Grain-boundary glass volume

Obsidian and flints are natural glasses. Such samples show a uniform diffusion in any direction. In contrast, the diffusion of F into meteorites must be a function of the grain size of the material. The apparent diffusion is a mixture of volume diffusion and grain-boundary diffusion. Grain-boundary diffusion is much faster... 

Figure 19. Residual stresses of grain-boundary phase and the silicon nitride grains as a function of the thermal expansion coefficient of the grain-boundary phase (calculated after [92]) used constants for Si3N4 E = 320, v = 0.27, a = 3.39 x 10 K and for the glass E = 140, v = 0.29, volume fraction of glass = 0.15 a) and dependence of the fracture toughness on the thermal expansion coefficients (data 1-3 after [92]) 1. mean thickness of the grains 0.55 2. 1-1.3 3. 1.5-1.7 (data 4 after [64]).

Grain boundary films in ceramics are not just restricted to the thin equilibrium films discussed so far. In a variety of other ceramics, thicker glass films (10 nm to several microns) are also observed, which have a significant effect on microstructure and properties. These thicker films represent a different regime of behavior and may vary in thickness with the volume fraction of liquid and from one boundary to another in a given sample of material. 

As the temperature rises, the viscosity of the glass falls, and viscous flow of the glassy layer from between the grains can result in creep. The available models predict that the effective viscosity of the material is inversely proportional to the cube of the volume fraction /of the boundary phase, i.e.. 

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