Isotropic processes

Once the resist has been patterned, the selected regions of material not protected by photoresist are removed by specially designed etchants, creating the resonator pattern in the wafer. Several isotropic (etching occurs in all directions at the same etch rate) and anisotropic (directional) etching processes are available. Wet chemical etching is an isotropic process that... 

A similar formula describes relaxation in the ground state. However, in obtaining the Eqs. (5.22) and (5.23) we assumed that relaxation takes place in isotropic processes with respect to directions in space. In this case the relaxation matrix is diagonal and does not depend on Q, Q, i.e. = rK KK QQi [132, 134]. This is the case, e.g., of radia-... 

Equation was derived without approximations. It is noteworthy that these solutions do not couple tensorial components of different orders and that they confirm that rotational diffusion and cis—>trans thermal isomerization are isotropic processes that do not favor any spatial direction. In Section 3.4, I discuss, through the example of azobenzene, how Equation 3.11 can be used to study reorientation processes during cis—>trans thermal isomerization after the end of irradiation. The next subsection gives analytical expressions at the early-time evolution and steady-state of photo-orientation, for the full quantification of coupled photo-orientation and photoisomerization in A<- B photoisomerizable systems where B is unknown. 

Basis for the relation = 3D V. dfi /dP = V - also in an isotropic process, volume strain rate = 3 x linear strain rate. 

Transport inside the zeolite crystals occurs through diffusion inside the zeolite pores. Although it is known that diffusion in zeoHtes is generally anisotropic [40], the random orientation of the crystals inside the reactor justifies the approximation that micropore diffusion can be described as an isotropic process. A mass balance for the zeohte crystals yields for the adsorbed phase concentration Cx in the crystals... 

There is still another approach to clarify the representation in Fig. 9.6. For the isothermal process, pV = nRT, which is a constant. Thus, the process must move parallel to the ordinate. For the isentropic process, we may consider the parametric representation (.t = pV = nRT, y = TS), where S is constant. Even for an isotropic process, the ideal gas law holds. On resolving the parametric representation, y/x = S/R, which indicates that the extrapolated lines cut the origin. 

The growth of a polymer-poor phase by SD or NG is an isotropical process, which takes place as soon as the solvent-nonsolvent contents supply the thermodynamic condition for dembdng. To understand the macrovoid formation, a quite interesting explanation was provided by McKelvey and Koros [28] as de-... 

In addition to realize smaller patterns with the same cross-sectional area, a silicon nitride layer was deposited on the surface after anisotropic etching of the deep trenches. The polymer was then deposited, and the silicon was etched by the isotropic process (only SFs). The results are shown in Fig. 12c, d. In this case, the patterns with a minimum lateral width of 5 pm are realized. 

Figure 23.27 shows microsections of a plated through hole and a blind via in polyimide film.The plasma-etch procedure is basically an isotropic process, as indicated by the undercut seen on the through hole considering the actual dimensions, however, this undercut is too small to cause any plating problems. 

All the theory developed up to this point has been limited in the sense that translational motion (the continuum degree of freedom) has been restricted to one dimension. In this section we discuss the generalization of this to three dimensions for collision processes where space is isotropic (i.e., collisions in homogeneous phases, such as in a... 

M-type ferrites are mainly used as permanent magnet material. They have largely replaced the alnicos as preferred permanent magnet material, as a result of the lower material and processing costs. These ferrites were first introduced under the trade name Ferroxdure, the isotropic form in 1952 (22) and the anisotropic (crystal oriented) form in 1954 (23), and are widely available commercially under various trade names such as Oxid and Koerox. They cover about 55% of the world market of permanent magnet materials, corresponding to 1100 million U.S. doUars (1991), as weU as 55% of the U.S. market, at 300 million. 

Within the plane of a nonwoven material, the fibers may be either completely isotropic or there may be a preferred fiber orientation or alignment usually with respect to a machine or processing direction. In the case of thicker dry-laid nonwovens, fiber orientation may be randomized in the third dimension, ie, that dimension which is perpendicular to the plane of the fabric, by a process known as needle-punching (7). This process serves to bind the fibers in the nonwoven by mechanical interlocking. 

When drawdown is high, the film may be uniaxially oriented and the properties of the final film isotropic. In the manufacture of strapping tape this effect is accentuated. If the cast or quenched film is to be used to feed an orientation tine, additional attention must be given to the amorphous—crystalline nature of the film ia the draw processes so that maximum strength can be achieved and uniform gauge and optical quality maintained. Slot casting is used for the orientation of these resins, polyesters, polyamides, and a variety of others. 

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