Profile angles

Fig. 3. determined from eraek-length data at 150 h as a funetion of resolved vertieal and horizontal eomponent of the surfaee profile angle [52J. 

In one of the first attempts to produce a systematic procedure for the identification of compounds based upon crystal morphology, Shead proposed to use profile angles as the analytical parameter [6,7]. This method was based on the use of sublimation to obtain thin crystal plates of simple geometrical forms. 

Fig. 3. Giscc determined from crack-length data at ISO h as a function of resolved vertical and horizontal component of the surface profile angle [52J.

Profile angle n. An angle, not necessarily an interfacial angle, used to describe a crystal. This angle is observed when the crystal is lying on a face. For example, a cube shows 90° an octahedron 60° or 120°. 

For the realization of complex geometries it may be necessary to use a CCM press which is equipped with pressing units in vertical and in horizontal direction. Alternatively, the pressure application can be realized with a complex tool design. However, there will always be an inhomogeneous pressure distribution inside the tool. This is affected by the profile angles which are mostly different to the direction of the applied pressure. 

Table 2. Relative errors made in the computation of the depth profile, the width, and the parameter c for the cracks from Fig.4a, Fig.4b, and Fig.4c and orientation angles C>=0°, =30 and 0=45°.

Equation 11-30 may be integrated to obtain the profile of a meniscus against a vertical plate the integrated form is given in Ref. 53. Calculate the meniscus profile for water at 20°C for (a) the case where water wets the plate and (b) the case where the contact angle is 40°. For (b) obtain from your plot the value of h, and compare with that calculated from Eq. 11-28. [Hint Obtain from 11-15.]... 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

As an extension of Problem 11, integrate a second time to obtain the equation for the meniscus profile in the Neumann method. Plot this profile as y/a versus x/a, where y is the vertical elevation of a point on the meniscus (above the flat liquid surface), x is the distance of the point from the slide, and a is the capillary constant. (All meniscus profiles, regardless of contact angle, can be located on this plot.)... 

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

STM and AFM profiles distort the shape of a particle because the side of the tip rides up on the particle. This effect can be corrected for. Consider, say, a spherical gold particle on a smooth surface. The sphere may be truncated, that is, the center may be a distance q above the surface, where q < r, the radius of the sphere. Assume the tip to be a cone of cone angle a. The observed profile in the vertical plane containing the center of the sphere will be a rounded hump of base width 2d and height h. Calculate q and r for the case where a - 32° and d and h are 275 nm and 300 nm, respectively. Note Chapter XVI, Ref. 133a. Can you show how to obtain the relevent equation ... 

With disk diameters above 5.25 in., all parameters, eg, water absorption and thermal expansion, become more critical which aggravates the expansion or warp of disks. If in the future disk rotation speeds have to be increased significantly to boost data transfer rates, higher demands will be placed on warp (tilt angle) and modulus to avoid creeping (ie, irreversible elongation in radial direction). A survey of the requirement profile for the substrate material of optical disks is given in Table 5 (182,186,187,189). 

Diffusivities of various elements ate determined experimentally. Dopant profiles can be determined. The junction depth can be measured by chemically staining an angle-lapped sample with an HE/HNO mixture. The -type region of the junction stains darker than the n-ty e region. The sheet resistivity can also be measured using a four-point probe measurement. These two techniques ate used for process monitoring. 

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