Crystallographic Grain Boundary Research Articles

Understanding cross boundary twin behaviours in AZ31 alloy by a composite Schmid factor

It is well known that twinning likely nucleates and forms pairs at grain boundaries (GBs) during the formation of hexagonal close-packed alloys. Therefore, the crystallography of GBs should be taken into account to assess the activation preference of twins (and pairs) at GBs. As Schmid factor (SF) is a grain-based parameter, it cannot predict from which GB segment, twinning prefers to nucleate. To solve this problem, recently we proposed a composite Schmid factor (CSF) that incorporates both the SF and a geometric compatibility factor (m’) between twin/slip systems in neighbouring grains. In this presentation, we first summarize the definition and calculation method of this parameter. Then, simultaneous twin nucleation and twin (or slip) stimulated twin behaviour in a twin chain were assessed by this parameter. For comparison, SF and m’ analyses were also performed. The advantages and limitations of this CSF in assessing twin behaviours were discussed.

Three-Dimensional Atomic Structure of Grain Boundaries Resolved by Atomic-Resolution Electron Tomography

Summary Grain boundaries (GBs) determine the properties of polycrystals, and tailoring the GB structure offers a promising method for the discovery and engineering of new materials. However, GB structures are far from well understood because of their structural complexity and limitations of conventional projection imaging methods. Here, we decipher three-dimensional atomic structure and crystallography of GBs in nanometals using atomic-resolution electron tomography. Unlike conventional descriptions, whereby they are either straight or curved planar planes with one-dimensional translational symmetry, we show that the high-angle GBs completely lose translational symmetry due to undulated curvature related to configurations of structural units. Moreover, we directly visualize kinks and jogs at the single-atom scale in dislocation-type GBs and investigate their mobilities. Our findings bring new insights to the conventional wisdom of GBs and show the importance of developing methods to include the non-planar nature of GBs to statistically evaluate the behavior of GBs in modeling studies.

An efficient Monte Carlo algorithm for determining the minimum energy structures of metallic grain boundaries

Sampling minimum energy grain boundary (GB) structures in the five-dimensional crystallographic phase space can provide much-needed insight into how GB crystallography affects various interfacial properties. However, the complexity and number of parameters involved often limits the extent of this exploration to a small set of interfaces. In this article, we present a fast Monte Carlo scheme for generating zero-Kelvin, low energy GB structures in the five-dimensional crystallographic phase space. The Monte Carlo trial moves include removal and insertion of atoms in the GB region, which create a diverse set of GB configurations and result in a rapid convergence to the low energy structure. We have validated the robustness of this approach by simulating over 1184 tilt, twist, and mixed character GBs in both fcc (Aluminum and Nickel) and bcc (α-Iron) metallic systems.

Correlating the five parameter grain boundary character distribution and the intergranular corrosion behaviour of a stainless steel using 3D orientation microscopy based on mechanical polishing serial sectioning

Using 3D-orientation microscopy consisting of electron backscatter diffraction (EBSD) and serial sectioning by mechanical polishing we investigated the correlation between grain boundary (GB) character expressed by its 5-rotational parameters and the GB precipitation and intergranular corrosion (IC) behaviour on an AISI 304L stainless steel. From the measurements, a volume of approximately 4.8 × 106 μm3 containing 451 grains and approximately 1500 GBs was reconstructed. Dominance of {111} planes for Σ3n (n = 1, 2, 3) GBs was found. In general, the IC behaviour of random high angle grain boundaries (RHAGBs) and low-Σ coincidence site lattice (CSL) boundaries (Σ ≤ 29) does not show a large difference. The corrosion behaviour of low angle grain boundaries (LAGBs) is strongly dependent on the misorientation angles, while the crystallographic GB plane becomes dominant for the behaviour of low-Σ CSL GBs and RHAGBs. It was found that the corrosion resistance is related on the atom packing density (APD) of the GB plane. High corrosion resistance appears for GBs with high APD values (in particular for the (111) planes with a maximum APD value).

