Diffusion in Stressed Thin Films
نویسنده
چکیده
The effect of mechanical stress on interdiffusion in a binary substitutional solid solution has been investigated from a theoretical point of view. Fick's first law, stating that the diffusional flux is proportional to the concentration (chemical potential) gradient, is the basic equation for diffusional mass transport. Limits of its validity, in particular in a state of non-hydrostatic stress, have not always been generally recognised. In this work the effect of non-hydrostatic mechanical stresses on diffusion is investigated theoretically. In cases of non-hydrostatic stress, chemical potentials for defining equilibrium are not applicable. Following a formalism proposed by Cahn and Larche [Larche and Cahn, (1973)], the so-called diffusion potentials have to be utilised for defining equilibrium instead of the chemical potentials. Thus, the diffusional flux under non-hydrostatic states of stress is taken proportional to the gradient of a diffusion potential. For the first time, complete flux equations have been derived both in the latticefixed frame of reference and the laboratory frame of reference. The diffusional flux is (also) proportional to the gradient of the (principal) components of the mechanical stress tensor and to the difference in the partial molar volume of the diffusing species. Fick’s first and second law have been solved numerically by an explicit finite difference method taking a Pd-Cu thin film diffusion couple having a planar, rotationally symmetric state of stress as a model example. The effects of both applied stress gradients as well as diffusioninduced stress gradients have been studied on the basis of a number of calculated concentration profiles considering both externally applied and diffusioninduced planar states of stress. A general conclusion is that the ‘larger’ atoms flow towards regions of tensile stress whereas ‘smaller’ atoms flow towards regions of compressive stress. 2. Interaction of stress and diffusion in a binary substitutional solid solution 12 2.
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تاریخ انتشار 2005