Schematics of the procedure to devise the image stress of a defect in a crystal (pink disk in the center) due to the presence of a free surface. (a) Traction forces at the free surface position in the infinite crystal. (b) Image stress introduced to cancel the traction stress. (c) The total stress field in the semi infinite crystal is and the resulting displacement field is visible as a dimple in the surface.
Relative errors of calculation using anisotropic elasticity of the image displacement and image energy of pure bcc Fe containing a nanometric dislocation loop. Relative error of (a) the image displacement, and (b) the image energy on the free surface of a semi infinite space. Relative error of (c) the image displacement, and (d) the image energy on the free surface of a thin film.
Image stress induced in-plane and out-of-plane displacement fields (u′,v′,w′) by a loop on the free top and bottom surfaces of a oriented bcc Fe single crystal thin film calculated using isotropic elasticity from Voigt and anisotropic elasticity. , , radius = 3 nm, depth = 14 nm, thickness = 28 nm.
Elastic parameters of Fe used for the calculations.
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