Translation domain boundaries

Regardless of whether the non-imaging of a species is due to preferential field evaporation or to preferential field ionization, the distinguisha-bility of alloy components in ordered alloys makes much easier the identification of lattice defects and of all types of domains, such as orientational and translational domains, and the discernment of order-disorder phase boundaries in ordered alloys, as well as facilitating the study of clustering and order-disorder phase transformation, etc.88 In most cases, image interpretations become self-obvious. For example in PtCo, which has the LI 0 structure, a Co layer can be distinguished from a... 

Fig. 10 A Translational and rotational (B) domain boundaries in a large-scale in-situ STM image of the hydrogen-honded dimer motif 111 of TMA on Au(lll)-(1 x l)/0.05 M H2SO4 in the presence of 3 mM TMA, Es = 0.33 V, ix = 111 pA. The arrow in A marks a characteristic kink site at a translational domain hoimdary. C High-resolution image of 111 on Au(lll)-(1 X 1), s = 0.30 V, ix = 200 pA. The primitive unit cell is indicated. D Proposed packing model of TMA in 111 [67]...

Fig. 37. (a) Translation domains in the B structure, in a plane parallel to (20T) 1, 2,3 are the different kinds of R atoms. Juxtaposition of two R atoms of the same kind is possible. Three translation domains and two anti-phase boundaries can occur in each crystal, (b) The two kinds of anti-phase boundaries they can be indexed s(132] and 3(132] which is equivalent to —1(132]. The same boundary between two regions is indexed in a different way in each region. 

As for the translation domains of B, they occur because the unit cell of the primitive lattice of B is three times larger than for A, so that each R atom of A can give an Rj or R2 or R3 atom of B, as seen previously. This gives three translation domains, separated by planar defects of translation vectors g[132] and -g[132] which are in this case antiphase boundaries. Each kind of epitaxy of B on A gives 6 x 3 = 18 equivalent domains. When we deal with B regions made of two twinned regions the number of domains is doubled. We can see that the study of the transformation domains is rather complicated for the B structure. It is probably... 

Figure 18 (a) Idealized model of the translation of the triple perovskite layers along die c axis, (b) Example of possible sites for additional oxygen at the domain boundary. 

Planar Interfaces. Planar interfaces are imaged as fringes parallel to the foil surface their characteristics depend on their geometric features. Translation interfaces (stacking faults, out-of-phase boundaries, etc.) separate two crystal parts related by a parallel translation R (Fig. 28 A), and domain boundaries separate domains that differ slightly in orientation (i.e.. for which the excitation errors are different As = S]-S2 (Fig, 28B) [154],... 

A) Translation interfaces with constant displacement vector R. B) Domain boundary between two regions for which the excitation error is slightly different the displacement R increases with increasing distance from the interface (the homologous diffraction vectors [/t and are slightly different Aff = S -9i)... 

The presence or absence of domain contrast across a fringe pattern helps to distinguish the two types of interface. If the two domains on either side of the interface exhibit the same brightness for all reflections, the fringes must be due to a translation interface they must exhibit a-char-acter. Domains exhibiting a difference in brightness are separated by a domain boundary and the fringes are of the -type. 

Many other examples of extended dislocations exist. Their further discussion will be deferred to the section on planar defects except for the case of superlattice dislocations. The ordered Cuj Au structure and antiphase domains have already been described in the introduction. While (a/2)<110> is a lattice translation vector in the face-centered cubic structure, it is not a lattice translation vector in ordered CujAu. Motion of a dislocation with b = ( /2)<110> in the ordered CujAu creates an antiphase domain boundary. Motion of a second dislocation through the structure with the same b restores the perfect order since a<110> is a lattice translation vector the structure of CujAu is simple cubic. Pairs of imperfect dislocations with, for example, b = (fl/2)[110] are thus expected. Such pairs, called superlattice dis-... 

When the physical geometry of the problem under consideration or the expected flow pattern has a cyclically repeating nature, cyclic or periodic boundary conditions can be used to reduce the size of the solution domain. Two types of cyclic boundary condition can be distinguished. The first is for rotationally periodic flow processes, where all the variables at corresponding periodic locations on the cyclic planes are the same. The second is for translationally periodic flow processes, where all the variables, except pressure, at corresponding periodic locations on the cyclic planes are the same. Examples of these two types are shown in Fig. 2.7. Such cyclic planes are in fact part of the solution domain (by the nature of their definitions) and no additional boundary conditions are required at these planes, except the one-to-one correspondence between the two cyclic planes. 

From an optical viewpoint, on the other hand, the difference between semiconductors and insulators lies in the value of Eg. The admitted boundary is usually set at 3 eV (see Appendix A for the energy units) and materials with Eg below this value are categorized as semiconductors, but crystals considered as semiconductors like the wurtzite forms of silicon carbide and gallium nitride have band gaps larger than 3 eV, and this value is somewhat arbitrary. The translation into the electrical resistivity domain depends on the value of Eg, and also on the effective mass of the electrons and holes, and on their mobilities. The solution is not unique moreover, the boundary is not clearly defined. Semi-insulating silicon carbide 4H polytype samples with reported room temperature resistivities of the order of 1010flcm could constitute the... 

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