Lattice continuity

In a crystal containing twin defects, the crystal lattices continue across the twin boundaries without a break. Another similar defect, the antiphase defect, is formed by a shift of the crystal by half a unit cell along the antiphase boundary. This defect can also contribute to strong image contrast as shown in Figure 10.3b. 

Fig. 1. The principal low-index surfaces of bcc, fee and hep crystals. For the hep lattice the ideal packing with da = 2 6/3 is assumed. Two stacking sequences of the hcp(llOO) plane are shown. In some cases the atoms are numbered according to the sequence of atomic planes. In the case of bcc(l 10) L stands for lattice and S for surface site on the bcc(l 11) surface F labels the faulted site in contrast to the lattice continuation L on fcc(l 11) the lattice site is labeled fee and the faulted site hep.

Solid solutions are formed when a solute is nonstoichiometrically incorporated into the crystal lattice of the solvent (Moore and Wildfong 2(X)9). Solid solutions can be classitied according to the solubility of the solute in the crystal lattice (continuous vs. discontinuous) or according to the way in which the solute molecules are distributed. In general, the term solid solution refers to systems that contain a crystalline carrier. 

Refine the averaged model by Monte Carlo simulated annealing of an intermediate resolution off-lattice continuous model. 

Adsorption sites are also labeled in a conventional way, e.g. fee-hollow site for adsorption at an fcc-lattice-continuation site above an fcc(lll) surface. Figures are provided to clarify the more common adsorption sites and local adsorption geometries. 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

The logic that leads us to this last result also limits the applicability of the ensuing derivation. Applying the fraction of total lattice sites vacant to the immediate vicinity of the first segment makes the model descriptive of a relatively concentrated solution. This is somewhat novel in itself, since theories of solutions more commonly assume dilute conditions. More to the point, the model is unrealistic for dilute solutions where the site occupancy within the domain of a dissolved polymer coil is greater than that for the solution as a whole. We shall return to a model more appropriate for dilute solutions below. For now we continue with the case of the more concentrated solution, realizing... 

The lattice model that served as the basis for calculating ASj in the last section continues to characterize the Flory-Huggins theory in the development of an expression for AHj . Specifically, we are concerned with the change in enthalpy which occurs when one species is replaced by another in adjacent lattice sites. The situation can be represented in the notation of a chemical reaction ... 

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