Grain-boundary surface tension

Figure 6.7 Average grain boundary energy, y b, surface energy of crystals at 0 K, ysS, and surface tension of liquid Al, Ag, Au, Ni and Pt as a function of melting temperature 7W 2/3[8, 11],...

Specific surface energy or surface tension of a solid Specific free energy of an interface between UC and U vapor Specific energy or tension of a liquid-solid interface Surface tension of a solid in a foreign vapor Surface tension of a grain boundary... 

All real crystals have atoms which occupy external surface sites and which do not possess the correct number of nearest neighbors as a consequence, Thus, a surface is a scat of energy and is characterized by surface tension. Furthermore, internal surfaces exist, grain boundaries and twin boundaries across which atoms are incorrectly positioned. In a crystal of reasonable size—say 1 cubic centimeter, these two-dimensional defects, called surface defects, contain only about 1 atom in 106, a rather small fraction. Even so, surfaces are important attributes of solids. 

If sand is moist, the slope of a sand pile can be higher. A sand castle can have vertical walls when it is built of moist sand in the morning, but as the afternoon wears on and the sand dries out, it cmmbles and collapses (mass wastes) until a stable slope forms. This is because the water makes the sand more cohesive. With the proper moisture content, there will be both water and air between most of the grains of sand. The boundary between the water and the air has surface tension— the same surface tension that supports water striders or pulls liquids up a capillary tube. In moist sand, surface tension holds the grains together like a weak cement. 

A more sophisticated approach for determination of the grain boundary segregation is similar to the determination of the surface tension of silicon melt. The novel approach of surface tension simulation has been successfully implemented in the thermochemical database. Hence, the assessment of the parameters for impurity segregation in solid silicon phase may greatly extend the application of the thermochemical database. The calculation results for C and O segregation are shown as dashed lines in Fig. 13.28. The McLean segregation isotherm can be reproduced using the approach similar to the surface tension simulation. 

Grain boundaries are internal interfaces and behave much like external surfaces, but now we have to be concerned with two crystal orientations, not one. Just as for surfaces, we have a pressure difference associated with the GB curvature and a driving force that tends to lead to an overall increase in grain size whenever possible. Grain morphology and GB topology are two aspects of the same topic. It is instructive to think of the model of soap foams a soap film is flat when in equilibrium and it has a finite thickness. Three soap films meet along a line—a TJ. If you blow on a soap film (apply a pressure) it bows out until the surface tension balances the applied pressure. 

For a grain structure to be in metastable equilibrium the surface tensions must balance at every junction between the GBs. It is theoretically possible to construct a three-dimensional polycrystal in which the boundary tension forces balance at all faces and junctions, but in a real random polycrystalline aggregate there are always going to be boundaries with a net curvature in one direction and thus curved triple junctions. Consequently, a random grain structure is inherently unstable and, on heating at high temperatures, the unbalanced forces will cause the boundaries to migrate toward their center of curvature. 

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