Transfer width

The most direct information obtained from LEED is the periodicity and intermediate range order within the transfer width of the surface under investigation. This can be gathered by visual inspection of the diffraction pattern and/or by relatively simple mathematical transformations of the spot profiles. 

Whereas the spot positions carry information about the size of the surface unit cell, the shapes and widths of the spots, i.e. the spot profiles, are influenced by the long range arrangement and order of the unit cells at the surface. If vertical displacements (steps, facets) of the surface unit cells are involved, the spot profiles change as a function of electron energy. If all surface unit cells are in the same plane (within the transfer width of the LEED optics), the spot profile is constant with energy. 

Structured (correlation). If the coherently ordered surface areas (islands, domains) are smaller than the transfer width of the LEED system and at the same vertical height, the width of these areas. Aw, is directly related to the width of the LEED spots in fe-space, Afen ... 

Contact Drying. Contact drying occurs when wet material contacts a warm surface in an indirect-heat dryer (15—18). A sphere resting on a flat heated surface is a simple model. The heat-transfer mechanisms across the gap between the surface and the sphere are conduction and radiation. Conduction heat transfer is calculated, approximately, by recognizing that the effective conductivity of a gas approaches 0, as the gap width approaches 0. The gas is no longer a continuum and the rarified gas effect is accounted for in a formula that also defines the conduction heat-transfer coefficient ... 

For vertical enclosed cells 10 in high and up to 2-in gap width, Landis and Yanowitz (Proc. Third Int. Heat Transfer Conf, Chicago, 1966, vol. II, p. 139) give... 

Data from tests employing nmltiple slots, with a correction calculated for slot width, were reported by Korger and Kizek [Tnt. J. Heat Mass Transfer, London, 9, 337 (1966)]. 

The width and shape of the energy loss peaks in HREELS are usually completely determined by the relatively poor instrumental resolution. This means that no information can be obtained from HREELS about such interesting chemical physics questions as vibrational energy transfer, since the influence of the time scale and mechanism of vibrational excitations at surfaces on the lifetimes, and therefore the line widths and shapes, is swamped. (Adsorbates on surfaces have intrinsic vibra-... 

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... 

Different values of will result if the integral limits (i.e., band width) or modulation transfer function in the integral change. All surface characterization instruments have a band width and modulation transfer function. If rms roughness values for the same surface obtained using different instruments are to be compared, optimally the band widths and modulation transfer functions would be the same they should at least be known. In the case of isotropic surface structure, the spatial frequencies p and q are identical, and a single spatial frequency (/>) or spatial wavelength d= /p) is used to describe the lateral dimension of structure of the sample. 

The modulation transfer function of the optical scatterometer is nearly unity. The spatial frequency band width, using 0.633-nm photons from a He-Ne laser, is typically 0.014—1.6 jim corresponding to a spatial wavelength band width 70— 0.633 pm. This corresponds to near normal sample illumination with a minimum... 

The significance of instrument band width and modulation transfer function was discussed in connection with Equation (3) to characterize the roughness of nominally smooth surfaces. The mechanical (stylus) profilometer has a nonlinear response, and, strictly speaking, has no modulation transfer function because of this. The smallest spatial wavelength which the instrument can resolve, 4nin> given in terms of the stylus radius rand the amplitude aoi the structure as... 

R, D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R, McNeil, and J. M. Bennett. Microstructure Characterization by Angle-Resolved Scatter and Comparison to Measurements Made by Other Techniques. To be published in AppL Opt. This work discusses the band width and modulation transfer function of the scatterometer, stylus profilometer, optical pro-filometer, and total integrated scattering systems, and gives results of mea suring several surhices using all techniques. 

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