Diffusion-Controlled Phase Transformations in Open Systems

Flux-Driven Lateral Grain Growth during Reactive Diffusion

“…Such flux-driven lateral grain growth during solid state reaction at frozen bulk diffusion should provide power laws, Eqs. (17), (18), with time exponents m = 0.20 for lat- eral grain size and n = 0.40 for phase width. It would be interesting for experimentalists also to measure the possible gradient of the lateral grain size, predicted by Model 2.…”

“…The reason is that in our case grain growth proceeds in the open system, so the growing layer can develop under gradients of chemical potentials as well as under passing fluxes. It is demonstrated in [13][14][15][16][17][18] that the fluxdriven morphology evolution in open systems can demonstrate quite a different behaviour from analogic morphology evolution in closed systems. For example, Flux-Driven Ripening (FDR) in soldering reaction proceeds (contrary to the conventional ripening with decreasing interface area and almost constant volume) with almost constant interface area but growing volume [13].…”

“…Flux-Driven lateral Grain Growth (FDGG) during thin film deposition also may leave the total grainboundary area constant and, depending on temperature, may lead to linear or parabolic dependence of mean grain size on the film thickness [14,16]. Flux-Driven Nucleation [15] and Flux-Driven Cellular Precipitation [17,18] demonstrate the influence of external flux on nucleation at interfaces and on precipitation at frozen bulk diffusion.…”

“…Typical numeric solution of Eqs. (17), (18) for the dependences nx 1/2 , mx 1/2 of time exponents on the dimensionless phase layer thickness x 1/2 with initial conditions x 0 = 0.25, y 0 = 1 is shown at Fig. 4.…”

Anisotropic Nucleation, Growth and Ripening under Stirring—A Phenomenological Model

“…Some years ago, a new method of production of rod-like and belt-like metal oxide structures (TiO 2 , V 2 O 5 ) was suggested involving intensive stirring of salted water with initially more or less equiaxially shaped oxide powder particles at elevated or even at room temperatures [ 1 , 2 ]. This new method connected the problem of anisotropic nucleation, growth, and ripening [ 3 , 4 , 5 , 6 ] with the problem of phase and structural transformations in open driven systems [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. In order to develop a theoretical interpretation of these interconnected phenomena, the first very simplified models were advanced recently in [ 18 ].…”