Coherent boundaries

Twins are commonly found or formed in all types of crystals. Their boundaries are of two general types coherent and incoherent. The coherent boundaries are usually also symmetric, so they offer little resistance to dislocation motion. However, the incoherent ones are not symmetric and may resist dislocation motion considerably. 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

This synergetic effect can be explained by the presence of coherent boundaries whose first consequence is to lower the potential barrier for electron transfer between the n-semiconductor TiOo and 7 0. The resulting elastic strains on both sides of the and the transmission of this becomes rutile. When this last transformation is complete, the interface vanishes and the reaction stops. 

Al O as it is by the presence of coherent boundaries with Ti02 anatase (Figure 8). 

Therefore, coherent boundaries should be present between each shell of the catalyst particle, with the following consequences for the catalysis namely, setting up of a metastable state of the catalyst, and a reduction in the energy barrier for electron transfer by the redox mechanism proposed for MCM catalysts (98-100) ... 

Figure 16.2 A boundary where compositions are disturbed by jumping the temperature, (a) The initial state, a perfectly coherent boundary, (b) The phase relations, (c) Profiles of composition very soon after a jump in temperature, (d) Profiles of composition at a longer time after the jump in temperature.

In contrast to XRD methods that may introduce sample preparation artifacts (see Jiang et al. 1997 Li et al. 1998), TEM integrated with selected-area electron diffraction (SAED) and energy dispersive spectrometry (analytical electron microscopy, AEM) measurements, provides direct, in situ observations on rock microtextures, crystallite size distributions, lattice imperfections of crystallites and interstratification (see the extensive reviews by Peacor 1992 and Merriman and Peacor 1999). TEM observations on selected portions of thinned (ion-milled) whole rock samples contradict the fundamental particle theory of Nadeau et al. (1984a,b,c summarized recently by Nadeau 1998). The observations show that phyllosilicate domains with interstratified structures form coherent boundaries, and therefore, MacEwan-type crystallites do exist in quasi-undisturbed rocks (Peacor 1998). In addition, AEM studies may provide reliable mineral-chemical data on the phases devoid of any external or internal impurities. 

The surface of adult cestodes forms a coherent boundary between the fluid compartment of the fibrous interstitium and the environment. The tegument contains several structurally distinct components (Fig. 12.1). 

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