Critical thickness

Examination of oven-aged samples has demonstrated that substantial degradation is limited to the outer surface (34), ie, the oxidation process is diffusion limited. Consistent with this conclusion is the observation that oxidation rates are dependent on sample thickness (32). Impact property measurements by high speed puncture tests have shown that the critical thickness of the degraded layer at which surface fracture changes from ductile to brittle is about 0.2 mm. Removal of the degraded layer restores ductiHty (34). Effects of embrittled surface thickness on impact have been studied using ABS coated with styrene—acrylonitrile copolymer (35). 

The pressure filter with tubular elements has also been used as a thickener, when the cake, backwashed by intermittent reverse flow, is redispersed by an agitator at the bottom of the vessel and discharged continuously as a slurry. In some cases the filter cake builds up to a critical thickness and then falls away without bio whack. 

Following the initial protective period, under certain conditions of temperature, alloy and gas composition , the oxidation goes through a transitional stage into breakaway. Several authors have reported that breakaway oxidation is initiated once the scale reaches a critical thickness or weight gain and only occurs below an initially protective duplex layer . 

No description of the useless region is necessary in light of the discussion that has been given of the critical thickness dc-... 

Sodium tungstate solutions have provided data for the testing of Equation 7-6. These data, obtained in the authors laboratory, show that absorption effects can be calculated for a series of solutions in which the calculated critical thickness (Equation 6-8) decreases from 0.4 cm for water, the solvent, to only 0.1 cm for the most concentrated solution tested. In order not to confuse the issue here, the details of the cor-... 

The first extensive1 study of x-ray excitation (1.17) as a method of producing x-ray spectra for analytical purposes was carried out by Glocker and Schreiber,17 who not only treated absorption effects very thoroughly and introduced the concept of critical thickness, but who... 

The differences between x-ray and electron excitation must obviously stem from differences in the interaction of x-rays (1.11) and of electrons (1.4) with matter. Electrons are retarded rather quickly when they strike a sample, and they lose much of their energy in classical collision processes (4.1). Because electrons transfer their energy so rapidly, the critical thickness (Equation 6-8) for electron excitation is very much less than we saw it to be for x-ray excitation a.calculation based on experiments on a variety of materials53 gives 1CT3 cm (105 A) as a good value for the depth to which 50-kv electrons penetrate aluminum, and bears out the previous statement. Because the energy of every electron decreases as it penetrates, the x-ray excited by any electron will be of... 

Attenuation of the analytical lines could be counterbalanced by increased line intensity at the sample. For a sample of greater than critical thickness, high intensity in an analytical line is favored by... 

Improper sampling can introduce errors originating at the surface (8.7) because x-ray emission spectrography operates only on a surface layer of critical thickness (6.4). Powders are particularly subject to errors that result from segregation and lack of uniformity in general (7.8, 7.15). Nonuniform residues from the evaporation of solutions can be troublesome. 

The samples have two important characteristics that facilitate these very difficult determinations First, the matrix (all of the sample but the element being determined) is essentially organic matter containing only traces of heavy metals. Second, the samples are of less than critical thickness (6.4). As a consequence, absorption and enhancement effects (7.3) are absent and the scattered background is relatively weak (7.4). 

Thickness, critical, see Critical thickness film, determination, see Film thickness, determination variation of line intensity with, 153-158... 

When hrjk < 1, thin layers of lagging increase the heat loss and it is necessary to exceed the critical thickness given by equation 9.266 before any benefit is obtained from the lagging. 

SRB, a diverse group of anaerobic bacteria isolated from a variety of environments, use sulfate in the absence of oxygen as the terminal electron acceptor in respiration. During biofilm formation, if the aerobic respiration rate within a biofilm is greater than the oxygen diffusion rate, the metal/biofilm interface can become anaerobic and provide a niche for sulfide production by SRB. The critical thickness of the biofilm required to produce anaerobie conditions depends on the availability of oxygen and the rate of respiration. The corrosion rate of iron and copper alloys in the presence of hydrogen sulfide is accelerated by the formation of iron sulfide minerals that stimulate the cathodic reaction. 

For a nonthinning, unbounded film, Vrij (10) showed via a thermodynamic analysis (i.e., a surface energy minimization) that when 3II/3h is greater than zero the film is unstable. Thus, in Figure 4 the critical thickness limit for metastable films,... 

Some materials have a small lattice mismatch with the substrate, less then 1%, and can adopt the same lattice constants at the interface. This, however, still results in some strain, which builds until released, forming slip dislocations etc.. The thickness at which defects occur is of considerable interest and referred to as the critical thickness [14, 15]. Strain can be minimized by adjusting the lattice constants of the... 

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