Dynamics of decomposition of CuCo alloys at the spinodal point

Abstract

As a typical system for the study of phase separation dynamics, decomposition of CuCo alloys has recently attracted much attention due to findings of giant magnetroresistence effect in Cu/Co, Cu/Fe etc. multilayer systems [1-5]. It was reported that a resistance drop in a magnetic field was also observed in decomposed Cug0Col0 alloys annealed at 400600 °C [6]. It has been revealed that inter-particle coupling of neighbouring magnetic phases (Co-rich) is responsible for the resistance drop, and the giant magnetoresistance effect depends mainly on two factors. One is alloy composition Co. When Co reaches a critical value, a Co-rich skelton structure will form. In this case no resistance drop will be observed because the magnetic coupling of Co-rich phases cannot be realized. The other factor is the wavelength of the decomposed structure, as a function of which the magnetic coupling between neighbouring Co-rich particles reaches a maximum. However, the classic theories on phase separation in a quenched system predicted that the wavelength as a function of composition will show an essential singularity at any point on the spinodal curve where the driving force for phase separation becomes zero [7-9]. So far, this problem has not been solved in the phenomenological framework although it was revealed experimentally that this singularity does not exist. In fact, at T = 773 K, for decomposed Cul_xCO x where x = 0.07-0.10, a resistance drop in a magnetic field was observed and the wavelength of the decomposed structure was several nanometers although the spinodal point Csl was 0.075 57 [6, 10]. Therefore, the classic theories seem to be invalid for describing decomposition near the spinodal curve. It then becomes necessary to develop a theoretical model to solve the problem of singularity at the spinodal curve. In this work we focus on this problem by solving the Cahn-Hill iard equation in a quenched CuCo system. Besides considering the role of non-linear diffusion terms, we also include Fourier-type thermal noise. We show that this problem can be solved successfully. The free energy AG(Co) of homogenized CuCo alloys was evaluated by calculation of phase diagram (CALPHAD) [11, 12], which can be formulated as: