Die direkte Messung von Stapelfehlerenergien

Different methods for determining stacking fault energies from dislocation configurations observed in the electron microscope are discussed. Configurations discussed are simple, threefold, and fourfold ribbons, arrays of many parallel ribbons, and dislocation nodes. The latter are treated taking the mutual interaction of the partials approximately into account. Results are given for measurementsin graphite, MoS$_{2}$, AIN, and talc

Surface effects associated with dislocations in layer crystals

Dislocation configurations in thin foils cannot be accurately interpreted unless the effects of anisotropy and surfaces on the stresses and energies of edge and screw dislocations are known. Expressions for these effects are derived here for a semi-infinite hexagonal crystal with dislocations in the basal plane. lt is then shown that in plate-like crystals, as used in electron-microscopic investigations, the finite thickness of the specimen leads to observable effects on the dislocation patterns. In particular, the width of a ribbon decreases as it approaches the surface, due to the reduced repulsion between the partials, so that care is needed in deducing stacking fault energies from ribbon widths. Also the energy of a dislocation is a function of its distance from a surface, so that if it is crossed by a surface step it suffers a "refraction" which, in simple cases, follows Snell's law. lt is further shown that dislocations will tend tobe aligned with surface steps, artd the interaction energy between a step and a parallel dislocation line can thus be derived from experimental data. Finally, a method is suggested for obtaining information on the elastic constants from electron microscopic data

The buckling of a thin plate due to the presence of an edge dislocation

lt is shown that an edge dislocation parallel to the surface of a thin foil causes buckling of this foil by an angle of about $\theta$ = b/t. (b = Burgers vector; t = thickness of the foil). The angle $\theta$ depends on the position of the dislocation. lt is maximum for a dislocation in the middle of the foil and it tends to zero as the dislocation approaches to the surface. lt is shown that the buckling is responsible for the discontinuous change in contrast along a dislocation as observed in transmission electron microscopy. The sense of buckling which can be determined by means of Kikuchi lines depends on the sign of the dislocation. The effect therefore provides an easy means to determine the sign of edge dislocations

STM observation of electronic wave interference effect in finite-sized graphite with dislocation-network structures

Superperiodic patterns near a step edge were observed by STM on several-layer-thick graphite sheets on a highly oriented pyrolitic graphite substrate, where a dislocation network is generated at the interface between the graphite overlayer and the substrate. Triangular- and rhombic-shaped periodic patterns whose periodicities are around 100 nm were observed on the upper terrace near the step edge. In contrast, only outlines of the patterns similar to those on the upper terrace were observed on the lower terrace. On the upper terrace, their geometrical patterns gradually disappeared and became similar to those on the lower terrace without any changes of their periodicity in increasing a bias voltage. By assuming a periodic scattering potential at the interface due to dislocations, the varying corrugation amplitudes of the patterns can be understood as changes in LDOS as a result of the beat of perturbed and unperturbed waves, i.e. the interference in an overlayer. The observed changes in the image depending on an overlayer height and a bias voltage can be explained by the electronic wave interference in the ultra-thin overlayer distorted under the influence of dislocation-network structures.Comment: 8 pages; 6 figures; Paper which a part of cond-mat/0311068 is disscussed in detai

GEOMETRICAL APPROACH TO THE COINCIDENCE

La caractérisation des joints en coïncidence, décrits par la relation d'orientation entre grains formant un joint, est obtenue par la comparaison avec des tables de coïncidences. Une approche formelle a été développée pour les systèmes cubique et hexagonal. Un grand nombre de tables a été établi pour le système hexagonal. Une méthode de quantification de la déviation entre un joint observé et des valeurs tabulées est proposée. Dans le cas des systèmes hexagonaux, une nouvelle notion est introduite pour exprimer la déviation entre le rapport c/a du matériau observé et la valeur approchée correspondante utilisée dans la table.The characterization of coincidence grain boundaries described by the orientation relationship between each crystal element is given by the comparison with tabulated coincidences. A formal approach has been developed for the cubic and the hexagonal systems. A large amount of tables has been established for the hexagonal crystals. A method is proposed for the quantification of the deviation between an observed grain boundary and tabulated cases. A new concept is proposed for expressing the deviation between the c/a ratio for a particular crystal and the corresponding approximate value of the table in the case of the hexagonal system