Strain Energy Effects in the Spinodal Decomposition of Cu-Ni(Fe) Nanolaminate Coatings

A model for spinodal decomposition must account for interface effects that include gradient and strain energy terms. The measurement of diffusion in the Cu-Ni(Fe) alloy for the special case of nanolaminate structured coatings is considered wherein the composition fluctuation is one-dimensional along <111>. An analytic approach is taken to model the kinetics of the transformation process that provides quantification of the strain energy dependence on the composition wavelength, as well as the intrinsic diffusivities and higher-order gradient-energy coefficients. The variation of the wave amplification factor R with wavenumber is modeled first to incorporate the boundary condition for growth at infinite wavelength. These results are used next to determine the gradient energy coefficients Kμ by modeling the interdiffusion coefficient ĎB variation with wavenumber, where a unique determination of the diffusion coefficient Ď is made. The value of the strain energy component that originates from interface strains associated with the epitaxial growth between layers is then determined by assessing the variation of wavelength-dependent amplification factors. A peak value of 9.4 × 107 J·m−3 for the strain energy is computed for Cu-Ni(Fe) nanolaminate coatings with 2–4 nm composition wavelengths.