Surface roughnesses

No manufactured surface, however it may appear to the naked eye, is absolutely perfect. The 

The measurement of roughness is taken as the average of the peaks and valleys over a given length. This roughness average is denoted by Rg and the values expressed in micrometers (urn). 

The Rg values specified should be selected from a range of preferred values contained in BS 1134 2010 shown in Table 5.4. The values are given as preferred in order to discourage 

The method of assessing surface roughness is either by stylus type instruments or by using surface roughness comparison specimens (Fig. 5.32). 

Small hand-held portable surface roughness testers (Fig. 5.33) are available which give a measurement of the average roughness of a surface The measurements are taken by a traversing drive unit carrying a diamond stylus 

Membrane surface roughness has a macroscopic and microscopic scale. Ghayeni et al. (1998) have reported large scratches on RO and NF membranes. While these large scale inhomogenities may cause attachment of large particles, we are interested in the microscopic roughness that determines the surface area available for adsorption and the thickness of the boundary layer. 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes 

A modification of Eq. X-31 has been made for fractal surfaces (see Section VII-4C). Contact angles near 90° on fractal surfaces are well described by [68] 

Roughness has important implications in wetting applications. While the eutectic solder, SnPb, normally forms a contact angle of 15-20° with copper, it completely wets the surface of rough electroplated copper and forms a fractal spreading front [69]. 

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

Microscopic roughness on solid surfaces can affect ellipso-metric measurements and thus the optical constants of a bulk material determined from the ellipsometric measurements. If thin surface films are studied by ellipsometric measurements that assume a smooth boundary between the substrate and film, the thickness and the optical constants thus obtained are in error if the substrate surface had microscopic roughness. The other side of 

Aspnes, Theeten, and Hottier made spectroscopic ellipsometry measurements of a surface with induced roughness, and examined calculations with various approximations based on the effective medium model represented by the following relation for the effective dielectric constant for a composite layer composed of materials 1 and 2 dispersed in a host medium  

FIGURE 7.48. Schematic illustration of macroscale roughness (a), microscale roughness (b), and atomic scale roughness (c). 

As an important parameter for surface quality, roughness is discussed in almost every article on cleaning and etching. However, in most cases it is treated as a quality control issue. As a result, the data on surface roughness reported in the literature for silicon surfaces are obtained under diverse conditions and are generally not comparable due to the fact that data are often reported without clear definition of the methods of determination and the area of sampling. 

Microroughness, or surface unevenness, at the atomic scale is always present on a real surface whether it is smooth or rough at the macroscopic scale. For a macro- 

TABLE 7.4. Roughness of Etched Silicon Surface in Various Solutions 

However, the effects of surface cleaning factors on microroughness reported in different studies are not consistent, probably due to the minute differences in the cleaning conditions and measurement procedure. 

In the preceding sections we have considered a well-defined surface structure typical for crystal faces prepared under ultra-high-vacuum (UHV) conditions. In practice, one more frequently deals with surfaces which are rough. These require a different description. 

One does not find two rough surfaces which are identical and even those which were obtained under the same processing parameters may differ from each other in an uncontrollable way. Such surfaces can be treated in a similar 

In many cases the height distribution can be well described by the Gaussian function 

An additional feature of a rough surface related to the length scale over which the height changes, is the correlation function 

It has the property that C(0) = cr. When r — ry increases, C(r — ry) decays to zero for a random surface with the rate depending on the distance over which points become uncorrelated. Often it is assumed that the correlation 

We start by discussing various means of incorporating surface roughness into the model systems in order to perform more realistic simulations. The means of subjecting the system to shear and load are discussed below. Thermostats are then discussed. Finally, we consider cases in which one can neglect the walls and treat the system as a bulk fluid. We finish with a discussion of different computational methodologies that are used in tribological simulations. 

The roughness of a surface can be characterized by averaging its height difference autocorrelation function over one or several statistically identical samples. The height difference autocorrelation function C2(Ar) is given by 

Various means of constructing self-similar surfaces are known.33 Some of them do not allow one to produce different realizations of surface profiles, for example, by making use of the Weierstrass function. These methods should be avoided in the current context because it would be difficult to make statistically meaningful statements without averaging over a set of statistically independent simulations. An appropriate method through which to construct self-similar surfaces i s to use a representation of the height profile h(x) via its Fourier transform h(q). 

