Interface coherent

Dehydration reactions are typically both endothermic and reversible. Reported kinetic characteristics for water release show various a—time relationships and rate control has been ascribed to either interface reactions or to diffusion processes. Where water elimination occurs at an interface, this may be characterized by (i) rapid, and perhaps complete, initial nucleation on some or all surfaces [212,213], followed by advance of the coherent interface thus generated, (ii) nucleation at specific surface sites [208], perhaps maintained during reaction [426], followed by growth or (iii) (exceptionally) water elimination at existing crystal surfaces without growth [62]. 

R.B. Schwarz, A.G. Khachaturyan, Thermodynamics of open two-phase systems with coherent interfaces, Phys. Rev. Lett. 74 (1995) 2523-2526. 

Gurtin M., 1993, The dynamics of solid-solid phase transitions 1. Coherent interfaces, Rat. Mech. 

The first important point is that satellites in incommensurate positions are observed in all superconductive bismuth cuprates. They are directed along the [100] or [010] directions and can appear along two perpendicular directions due to the existence of domains at 90°, characterized by a perfect coherent interface (Figure 30a). 

O Keeffe (1991Z)) has used bond valences to model the coherent interface that occurs between the semiconductors Si and MSi2 with M = Ni or Co (27139). Although these systems contain Si-Si bonds and therefore do not obey the assumptions of the bond valence model (condition 3.2), the mathematical formalism of the model still works because of the high symmetry. As both Si-Si and Si-Ni bonds are found in NiSi2, the cubic structure is strained (cf. BaTiOs in Section 13.3.2) and this strain affects the structure of the interface. Of the six possible interfacial structures examined, the two with the lowest BSI eqn (12.1) are those that are believed to occur in NiSi2 and CoSi2 respectively, and in both cases the strain introduced at the interface is correctly predicted. 

The inflexion in curves (A) and ( ) occurs after a decomposition of about 30% of substance. The plots of the acceleratory period are approximately parabolic. The mechanism of the decomposition probably consists of nucleation of sub-grains at the edges and progression of the reaction into the grains with a non-coherent interface. 

Stress builds up at a coherent interface between two phases, a and / , which have a slight lattice mismatch. For a sufficiently large misfit (or a large enough interfacial area), misfit dislocations (= localized stresses) become energetically more favorable than the coherency stress whereby a semicoherent interface will form. The lattice plane matching will be almost perfect except in the immediate neighborhood of the misfit dislocation. Usually, misfits exist in more than one dimension. Sets (/) of nonparallel misfit dislocations occur at distances... 

Let us extend these relations to the equally important case of coherent interfaces, lb do so, it is necessary to include the strain energy of the a and p phases. To this end, we formulate the thermodynamic relations in terms of SE s (A , V) [W.C. Johnson, H. Schmalzried (1992)]. Under the condition of coherency, the number of lattice sites is conserved. Instead of Eqn. (10.7), we obtain... 

In order to determine the equilibrium state of systems including coherent interfaces, the conditions of thermal, chemical, and mechanical equilibrium have to be met, that is, for the first two... 

The simplest case occurs when the a-phase and /3-phase crystals have different compositions but still match almost exactly in all three dimensions. The critical nucleus can then form with a coherent interface and is therefore of relatively low energy.1 Also, any strain energy will be small. This condition is met during the precipitation of Ag-rich precipitates in a A1 + 4 at. % Ag matrix [8] and Co-rich precipitates in a Cu + 1 at. % Co matrix [9] where the precipitates are coherent and essentially spherical in shape. 

In a further operation, these stresses can be eliminated by introducing an array of dislocations in the interface as in Fig. B.7c. The resulting interface consists of patches of coherent interface separated by dislocations. The cuts and displacements necessary to introduce the dislocations destroy the overall coherence of the interface, which is therefore considered to be semicoherent with respect to the reference... 

It is often useful to describe the dislocation content of coherent and semicoherent interfaces in terms of another framework which employs coherency dislocations and anticoherency dislocations. The basic idea is illustrated in Fig. B.8, which shows the same two boundaries shown previously in Fig. B.76 and c. The coherency dislocations possess a stress field equivalent to the long-range coherency stresses associated with the coherent interface. They are not real dislocations in the... 

For crystalline-crystalline interfaces we further discriminate between homophase and heterophase interfaces. At a homophase interface, composition and lattice type are identical on both sides, only the relative orientation of the lattices differ. At a heterophase interface two phases with different composition or/and Bravias lattice structure meet. Heterophase interfaces are further classified according to the degree of atomic matching. If the atomic lattice is continuous across the interface, we talk about a fully coherent interface. At a semicoherent interface, the lattices only partially fit. This is compensated for by periodic dislocations. At an incoherent interface there is no matching of lattice structure across the interface. 

In another study, Shashkov and Seidman (1996) used atom-probe field-ion microscopy to examine the adsorption of Ag dissolved in solid Cu at semi-coherent interfaces between Cu-Ag and MgO precipitates obtained by internal oxidation of... 

These models are the preferred geometry in electronic structure methods originating from solid state physics. Periodic boundary conditions are applied to a unit cell representing the M/C interface. Therefore, slab models are restricted to coherent interfaces, which means that periodicity parallel to the interface is present — this corresponds to a locked in interface structure. Of course, the periodicity may have a long repetition length. 

Having settled on some metal and ceramic surfaces that we think will match, we must determine the relative orientation and translation of these surfaces with respect to each other. Certain directions in the metal and ceramic are likely to be aligned for a stable interface. There will often be multiple minima, corresponding to different lock-in possibilities for the coherent interface. Lastly, the size and shape of the interface unit cell needs to be determined, if we assume a coherent interface, which is implicit if periodic boundary conditions are applied. A realistic unit cell will of course correspond to low strain on both the metal and ceramic side. 

Barium styphnate can be prepared either as a monohydrate or a trihydrate and the kinetics of tiie dehydrations and the decompositions of both forms have been studied by Tompkins and Young [139]. The decomposition of the dehydrated monohydrate (542 to 581 K) exhibited a sigmoid curve which initially fitted the power law and the induction period was very short E = 153 kJ mol ). Reaction at a non-coherent interface proceeded along grain boundaries and into the sub-grains. 

Their Tammann temperatures are low. As a consequence, these lattices are in a metastable state, near these temperatures. If two structures are closely related, as we shall see in the next section, the two solids will be able to form either coherent interfaces or solid solutions. In these cases, "hybrid crystals, in which microdomains of both phases coexist, can be formed according to UBBELOHDE s theory (43), which considers strain energy E and internal surface energy ri (44). The free enthalpy of a domain (1) in a matrix of structure (2) is given by ... 

---