Coherency strain energy and chemically induced grain boundary migration in $Al_2O_3$

Abstract

In most previous investigations on the chemically induced interface migration (CIM), the major emphasis has been laid on the driving force for the phenomenon. The driving force is now believed to be the coherency strain energy built in a thin coherent diffusionmal layer on a receding grain during the migration. Some quantitative analyses have also been made for several systems, based on the calculation of coherency strain energy. The analyses, however, were limited to cubic systems. In order to confirm the coherency strain model for the migration, the coherency strain energy of non-cubic systems must be calculated and critical experiments for the systems are needed. In the present investigation, we have first derived a general equation of coherency strain energy applicable to all crystal systems and studied the effect of coherency strain energy on the chemically induced grain boundary migration (CIGM). A special emphasis has been laid on the initiation and migration direction in CIGM, which were not well understood yet. Alumina with trigonal symmetry, one of the most common oxides of practical importance, has been taked as a model system. This thesis consists of seven chapters including general introduction (Chap. I) and concluding remarks (Chap. VII). In chapter II, based on the macroscopic theory of elasticity, a general equation of coherency strain energy applicable to all crystal systems is derived by modifying Hilliard``s method and the calculated results for some selected materials are graphically represented as the coherency strain energy map (CSEM). The complete equation is equivalent to those of Eshelby and Hay. If stress-free strain data is available, the absolute value of the strain energy can be determined. If instead, an assumption of hydrostatic stress for the internal stress induced by alloying or dealloying is used to determine the relative variation of coherency strain energy with crystallographic orientation and the plane with minimum or maxim...