Residual stress gradients along ion implanted zones — cubic crystals
Large internal strains and stresses can be produced by low temperature implantation over small distances from the free surface in a thick substrate. These are typically non-uniform and have large composition gradients. In dilute bcc solutions, containing unclustered interstitial implants, the residual macroscopic strains may be treated as isotropic. The calculation of residual strain (or stress) is based upon anisotropic elasticity theory and internal stress is given in terms of the dipole tensor for individual defects in single crystal films. In a completely elastic zone, forces act to maintain a rigid outside surface and cause the strain distribution to be zero along directions parallel to the free surface. This produces a strain magnification along the perpendicular direction from Poisson contractions. If the implanted zone is completely relaxed by plastic deformation, the strains are described by the free expansion strains due to both implants and lattice damage. There is no angular dependence of the free expansion strain in this extreme condition. One can determine whether a zone is completely elastic, completely relaxed by plastic deformation, or in some intermediate state from plots of strain against sin2χ, where χ is the angle of tilt relative to the surface normal. These results may be obtained from X-ray Bragg intensity data by measuring shifts and line broadening from (hkl) planes at different tilt angles. Theoretical results are given for both single crystal and polycrystalline materials in terms of residual strain and stress.
KeywordsResidual Stress Residual Strain Anisotropic Elasticity Macroscopic Strain Crystal Film
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