Question

(a) Do you expect the surface energy to be greater than, the same as, or less than the grain boundary energy, why? (b) A small angle grain boundary has a less grain boundary energy than a high-angle one. Why?

Answer 1

A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are 2D defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship.

a),the answer is a)greater than.

the reason is
On a grain boundary some of the 'dangling bonds' of each surface are no longer dangling and there is some bondage between grains. A dangling bond is of higher energy than a real bond, so less dangling bonds, less potential energy.

b)

The energy of a low-angle boundary is dependent on the degree of misorientation between the neighbouring grains up to the transition to high-angle status. In the case of simple tilt boundaries the energy of a boundary made up of dislocations with Burgers vector b and spacing h is predicted by the Read-Shockley equation:

where:

with is the shear modulus, is Poisson's ratio, and is the radius of the dislocation core. It can be seen that as the energy of the boundary increases the energy per dislocation decreases. Thus there is a driving force to produce fewer, more misoriented boundaries (i.e., grain growth).

The situation in high-angle boundaries is more complex. Although theory predicts that the energy will be a minimum for ideal CSL configurations, with deviations requiring dislocations and other energetic features, empirical measurements suggest the relationship is more complicated.