Boundaries antiphase

For the phase stability analysis we follow the method given by Kanamori and Kakehashi of geometrical inequalities and compute the antiphase boundary energy defined by... 

Figure 1 (a) The nearest neighbor pair interactions and (b) antiphase boundary energies as functions of energy for Pdj,Vi j, alloys x=0.25, x = 0.5 and x = 0.75 ( from top to bottom). Vertical lines mark the Fermi energy for the three different concentrations. 

Fig. 5 illustrates a peculiar kinetic phenomenon which occurs when an initially disordered alloy is first annealed at temperature T corresponding to area b in Fig. 1 and then quenched to the final temperature T into the spinodal instability area d antiphase boundaries "replicate , generating approximately periodic patterns. This phenomenon reflects the presence of critical, fastest growing concentration waves under the spinodal instability (the Calm waves ). Lowering of the temperature to T < T results in lowering of the minority concentration minimum ("c-well ) within APB, while the expelled solute atoms build the c-bank adjacent to the well . Due to the... 

We studied vacancy segregation near interphase and antiphase boundaries using the MFA and PCA approaches described in Sec. 6 below. For the A-B alloy with vacancies, the stationary distribution of mean vacancy occupations =< > can be explicitly... 

In this Section we use Eqs. (2)-(10) to derive several relations for the free energy F ci of a stationary noiiuniform alloy. These relations can be used to study properties of interphase and antiphase boundaries, nucleation problems, etc. 

ROUGHENING OF AN ANTIPHASE BOUNDARY NEAR A BULK FIRST ORDER TRANSITION... 

The interatomic interaction is described by an EAM potential specifically developed for NiAl in the B2 structure [12]. Compared to the older potential [16], which was used in most of the previous atomistic studies, our new potential gives considerably higher antiphase boundary (APB) energies = 0.82 J/m, yj pg = 1.06 J/m in good agreement with the APB... 

Using the constructed potentials the y-surface for the (111) plane was calculated. (For more details see Girshick and Vitek 1995). T e lowest energy minimum on this surface corresponds to the ideal Llo structure. However, there are three different metastable stacking fault type defects on (111) the antiphase boundary (APB), the complex stacking fault (CSF) and the superlattice intrinsic stacking fault (SISF). The displacements... 

Antiphase boundary (APB) conservative vacancy segregation at Arrhenius plot Asymmetrical mixtures Atomic-sphere approximation (ASA) ASA-LSDA... 

The recommended Mg-Au phase diagram is that of ref. 3 amended by the addition of several new compounds close to MgAu3 they are a family of close-packed structures modulated both by antiphase boundaries of the superstructure and by a... 

Figure 1.1 Defects in crystalline solids (a) point defects (interstitials) (b) a linear defect (edge dislocation) (c) a planar defect (antiphase boundary) (d) a volume defect (precipitate) (e) unit cell (filled) of a structure containing point defects (vacancies) and (/) unit cell (filled) of a defect-free structure containing ordered vacancies. ...

If both these partial dislocations exist in the crystal, they will be linked by an antiphase boundary (Fig. 3.12d). 

For energetic reasons, internal boundaries are almost always planar in crystals. This is not a mle, though, and in some circumstances curved boundaries can occur. These are frequently found when the boundary is simply a variation in metal atom ordering of the type characterized by antiphase boundaries (see below). 

Antiphase boundaries (APBs) are displacement boundaries within a crystal. The crystallographic operator that generates an antiphase boundary in a crystal is a vector R parallel to the boundary, specifying the displacement of one part with respect to the other (Fig. 3.27), whereas the crystallographic operator that generates a twin is reflection (in the examples considered above). 

Similar antiphase boundaries form in metals with structures based upon a hexagonal close-packed array of metal atoms, such as magnesium. Condensation of vacancies upon one of the close-packed metal atom planes to form a vacancy loop, followed by subsequent collapse, will result in a hypothetical sequence. . ABABBABAB This arrangement will be unstable because of the juxtaposition... 

As in the case of twin planes, the antiphase relationship may affect only one part of the structure, for example, the cation substructure, while leaving the anion substructure unchanged. This is particularly common when the anion array can be considered to consist of a close-packed array of ions, which remains unchanged by the antiphase boundary (Fig. 3.28). 

Figure 3.27 Antiphase boundaries (a, b) antiphase boundaries are formed when one part of a crystal is displaced with respect to the other part by a vector parallel to the boundary.

Figure 3.28 Antiphase boundary affecting only one atom type in a crystal.

Because the vector describing an antiphase boundary always lies parallel to the boundary, there is never any composition change involved. 

Au is an excellent electrode material. It is inert in most electrochemical environments, and its surface chemistry is moderately well understood. It is not, however, the substrate of choice for the epitaxial formation of most compounds. One major problem with Au is that it is not well lattice matched with the compounds being deposited. There are cases where fortuitous lattice matches are found, such as with CdSe on Au(lll), where the Vs times the lattice constant of CdSe match up with three times the Au (Fig. 63B) [115,125]. However, there is still a 0.6% mismatch. A second problem has to do with formation of a compound on an elemental substrate (Fig. 65) [384-387]. Two types of problems are depicted in Fig. 65. In Fig. 65A the first element incompletely covers the surface, so that when an atomic layer of the second element is deposited, antiphase boundaries result on the surface between the domains. These boundaries may then propagate as the deposit grows. In Fig. 65b the presence of an atomically high step in the substrate is seen to also promote the formation of antiphase boundaries. The first atomic layer is seen to be complete in this case, but when an atomic layer of the second element is deposited on top, a boundary forms at the step edge. Both of the scenarios in Fig. 65 are avoided by use of a compound substrate. 

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