Cosines, Law

Lambert s cosine law Lambic beer Lamb modes Lambs Lamb wave Lamellae Lamepon Laminar flow Laminated fabrics Laminated glass... 

Metallization layers are generally deposited either by CVD or by physical vapor deposition methods such as evaporation (qv) or sputtering. In recent years sputter deposition has become the predominant technique for aluminum metallization. Energetic ions are used to bombard a target such as soHd aluminum to release atoms that subsequentiy condense on the desired substrate surface. The quaUty of the deposited layers depends on the cleanliness and efficiency of the vacuum systems used in the process. The mass deposited per unit area can be calculated using the cosine law of deposition ... 

Figure 12 An illustration of the cosine law distribution for frequency of (a) incident and (b) scattered molecules. The length of an arrow is proportional to the frequency of molecules incident or scattered at the angle indicated.

Figure 13 The contrast between (a) specular reflection and (b) cosine law scattering.

The angular dependence of the secondary ion intensity is expected to follow a simple cosine law, in particular for randomly oriented polycrystalline surfaces. The explanation for this is that upon impact the collision cascade takes care of an isotropic distribution of the energy through the sample. Hence the intensity of collision... 

Lambert-Beer law, 24 89. See also Beer-Lambert expression Lambert cosine law, 23 121 Lambs... 

The intensities of diffuse reflectance and fluorescence are both distributed over the solid angle according to Lambert s cosine-law. An ultraviolet-visible (UV/VIS)-... 

The radiance observed from a body depends on the elevation angle 0, which is the angle from the surface normal at which the measurement is made. If 8 is independent of 0, the radiance at 6, is given by Lambert s cosine law ... 

Electron Beam Evaporation. Most electron beam evaporation sources have a probability distribution that can be approximated by the cosine law ... 

Figure 6. Molecular-beam distribution for electron beam evaporation source obeying the cosine law.

Equation 24 typically appears in introductory texts on semiconductor processing (12). Despite the fact that the cosine law distribution is relatively flat, equation 24 shows that the relative incident flux or thickness uniformity falls off dramatically. For example, at l/H = 0.5, t(l)/tmax = 0.64, even though cos (< )) = 0.89, that is, the incident flux at a planar substrate has fallen to 64% of its maximum value. 

Since the observer views radiation from all parts of the extended area A, but at different angles a, Lambert s cosine law, which states that the intensity in a given direction will change in proportion to the cosine of the angle from the normal, has to be taken into account.) Equ. (10.45a) is equivalent to... 

Molecular flow occurs under conditions where Kn > 0.5 - the mean free path of the particles exceeds the smallest dimension of the flow channel. Under such conditions, with thin-walled orifices, for example, gas particles will pass through almost without collision. With pipes and ducts, however, this is not the case. Particularly for low Kn values (1-10) of the particles that enter the duct, some may reach the exit whilst the remainder return to the entrance after a number of collisions with the duct walls. What is important about such collisions is that, on collision with a wall, the particles are regarded as being immobilised for a very short time before emerging in any direction with equal probability (according to the cosine law). This describes diffuse or random scattering where no particular direction is favoured. To describe this process, the concept of transmission probability (Pr) was introduced by Clausing. 

The 6 123 angle at atom 2, which forms bonds with 1 and 3, is calculated from the cosine law... 

The transport of species along the chromatography column is assumed to be dependent only on the solid angle of the desorption direction and on the dimensions of the column. The solid angles of desorption from a plane surface into the vacuum are calculated according to Knudsen [19] assuming a cosine law ... 

In microporous materials where Knudsen diffusion prevails, De cannot be calculated by solving Fick s law. The use of a discrete particle simulation method such as dynamic MC is appropriate in such cases (Coppens and Malek, 2003 Zalc et al., 2003, 2004). In the Knudsen regime, relatively few gas molecules collide with each other compared with the number of collisions between molecules and pore walls. One of the fundamental assumptions of the Knudsen diffusion is that the direction in which a molecule rebounds from a pore wall is independent of the direction in which it approaches the wall, and is governed by the cosine law the probability d.v that a molecule leaves the surface in the solid angle dm forming an angle 0 with the normal to the surface is... 

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