More Complete Expressions for the Classical Nucleation Rate

5 More Complete Expressions for the Classical Nucleation Rate 

With the background above, more complete expressions for the classical nucleation rate can be explored. 

Single-Component System with Isotropic Interfaces and No Strain Energy. This relatively simple case could, for example, correspond to the nucleation of a pure solid in a liquid during solidification. For steady-state nucleation, Eq. 19.16 applies with AQC given by Eq. 19.4 and it is necessary only to develop an expression for /3C. In a condensed system, atoms generally must execute a thermally activated jump over a 

zcXg is the number of sites in the matrix from which atoms can jump onto the critical nucleus, vc is the effective vibrational frequency for such a jump, and G is the free energy of activation for the jump. 

Two-Component System with Isotropic Interfaces and Strain Energy Present. An example of this case is the solid-state precipitation of a 5-rich (i phase in an A-rich a-phase matrix. For steady-state nucleation, Eq. 19.16 again applies. However, for a generalized ellipsoidal nucleus, the expression for AQ will have the form of Eq. 19.28. Also, /3 must be replaced by an effective frequency, as discussed in Section 19.1.2. 

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