Epitaxial relationships

The crystallographic requirement for tire formation of G-P zones is that the material within the zones shall have an epitaxial relationship with the maUix, and tlrus the eventual precipitate should have a similar unit cell size in one direction as tha maUix. In dre Al-Cu system, the f.c.c. structure of aluminium has a lattice parameter of 0.4014 nm, and the tetragonal CuAl2 compound has lattice parameters a — 0.4872 and b — 0.6063 nm respectively. 

Huse has pointed out that strain is to be expected in most thin-film systems, since even in the incommensurate case the intrinsic surface stress will strain the film (18). As a result, we conclude that incomplete wetting is expected for all crystalline films, except in the case where there is an epitaxial relationship between film and substrate and that the film is maintained at its bulk equilibrium lattice spacing. 

The extent to which small particles of Pd and Pt show evidence of oxidation after exposure to air Is also highly variable. It Is difficult to confirm the evidence of X-ray diffraction and EXAFS (25) that most particles In the 15-20A size range consist entirely of oxide. We have found that such particles usually give single crystal patterns attributable to the metals. There Is, however, considerable evidence that, in the case of Pt on alumina, the Pt crystals have a well-defined epitaxial relationship with the crystallites (20-50A diameter) of the nominally "amorphous" alumina substrate. 

Similar observations of epitaxial relationships have been observed for small crystals of Ru and Au on MgO (26). Figure 3(a)... 

However, a PS-fo-PI/PI blend shows direct L G transitions without appearance of the PL phase. The L microdomain is more favourable than the PL phase since the volume fraction of the PI block component and the symmetry of microdomains is increased by the addition of PI homopolymer. Hence, the PL phase may not be formed as an intermediate structure if relatively high molecular weight PI homopolymer is added. The latter is not able to effectively fill the corners of the Wigner-Seitz cells in consequence packing frustration cannot be released and the PL phase is not favoured [152]. In contrast, the addition of low molecular weight PI homopolymer to the minor component of the PL phase reduces the packing frustration imposed on the block copolymers and stabilizes it [153]. Hence, transition from the PL to the G phase indicates an epitaxial relationship between the two structures, while the direct transition between L and G yields a polydomain structure indicative of epitaxial mismatches in domain orientations [152]. 

In order to establish such a correlation, however, a statistical analysis of a very large number of patterns would be necessary. This is one possible area for application for the pattern recognition techniques mentioned above. For thin single crystal substrates, any epitaxial relationship of the metal particles to the support is clearly evidenced because the patterns are superimposed in nanodiffraction. A comparison can be made of the patterns obtained with the beam on and just off the particle. 

Another demonstration of the impact of upd on bulk deposition is provided by Pb and T1 deposition on Ag(lll) and Ag(lOO), where the orientation of the three-dimensional crystallites reflects the epitaxially relationship established by the upd layer [341]. For example, in the case of Pb deposition on Ag(lll) [395], a two-dimensional layer, Ag(lll)[110] compressed 2D hep Pb [110] R 4.5°, is initially formed followed by nucleation of a three-dimensional cluster having the same orientational relationship, Ag(lll)[110] 3DPb(lll)[110] R4.5°. 

The microscopy results characterizing the Cu/ZnO catalyst are in accord with EXAFS data representing the dynamic morphology changes (39—41), and they also provide an important additional insight On the basis of the lattice-resolved images, the nature of the exposed facets of the projected copper nanoclusters and the epitaxial relationship between the copper and ZnO can be identified. The majority of the copper nanocrystals appear to be in contact with the ZnO support with their (111) facets, as was also observed for copper particles prepared by vapor... 

It can also be observed from the schematic of the interactions shown in Fig. 10 that interaction zones that provide the possibility for sharing sulfur atoms by the two different phases exist. The structure of these interaction zones are crucial to understanding the interaction of sulfides with supports and promoter phases. The basal plane interaction with a second phase can be expected to be weak, but charge transfer might be expected if metal atoms are exposed on the second phase. Such an interaction would be similar to an intercalation interaction. The edge interaction will be much stronger, and here a transition zone with a possible epitaxial relationship between MoS2 and the second phase is expected. It is in this zone that we can expect to find the surface phases as described above (for example, the CoMoS phase). But in the cases described here, the surface phase becomes a line phase at the boundary between the two bulk phases. It is our belief that the detailed study of these phases represents a key area for future research in TMS catalysis. 

