Many of the dihedral angles where grain boundaries meet the free surface in MgO

Question

Many of the dihedral angles where grain boundaries meet the free surface in MgO and Al2O3 are less than 120°, corresponding to a surface energy that is less than the grain boundary energy ( grain boundary energy> surface energy). It is intuitively surprising to find that grain boundary energy> surface energy since free surface has more broken bonds than the grain boundary and might be expected to have higher energy. This feature is unique to ceramics and has not been observed in metals. Propose possible reasons why grain boundary energy> surface energy?

Explanation / Answer

Relative grain boundary energies can be simply related to true dihedral angles, which are the angles between grain boundary planes meeting at triple edges in polycrystals. Some limited efforts in the measurement of true dihedral angles have used the technique of serial sectioning, which is usually cumbersome and time consuming. In a polycrystalline space-filling microstructure, the meeting of three grains forms a triple edge. The geometry of the grain boundaries (or interfaces) can be characterized in terms of the angles between planar interfaces that meet at the triple edge. Thermodynamic and kinetic conditions, under which grain boundaries can be described as thick, are considered. It is shown that in many cases such thick grain boundaries consist of thin films of a phase different from that in the adjacent grains. Such films can be liquid, amorphous or can have a crystalline structure different from that in adjacent grains. A variety of materials are considered, from pure metals to high-temperature superconducting ceramics. The influence of the phase state of grain boundaries on the properties of polycrystalline materials (such as mechanical properties and grain growth behaviour) is considered.Consistent with the results of the calculated energies for fcc metals, the grain boundary energies of bcc metals are more sensitive to the grain boundary plane orientation than to the lattice misorientation. Subsets of the data support the hypothesis that low index planes, which have low surface energies, are often found in low energy grain boundaries. Pure metals are made of several randomly oriented grains or crystals. The surface which is shared by two neighboring grains is the boundary between the two. Microstructure represents a 2 dimensional section of such an arrangement. The grains that are visible represent crystals and the lines are the boundaries. The atoms in respective grains on the two sides of a boundary are arranged in a periodic fashion. However there may not be a definite relation between the two. This means that just across the boundary there is a sudden change in the atomic array. Therefore a grain boundary may represent a surface where the atoms may not be arranged in a periodic fashion. This may also be visualized as a network of dislocations although it may be difficult to guess its structure. Nevertheless the nature of the boundary will certainly be affected by the shape of the neighboring grains and their orientations

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