Integral lattices

S. Wolf, Silicon Processing for the VLSI Era (Volume 2, Process Integration, Lattice Press, Sunset Beach, CA, 1990) p. 186. 

In order to construct the reducible representation of the translations or of the librations, at a particular point in the Brillouin zone (for a particular wave vector q), we must investigate the transformations of the basis functions under the pertinent symmetry operations. As basis functions we use the translationally symmetrized functions which already belong to irreducible representations of the group of pure translations by integral lattice vectors. The basis functions were given in Eq. (2.11). They are... 

Crystal growth is a diffusion and integration process, modified by the effect of the solid surfaces on which it occurs (Figure 5.3). Solute molecules/ions reach the growing faces of a crystal by diffusion through the liquid phase. At the surface, they must become organized into the space lattice through an... 

Statistical mechanics methods such as Cluster Variation Method (CVM) designed for working with lattice statics are based on the assumption that atoms sit on lattice points. We extend the conventional CVM [1] and present a method of taking into account continuous displacement of atoms from their reference lattice points. The basic idea is to treat an atom which is displaced by r from its reference lattice point as a species designated by r. Then the summation over the species in the conventional CVM changes into an integral over r. An example of the 1-D case was done successfully before [2]. The similar treatments have also been done for... 

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