Grain boundaries nucleation

The nucleation rate is, in fact, critically dependent on temperature, as Fig. 8.3 shows. To see why, let us look at the heterogeneous nucleation of b.c.c. crystals at grain boundaries. We have already looked at grain boundary nucleation in Problems 7.2 and 7.3. Problem 7.2 showed that the critical radius for grain boundary nucleation is given by... 

Grain boundary nucleation will not occur in iron unless it is cooled below perhaps 910°C. At 910°C the critical radius is... 

K.C. Russell. Grain boundary nucleation kinetics. Acta Metall., 17(8) 1123—1131, 1969. 

J.W. Cahn. The kinetics of grain boundary nucleated reactions. Acta Metall., 4(5) 449-459, 1956. 

Figure 4 shows this plot for the transformation when the ferrous and ferric hydroxides were precipitated separately by the quick addition of the sum of 2E ammonia and mixed together subsequently. The plot consists of two straight lines of slopes 1 and 2.5. When 2E ammonia was added to the mixture of ferrous and ferric solutions quickly the slopes were 1 followed by 1.85 when added slowly, the slopes were 1 and 1.82. Slope 1 indicates grain boundary nucleation after saturation. Slopes between 1.5 and 2.5 are indicative of diffusion controlled growth from small dimensions (Hi). Note that the curve for 2E Q seems to begin with a larger slope. 

The transformation of the jointly precipitated (Step I) mixture of ferrous and ferric hydroxides to magnetite (Step II) was studied by the continuous measurement of the magnetic moment. It was found that at large excess ammonia, added in Step I, magnetite forms at a fast rate and the transformation is complete. At small excess ammonia the transformation is slow and incomplete. The application of Avrami s theory to the data indicated grain boundary nucleation in the former case and grain boundary nucleation after saturation followed by diffusion controlled growth in the latter case. Mechanisms are proposed for both cases. 

The general form of the equation was developed by Cahn [73], A brief explanation is presented here. The nucleation sites of new phases would be grain boundaries, grain edges, and/or grain comers. In the case of grain boundary nucleation, the volume fraction of a new phase after some time can be expressed as follows. Cahn considered the situation illustrated in Fig. 21.8 and calculated the volume of the semicircle. 

Pumphrey, P.H. andEdington, J.W. (1974) The structure of the semicoherent interface between grain boundary nucleated MjjCg and austenitic stainless steel. Acta Metall, 22(1), 8994. 

Nucleation in solids is very similar to nucleation in liquids. Because solids usually contain high-energy defects (like dislocations, grain boundaries and surfaces) new phases usually nucleate heterogeneously homogeneous nucleation, which occurs in defect-free regions, is rare. Figure 7.5 summarises the various ways in which nucleation can take place in a typical polycrystalline solid and Problems 7.2 and 7.3 illustrate how nucleation theory can be applied to a solid-state situation. 

Fig. 7.5. Nucleation in solids. Heterogeneous nucleotion con take place at defects like dislocations, grain boundaries, interphase interfaces and free surfaces. Homogeneous nucleation, in defect-free regions, is rare.

An alloy is cooled from a temperature at which it has a single-phase structure (a) to a temperature at which the equilibrium structure is two-phase (a -i- ji). During cooling, small precipitates of the P phase nucleate heterogeneously at a grain boundaries. The nuclei are lens-shaped as shown below. 

In reality, below 550°C the driving force becomes so large that it cannot be contained and the iron transforms from f.c.c. to b.c.c. by the displaeive mechanism. Small lens-shaped grains of b.c.c. nucleate at f.c.c. grain boundaries and move across the... 

Fig. 8.7. The displacive f.c.c. —> b.c.c. transformation in iron. B.c.c. lenses nucleate at f.c.c. groin boundaries and grow almost instantaneously. The lenses stop growing when they hit the next grain boundary. Note that, when a new phase in any material is produced by o displacive transformation it is always referred to os "martensite". Displacive transformations ore often called "martensitic" transformations os o result.

Figures 11.2-11.6 show how the room temperature microstructure of carbon steels depends on the carbon content. The limiting case of pure iron (Fig. 11.2) is straightforward when yiron cools below 914°C a grains nucleate at y grain boundaries and the microstructure transforms to a. If we cool a steel of eutectoid composition (0.80 wt% C) below 723°C pearlite nodules nucleate at grain boundaries (Fig. 11.3) and the microstructure transforms to pearlite. If the steel contains less than 0.80% C (a hypoeutectoid steel) then the ystarts to transform as soon as the alloy enters the a+ yfield (Fig. 11.4). "Primary" a nucleates at y grain boundaries and grows as the steel is cooled from A3...

Figure 6.2. Sloichiomclric CuPl, ordered at 550°C for 157 hours. Viewed under polarised light in reflection. Shows growth of ordered domains, heterogeneously nucleated at grain boundaries and surface scratches (after Irani and Cahn 197.5).

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