Structure and Energy of Grain Boundaries

Tilt boundaries occur if the axis of rotation between the two grains is located in the boundary (interface). In contrast, if the axis of rotation is perpendicular to the boundary, the boundary is called a twist boundary and consists of a collection of screw dislocations (Fig. 3-6b). An equation similar to Eqn. (3.14) holds for twist (and mixed) boundaries. Since dislocation theory is well understood, it is possible to quantitatively treat small-angle grain boundaries [J.P. Hirth, J. Lothe (1982)]. 

It is known from experiment that the boundary energy and diffusivity are a function of the grain boundary orientation angle and often show minima at certain specific orientations [Q. Ma, R.W. Balluffi (1993) A.N. Aleshin, etal. (1977)]. This 

Grain boundary models were developed primarily for metals. We can assume that the above mentioned ideas on the structure and energy of grain boundaries also hold, in essence, for ionic, covalent, and van der Waals crystals as well [M. W. Finnis, M. Riihle (1993)]. 

Since we are considering equilibrium boundaries and interfaces, let us introduce some phenomenological thermodynamics. If 6 symbolizes the orientation (location) of two crystal parts (phases) relative to each other, and s designates a structure parameter that symbolizes the atomic structure of the boundary (composition and structural details), then 

We conclude that the isothermal, isobaric interface structure is a function of 1) the orientation and 2) the component chemical potentials in the adjacent crystals. The first point has been exploited explicitly in calculations of boundary energies, Eb (= Eloial — El-En), using appropriate interatomic potentials and relaxation pro- 

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We have repeatedly emphasized the complementary (and sometimes antagonistic) role of empirical and first-principles calculations of the many structures that inhabit materials. The structure and energy of grain boundaries is clearly yet another defect... 

The structure and energy of grain boundaries are very much affected by the stoichiometry of the component atoms and by the addition of interstitial atoms. 

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