An Investigation On The Preference Of The Precipitation Crystallography In FCC/BCC Systems

Precipitation hardening is an effective way to enhance the strength of materials. Thestrengthening effect is affected by the morphologies, size, and distribution of the pre-cipitates, which is closely related to the knowledge of the precipitation crystallography.However, the formation and the preference of the precipitation crystallography in manyalloys are still unknown. It is an attempt in this work to investigate the preference of theprecipitation crystallography in FCC/BCC Systems with a combination of the crystallo-graphical models and energetic studies based on the atomic potentials.In the early stage of the phase transformation (coherent stage), the BVC (BurgersVector Content) model and SVD (Singular Value Decomposition) method is suggestedto analysis the misfit distribution. The misfit distribution can be conveniently character-ized by the singular values and singular vectors defined by the SVD of the transformationdisplacement field. In the condition of the IL (Invariant Line), the OR (Orientation Re-lationship) with minimum BVC in FCC/BCC Systems is not unique, which is consistentwith the experimental work. In addition, the possible OR in this stage is calculated.In the later stage of precipitation (semicoherent stage), it is found the O-line modelis applicable in this stage based on a fit/misfit analysis. The percentage of good match-ing atoms in this interface is always nearly30%. Formulae are provided for crystal-lographic features, including OR, HP orientation, dislocation direction and dislocationspacing, for two cases with different Burgers vectors, i.e. Case I:[110]_f/2|[100]_b,CaseII:[101]_f/2|[111]_b/2. These formulae are expressed as functions of the lattice parameterratio and the angle between two Burgers vectors. Taken these analytical results as an in-put, the interfacial energies of pure iron, Ni-Cr, Fe-Cu have been studied. According tothe energetic studies, the interface with the lowest interfacial energy contains the parallelBurgers vectors. For a given Burgers vector, the local minimum of the interfacial energymaycorrespondtoalocalmaximumofthedislocationspacingormaynot. Theinterfacialenergy of the general interfaces containing parallel Burgers vectors is also investigated.It is also found the interface, containing the O-line and parallel Burgers vectors, is morepreferable than those only containing parallel directions. Energetic study further showsthattheinterfaceat nearK-S ORhas lower interfacialenergy comparingwiththatofN-WOR, though the dislocation spacing is smaller. The effects of the lattice parameter ratio, composition and elastic constant on the interfacial energy have been studied, and it isshown that the preference of near K-S OR is not alternated around conventional latticeparameter ratio1.255. Moreover, the relaxed atomic structures are also analyzed. Basedon the results from coherent and semicoherent stage, the mechanism of possible crystal-lographical evolution between two stages is proposed, and it may developed by rotationmechanism or by a two dimensional mechanism.In addition, two methods have been developed to solve the orientations of interfacescontaining one set of dislocations. These interfacial orientations are found to lie on thesurface of an elliptic cone. The equation and the geometrical axes of the cone can besimplysolvedbyreferringtothediffractionpatternsnormaltotheBurgersvectors. Thesemethods are general and can be easily applied.