Three-Dimensional Characterization of Sintered UO2+x: Effects of Oxygen Content on Microstructure and Its Evolution

The oxygen content during the intermediate and final stages of sintering can have a strong effect on the microstructural evolution of oxide fuels. Two depleted urania (d-UO2.0 and d-UO2.14) samples, sintered up to a theoretical density of 90%, were serial sectioned using a focused ion beam and characterized with electron backscatter diffraction (EBSD). The EBSD data were used to make three-dimensional reconstructions of the microstructures to evaluate their characteristics at an intermediate stage of sintering. The oxygen content was found to affect grain shape and grain boundary (GB) mobility, as curved and elongated grains were observed in UO2.0, as well as stronger pore-GB interactions, which is an indication that microstructure was less evolved in UO2.0. Both samples presented a similar fraction ([approximate]20%) of special, coincident site lattice boundaries, with larger amounts of Σ3n GBs, and a rather large fraction of Σ11 GBs for UO2.14. Crystallographic GB planes were also determined to study the distributions of all GB parameters. The UO2.0 sample had a large fraction of GB planes close to the Σ3 twinning planes, which suggests that lower-energy interfaces are used to minimize energy in this sample, potentially due to lower overall GB mobility as compared to UO2.14.

Crystallographic orientations of high-angle grain boundaries in dynamically recrystallized quartz: First results

The crystallography and geometry of high-angle grain boundaries from dynamically recrystallized quartz have been studied. On the basis of combined electron backscatter diffraction and universal stage measurements, the complete crystallographic orientation of the grain boundaries could be calculated. The u-stage rotation of the grain boundaries to a vertical position reveals that they are never curved but always consist of straight segments. Our results show that these segments preferentially occupy rhombohedral, trapezohedral and bipyramidal orientations, i.e., orientations in a ∼ 25–50° girdle to the c-axis. A specific, albeit low, number of segments with special crystallographic orientation, with respect to a neighbouring quartz grain, often shows another special orientation with respect to the other neighbouring grain. Preferred combinations of grain boundary orientations related to both neighbouring grains are (i) low-index rhombohedral and high index trapezohedral, (ii) low-index bipyramidal and low-index trapezohedral or high-index rhombohedral, and (iii) low-index trapezohedral and low or high index trapezohedral. In certain cases, such as at triple junctions, the boundaries occupy specific trapezohedral orientations with a constant angle to the c-axis. This argues for energy isotropy of trapezohedral planes with the same angle to the quartz c-axis. In general, good match coincidence site lattice (CSL) orientations are not preferentially occupied so that most of the studied grain boundaries represent general boundaries. The formation of straight segments in special crystallographic orientations indicates the crystallographic control and implies an energy reduction of certain general boundaries.

Percolation Properties of Internal Wetted Polycrystals: Effect of Stresses and Material Structure

It is well established from studies of bicrystals that the wetting behavior of grain boundary (GB) depends on the GB crystallography and stress. However, only in several researches of polycrystalline materials properties this boundary-boundary variability is taken into account. In polycrystalline materials the whole network of GB is never completely wetted. The number of wetted boundaries and the topology of their network vary as a function of many factors such as texture, intensity and sign of residual or applied stresses, impurities, content, and specimen size. The role of these factors is not clearly understood yet. This article is devoted to the effect of material structure and stresses on the relative number of wetted GBs and on the connectivity of intergranular liquid in polycrystalline materials. Percolation approach is employed to describe the liquid phase connectivity in internal wetted polycrystals. Some examples are regarded. The relative number of wetted GBs in Zn/Ga system is established on the basis of the distribution of GB orientations and GB wetting statistics. The influence of stresses on the network topology and percolation threshold (the critical concentration of wetted boundaries at which an infinite network appears) value is discussed. The computer modeling is fulfilled to evaluate the threshold as the function of grain shape. The topology of liquid phase inclusions is discussed in terms of critical indexes.

