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Title: Zero modes on zero-angle grain boundaries in graphene

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 91; Journal Issue: 12; Journal ID: ISSN 1098-0121
American Physical Society
Country of Publication:
United States

Citation Formats

Phillips, Madeleine, and Mele, E. J. Zero modes on zero-angle grain boundaries in graphene. United States: N. p., 2015. Web. doi:10.1103/PhysRevB.91.125404.
Phillips, Madeleine, & Mele, E. J. Zero modes on zero-angle grain boundaries in graphene. United States. doi:10.1103/PhysRevB.91.125404.
Phillips, Madeleine, and Mele, E. J. 2015. "Zero modes on zero-angle grain boundaries in graphene". United States. doi:10.1103/PhysRevB.91.125404.
title = {Zero modes on zero-angle grain boundaries in graphene},
author = {Phillips, Madeleine and Mele, E. J.},
abstractNote = {},
doi = {10.1103/PhysRevB.91.125404},
journal = {Physical Review B},
number = 12,
volume = 91,
place = {United States},
year = 2015,
month = 3

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevB.91.125404

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Cited by: 2works
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  • This paper discusses the dislocation structure of small angle tilt and twist boundaries in ordered Ni{sub 3}Al, with and without boron, investigated using transmission electron microscopy. Dislocation with Burgers vectors that correspond to anti-phase boundary (APB)-coupled superpartials were found in small angle twist boundaries in both boron-free and boron-doped Ni{sub 3}Al, and a small angle tilt boundary in boron-doped Ni{sub 3}Al. The boundary structures are in agreement with theoretical models proposed by Marcinkowski and co-workers. The APB energy determined from the dissociation of the grain boundary dislocations was lower than values reported for isolated APBs in Ni{sub 3}Al. For smallmore » angle twist boundaries the presence of boron reduced the APB energy at the interface until it approached zero. This is consistent with the structure of these boundaries containing small regions of increased compositional disorder in the first atomic plane next to the interface.« less
  • Small angle [001] twist boundaries and [001](110) tilt boundaries in B-free and B-doped Ni-rich Ni{sub 3}Al (76 at. % Ni) were examined using conventional electron microscopy techniques as well as Energy Dispersive X-ray Spectroscopy (EDS), annular dark field (ADF) imaging and spatially resolved electron energy loss spectroscopy (EELS), in an UHV scanning transmission electron microscope. The interface structure consists of periodically spaced pairs of a/2<110> partial dislocations, linked by an antiphase boundary (APB). An analysis of the separation of the partials gives APB energies which are lower than in bulk Ni{sub 3}Al and which decrease with increasing misorientation angle. EDS,more » EELS and ADF imaging demonstrate that the APBs are Ni-rich. The observations on the APB chemistry and energy taken together lead to the conclusion that Ni-enrichment lowers grain boundary energy by decreasing the number of high energy Al-Al interactions across the APB. These results on small angle boundaries lead to the suggestion that Ni-enrichment also decreases the number of high energy Al-Al interactions across the interface at large angle boundaries.« less
  • Earlier calculations on (100) high-angle twist boundaries in Al are extended to Cu, Ag and Au. Recent pseudopotentials of Dagens together with three empirical potentials for Cu are applied. Boundaries with values of sigma, the inverse density of coincidence sites, ranging between 5 and 73 are considered. In contrast to earlier results for the Al pseudopotential of Dagens et al, the relaxed grain-boundary energy, Esigma, is found to increase smoothly as function of the twist angle, theta, for all six potentials considered here; i.e. ''cusps'' in the Esigma (theta) curve are not observed. Rather, similar boundary structures are obtained formore » the noble-metals; these differ drastically from those derived by means of the pseudopotential for Al. From a comparison with (100) twist boundaries in ionic crystals with NaC1 structure it is concluded that also in the f.c.c. metals a volume expansion at the interface which increases smoothly with theta should be present. Interfacial structures determined without consideration of this expansion are hence concluded to be systematically in error. The article concludes with a summary of the properties of (100) twist boundaries in the f.c.c. and NaC1 structures which are thought to be valid independent of the detailed form of the interatomic potential chosen.« less
  • A new computer code is described which permits the investigation of the energy and structure of coincident-site lattice (CSL) grain boundaries in metals. As an improvement over computer programs used by other workers, the full second-derivative (force-constant) matrix associated with a given interatomic potential is applied for the iterative energy minimization. Using this extremely efficient and reliable procedure the effect of the form of the interatomic potential and its truncation radius on the predicted grain-boundary energy and structure is investigated. Six different potentials for aluminum, ranging from a Morse potential to a pseudopotential, are applied to the simulation of themore » energy and structure (100) CSL twist boundaries with values of ..sigma.., the inverse density of CSL sites, ranging between ..sigma.. = 5 and ..sigma.. = 73. It is found that not only do both the energy and structure of a given boundary vary greatly from one potential to another, but also that the relative energies of different boundaries, i.e. the boundary-energy vs misfit-angle curves, depend on the potential. In contrast to recent claims of Brokman and Balluffi, no cusps in these curves are found for potentials which ignore the charge-density oscillations. The two basic assumptions of the Brokman-Balluffi cusp model are found to be valid only for extremely simple potentials with very short cutoff radii. It is suggested that (1) charge-density oscillations may be important for predicting grain-boundary properties, and (2) no obvious relationship exists between grain-boundary geometry (..sigma..) and the energy. 39 references, 18 figures, 1 table.« less
  • Regular networks of localized grain boundary dislocations (GBDs) have been imaged by means of transmission electron microscopy in three different types of high-angle grain boundaries in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}}, implying that these boundaries possess ordered structures upon which a significant periodic strain field is superimposed. The occurrence of these GBD networks is shown to be consistent with the GBD/Structural Unit and Coincidence Site Lattice (CSL)/Near CSL descriptions for grain boundary structure. Thus, these dislocations appear to be intrinsic features of the boundary structure. The spacing of the observed GBDs ranged from {similar to}10 nm to {similar to}100 nm. Thesemore » GBDs make the grain boundaries heterogeneous on a scale that approaches the coherence length and may contribute to their weak-link character by producing the superconducting micro-bridge'' microstructure which has been suggested on the basis of detailed electromagnetic measurements on similar samples.« less