Planar Faults and Phase Diagrams

The emergence of the types of polytypes described above may be rationalized on the basis of a variety of different ideas. Rather than exploring the phenomenon of polytypism in detail, we give a schematic indication of one approach that has been used and which is nearly identical in spirit to the effective Hamiltonian already introduced in the context of stacking fault energies (see eqn (9.18)). In particular, we make reference to the so-called ANNNI (axial next-nearest-neighbor Ising) model which has a Hamiltonian of the form 

The basic idea is to represent the energy of a given stacking sequence in terms of effective Ising parameters. The relative importance of first (/i) and second (J2) neighbor interactions gives rise to a competition that can stabilize long-period 

One of the dominant themes upon which much of our analysis has been predicated is the idea that a solid is populated by structures at many different scales. At the most fundamental level, a crystal may be thought of as an uninterrupted arrangement of atoms according to the simple decomposition 

As a reminder of the way interfaces, as key microstructural elements, can impact material response, we note one of the celebrated relations between a material s microstructure and its physical response, namely, the Hall-Petch relation which holds that the yield strength of a material scales as 

As is evidenced by fig. 9.38, there are a number of points of entry into a discussion of polycrystalline microstructures. In particular, fig. 9.38 shows that at the simplest level (frame (a)) we can consider bicrystal geometries. In keeping with 

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