Influence of bulk composition on grain boundary segregation inB2Fe−Al:An atomic-scale simulation study

The atomic structure of the (310)[001] symmetrical tilt grain boundary (GB) in $B2\mathrm{F}\mathrm{e}\ensuremath{-}\mathrm{A}\mathrm{l}$ ordered alloys was studied at $T=0\mathrm{K}$ by numerical simulations using N-body empirical potentials. As expected from the high degree of order of $B2\mathrm{F}\mathrm{e}\ensuremath{-}\mathrm{A}\mathrm{l}$ the coincidence site lattice (CSL) theory is found a relevant approximation for GB crystallography, the stable GB variants being close to the usual symmetric and pseudosymmetric CSL models, with no GB vacancies. However, as regards GB chemistry, the extension to interfaces of the independent point defect approximation, rigorous for bulk ordered compounds, and assessment of its validity by a full treatment of interactions between GB point defects reveal a strong dependence of GB properties on alloy off-stoichiometry: single-layer Fe segregation holds in Fe-rich Fe-Al, whereas in Al-rich alloys, a complex multilayer Al segregation appears, with the possibility of a GB phase transition, and GB glide weakly dependent on GB chemistry seems easy in the [001] direction. These elements may help explain the experimentally well-known high dependence of the mechanical properties of $B2\mathrm{F}\mathrm{e}\ensuremath{-}\mathrm{A}\mathrm{l}$ on bulk composition.

Electronic Structure of Pristine and Solute‐Incorporated SrTiO3: III, Perfect‐Crystal, Grain‐Boundary Geometry, and Acceptor Doping

Electronic structure is investigated for donor‐impurity‐incorporated perfect‐crystal and 36.8° symmetric tilt Sigma5 (310) grain‐boundary geometries of SrTiO3. The relaxed model of the atomic structure of the grain boundary used in the present investigations is the same as that used in Part II, as derived by Ravikumar et al. using lattice‐statics simulations based on pair‐potential calculations. As in Part II, the methodology of one‐electron first‐principle cluster calculations, which is discussed in Part I, is extended to clusters with single‐donor impurity substitutions at the central titanium and strontium sites. The effects of niobium substitution at a titanium site and lanthanum substitution at a strontium site in the bulk and at the grain‐boundary core have been investigated by determining the aspects of the electronic structure discussed for the acceptors. The influence of grain‐boundary crystallography on donor impurity incorporation has been evaluated in terms of variations in densities of states, spatial charge densities, and charge populations at the grain boundary. As in Parts I and II, no additional local lattice relaxations around the impurity are considered for the impurity‐incorporated clusters. Donor compensation mechanisms reported in the literature are discussed in connection with the electrical activity of the material. The calculations reveal that, in perfect‐crystal geometry, although lanthanum exhibits almost the expected donor behavior at the strontium site, niobium does not exhibit very good donor behavior at the titanium site. Moreover, a decrease in the donor behavior of these impurities is observed in the grain‐boundary geometry. Such variations in the electronic behavior of donors are due to the crystallographic variations at the grain boundary and are likely to decrease the grain‐boundary‐charge and associated space‐charge effects in the presence of donors as compared with the increase of such effects in the presence of acceptors. Consequently, a decrease in space‐charge‐induced segregation of donors at grain boundaries and the effects thereof can be expected.

