Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Abstract

The kinetics of c 0 -type (Ni 3 X) precipitate growth and solute depletion in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, Ni-Ti and Ni-Al-Cr alloys is successfully predicted by the trans-interface diffusion-controlled theory of coarsening using non-integer temporal exponents, n, satisfying 2 B n B 3, which are obtained from analyses of particle size distributions (PSDs). The origin of non-integer n is concentrationdependent diffusion through the c/c 0 interface. The literature on diffusion of Al and Ni in Ni 3 Al is specifically examined. It is shown unequivocally that the concentration-dependent diffusion of Al can account semi-quantitatively for the value of n that successfully describes the PSDs and kinetics of coarsening of the c 0 precipitates. There is no need to invoke a particle size-dependent c/c 0 interface width, as was done in prior work. It is argued that existing theory and computational modeling of coarsening in systems with highly disparate diffusion mobilities in both phases do not correctly represent the mobilities in the matrix, precipitate, and interface in Ni-Al alloys. These theories predict temporal exponents satisfying 3 B n B 4, for which there is no experimental support.

Cellular Automata Modeling of Ostwald Ripening and Rayleigh Instability

“…However, Ardell and Ozolins [ 10 ] pointed out that, when particles grow to very large sizes, the coarsening behavior becomes matrix diffusion controlled. Because when the particles are very large, the concentration gradients in the matrix become so small that diffusion of solute in the matrix is actually slower than it is through the interface [ 14 ], and it will be matrix diffusion controlled instead of interface transfer controlled. So when the controlling mechanism changes to matrix diffusion, the current CA model is no longer applicable.…”

“…This theory is limited to the steady state of Ostwald ripening for the extreme case with vanishingly low particle fraction, and predicts the growth law, , with the exponent m = 3, where is the average particle radius, t is the time and K is the coarsening rate constant. The most recent model was developed by Ardell and Ozolins [ 10 ] and later elaborated by Ardell [ 11 , 12 , 13 , 14 ]. They assume that the coarsening process is trans-interface-diffusion-controlled (TIDC), instead of the classical theory with the assumption of matrix diffusion controlled.…”

“…They assume that the coarsening process is trans-interface-diffusion-controlled (TIDC), instead of the classical theory with the assumption of matrix diffusion controlled. The TIDC theory predicts the exponent m of the growth law in the range of 2 and 3 either by invoking a particle size-dependent interface width [ 11 , 12 ] or by invoking concentration-dependent diffusion coefficient [ 14 ]. Apart from analytical models, numerical models of Ostwald ripening have been reported, such as phase field model [ 15 , 16 , 17 , 18 ], Monte Carlo model [ 19 , 20 , 21 , 22 ], and cellular automata (CA) model [ 23 ].…”

Cell-Free Biomimetic Mineralization Strategies to Regenerate the Enamel Microstructure

“…Due to the large surface area of the shell structure, small crystals within the structure are energetically unfavorable and easily dissolve and diffuse into solution. The crystals are redeposited onto HA, promoting their growth [79]. Ca 2+ gradually dissociates from the EDTA-Ca complexes and displays preferential binding to the crystal's polar (001) direction [71].…”