Epitaxy relations

The structural form of brookite (TiO ) is expected to be bounded by 210 and 111, both being F faces by PBC analysis, but the actual growth form observed is platy Habitus bounded by largely developed 100, which is an S face. The misfit ratio between the PBC on the (0110) face of quartz and that on (100) ofbrookite is the smallest among any misfit ratios between the two crystal species. From this, it was found that the platy Habitus ofbrookite arose because quartz adsorbed in an epitaxial relation on 100 ofbrookite, thus diminishing thegrowthratekof(lOO) [30]. 

The corresponding relation between the host and guest crystals when evaluating the misfit ratio may be a one-to-one lattice relation in the same direction (a X b to a xb axes), or in different axial directions (aX b axes versus aX <110> axes), or on the basis of one unit cell versus a few unit cell sizes (see Fig. 7.13). Royer s misfit ratio is generally a two-dimensional correspondence, but Hartman [13] extended this relation to the misfit ratio in PBCs (see Section 4.2), which is a one-dimensional correspondence. Royer s epitaxial relations correspond to a relation between the F faces of the host and guest crystals containing more than two PBCs, and an epitaxial relation is not allowed between S faces or K faces. In Hartman s analysis, rela-... 

The freedom of the dangling bonds on the crystal surface increases with increasing temperature. As a result, there is a critical temperature below which an epitaxial relation cannot be realized. This temperature is called the epitaxial temperature, and it depends on interface orientation. If the misfit ratio is small, the epitaxial temperature is low if the misfit ratio is large, the epitaxial temperature is high, and an epitaxial relation will not be achieved unless the temperature is higher than the epitaxial temperature. 

Another element controlling the epitaxial relation is the state of the dangling bonds on the surface of the host crystal. When the dangling bonds are no longer active owing to adsorbed molecules, the epitaxial relation is not realized. This is why host surfaces cleaved in air have different epitaxial temperatures from those cleaved in a vacuum. 

The following three mechanisms are suggested for the growth of a guest crystal in an epitaxial relation on the surface of low-index faces of a host crystal. 

Mechanism forming a thin film in an epitaxial relation through a monolayer spreading parallel to the interface. This is called the Frank-van der Merve mechanism. 

In addition to epitaxial relations, characteristic textures appear due to the intergrowth of crystals of two different species in a certain crystallographic relation. Various terms have been used in the mineralogical field to describe textures, as summarized in Table 7.2 [15], [16]. Observations of descriptive and taxonomy type have been accumulated, since they show the origin of rocks and ores, but understanding the mechanism of their formation still remains a future subject of research. 

Coaxial intergrowth is a paragenetic relation that describes crystals of two different species growing with a common axis the misfit ratios between the two crystals in the direction of the common axis are small, without exception. The formation of coaxial intergrowth can be understood to be one crystal conjunct to the other in an epitaxial relation, where both continue to grow. If a liquid of eutectic A-B component is solidified from one side (unidirectional solidification), crystals of the two phases A and B precipitate in dotted, columnar or lamellar (with common axis) form, and show unique textures for unidirectional solidification. This is a well known phenomenon in metallurgy. 

Studying the crystallographic orientation and determining epitaxy relations... 

If two crystals are placed side by side, it is possible to define vector relations that express the characteristic crystallographic directions of one of the ctystals in a set of coordinates defined by the cell of the other crystal. These are referred to as epitaxy relations. By extrapolation, when the grains that comprise a polyctystalUne film all have virtually the same orientation, it is possible to define ctystallographic axes specific to this orientation and to find the relation between these axes and those, for example, of the single ctystal on which the film is deposited. If the film and the substrate share the same ctystal nature, we are dealing with homoepitaxy, otherwise, it is referred to as heteroepitaxy. Epitaxy relations are three-dimensional and therefore they are usually written as follows ... 

We will illustrate this quantitative characterization method of the microstructure with a study [BOU 03] conducted on a sample comprised of a lithium niobate film which is which is about 500 nm thick, deposited on a sapphire substrate cut parallel to the (0006) planes. This film was produced by laser ablation and is epitaxial so as to have the (0006) planes of LiNbOs parallel to the interface and the in-plane orientation is characterized by two variables. The epitaxy relations can be written ... 

These observations are assumed to result for the epitaxial relations between platinum and the lanthanum-alumina support. 

The possibility of growing epitaxial zeolite films on micrometer-sized, structurally different zeolite support crystals was explored with the aim to develop polyfunctional zeolite materials with spatially separated adsorptive and/or catalytic functions. Support crystals of one zeolite type were added to a hydrogel for crystallization of a second zeolite type. Tuning of the crystallization conditions led to the formation of a MAZ-on-EMT overgrowth material consisting of an oriented, continuous film of MAZ crystallites completely covering the surface of the EMT support crystals. The epitaxial relations between the two phases were established using HRTEM and SAED. 

During the mineralization process of calcium carbonate induced by a 6-sheet template made of a phospholipid-peptide conjugate, it was also shown that the orientations of the crystals were related to geometrical matching lattice and stereochemical complementarity between the functional groups of the template and the positions of the ions in the nucleation plane. However, the nucleation of different crystal faces can be achieved depending on the ability of the template to adapt to the structure of the inorganic phase, without the need for an epitaxial relation between the two components. ... 

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