Growth kinetics of precipitation

The problem now is to solve Pick s second law, expressed in spherical coordinates, under the assumption that 1. The concentration of the precipitating component at time t Ois every- 

a relaxation time t = rl/3rpD for the precipitation process can be given, c is the average concentration of the precipitating component in the region of influence 4/3-7rr, and is small compared to Furthermore, under the conditions of applicability of eq. (7-40) the following mass balance can be written  

First of all, however, in light of the preceding general discussion, let us consider, as an example, the precipitation of cementite e C out of an iron matrix which is supersaturated with carbon [40]. Difficulties arise because of the difference between the molar volume of the precipitate and the volume per mole of the precipitating components in the matrix. This causes a stress field to be formed around the precipitate. As long as no internal voids or creep processes occur, in the steady state case there will be a coupled diffusional flux of carbon towards the precipitate and of iron towards the supersaturated matrix, because the volume of the Fq C precipitate is greater than the volume of 3Fe. This problem was first analyzed by Hillert [41] for the system Fe-C. This analysis, however, has a quite wide and general applicability. 

The growth of an FejC particle in a supersaturated austenite matrix can be described on an atomistic basis as follows. The rate-determining step is the relatively slow diffusion of iron via vacancies. The flux of iron occurs away from the surface of the cementite particles towards the matrix. The main contribution to the driving force is the pressure difference between 

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Nielsen, A. E. 1964. Diffusion controlled growth. Kinetics of Precipitation. Pergamon Press, Oxford, UK. p. 34. 

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