Impurities location

Figure 2. The nearest-neighbor concurrence C(l,2) for different values of the anisotropy parameter y = 1, 0.7, 0.3, 0 with an impurity located at = 3 as a function of the reduced coupling constant A = 7/2/i, where J is the exchange interaction constant and h is the strength of the external magnetic field. The curves correspond to different values of the impurity strength a = 0,0.5,1,1.5 with system size iV = 201.

An impurity located at a lattice site introduces strain that, in general, tends to reduce stability. Impurities may become mobile at elevated temperature and may accumulate within the distorted material that constitutes dislocations, internal surfaces, etc. (see below), or even as included or separate particles. 

The effects exerted by surface impurities, and by impurities located in the adjacent-to-surface layer at a depth exceeding the Debye length, on electrical conductivity and the electron work function will be different. 

Interstitial defects result from an impurity located at an interstitial site or one of the lattice atoms being in an interstitial position instead of being at its lattice position. Interstitial refers to locations between atoms in a lattice structure. 

Fig. 4.11 Transition from HPL to double-gyroid in films of PFS18-b-PLA48 2 a Top view onto double-gyroid crystals surrounded by HPL which were nucleated by an impurity located in the center, b Closeup of the framed area of (a) showing a cross-section of the interface between the double-gyroid and HPL. c Top view onto a multiple double-gyroid crystals growing from a nucleation point forming a sunflower, d Magnified view of the flamed area of (c)...

Substitution of a dopant for an element of the perfect crystal leads to a distortion of the perfect lattice from which electrons can scatter. If that substitutional dopant is ionized, the electric field of that ion adds to the scattering. Impurities located at interstitial sites (i.e., between atoms in the normal lattice sites) also disrupt the perfect crystal and lead to scattering sites. Crystal defects (e.g., a missing atom) disrupt the perfect crystal and appears as a scattering site in the free space seen by the electron. In useful semiconductor crystals, the density of such scattering sites is small relative to the density of sihcon atoms. As a result, removal of the silicon atoms through use of the effective mass leaves a somewhat sparsely populated space of scattering sites. 

Therefore, in order to study the electron structure of Be-containing solid solutions a large number of calculations have been performed by Ivanovsky and coworkers (Ivanovsky and Anisimov, 1988 Ivanovsky et al, 1988c) for the TiC-Be and NbC-Be systems using the self-consistent LMTO-GF method. Different possible positions of impurity centres in the bulk crystals have been considered. LDOSs of isolated Be impurities located at the sites of C (1) or metal (2) sublattices and the DOS of the initial carbides are shown in Fig. 5.13. 

The surface states considered so far are related to the clean and well-ordered surface of a crystal and they are called therefore intrinsic surface states. Defects or impurities located at a surface can form electronic states whose wave functions are localized in their vicinity and thus at the surface too. They are called extrinsic surface states. Such states do not possess a 2D translational symmetry and an electron occupying such a state cannot propagate along the surface. 

Because there are a large number of sites along the dislocation line, a large number of impurity atoms can be accommodated in the dislocation core. The interaction energy of an impurity located at position r and angle 0 with respect to a pure edge dislocation, where the impurity has a size AR different from the matrix atom radius R can be shown to be ... 

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