Thin films of carbides and nitrides of Group 6 metals were synthesized by reaction of a metal film with a reactive gas at high temperature and by reactive sputtering. The phases obtained depended on the experimental conditions. High temperatures metastable phases (/i-WC, v and 6-MoC]. ) were obtained by reactive sputter deposition of films. The carbon concentration in such films depended on the temperature of the substrate and on the pressure. In some cases ordered sublattices of carbon and nitrogen were observed and epitaxial relationships between the deposit and the substrate were studied. 

Fig. 5.18 SAXS patterns for copolymer PBOmPBOln3 showing that q is the same for the ordered melt and the metastable crystalline structure, suggesting an epitaxial relationship between these phases (Ryan el al. 1997).

Looking at the microstructure for samples above and below the maximum in coercivity, Fig. 21 shows that the FePt islands become interconnected above the coercivity maximum while below the maximum the islands are well separated. In the insets of Fig. 21(a) and (b) are the selected area diffraction (SAD) patterns for the samples. These indicate a single crystal FCT pattern with (001) orientation. Adjacent to the FePt diffraction spots are the (001) MgO single crystal spots indicating a slight mismatch in the lattice spacing of the two materials and a good epitaxial relationship between the two. 

Table 7.4 summarizes the out-of-plane and in-plane epitaxial relationships of ZnO films and sapphire substrates, the c-axis and a-axis lattice constants of ZnO, the ZnO full peak widths at half maximum (FWHM) of 20-to and uj scans, and the tilt of the ZnO structure along surface normal [47]. Because of the low intensity of the asymmetric (10l4) reflection, the a-lattice constant has larger uncertainty compared to the c-axis lattice constant. The epitaxial relationships correspond to the results of Ohtomo (see Table 1 in [22]). 

The knowledge of the structure and the morphology of the metal clusters is necessary if we want to understand the reaction kinetics at the atomic level. The more versatile technique to study the structure and the morphology of supported metal cluster is TEM. It can provide directly the structure and the epitaxial relationships on a collection of clusters in the diffraction mode. By High Resolution TEM it is possible to get this information at the level of one cluster [83]. By using high-resolution profile imaging it is possible to measure the lattice distortion at the interface [84], These capabilities are very unique for TEM. Such structural information can be obtained in situ by diffraction techniques but only on a collection of clusters [14, 29]. To illustrate the structural characterization by TEM we present the case of Pd clusters on MgO(l 0 0), which will be discussed in the next sections. 

Growth on (1120) A-plane sapphire yields an epitaxial relationship of (0001)g,n//(1 120)ai2O3 with inplane orientations of [1120]g.n//[0001]Ai2O3 and [1120]g,n//[1120]ai2O3 [2,4], This results in approximately a 30% lattice mismatch for both in-plane orientations by comparing the oxygen sublattice distance with the GaN lattice. 

Surface orientation of the sapphire substrate used for most growth of GaN and its alloys is the c-plane, i.e. (0001), but growth on other orientations such as the a-plane (11-20) and r-plane (1-102) is also conducted. The epitaxial relationship is summarised in TABLE 4 [23], There is a discussion on the relationship on the (01-12) surface in [23], The relationships on the (0001) surface are schematically illustrated in FIGURE 3 [24,25],... 

FIGURE 3 Schematic illustration of epitaxial relationship between GaN and sapphire (0001) (a) (b) shows the top view, GaN (closed circles) and sapphire (open circles) representing the rotation of the GaN basal plane by 30°. 

The preparation of mixed oxide catalysts from hy-droxycarbonates is not restricted to Ni/Al203, but also possible for several other systems. One example is the technically very important methanol catalyst based on CuO/ZnO. It can be prepared from a hydrotalcite-like precursor as well [57], but mostly a hydrozincite or au-richalcite precursor is used [58]. On reduction of auri-chalcite precursors, epitaxial relationships between the copper and the ZnO were observed. Such preferential formation of certain orientations is also the decisive factor in the last example discussed here. 

Fig. 62. Phi scan X-ray diffraction patterns of (a) the SrTi03 220) reflections, (b) the SrTi03 202 reflections, and (c) the LaA103 substrate 220 reflections, showing the epitaxial relationship between the SrTiO, film (deposited from Sr(hfac),(tetraglyme) and Ti(0-i-Pr)4) and the (100) LaAI03 substrate. (Redrawn from Ref. 323.)...

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