Electronic Structure of Pristine and Solute‐Incorporated SrTiO3: II, Grain‐Boundary Geometry and Acceptor Doping

Grain boundaries in ceramics have a major influence on various mechanical and electrical properties of the material system. Nonlinear electronic properties of electroceramics are directly linked with the grain‐boundary phenomena caused by the variations in the crystallography and the chemical environment, and consequent variations in the electronic structure of the grain boundaries. In this Part II of the three‐part report, the electronic structure of pristine and acceptor‐impurity‐incorporated 36.8° symmetric tilt σ5 grain boundary in SrTiO3 is investigated. A relaxed model of the atomic structure of this grain boundary derived by Ravikumar et al. using lattice statics simulations based on pair‐potential calculations has been used for electronic structure calculations. This model is a very good approximation to the true relaxed structure, because it accurately reveals some of the structural features observed experimentally. The methodology of one‐electron first‐principle cluster calculations discussed in Part I has been used to study the pristine titanium‐ and strontium‐centered grain‐boundary clusters. Clusters with a single acceptor impurity at the central titanium site also have been considered in order to investigate the effects of impurities at the grain boundaries. As in Part I, no additional local lattice relaxations have been considered for the impurity‐incorporated clusters. Calculations involve determination of the aspects of the electronic structure outlined in Part I. The influence of grain‐boundary crystallography on local electronic structure is evaluated in terms of variations in densities of states and spatial charge densities. The influence of the grain boundary on local charge transfer and on impurity‐induced changes in charge populations also is investigated. The role of impurity incorporation at the grain boundaries is discussed in comparison with impurity incorporation in the bulk. The calculations reveal an increased covalence in the nature of the Ti‐O and Sr‐O bonds at the SrTiO3 grain boundary. The optical bandgap at the grain boundary is reduced because of the broadening of the O 2p valence and Ti 3d conduction states toward the Fermi level. An enhancement in the acceptor nature of transition‐metal impurities is observed at the grain boundary with an increase in the degree of association between the impurity ions and the oxygen neighbors. The variations in the electronic structure resulting from the variations in the crystallography at the grain boundary have implications on grain‐boundary segregation, space‐charge, and conductivity phenomena associated with the impurities.

On the Applicability of the CSL Model to Grain Boundaries in Non-Cubic Materials

Crystallography of grain boundaries in crystal structures of lower symmetry is considered. It is suggested that only twin boundaries are singular in nature. Difficulties in the application of the CSL model to analyzing interfaces in non-cubic materials are discussed. It is shown that the reciprocal volume density of coincident sites, Σ, is not the primary parameter determining the grain boundary structure and properties.

The Effects of Thermomechanical Processing on Interfacial Crystallography in Metals

Thermomechanical processing can be used effectively to manipulate the crystallography of grain boundaries in metals and alloys. Several examples are quoted here accompanied by an elucidation of the factors which influence the grain boundary network geometry. Twinning is the principal means of introducing improved boundaries into the microstructure, and this paper examines the reasons for this and proposes a model for the proliferation of 23 boundaries, as distinct from Σ3 twins, in the microstructure. It is concluded that the relative specialness of boundaries adjoining coherent twins, rather than the absolute specialness, is the critical factor.

Studies of the crystallography of arbitrary grain boundaries by O-lattice construction: Application to bulk YBa2Cu3O7-δ

Abstract We report our procedure for analysing the crystallography of arbitrary grain boundaries (arbitrary relative orientation with an arbitrary path of the interface between adjacent crystals). The approach is based on constructions of the O-lattice and b-net to derive the possible Burgers vector of arrays of grain-boundary dislocations for any given geometry of the grain boundary (boundary misorientation and boundary plane normal) using Bollmann's O-lattice theory. The configurations of the boundary dislocations associated with these Burgers vectors are then refined by taking the dislocation reaction into account, and comparing them with the experimentally determined Burgers vectors, line directions and line spacings of the dislocations using a modified Frank dislocation model. We applied our procedure to analyse the grain boundary in orthorhombic YBa2Cu3O7-δ superconducting oxides. Our results suggest that the methodology is valuable in determining the structure of arbitrary grain boundaries and is v...

