Interface plane scheme

For tilt boundaries, the value of E can also be calculated if the plane of the boundary is specified in the coordinate systems for both adjoining grains. This method is called the interface-plane scheme (Wolfe and Lutsko, 1989). In a crystal, lattice planes are imaginary sets of planes that intersect the unit cell edges. The tilt and twist boundaries can be defined in terms of the Miller indices for each of the adjoining lattices and the twist angle, , of both plane stacks normal to the boundary plane, as follows ... 

Within this contimiiim approach Calm and Flilliard [48] have studied the universal properties of interfaces. While their elegant scheme is applicable to arbitrary free-energy fiinctionals with a square gradient fomi we illustrate it here for the important special case of the Ginzburg-Landau fomi. For an ideally planar mterface the profile depends only on the distance z from the interfacial plane. In mean field approximation, the profile m(z) minimizes the free-energy fiinctional (B3.6.11). This yields the Euler-Lagrange equation... 

We refer to the planes which close the box parallel to the boundary as the terminating planes. Between the terminating planes, the box includes one or more translational unit cells of the system parallel to the boundary. We therefore have to assume that the system is periodic parallel to the boundary, but this assumption is anyway necessary for practical schemes of calculation. The terminating planes should be far enough away from the interface to be locally in the undistorted bulk material. 

The study of the enantioselective hydrosilylation reaction was performed with a series of combined quantum mechanics/molecular mechanics (QM/MM) calculations [26, 30] within the computational scheme of ab initio (AIMD) (Car-Parrinello) [62] molecular dynamics. The AIMD approach has been described in a number of excellent reviews [63-66], AIMD as well as hybrid QM/MM-AIMD calculations [26, 47] were performed with the ab initio molecular dynamics program CPMD [67] based on a pseudopotential framework, a plane wave basis set, and periodic boundary conditions. We have recently developed an interface to the CPMD package in which the coupling with a molecular mechanics force field has been implemented [26, 68],... 

Polymers at interfaces are an important part of a large number of polymeric technological applications. The orientation, specific interactions, and higher order structures of amphiphilic molecules at a quasi two- dimensional plane form the basis of a variety of interesting phenomena [3-6], Scheme 3.1 shows a schematic representation of this behavior. 

Fig. 5. Illustration of the scheme of surface-tailored zeolite-water interface with adsorbing fluoride ions found in the region bound between planes 0 and IHP. The interaction leads to the formation of inner-sphere complexes of surface-tailored zeolite/fluoride. Sodium ions do not penetrate the IHP.

The force driving the coating flow is usually gravity and/or an externally applied pressure. One boundary surface of the liquid layer is its interface with the supporting fluid, the other a fluid interface. If the ambient fluid is a dynamically passive gas, the film has a free surface as it flows down inclined planes. Coating flows are free-surface flows and as such are difficult be solved mathematically. The free surface is an integral part of the solution. In the solution scheme, it must be guessed... 

Suppose that we want to find the distribution of temperature in the die and the hot body, which come into contact with each other during the process of die-forming. For simplicity, we assume that the die and the body are in contact along a plane, and heat transfer in this system proceeds in the direction normal to this plane. The scheme of mutual location of the die and the body in contact, and the qualitative distribution of temperatures in the interface region, are presented in Fig. 25. 

Figure 7.2a and b depicts the numbering scheme and the model for the molecular orientation of the 1-butyl-3-methylimidazolium cation, [C4mim] in ionic liquids at the air-liquid interface, respectively. SFG results show that the butyl chain of the cation extends towards the gas phase witii the imidazolium ring lying parallel to the surface plane. This configuration has been found to be consistent, regardless of the anion [32], for 1-butyl-3-methylimidazolium room-temperature ionic liquids, particularly where the anions are composed of Br , r, [PFg] ,... 

To simulate the spontaneous dynamic motion of cracks, we use a 2-D plane strain cohesive/volumetric finite element (CVFE) scheme that has shown great success in the simulation of various dynamic fracture events in brittle media (Xu and Needleman, 1994, Camacho and Ortiz, 1996, Geubelle and Baylor, 1998). As its name indicates, the numerical method is based on the combination of conventional (volumetric) elements used to model the mechanical response of the ceramic material and interface (cohesive) elements introduced to simulate the intergranular failure process. Figure 1 schematically illustrates the CVFE concept. The volumetric elements... 

Contact between dissimilar metals occurs frequently in electronic devices, components, and systems. Among the many metallization schemes found in thin film and integrated circuits are Ti/TiN/Al/TiN (see Section 9.4.1) and Ti/Pd/Au. Gold wires bonded to aluminum pads or to alumi-num/copper interfaces in devices are also commonplace. In equipment cabinets, copper ground planes may be connected to the steel frame. Dissimilar metals in electrical contact in the presence of an electrolyte solution may lead to galvanic corrosion in which the more active metal will corrode, while the more noble metal is protected from corrosion. Ranking of metals in terms of their relative activity is known as the galvanic series (Jones, 1992). 

Figure 9.1 Scheme of the system under study in the case of a plane interface. 

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