Abstract
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.
Highlights
The diffusional transformation of spinodal decomposition [1,2,3,4,5,6,7,8,9,10] proceeds by the growth of a periodic composition fluctuation as the α-phase matrix decomposes at temperatures within the spinodal into α'Coatings 2015, 5 and αphases, without a change in the crystal structure
This study considers the effects of strain energy from a one-dimensional modulation in nanolaminate structures on the kinetics of the spinodal decomposition process
In a comparison of results for aging at 320, 345 and 400 °C, growth of the composition fluctuation is seen within the spinodal at temperatures below
Summary
The diffusional transformation of spinodal decomposition [1,2,3,4,5,6,7,8,9,10] proceeds by the growth of a periodic composition fluctuation as the α-phase matrix decomposes at temperatures within the spinodal into α'Coatings 2015, 5 and αphases, without a change in the crystal structure. The case for multilayered structures is investigated wherein it can be modeled that the motion of an interface is affected by interactions with second nearest interfaces, leading towards the tendency of doubling the composition wavelength over time. The free energy f at a temperature Ti is considered for an alloy system composed of elements A and. The local minima in the free energy curve, i.e., at f = ∂f/∂c = 0, provide the locus of points at temperatures Ti that form the miscibility gap. The phase transformation process of spinodal decomposition [1,2,3,4,5,6,7,8,9,10] proceeds via uphill diffusion when the second-order derivative of the Helmholtz free energy f with respect to composition c is less than zero, i.e., f = ∂2f/∂c2 < 0. Decomposition for one-dimensional diffusion is found [20]
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