Grain boundary energy anisotropy: a review

Rohrer, Gregory S.

doi:10.1007/s10853-011-5677-3

Cited by 407 publications

(212 citation statements)

References 79 publications

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“…The approximate error associated with the numerical procedure used to determine hi can be estimated by random subdivision of the set of triple junctions into groups and subsequent comparison of the results of hi for each group. The triple-junction method has been successfully applied to determine the relative GB energies in metal and ceramic structures and it will be used in the following to determine the surface tension of symmetric tilt GBs in lamellar BCP systems [26]. Figure 1(b) illustrates a symmetric tilt GB in a layered (BCP) structure-the boundary (indicated as a bold line) symmetrically bisects the rotation angle about an axis within the boundary plane.…”

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confidence: 99%

Measuring Relative Grain-Boundary Energies in Block-Copolymer Microstructures

2012

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The (relative) energies of symmetric tilt grain boundaries in a strongly segregated lamellar block copolymer are determined by analysis of the dihedral angles at grain-boundary triple junctions. The analysis reveals two regimes: at low and intermediate misorientations (corresponding to a tilt-angle range 0 85 ) the grain-boundary energy is found to depend on the tilt angle as EðÞ $ x , with 2:5 > x ! 0. At large misorientations the grain-boundary energy is found to be independent (within the experimental uncertainty) of the angle of tilt. The transition between the two scaling regimes is accompanied by the transition of the grain-boundary structure from the chevron to the omega morphology. Grain-boundary energy and frequency are found to be inversely related, thus suggesting boundary energy to be an important parameter during grain coarsening in block-copolymer microstructures, as it is in inorganic polycrystalline microstructures. The ability to self-organize into periodically ordered microdomain morphologies makes block-copolymerbased materials intriguing platforms to facilitate transformative technological breakthroughs in a range of areas, including dynamic photonic sensors, solid state ion conductors, and bulk heterojunction materials for polymer photovoltaics [1][2][3][4][5]. In these applications, nonequilibrium structural defects such as grain boundaries (GB) are expected to play an important role in determining material performance because of their impact on the long-range order and tortuosity of diffusion pathways. The occurrence of GB defects is inherent in quiescent organized blockcopolymer (BCP) microstructures and can be related to the nucleation and growth of ordered grains during the structure evolution process, the interaction of disclinations, or mechanically induced kinking because of inhomogeneous solvent evaporation during the late stages of film formation. The basic phenomenology of GB structures in BCP materials was first discussed by Gido and Thomas who classified and evaluated the various GB types associated with tilt and twist deformations of lamellar BCPs [6][7][8][9]. Subsequent experimental studies revealed the relevance of process parameters (such as the application of shear fields), molecular architecture, and composition on GB formation as well as the implications of GB defects on, for example, the permeability of BCP materials [10][11][12][13][14][15][16][17].Despite the abundance of GB defects and their demonstrated relevance on the physical properties of BCP materials, very little is known about the governing parameters that determine the formation of the various types of GB structures in BCPs or the evolution of GB structures during, for example, thermal annealing. One parameter that is of particular interest is the energy penalty associated with GB formation as it provides insight into both the mechanism and driving force of grain coarsening during annealing. The current understanding of GB energies in BCPs is limited to simulation studies, for example, by Schick and co-worke...

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Measuring Relative Grain-Boundary Energies in Block-Copolymer Microstructures

2012

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“…Specifically, the cells of rectangle shape (NB: the hexagonal shape can be transformed into rectangle shape) could always be matched easily after some unit repeating operations, which is in pursuit of existence of a coincidence site lattices 43,44 (CSL). Comparatively, the cells of parallelogram with unequal neighboring sides and a non-right angle are difficult to be matched with the others.…”

Section: The Matching Of Shape and Lattice Constants Of The Cellsmentioning

confidence: 99%

“…This difference of interfacial energies could be explained by the fact that the partial saturation of interfacial dangling bonds is not capable enough to offset the instabilities of high energy surfaces. Experimentally, it is observed 44 that the grain boundaries comprised of low energy surfaces have relatively low energies. Our finding is in line with the experimental ones, and indicates that consideration of surface energies should be taken into when choosing interface combinations.…”

Section: The Search Of Relative Position Of Two Phasesmentioning

confidence: 99%

Modeling and stabilities of Mg/MgH2 interfaces: A first-principles investigation

et al. 2014

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We have theoretically investigated the modeling and the structural stabilities of various Mg/MgH2 interfaces, i.e. Mg($10\bar 10$101¯0)/MgH2(210), Mg(0001)/MgH2(101) and Mg($10\bar 10$101¯0)/MgH2(101), and provided illuminating insights into Mg/MgH2 interface. Specifically, the main factors, which impact the interfacial energies, are fully considered, including surface energies of two phases, mutual lattice constants of interface model, and relative position of two phases. The surface energies of Mg and MgH2, on the one hand, are found to be greatly impacting the interfacial energies, reflected by the lowest interfacial energy of Mg(0001)/MgH2(101) which is comprised of two lowest energy surfaces. On the other hand, it is demonstrated that the mutual lattice constants and the relative position of two phases lead to variations of interfacial energies, thus influencing the interface stabilities dramatically. Moreover, the Mg-H bonding at interface is found to be the determinant of Mg/MgH2 interface stability. Lastly, interfacial and strain effects on defect formations are also studied, both of which are highly facilitating the defect formations. Our results provide a detailed insight into Mg/MgH2 interface structures and the corresponding stabilities.

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“…In fact, this inverse correlation persists throughout the domain of grain boundary types of all of the materials that have been examined. (Dillon and Rohrer, 2009b, Rohrer, 2011a, Saylor et al, 2003a This inverse correlation is thought to arise from the preferential elimination of higher energy boundaries during grain growth. Rohrer, 2009a, Rohrer, 2011a) <Figure 18 near here> Three--dimensional microstructural data is particularly important when the connectivity of a microstructure is important, as is the case for a solid oxide fuel cell.…”

Section: X-ray Tomographymentioning

confidence: 99%