Gregory S. Rohrer

Distribution of grain boundaries in magnesia as a function of five macroscopic parameters

Abstract A semi-automated method has been used to measure all five macroscopically observable parameters of 4.1×10 6 boundary plane segments making up 5.4 mm 2 of boundary area in a hot-pressed magnesia polycrystal. The observations allow a complete description of the distribution of crystal orientations, grain boundary misorientations, and the crystallographic orientations of grain boundary planes. Among the low misorientation angle grain boundaries, there is a preference for tilt boundaries, especially those with boundary plane normals in the direction. At all fixed misorientations, there is a preference for boundaries with a boundary plane normal in the direction. These boundaries are generally asymmetric and occur at least twice as frequently as the average boundary for each fixed misorientation.

Open‐core screw dislocations in GaN epilayers observed by scanning force microscopy and high‐resolution transmission electron microscopy

Structural investigations of organometallic vapor phase epitaxy grown α‐GaN films using high‐resolution transmission electron microscopy and scanning force microscopy have revealed the presence of tunnel‐like defects with 35–500 A radii that are aligned along the growth direction of the crystal and penetrate the entire epilayer. These defects, which are termed ‘‘nanopipes,’’ terminate on the free surface of the film at the centers of hexagonal growth hillocks and form craters with 600–1000 A radii. Either one or two pairs of monolayer‐height spiral steps were observed to emerge from the surface craters which allowed us to conclude that nanopipes are the open cores of screw dislocations. The measured dimensions of the defects are compared to Frank’s theory for the open‐core dislocation.

The Distribution of Internal Interfaces in Polycrystals

Recent advances both in experimental instrumentation and computing power have made it possible to interrogate the distribution of internal interfaces in polycrystals and the three dimensional structure of the grain boundary network with an unprecedented level of detail. The purpose of this paper is to review techniques that can be used to study the mesoscopic crystallographic structure of grain boundary networks and to summarize current findings. Recent studies have shown that grain surfaces within dense polycrystals favor the same low energy planes that are found on equilibrium crystal shapes and growth forms of crystals in contact with another phase. In the materials for which comprehensive data exists, the distribution of grain boundaries is inversely correlated to the sum of the energies of the surfaces of the grains on either side of the boundary.

The relative free energies of grain boundaries in magnesia as a function of five macroscopic parameters

Abstract Using measurements of the geometric and crystallographic characteristics of approximately 10 4 triple junctions in a MgO polycrystal, the relative grain boundary energy has been determined as a function of five macroscopic parameters. The relative energy of a particular grain boundary is inversely correlated with its frequency of occurrence. At all misorientations, grain boundaries with {1 0 0} interface planes have relatively low energies. For low misorientation angle grain boundaries, the results are consistent with the predictions of dislocation models. At high misorientation angles, the population and energy are correlated to the sum of the energies of the free surfaces that comprise the boundary.

Structure of the Reduced TiO2(110) Surface Determined by Scanning Tunneling Microscopy

The scanning tunneling microscope has been used to image a reduced TiO2(110) surface in ultrahigh vacuum. Structural units with periodicities rangng from 21 to 3.4 angstroms have been clearly imaged, demonstrating that atomic resolution imaging of an ionic, wide band gap (3.2 electron volts) semiconductor is possible. The observed surface structures can be explained by a model involving ordered arrangements of two-dimensional defects known as crystallographic shear planes and indicate that the topography of nonstoichiometric oxide surfaces can be complex.

Spatially selective visible light photocatalytic activity of TiO2/BiFeO3 heterostructures

Heterostructures of thin titania films on BiFeO3 substrates were grown by pulsed laser deposition. The heterostructures, when excited by visible light with energies between 2.53 and 2.70 eV, photochemically reduce aqueous silver cations from solution in patterns that mimic the structure of the ferroelectric domains in the substrate. Under the same conditions, titania by itself reduces insignificant amounts of silver. The observations indicate that electrons generated in the substrate are influenced by dipolar fields in the ferroelectric domains and transported through the titania film to reduce silver on the surface.

A scanning tunneling microscopy and spectroscopy study of the TiO2-x(110) surface

The surface structure of reduced TiO2−x(110) has been studied in ultrahigh-vacuum by scanning tunneling microscopy and tunneling spectroscopy. A variety of surface structure types with periodicities larger than the bulk TiO2 unit cell have been clearly resolved. These periodic structures, which have repeat distances ranging from 3.2 A to greater than 30 A, coexist with one another on the reduced surface and have domain sizes of < 1000 A. Tunneling spectra acquired from this surface show the bulk conduction band edge 0.5 eV above the Fermi level and a bandgap greater than 2.5 eV. These observations are compared to a surface structure model that assumes the presence of varying concentrations of bulk crystallographic shear plane defects that accommodate non-stoichiometry in this material.

Deriving grain boundary character distributions and relative grain boundary energies from three-dimensional EBSD data

Abstract Three-dimensional electron backscatter diffraction data, obtained by serial sectioning a nickel–base superalloy, has been analysed to measure the geometric arrangement of grain boundary planes at triple junctions. This information has been used to calculate the grain boundary character distribution (GBCD) and the grain boundary energy distribution (GBED). The twin content from the three-dimensional GBCD calculation compares favourably with the twin content estimated by stereology. Important factors in the analysis are the alignment of the parallel layers, the ratio of the out-of-plane to in-plane spacing of the discrete orientation data and the discretisation of the domain of grain boundary types. The results show that grain boundaries comprised of (111) planes occur most frequently and that these grain boundaries have a relatively low energy. The GBCD and GBED are inversely correlated.

Sparse data structure and algorithm for the phase field method

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

Extracting Grain Boundary and Surface Energy from Measurement of Triple Junction Geometry

Measurement of the geometry of triple junctions between grain boundaries in polycrystalline materials generates large sets of dihedral angles from which maps of the grain boundary energy may be extracted. A preliminary analysis has been performed for a sample of magnesia based on a three-parameter description of grain boundaries. An extended form of orientation imaging microscopy (OIM) was used to measure both triple junction geometry via image analysis in the SEM and local grain orientation via electron back scatter diffraction. Serial sectioning with registry of both in-plane images and successive sections characterizes triple junction tangents from which true dihedral angles are calculated. We apply Herrings relation at each triple junction, based on the assumption of local equilibrium at the junction. By limiting grain boundary character to a (three parameter) specification of misorientation for the preliminary analysis, we can neglect the torque terms and apply the sine law to the three boundaries. This provides two independent relations per triple junction between grain boundary energies and dihedral angles. Discretizing the misorientation and employing multiscale statistical analysis on large data sets allows (relative) grain boundary energy as a function of boundary character to be extracted from triple junction geometry. A similar analysis of thermal grooves allows the anisotropy of the surface energy to be measured in MgO.