The Role of Chemical Driving Force in Discontinuous Coarsening
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THE ROLE OF CHEMICAL DRIVING FORCE IN DISCONTINUOUS COARSENING M. Hillert
Div. of Physical Metallurgy Royal Inst. of Technology S-1O0 44 Stockholm, Sweden ABSTRACT The precipitation of a new phase sometimes results in the simultaneous growth of one of the matrix grains at the expense of another one, so called discontinuous precipitation. The two growing crystals may arrange themselves in the lamellar fashion, known from eutectoid transformations. The mathematical analysis of this diffusion-controlled reaction would be incomplete if the nature of the driving force for the matrix grain is not identified. There have been many suggestions regarding the nature of the driving force. The recent discovery that grain boundaries in a single-phase material can migrate in connection with grain boundary diffusion supports the hypothesis of a chemical driving force, acting in discontinuous precipitation. Another reaction where the chemical driving force may be important is discontinuous coarsening. The theory for this reaction is developed in sufficient detail to show the role of the chemical driving force. INTRODUCTION When a precipitation occurs at a grain boundary it sometimes happens that it grows into one of the grains in cooperation with the other grain. The resulting microstructure may resemble a lamellar eutectic or eutectoid structure. This kind of precipitation is called discontinuous precipitation.
FIG.
1. Shape of interface during discontinuous FIG. 2. precipitation
Balance of forces
Figure 1 shows a schematic picture of the growth front. Smith [1] has emphasized the importance of the migrating grain boundary (oo/aI in Fig. 1) and suggested that the rate-controlling mechanism should be grain boundary diffusion by which the supersaturation in the a0 grain is fed to the growing grains without any need for volume diffusion. Chemical Driving Force The question that made the o /a grain boundary migrate was discussed several times over the years and various suggestions were made. However, they were not considered when mathematical expressions for the growth rate were constructed, until the present author [2,3,41 took a detailed look at the balance of forces at the interface, Fig. 2. Assuming local equilibrium of the surface tensions at the three-phase junctions, one can in principle calculate the angles and, in particular, one can evaluate what fractions L'A Mat.
Res. Soc. Symp.
Proc. Vol.
21 (1984)
Elsevier Science Publishing Co.,
Inc.
416
and LB of the a/B surface tension must be carried by the a and B lamellae, respectively. In order to apply this consideration to the theory of growth it is necessary to find the driving forces which can make the lamellae grow in spite of the restraining force. There is undoubtedly a chemical driving force for the growth of the precipitating phase, B. A chemical driving force was now postulated for the al. grain also [2]. The argument can be best described by introducing a curve for the a /aI and x /BI boundary in the Gibbs energy diagram for the system, Fig. 3. T~e point o
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