Anisotropic elastic fields of twist boundaries

Abstract

Al~tract-Relations for linear anisotropic elastic fields of parallel arrays of dislocations are developed. These fields are used to compute the displacement fields of twist boundaries composed of a square grid of screw dislocations. For gold, the results are shown to agree to first order with fields deduced from X-ray diffraction studies and from atomistic simulations for twist boundaries in gold. R6aum6-4)n d~veloppe des relations concernant les champs ~lastiques anisotropes lin~aires cr66s par des arrangements paralldles de dislocations. Ces champs sont utilis~s pour calculer les champs de d6placement de joints de torsion compos6s d'une grille carr6e de dislocations vis. Pour l'or, on montre que les r6sultats sont en accord au premier ordre avec les champs d6duits de 6tudes par diffraction des rayons X et des simulations atomiques pour des joints de torsion. Ztmmnmenf~aag-Ausdriicke werden abgeleitet fiir lineare anisotrope elastische Felder von Anordnungen paralleler Versetzungen. Mit diesen Feidern wird das Versehiebungsfeld von DriUkomgrenzen, die aus einem quadratischen Netz von Schraubenversetzungen bestehen, bereehnet. Ffir Gold wird gezeigt, dab die Ergebnisse in erster Ordnung mit Feldern fibereinstimmen, die aus R6ntgenmessungen und aus atomisticschen Simulationen f/Jr Drillkorngrenzen in Gold folgen.

Solute-atom segregation/structure relations at high-angle (002) twist boundaries in dilute Ni?Pt alloys

“…15 to 21). First, it is shown that at high angles the (002) planes exhibit a considerable degree of relaxation in the direction normal to the interface, with the positions of certain sites deviating from the average position of the plane by up to 10% of the interplanar spacing; this value is in good agreement with both experiments [32] and calculations [58]. On the Ni-rich side the strongly enhanced sites tend to lie closer to the plane of the interface, while on the Pt-rich side they relax away from the interface.…”

“…It has to do with the pattern of atomic relaxations in the (002) planes near the interface. It is well known from analytical models [58], computer simulations and experiments [32,59], that local relaxations at (002) symmetrical twist boundaries lead to considerable variations in the positions of atomic sites not only in the plane parallel to the interface, but also in the direction normal to the interface within one (002) plane--up to 20% of the interplanar distance. Therefore, the relaxed structure of a (002) plane near the interface is not smooth, as in the bulk, but atomically rough, with different types of sites located closer to the interface or farther from it with respect to the average position of the plane normal to the interface.…”

A multi-phase field model of planar dislocation networks

“…The field ξ α (x 1 , x 2 ) may also be regarded as a counter that keeps track of the number of dislocations of type α that have crossed over the point (x 1 , x 2 ). For notational convenience, we introduce the diagonal matrix 15) whereupon the Peierls potential takes the form…”

“…In a continuum setting, sub-grain dislocation networks have been studied analytically [4,5,[11][12][13] and computationally [9,[14][15][16]. Analytical studies have been for the most part limited to infinite planar dislocation arrays and based on simple kinematics and geometrical arguments such as Frank's relation or on line-tension models that neglect elastic interactions and the structure of the dislocation nodes [4,11,13].…”

Mapping strain fields in ultrathin bonded Si wafers by x-ray scattering

“…In the present work we apply x-ray scattering to measure the strain amplitudes in samples with an ultrathin bonded upper crystal and analyze the results using an isotropic elastic approximation. 1,2,10,11 Silicon-on-insulator ͑SOI͒ wafers with a 200 nm Si͑001͒ crystal on top of the SiO 2 were thinned by dry oxidation. The required layer thickness was determined using ellipsometry.…”