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Liquid-Phase Sintering
Published in M. N. Rahaman, Ceramic Processing and Sintering, 2017
Compared to solid-state sintering, the presence of the liquid phase leads to enhanced densification through (1) enhanced rearrangement of the particulate solid and (2) enhanced matter transport through the liquid. Figure 10.1 shows a sketch of an idealized two-sphere model in which the microstructural aspects of liquid-phase sintering are compared with those of solid-state sintering. In liquid-phase sintering, if, as we assume, the liquid wets and spreads to cover the solid surfaces, the particles will be separated by a liquid bridge. The friction between the particles is significantly reduced so that they can rearrange more easily under the action of the compressive capillary stress exerted by the liquid. In solid-state sintering by, for example, grain boundary diffusion, an important parameter that controls the rate of diffusion is the product of the grain boundary diffusion coefficient Dgb and the grain boundary thickness δgb. In liquid-phase sintering, the corresponding parameter is the product of the diffusion coefficient DL of the solute atoms in the liquid and the thickness of the liquid bridge δL. Since δL is typically many times greater than δgb and diffusion through a liquid is much faster than in solids, the liquid therefore provides a path for enhanced matter transport.
Interface Electrical Phenomena in Ionic Solids
Published in P.J. Gellings, H.J.M. Bouwmeester, Electrochemistry, 2019
Transport along interfaces, commonly considered as grain boundary diffusion in the literature, corresponds with diffusion parallel to interfaces, such as grain boundaries, and is limited to a thin grain boundary layer of thickness δ (Figure 4.43). This transport is usually much faster than the transport in the bulk phase. The enhancement effect is related to the microstructure of the interface region. The correct determination of the grain boundary diffusion coefficient of defects requires knowledge of the enrichment coefficient of the grain boundary by these defects.
A dislocation assisted self-consistent constitutive model for the high-temperature deformation of particulate metal-matrix composite
Published in Philosophical Magazine, 2021
M. Rezayat, M.H. Parsa, H. Mirzadeh, J.M. Cabrera
It means that if the deformation zone was fully recrystallized, the stress intensity drops to . Although for a certain condition of deformation, the ratio of is constant, the fraction of DRXed area is increasing with strain. Considering the velocity of dislocation climb (as the main recovery mechanism) and velocity of grain boundary migration, the ratio of dislocation density in recrystallized and recovered structure can be found from [64]: where Dsd is the self-diffusion coefficient, Dgb is the grain boundary diffusion coefficient, and Vm is the molar volume of aluminum (9.99×10−6 m3/mol). Laasraoui and Jonas [65] used Equation (17) to calculate the dynamic recrystallization fraction during deformation as:
Simulation of silver nanoparticles sintering at high temperatures based on theoretical evaluations of surface and grain boundary mobilities
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2020
When pressure is applied during sintering, material transport occurs along the grain boundary, which results not only in the growth of the neck but also in densification (center-to-center approach of the particles). Atom movement from the grain boundary under compression to the neck surface under tension is the same as that of vacancy movement in the reverse direction, which makes the grain boundary act as a site for vacancy annihilation. The relative centerwise shift of two particles occurs when the vacancies are annihilated at the grain boundary. The normal displacement rate of the relative motion is given as [14]: where is the diffusion thickness of the grain boundary, is the grain boundary diffusion coefficient, and is the normal stress. The relative velocity between two particles is defined negative as removal of matter occurs at the grain boundary and they move closer. The equilibrium dihedral angle, is given by the ratio of the grain boundary energy, to the surface energy,
Simulation of the microstructural evolution during dynamic recrystallisation with a modified cellular automaton
Published in Philosophical Magazine Letters, 2020
The driving force for the growth of a dynamic recrystallisation grain mainly arises from the difference between the dislocation densities on opposite sides of grain boundaries. The growth velocity (V) may be expressed approximately as [2]:where P is the driving force of the growth of a DRX grain, r is the radius, and M is the grain-boundary mobility that can be calculated from [2]whereHere, C4 is a constant of value 2.0 in this paper, is the grain-boundary diffusion coefficient, k is the Boltzmann constant, Tm is the melting temperature, and Qb is the grain-boundary activation energy.