Stress effects and non-linearities in diffusional mixing of multilayers

In classical treatments of diffusional mixing of multilayers it is usually supposed that i) the intrinsic diffusion coefficients, Di, are independent of concentration, and they are equal (the Kirkendall shift is zero) [1]; ii) the stress effects are discussed in the framework of the Cahn-Hilliard-theory [1,2]; iii) the deviation from the continuum description can be analysed for a sinusoidal concentration distribution in the discrete Fick equations. These limitations are discussed here and numerical simulations are used to show the effects of the strong concentration dependence of Di. The role of stresses are discussed in the framework of the treatment given by Stephenson [3], which contains the effect of simultaneous stress relaxation (Kirkendan-shift) as well. For the correct description of the Kirkendall-effect a generalised analytical expression for the gradient energy term is also given. The consequences of above effects on the decay of the intensity of the first small angle Bragg peak, due to the concentration modulation, is illustrated.