Root-mean-square surface

A hollow optical fiber (HOF) is a totally different type of optical fiber [42 16]. Figure 2.3A shows the structure of an HOF. An HOF is made of a glass tube with an inner coating of silver and a dielectric film, which enhances reflectivity. Matsuura et al. reported that the root mean square surface roughness of the silver film was 12 nm in their fabricated HOF [44]. 

Figure 20 AFM image (tapping mode, height image) of a dry cellulose film. The cellulose concentration was 0.5%w/w. The root-mean-square surface roughness was 5.0 nm (courtesy of M. Liu, University of Birmingham, UK).

Figure 4.10 Root-mean-squared surface roughness as a function of length scale and time, averaged over 8 locations, at one set of experimental conditions given in Table 4.2.

As mentioned previously, CTRs arise as a result of the abrupt termination of a crystal lattice, and the diffuse diffracted intensity connects Bragg points in reciprocal space. In this case, the scattering vector is normal to the surface, and as a result, this technique is very sensitive to surface and interface roughness but not to in-plane atomic correlations. Thus, it yields information that is complementary to that obtained by grazing incidence diffraction. The most important feature of CTR is the characteristic decay of the scattered intensity described by Eq. (38). For surfaces that are not perfectly terminated (i.e., rough) the intensity will decay faster than predicted by this equation, and this can be used as a measure of root-mean-square surface roughness. 

Figure 12-5. Center-line average and root-mean-square surface roughness, cencer-line average peak height is given by Ul dl...

In addition to deformations due to stress and stress-gradients, the surface roughness of the thin films used to fabricate optical M EM S components can also have an impact, as deposited polysilicon can have significant roughness. The root mean square surface roughness of polysilicon in the MUMPS process has been measured and found to be approximately 12nm. 

Surface roughness of various PEDOT PSS-types differing in their ratio of PEEXDT to PSS determined by atomic force microscopy. The layers were spin coated on ITO-coated glass (R = 1.8 nm) at a spin speed of 33 rps and baked at T = 200°C for 5 min on a hot plate. The root-mean-square surface roughness was calculated for an area of 1 pm square. 

For multi-dimensional potential energy surfaces a convenient measure of the gradient vector is the root-mean-square (RMS) gradient described by... 

On average, the reflectivity decays in proportion to 0 or since both interfaces are sharp. However, if either surfaces is rough, then marked deviations are seen and the reflectivity is damped by a factor of exp -2k o, where a is the root-mean-square roughness. Thus, the reflectivity is very sensitive to surface roughness and to concentration gradients at interfaces. 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

Nitrile rubbers, including fiber-reinforced varieties, are used both as radial shaft-seal materials and as molded packing for reciprocating shafts. They have excellent resistance to a considerable range of chemicals, with the exception of strong acids and alkalis, and are at the same time compatible with petroleum-based lubricants. Their working temperature range is from —1°C to 107°C (30°F to 225°F) continuously and up to 150°C (302°F) intermittently. When used on hard shafts with a surface finish of, at most, 0.00038 mm root mean square (RMS), they have an excellent resistance to abrasion. 

Another characteristic of a polymer surface is the surface structure and topography. With amorphous polymers it is possible to prepare very smooth and flat surfaces (see Sect. 2.4). One example is the PMIM-picture shown in Fig. 7a where the root-mean-square roughness is better than 0.8 ran. Similar values are obtained from XR-measurements of polymer surfaces [44, 61, 62], Those values compare quite well with observed roughnesses of low molecular weight materials. Thus for instance, the roughness of a water surface is determined by XR to 0.32 nm... 

Fig. 7a, b. PMIM-image of (a) a poly-p-bromostyrene surface [118], (b) a PS/polybutadiene diblock copolymer, PS-b-PB, at approximately 100 fold magnification. The lateral resolution is of the order of 1 pm while the height resolution is of the order of 0.6 nm. The root-mean-square roughness averaged over the area shown is 0.8 nm in (a) close to the resolution limit of the technique. It is much larger (10 nm) in (b) due to the formation of steps after annealing. The scale in z-direction in (a) and (b) is different by a factor of 7... 

The average value of the asymmetrical fluctuation is defined as the root mean square (rms) value. Using the Rayleigh theorem,94 the average value of the surface concentration fluctuation, for example, can be written as... 

The Si wafer industry has achieved very flat Si surfaces by electropolishing a root-mean-square (rms) roughness of 0.3 nm is customary, even for highly-doped degenerate Si. For a 100-nm Au layer deposited atop a 10-nm Ti adhesion layer atop an electropolished Si wafer, an rms roughness of 0.4 nm was measured by AFM [38]. 

For proteins the X-ray structures usually are not determined at high enough resolution to use anisotropic temperature factors. Average values for B in protein structures range from as low as a few A2 for well-ordered structures to 30 A2 for structures involving flexible surface loops. Using equation 3.6, one can calculate the root mean square displacement fu2 for a well-ordered protein structure at approximately 0.25 A (for B = 5 A2) and for a not-so-well-ordered structure at... 

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