Grain size interaction theory

Above the threshold, deformation occurs as a consequence of direct particle interaction. Several mechanisms of interaction have been suggested solution-precipitation flow of fluid between particles and cavity formation at the particle matrix interface. These theories of creep suggest several rules to improve creep behavior (1) increase the viscosity of the matrix phase in multiphase materials (2) decrease the volume fraction of the intergranular phase (3) increase the grain size (4) use fiber or whisker reinforcement when possible. As the creep rupture life is inversely proportional to creep rate, lifetime can be improved by improving creep resistance. 

A comprehensive theory of sintering should be capable of describing the entire sintering process as well as the evolution of the microstructure (i.e., grain size, pore size, and the distribution of the grain and pore sizes). However, in view of the complex nature of the process, it is unlikely that such a theory will be developed. A more realistic approach, which is adopted in this book, is to first develop an understanding of the densification and coarsening phenomena separately and then explore the consequences of their interaction. 

The simplest approach conventionally employed to describe the grain screening in colloidal plasmas is the Debye-Hiickel (DH) approximation, or, its modification for the case of the grain of finite size, the DLVO theory [6,7], The DH approximation represents the version of Poisson-Boltzmann (PB) approach linearized with respect to the effective potential based on the assumption that the system is in the state of thermodynamical equilibrium. The DH theory yields the effective interparticle interaction in the form of the so-called Yukawa potential which constitutes the basis for the Yukawa model. 

Simple approach based on the effective mass theory has been developed and successfully applied to simulate electronic properties of monocrystalline and grained nanocrystalline films accounting for the confinement effect and interactions between the grains. Quantum confinement was found to influence band gap values only for the films with the thickness less than 5 nm. The highest gap varied from 0.63 to 0.91 eV depending on the film thickness as well as on the lateral size of the grains. Inclusion of the grains inside the film induces a eonsiderable increase of the gap as compared to the monocrystalline film of the same effective thickness. 

Migration and coalescence of voids as weU as their interactions with grain boundaries (GBs) in the presence of the electric wind force is crucial for understanding the failure mechanism. The first fundamental theory of void migration was developed by Krivoglaz [34] for an isolated spherical void and was later modified by Ho [35] for voids in the vicinity of an external surface. At that, the theory of electron wind force [36, 37] was used to demonstrate a (l/R)-size dependence of void velocity. However, the interaction of a void with GBs during electromigration (EM) was not considered. 

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