Grain-boundary morphology and crystallography in recrystallized hornblende

Grain-boundary morphology and crystallography in recrystallized hornblende

A crystalline aggregate with icosahedral symmetry: Implication for the crystallography of twinning and grain boundaries

Abstract Polycrystalline aggregates with overall icosahedral symmetry have been found in rapidly solidified Al—Mn—Fe—Si alloys. The orientation relationship between crystals is such that icosahedral motifs in all the crystals are parallel. Although the cubic axes undergo fivefold rotation about irrational 〈1, τ, 0〉 axes, only five orientations occur among hundreds of crystals. This is a special orientation relationship, but there is neither a coincidence nor a twin lattice (S = σ = ∞). The concepts of twinning and special grain boundaries are re-examined, and a new definition of special orientations (hypertwins) based on the reduction of the number of arithmetically independent lattice vectors is proposed. It includes both old and new special orientations and can be easily interpreted in terms of quasilattices.

Grain boundary dislocation networks in YBa2Cu3O7-δ

The crystallography, morphology, and structure of typical grain boundaries in sintered samples of the high temperature superconducting oxide YBa2Cu3O7-δ(123) have been investigated by transmission electron microscopy using two-beam diffraction contrast imaging and selected area diffraction techniques.Since most of the grains present in sintered samples of 123 are plate shaped with the plate normal parallel to the c-axis of the crystal, the grain boundaries can be divided into two classes: (a) those for which the boundary plane normal is nearly parallel to the c-axis of one of the abutting grains (basal-plane-faced boundaries), and (b) those which are not basal-planefaced. Regular networks of grain boundary dislocations have been observed in high-angle grain boundaries of both types. These networks extend the length of the imagable portion (i.e., sufficiently thin) of the boundary without changing their basic geometry. The line contrast produced by the networks shows several of the key characteristics of dislocation images.

Composition variations near grain boundaries in YBa2Cu3O7-δ

Detailed electromagnetic characterization of samples of YBa2Cu3O7-δ (123) have shown this material, at least in its sintered form, is composed of islands of good superconductor which are separated from one another by “weak links” consisting of regions of poor superconductor or normal material. A number of researchers have suggested that these weak links are associated with grain boundaries. Therefore, conventional transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) coupled with energy dispersive x-ray analysis (EDAX) have been used to investigate the morphology, crystallography, and composition of typical grain boundaries in this material.The electromagnetic properties of the specific samples from which the TEM specimens were prepared had been studied in detail. Briefly, these samples possessed relatively low normal state resistivities and nearly field independent transport critical current densities, indicating that they were of relatively high quality.For these initial studies, specimens for TEM and STEM/EDAX were prepared by dimpling plus ion milling (3-4kV, 0.5mA per gun, liquid nitrogen cooled stage).

Dependence of phosphorus segregation on grain boundary crystallography in an FeNiCr alloy

Relation between the amount of P-segregation and grain boundary crystallography in an FeNiCr alloy was studied. A grain boundary etching method was utilized for analyzing P-segregation, and the crystallography of grain boundaries was characterized by making channelling pattern and trace analysis. Macroscopic geometric characteristics of grain boundaries which were found to be effective in suppressing the amount of P-segregation are (1) low-angle disorientation (2) σ3 orientation relation, (3) \\ ̃ gs3 (quasi-twin) orientation relation (4) boundary orientation close to the orientation of the coherent twin boundary,(5) boundary plane having low indices, and (6) boundary straightness. It was suggested that an essential geometric factor on the atomic scale which controls the amount of P-segregation in high-angle boundaries is their coherency or free volume.

A practical approach to the determination of the crystallography of grain boundaries

Methods available for determining the crystallography of grain boundaries are surveyed. It is suggested that the reason why relatively few studies of the crystallography of large numbers of boundaries have been made is the intensity of labour involved in the data analysis. A scheme is described which allows a large sample population of grain boundaries to be handled with maximum efficiency, whilst maintaining high precision in the parameters which describe the boundary. It also permits a comparison of these parameters with those which describe special cases (e.g. high-density coincidence site lattice, etc). The method involves a combination of stereographic manipulation and matrix algebra.

A practical approach to the determination of the crystallography of grain boundaries

A practical approach to the determination of the crystallography of grain boundaries