Growth interface-controlled

Equation (6.11) is valid for the initial particle growth. Interface control of the growth kinetics would lead to a linear rate law. Details can be found, for example, in [H. Schmalzried (1981)]. 

Decomposition of a single solid J- Nucleation - Growth Interface phenomena. Geometric control... 

Contracting volume (CV) Three-dimensional growth diffusion controlled with decreasing interface velocity 168, 171... 

The new reference frame is known as the interface-fixed reference frame, and the old reference frame is called the laboratory-fixed reference frame. The melt consumption rate u depends on whether the growth is controlled by interface reaction, or by diffusion, or by externally imposed conditions such as cooling. 

Initially, when the ApBq layer is very thin, the reactivity of the A surface is realised to the full extent because the supply of the B atoms is almost instantaneous due to the negligibly short diffusion path. In such a case, the condition kom kW]/x is satisfied. Therefore, if the surface area of contact of reacting phases A and ApBq remains constant, chemical reaction (1.1) takes place at an almost constant rate. In practice, this regime of layer growth is usually referred to as reaction controlled. The terms interface controlled regime and kinetic regime are also used, though less suited. 

The two most important nucleation processes are continuous nucleation, that is, when the nucleation rate is temperature dependent according to an Arrhenius equation, and the site saturation process, that is, when all nuclei are present before the growth starts. The two growth processes normally considered are volume diffusion controlled and interface controlled. Finally, the process that interferes with growth is the hard impingement of homogeneously dispersed growing particles. 

Decohesion and void growth are controlled by the debonding stress at the particle/matrix interface it only occurs when the local debonding stress is lower than the fracture stress (crazing stress) of the matrix itself G is correlated with the local toughness at the interface it is dependent on the particle/matrix adhesion energy. 

Diffusion of oxygen and/or metal atoms near the surface then occurs and the initial oxide layer is formed. The further growth of this layer involves two steps (a) reaction at the metal/oxide and oxide/oxygen interfaces, and (b) transport of material through the oxide layer. As the oxide layer gets thicker, the rate of growth is controlled by (b) which becomes the slower of the two steps. If the volume of the oxide produced is less than that of the parent metal, the simple rate law for an unimpeded reaction is observed... 

Fig. 13. Coexistence, hysteresis and kinetics, (a) Schematic of interface-controlled growth of phase ft into phase a (b) superposition of spectra and thermal hysteresis (c) time evolution of volume fraction of phase ft Avrami model (Eq. (14)) for different exponents n.

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