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Kinetics of Materials - R. Balluff_ S. Allen_ W. Carter (Wiley_ 2005) Episode 12

Tham khảo tài liệu 'kinetics of materials - r. balluff_ s. allen_ w. carter (wiley_ 2005) episode 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 19.2 HETEROGENEOUS NUCLEATION 481 Ỵaa ỴaP 2 COS ự Figure 19.14 Regimes in which grain corner edge boundary and homogeneous nucleation are predicted to be dominant. From Cahn 18 . _ yb2 . In 47T screw dislocation 19.50 El 19.2.2 Nucleation on Dislocations Dislocations in crystals have an excess line energy per unit length that is associated with the elastic strain field of the dislocation and the bad material in its core. In many cases the formation of a particle of the new phase at the dislocation can reduce this energy enabling it to act as a favorable site for heterogeneous nucleation. The original treatment of heterogeneous incoherent nucleation on dislocations was by Cahn 19 The general topic including coherent nucleation on dislocations has been reviewed by Larché 20 Incoherent Nucleation. Consider first incoherent nucleation on dislocations 19 . For linearly elastic isotropic materials the energy per unit length El inside a cylinder of radius r having a dislocation at its center is given by r Ro and __ lib2 r El ---- In -7 edge dislocation 19.51 4tt 1 - V Ro where b is the Burgers vector and Ro is the usual effective core radius. Poisson s ratio V is approximately 0.3 for many solids so to a fair approximation the energy difference between edge and screw dislocations can be ignored. Following Cahn Ei ln 19.52 z y - to y where B ụ-bI 2 r . Allowing the entire region inside a radius r to transform to incoherent 3 will allow essentially all of the dislocation energy originally inside the transformed region to be released. Thus the dislocation catalyzes incoherent nucleation by eliminating some of the dislocation s total energy. It is important to note that the dislocation will still effectively exist in the material along with its strain energy outside the transformed region even though the incoherent 3 has replaced the core region. For example a Burgers circuit around the dislocation in the matrix material surrounding the incoherent 3-phase cylinder will still