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Mat. Res. Soc. Symp. Proc. Vol. 505 0 1998 Materials Research Society

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d Figure 1: Schematic illustration of the nucleation of slip in a single disk-shaped grain, after Thompson [5]. The grain is considered in isolation, in the treatment that leads to Equation 2. where b is the Burgers vector of the dislocation, Wd is the energy per unit length of the dislocations in their final positions, trapped in the grain boundaries or the film-substrate interface, d is the grain diameter, h is the film thickness, Xis the angle between the normal to the plane of the film and the Burgers vector direction, and 0 is the angle between the film plane and the slip plane: cos)coso is the Schmid factor. Thompson's expression clearly indicates that the yield stress also depends upon the crystal orientation (through X and 0); or in the ensemble, upon the texture of the film. The models of both Nix [4] and Thompson [5] are based upon the assumption that dislocation loops are nucleated at the free surface of the film, as indicated schematically in Figure 1. Sanchez and Arzt [1] have also considered how the crystallographic texture of a film should affect its yield stress. For the glide of threading dislocations through a capped (e.g. oxidized) film a on rigid substrate they suggested that a h = CijkG'-

(3)

where G* is the effective shear modulus of the capped film-substrate system They assumed that the grain height is equal to the film thickness and that a , is independent of grain orientation and is dependent only on the length of the glide plane in the grain. The effect of the grain orientation

(which remains the same for an uncapped film) is determined by the factor Cijk given by Cijk-

cosicoSX

(4)

where (ijk) denotes the particular grain fiber orientation. The Sanchez-Arzt model is based upon dislocation-bowing in the plane of the foil, and is appropriate for films that are rigidly constrained on both surfaces, rather than one, but it is similar in most other respects to the Nix and Thompson models. EXPERIMENTAL Polycrystalline gold films were made by thermal evaporation of gold from a tungsten basket onto freshly cleaved, nominally (100) sodium chloride substrates. The nominal film thickness was 120nm and the deposition was carried out at a rate of about lnm per second with the substrate at uncontrolled room temperature in a chamber pressure of about 4xl0- torr. After the deposition, the film that was to be annealed on gold TEM grid, was floated off the rock salt surface in distilled water and collected on the gold TEM grid. The films on substrate and the films on TEM grids were annealed at 550°C for 1 hour. The size of the grains was estimated by the mean linear intercept method. Kikuchi patterns from convergent beam electron diffraction were used to measure individual orientations and to determine grain boundary normals. Two-beam contrast analysis was used to determine the Burgers vectors of dislocations.

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300nm Figure 2: Bright-field TEM image of a yielded grain (#1) surrounded by unyielded neighbors (#2 - #7). Th