In reciprocal space, self-similar surfaces described by Eqs. [8] and [9] are typically characterized by the spectrum S(q) defined as 

The full characterization of the stochastic properties of a surface requires consideration of higher order correlations of the height function. However, it can be difficult to construct surfaces in this manner without experimental input. As an approximation, it may be reasonable to neglect the higher order terms. 

No manufactured surface however it may appear to the naked eye is absolutely perfect. The degree of smoothness or roughness of a surface depends on the height and width of a series of peaks and valleys which give the surface a certain texture. This surface texture is characteristic of the method used to produce it. For example, surfaces produced by cutting tools have tool marks in well-defined directions controlled by the method of cutting, and equally spaced according to the feed rates used. 

The values specified should be selected from a range of preferred values contained in BS 1134-1 1988 shown in Table 5.4. The values are given as preferred in order to discourage unnecessary variation of the values expressed on drawings. Where a single value is stated on a drawing it is understood that work with any value from zero to the stated value is acceptable. 

Name three materials from which straightedges are made. 

In a systematic molecular study, the following observations have been made regarding the effect of surface roughness on no-slip boundary condition. 

For microchannel flow with atomically smooth walls, the no-slip condition at the walls is valid if the global Knudsen number Kng = A/h 0.01, where h is the channel height and d is the mean free path of gas. 

Wu and Cheng [26] derived a Nu correlation based on experimental results in trapezoidal Si microchannels. The surface roughness k is taken into account, in addition to geometric aspects  

The morphology of the sputtered aluminium film on a glass substrate (1000 nm thickness) before and after anodisation was studied by AFM microscopy. The surface roughness of both films is approximately 35 nm. The 

Barrier Aluminium Oxide Fiims as Gate Dielectrics for Organic Transistors 

The above results showed that an aluminium oxide film with the best dielectric properties was prepared in neutral electrolyte of 0.01 M tartaric acid at low current densities and formation voltages 30 V. 

The average capacitance and specific resistivity of the barrier aluminium oxide films are determined to be 430. .. 470nF/cm and 1.3. .. 2.4 10 Qcm, respectively. By using the anodisation factor of 1.2 nm/V for the films formed at low formation voltage, dielectric constants of 5.8. .. 6.4 are calculated from the measured capacitance values. The comparatively low dielectric constant is in agreement with the formation of an amorphous anodic aluminium oxide film as discussed above rather than a crystalline structure for which a higher dielec- 

The thickness and properties of the barrier aluminium oxide layer were investigated by eleetrochemieal impedanee speetroscopy. The total thickness of the films was determined by seanning electron microscopy of cross-sections. Then, the thiekness of eaeh layer within the aluminium oxide films was calculated. Formation eurrent density, formation voltage, anodization time, and sur-faee roughness of the substrate influenced the electrical and structural properties of the barrier aluminium oxide layer. 

Johnson and Dettre were able to show that of all possible positions of the foot of the drop inside a given groove, there was only one where the free energy 

FIGURE 2.11 A drop on an idealized rough surface. Reprinted with permission from Johnson and Dettre (1964). Copyright 1964 American Chemical Society. 

Besides the above three important features, there are many others, some of which are mentioned briefly below. One question that is often asked is if the horizontal force balance at the contact line leads to Young s equation, what happens to the normal component Ylv sin X It appears that such a component does exist and tends to distort the solid surface. Since in most cases the magnimde of this force is small and the modulii of elasticity of the solids are large, no significant distortion can be observed. (However, Bailey (1957) has actually observed the distortion of the solid near the contact line region of a mercury drop on a mica sheet 1 pim thick.) 

Liquid imbibition into the solid substrate can also alter the results (Yuk and Jhon, 1986, 1987). As discussed in Chapter 1, crystal structures affect the surface energies and hence the contact angles, even on low energy polymer surfaces (Fort, 1965). 

