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

Abstract

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 × 10 7 J·m −3 for the strain energy is computed for Cu-Ni(Fe) nanolaminate coatings with 2-4 nm composition wavelengths.

Interdiffusion at Room Temperature in Cu-Ni(Fe) Nanolaminates

“…The result seen in the data plots of Figures 3 and 4 is a bimodal distribution in R(B) versus B curve as the outcome of room temperature aging. A decrease in wavenumber β, and corresponding increase in λ for maximum growth is seen from a value of 1.8 nm reported [22] at 320 • C to a 3.7 nm at room temperature as found in Figure 3 and listed in Table 1.…”

“…The accuracy in determining the diffusivity coefficients for these curves 2 and 1 at B 2 = 0 is limited by a total error of 30-35%, respectively. This error is orders of magnitude greater than theĎ value of −1 × 10 −26 nm 2 ·s −1 at 23 • C which could be extrapolated [22] from high-temperature data for Ni 63 self-diffusion [29] wherě D(T) at T −1 = 0 equalsĎ 0~1 cm 2 ·s −1 . To reconcile this difference, the third data-point fit is considered where theĎ value of −1 × 10 −26 nm 2 ·s −1 at 23 • C is assumed, and the required values of the gradient energy coefficients are computed (as listed in Table 2) along with the required order of magnitude for the amplification factor R. In this third fit, it's found that the gradient energy coefficients would have to be 10-12 orders of magnitude smaller than measured, and that the corresponding R values would need to be 16 orders of magnitude smaller than actually measured.…”

“…The ratio between the normalized satellite and Bragg peaks is compared between the as-deposited condition, and after 30 years aging at room temperature. An initial nonlinear response [19,22] in the ln-scale, normalized-satellite intensity variation with anneal time, i.e., amplification factor R, that can occur from a strong composition dependence in Cu-Ni [27,28] is not anticipated in this study since the growth of the final wavelength λ (nm) initial wavelength λ (nm) Figure 1. The θ/2θ X-ray diffraction scans shows the satellite peaks below (−1) the (111) Bragg reflections of the Cu-Ni(Fe) nanolaminates with composition wavelengths of 3.04 nm (green curve) and 3.15 nm (blue curve) and the (Cu) base layer for epitaxial growth.…”

“…Figure 6. The Arrhenius plot of experimental diffusivity Ď (cm 2 ·s −1 ) data with the ratio of melt point Tm to test temperature T for the Cu-Ni(Fe), Ni-Cu, Fe-Cu, Ni-Ni, Si-Al, and HfN-ScN systems is shown along with generic diffusivity curves [32] for identifying the bulk-, dislocation-, and grain boundarybased diffusion mechanisms ( Jankowski [22] Wang, et al [44]; present).…”

“…The ratio between the normalized satellite and Bragg peaks is compared between the as-deposited condition, and after 30 years aging at room temperature. An initial nonlinear response [19,22] in the ln-scale, normalized-satellite intensity variation with anneal time, i.e., amplification factor R, that can occur from a strong composition dependence in Cu-Ni [27,28] is not anticipated in this study since the growth of the composition fluctuation at room temperature is measured using nanolaminates that had initially undergone significant homogenization [19] at temperatures outside the spinodal to greatly reduce the amplitude of the composition profile to a small fluctuation-a necessary condition for the diffusion model. The variation of the amplification factor R with the dispersion relation B of the Cu-Ni(Fe) structure is plotted in Figure 3.…”