Anti-phase boundary

In Figure 1(b) we have plotted the negative of anti-phase boundary energy e = — ( as a function of band filling for Pd Vi- with x = 0.25, 0.5 and 0.75. The number of zeros is in agreement with the arguments based on moments (there has to be at least four zeros). ... 

Anti-phase boundaries are interfaces leading a phase shift in the scattering amplitudes between two domains. They may be distinguished from those where the two domains differ in orientation. 

BWG and anti-phase boundary energies. The bond-breaking method first described by Flinn (I960) allows an estimate to be made for the structural component of anti-phase boundary (APB) energies. As good agreement can be obtained... 

Fig. 2.11 Structure in the vicinity of the shear plane for the shear operation (/ifcZ) [011] of a TiOj-type structure, (a) (121)5[0il] (b) (132) [0il] (c) (011)2[0il] the structure obtained after only operation (3) on TiO2 without the elimination of an oxygen-only plane. The structure is called an APB (anti phase boundary) or twin structure, and is similar to the shear structure of (110)j[li0] of ReOj (see Fig. 2.6(a)). Note the atomic arrangement in the zones framed by dotted lines (see also Fig. 2.113).

A discussion of types of inter-layer bonding, layer types and layer matching is followed by a consideration of disorder in such structures, as well as symmetry aspects and some growth mechanisms. Structures transitional between this type of structure and commensurate structures, i.e. structures which are really non-commensurate layers joined at anti-phase boundaries which restore commensurability, are then considered and classified with a detailed consideration of known examples from inorganic chemistry and mineralogy. Finally, some broad, general conclusions are enumerated. 

T and H components are the same as in the yttrium oxyfluorides etc., but now they occur as strips intergrown in each layer the entire structure is divided by anti-phase boundaries perpendicular to the layers, with a slip vector R equal to half the unit-cell vector in the layer-stacking direction. These structures (often slightly monoclinic ) are CC types, with finite incommensiurate portions. They will be considered more fully in Chap. 6 below. Meanwhile, we will simply point out that anti-phase-boundary structures of this sort are strictly limited to ternaries with two cations and one anion. The related ternaries considered earlier in this section - those containing one cation and two anions - do not have these boundaries they are truly non-commensurate. This difference we take to be significant. 

On the other hand, if such flexibility is absent the layer misfit may be compensated by rolling up the double layers, producing a cylindrical (CC) structure on an atomic scale, as in chrysotile An alternative possibility is the undulatory double layers of, for example, antigorite where the misfit-compensating curvature changes its sense at regular intervals as a result of layer-switching [anti-phase boundaries, cf. (Zr,Nb)Oj, Sects. 4.4 and 6]. 

In the three-step process, the thickness of the SiC layer was monitored as a function of time in the carburization and BEN steps, and its thickness reached a maximum at 3-5 min of the BEN treatment [267]. A mesh structure was also observed. The hillock (protrusion) structure was extended along [110] or [110], and hence the boundaries between the hillock structures were considered to be anti-phase boundaries between the anti-phase domains of 3-SiC. 

The most obvious heterogeneous mechanism follows from our discussion in Section 2 where we showed that shear planes could be related to metal interstitial defects, but that a pre-existing anti-phase boundary (APB) is required. Thus shear-plane formation may occur by metal interstitial capture at pre-exist ng APBs (Bursill et More particularly, it is proposed that metal interstitial ions produced by... 

Minerals are often riddled with microstructures when observed under the electron microscope. Although the observation and classification of microstructures such as twin boundaries, anti-phase boundaries, exsolution lamellae etc., has been a longstanding activity of mineralogists and crystallographers it has only been very recently that we started to understand the enormous importance of microstructures for the physical and chemical behaviour of minerals. 

Brace AD, Taylor W, Murray AF (1980) Precursor order and Raman scattering near displacive phase transitions. J Phys C Solid State Phys 13 483-504 Brace A, Cowley RA (1981) Structural phase transitions. Taylor and Francis, London Chrosch J, Bismayer U, Salje EKH (1997) Anti-phase boundaries and phase transitions in titanite an X-ray diffraction study. Am Mineral 82 677-681... 

The PdCu3 particles were obtained with the a ordered structure, (type AuCu3), after annealing at 500 °C in H2 for 5 days. Particles smaller than 20 nm are found in two main epitaxial orientations (001) and (110) on MgO (001), with a continuous structure and stacking faults. Larger particles had periodic anti-phase boundaries as observed in the bulk, with a modulation of 4 unit cells, corresponding to an atomic composition between 24.5 and 27% of Pd... 

Particles with the continuous ordered structure of PdCu3, with stacking faults, are obtained after a long annealing. Their are cap-shaped and mainly oriented (100) and (110) on MgO. For larger sizes (> 10-20 imi), long period superstructures with anti phase boundaries are obtained, with the same spacing as in the bulk alloy for equivalent concentrations. 

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. 

Fig. 39. Anti-phase boundary ending on a (313) twin, with plane of paper parallel to (201). The twinning is the same on each side of the anti-phase boundary if a step of one reticular plane occurs on the twin.

In a model [197]. the superstructure is assumed to consist of identical slabs of basic structure with thickness D limited by planes normal to e . Usually the slab thickness is equal to an integer number n of unit cell parameters a of the basic structure i.e.. D = na, but this need not be the case. Successive. slabs are separated by planar interfaces (stacking faults, anti-phase boundaries, discom-mensuration walls, etc.) with a di.splacement vector R and a unit normal e . 

Fig. 6.44. Formation of an anti-phase boundary during slip of a dislocation through an ordered lattice structure containing two elements...

On the other hand, to explain the magnetisation and a reduced Ms in n-type metallic double perovskite system, Sr2 xCaa FeMo06 (0 < x < 2), Goodenough and Dass invoked the idea of anti-phase boundaries (APB). 

Figure 5.11 Schematic of an anti-phase boundary in an (001) plane of Sr2FeMoOg. Reprinted with permission from Goodenough and Dass, 2009 [82]. Copyright (2000)...

The y precipitates are equiaxed when small, then non-equiaxed as they grow and eventually become plate-like shaped. The y precipitates transform into plates far more readily than y precipitates, which is attributed to the absence of anti-phase boundaries in the Y phase. Despite the non-equiaxed shapes, (r)3 depends approximately linearly on aging time t. The experiments show that the kinetics of coarsening of y precipitates is much slower than that in the reverse system. This is consistent with behavior expected from diffusion in the two phases. 

D. W. Pashley and A. E. B. Presland, The observation of anti-phase boundaries during the transition from CuAu I to CuAu II, J. Inst. Met. 87 (1958-59). 

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