Kinetics of spinodal decomposition and strain energy effects in Cu-Ni(Fe) nanolaminates
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Kinetics of spinodal decomposition and strain energy effects in Cu-Ni(Fe) nanolaminates Alan F. Jankowski Texas Tech University, Edward E. Whitacre Jr. College of Engineering, Mechanical Engineering Department, P.O. Box 41021, Lubbock, TX 79409-1021, U.S.A. ABSTRACT The phase transformation of spinodal decomposition proceeds without nucleation and is affected by the alloy composition, temperature, interfaces and gradient energy, as well as the presence of lattice strain. As a consequence, a coherent spinodal can be depressed well below the chemical spinodal within the miscibility gap. Phase separation from a solid solution within the spinodal leads to the formation of characteristic composition wavelengths. In the nickel-based alloy system, a nanolaminate structure is used to initially create an artificial composition fluctuation with unique nanoscale wavelengths. The direct measurement of diffusivity at low temperatures in Cu-Ni and Cu-Ni(Fe), from the spinodal towards room temperature, requires sensitivity to the nanoscale fluctuations in composition. For this purpose, x-ray diffraction scans are used to assess changes in the short-range order of the composition fluctuation and the corresponding changes in the gradient energy, from which an evaluation of lattice distortion effects reveals a peak in strain energy for 2-3 nm composition wavelengths. INTRODUCTION In spinodal decomposition [1-10], the alloy transforms from the parent α-phase solid solution into α' and α phases by the growth of a periodic composition fluctuation without a change in crystal structure. Consider the free energy diagram in Fig. 1 of an A-B alloy system at temperature Ti. There is no barrier for decomposition as the transformation proceeds via uphill diffusion, that is, as f < 0. For the free energy curve at temperature Ti the composition C* rests within the spinodal region as seen in the shaded region of the phase diagram in Fig. 1. The Cα' and Cα compositions mark the bounds of the miscibility gap at Ti as determined by the minima in the free energy curve for the alloy. The locus of points for those compositions at temperatures that are between the bounds defined by f =0 is termed the chemical spinodal. Decomposition for one-dimensional diffusion is first explained [1] by considering an interfacial energy term between adjacent atomic planes. Experimental evidence for a corresponding structure is found earlier where satellite reflections are observed about the Bragg peaks in x-ray diffraction patterns for a quenched Cu-Ni-Fe alloy [11] that was annealed within the miscibility gap. The additional consideration of a gradient energy term [3-4] allowed for the identification of a critical wavelength, whereas the presence of lattice coherency effects [5] can depress the transformation temperature further to produce a coherent spinodal that rests within the (incoherent) chemical spinodal. The decrease of the spinodal can be significant [12] for some alloy systems such as Au-Ni with large lattice misfit, whereas it’s potentially smaller for bulk
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