of electronic structure of materials are correlated with the classification proposed.     

Dielectric response of a (1000 nm)SrTiO<Subscript>3</Subscript> layer epitaxially grown on (001)La<Subscript>0.67</Subscript>Ca<Subscript>0.33</Subscript>MnO<Subscript>3</Subscript> to temperature variation and electric field

The structure and dielectric characteristics of the (1000 nm)SrTiO₃ spacer in a (001)SrRuO₃ ‖ (001)SrTiO₃ ‖ (001)La_0.67Ca_0.33MnO₃ trilayer heterostructure grown on a (001)(LaAlO₃)_0.3+(Sr₂AlTaO₆)_0.7 substrate have been studied. Both oxide electrodes, as well as the strontium titanate layer, were cube-on-cube epitaxially grown. The unit cell parameter in the SrTiO₃ layer measured in the substrate plane (3.908±0.003 Å) practically coincided with that determined along the normal to the substrate surface (3.909±0.003 Å). The temperature dependence of the real part of the permittivity ?′ of the SrTiO₃ layer in the range 70–180 K fits the relation (?′)^?1 ～ ? ₀ ^?1 C ₀ ^?1 (T-T _C ) well, where C₀ and T_C are the Curie constant and the Curie-Weiss temperature, respectively, for bulk strontium titanate crystals and ?₀ is the free-space permittivity. The data obtained on the temperature dependence of the permittivity of SrTiO₃ films enabled us to evaluate the effective depth of electric field penetration into the manganite electrode (L _e ≈ 0.5 nm) and the corresponding capacitance (C _e ≈1×10^?6 F/cm²) of the interface separating the (001)SrTiO₃ layer from the (001)La_0.67Ca_0.33MnO₃ bottom electrode.     

Saturation magnetization distribution in the vicinity of a grain boundary in a plate of a triaxial silicon-iron-type ferromagnet

The one-dimensional saturation magnetization distribution M _S(x) in the vicinity of grain boundaries (GBs) is studied in $(01\bar 1)$ plates of soft magnetic alloys of the Fe-3% Si type in the framework of the theory of micromagnetism. The mechanisms of the emergence of spatial inhomogeneities of the saturation magnetization near planar GBs are discussed. Calculations show that macroscopic regions Δx≈10 mm in extent arise near GBs because of the μ* effect. This result is supported by the experimental data.