Systematics of the cellular precipitation reactions
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of the C e l l u l a r
Precipitation
Reactions
ERHARD HORNBOGEN A systematic description is given of cellular reactions with special account to the discontinuous precipitation. The following special aspects of this reaction are discussed: The constitutional, nucleation, and other conditions for its occurrence; the role of grain boundaries, d i s locations, and vacancies for the mechanism; the effect of continuous precipitation before discontinuous precipitation; multiple discontinuous reactions; effects of grain boundary structure, third elements, and external s t r e s s ; reactions in highly defect crystals and amorphous solids. It is shown that all phenomena can be understood either by effects on driving force or mobility of the reaction front. DISCONTINUOUS precipitation (d.p.) belongs to the large family of autocatalytic reactions. The adjective discontinuous r e f e r s to the composition of the matrix lattice, which changes discontinuously a c r o s s the r e action front, Fig. 1. The t e r m s cellular-, r e c r y s t a l lization-, and grain boundary-reaction are also in use and relate to other typical features of this reaction: it leads to the formation of ceils with a usually lamellar morphology of the phases, the matrix orientation is changed, and it requires grain boundaries to serve as a reaction front. The most important characteristic seems to be, however, the autocatalytic nature of the reaction: it is able to move or reproduce lattice defects in its reaction front that are able to accelerate nucleation and/or growth of the equilibrium phases. There are several other reactions which are r e lated to d.p. because they make use of grain bounda r i e s or incoherent phase boundaries as a reaction front. Their characteristics are shown schematically in Fig. 2. The presence of a grain boundary in the r e action front is a very frequent, but not a n e c e s s a r y condition for d.p. (see chapter 1.2). Most of the work on d.p. is concerned with the grain boundary reaction. In the attempts to provide a quantitative description the growth of cells has usually been treated under special conditions: a) grain boundaries with isotropic structure are active for nucleation and/or growth, b) no changes taking place ahead of the reaction front, c) no third elements interact with the reaction front, d) no line or areal defects except the grain bounda r i e s play a role. Based on these conditions theories have been worked out that attempt to correlate the velocity of the r e a c tion front G, interlamellar spacing S, degree of segregation in the matrix lattice c X / c e (Co, Ce, c x are the concentration of supersaturated solid solution, equilibrium solid solution, and actual concentration after d.p. respectively) and the temperature dependence of all these p a r a m e t e r s . Several theories of the growth rate have been developed. They can be distinguished
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