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For defect sizing by TOED, use of L waves involves a penalty in resolution of almost a factor of two at a given frequency because of difference in velocity as compared to shear waves and use of SV waves runs into difficulties because of the mode conversion problems. Further, problems due to couplant thickness variations, surface roughness affects, beam skewing and distortion problems in anisotropic welds can also be expected. On the contrary, SH waves are not affected... 

Adjustable coupling sensitivity aceording to surface roughness... 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

In the context of the structural perturbations at fluid-solid interfaces, it is interesting to investigate the viscosity of thin liquid films. Eaily work on thin-film viscosity by Deijaguin and co-workers used a blow off technique to cause a liquid film to thin. This work showed elevated viscosities for some materials [98] and thin film viscosities lower than the bulk for others [99, 100]. Some controversial issues were raised particularly regarding surface roughness and contact angles in the experiments [101-103]. Entirely different types of data on clays caused Low [104] to conclude that the viscosity of interlayer water in clays is greater than that of bulk water. 

The modification of the surface force apparatus (see Fig. VI-4) to measure viscosities between crossed mica cylinders has alleviated concerns about surface roughness. In dynamic mode, a slow, small-amplitude periodic oscillation was imposed on one of the cylinders such that the separation x varied by approximately 10% or less. In the limit of low shear rates, a simple equation defines the viscosity as a function of separation... 

In the case of powders formed by grinding and particles formed by aggregation, surface roughness can be so extreme that, curiously, it can be treated by mathematical geometry (see Mandelbrot, Ref. 102 also Ref. 103). We can... 

Strongin D R, Carrazza J, Bare S R and Somoqai G A 1987 The importance of Cj sites and surface roughness in the ammonia synthesis reaction over iron J. Catal. 103 213... 

Guenther K FI, Wierer P G and Bennett J M 1984 Surface roughness measurements of low-scatter mirrors and roughness standards Appl. Opt. 23 3820... 

For primary insulation or cable jackets, high production rates are achieved by extmding a tube of resin with a larger internal diameter than the base wke and a thicker wall than the final insulation. The tube is then drawn down to the desked size. An operating temperature of 315—400°C is preferred, depending on holdup time. The surface roughness caused by melt fracture determines the upper limit of production rates under specific extmsion conditions (76). Corrosion-resistant metals should be used for all parts of the extmsion equipment that come in contact with the molten polymer (77). 

Convection Heat Transfer. Convective heat transfer occurs when heat is transferred from a soHd surface to a moving fluid owing to the temperature difference between the soHd and fluid. Convective heat transfer depends on several factors, such as temperature difference between soHd and fluid, fluid velocity, fluid thermal conductivity, turbulence level of the moving fluid, surface roughness of the soHd surface, etc. Owing to the complex nature of convective heat transfer, experimental tests are often needed to determine the convective heat-transfer performance of a given system. Such experimental data are often presented in the form of dimensionless correlations. 

Optimum surface roughness usually is 0.05—0.5 pm a very smooth surface contains very Htde lubricant within its depressions, whereas rough peaks penetrate the lubricant to promote wear. Improved corrosion resistance may be obtained with a suitable subcoating surface conversion treatment or by inclusion of inhibitors in the coating. 

Surface Finish. As well as influencing the rate of metal removal, electrolytes also affect the quality of surface finish obtained in ECM. Depending on the metal being machined, some electrolytes leave an etched finish. This finish results from the nonspecular reflection of light from crystal faces electrochemicaHy dissolved at different rates. Sodium chloride electrolyte tends to produce a kind of etched, matte finish when used for steels and nickel aHoys. A typical surface roughness average, Ra is about 1 ]lni. 

Optical Properties. Owing to the high crystallinity of HDPE, most thick-waHed articles made from HDPE resins are opaque. Significant surface roughness can also add to the opacity. Thin HDPE film, in contrast, is translucent, but its transparency is significantly lower than that of LDPE or LLDPE film. The ultraviolet transmission limit of HDPE is around 230 nm. 

Particle Velocity on a. Surfa.ce. Smaller particles, those that are more irregular in shape and/or those that have a higher surface roughness, typically have a higher frictional drag on a hopper or chute surface. 

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