High temperature behavior

Let us now compare the general population numbers of Equation 11.27 for two levels. The first, level k, is taken to be some level with energy less than the chemical potential. The second, level m, has an energy greater than the chemical potential. From Equation 11.27, we obtain the ratio 

As temperature increases, the exponentials in the numerator and the denominator approach zero. Therefore, 

This result is independent of d, and therefore, fermions and bosons are distributed in the same way as the hypothetical indistinguishable boltzons at high temperatures. We conclude that Boltzmann statistics are appropriate in that case. 

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There are differences in the high temperature behavior. While oxaziridines almost always isomerize to acid amides, a similar reaction of diaziridines, which should lead to amidines, has not been observed. Sensitivity towards bases, often encountered in oxaziridines, is observed only in some special substituted diaziridines. The tendency of some classes of oxaziridines to transfer the nitrogen function also lacks in the diaziridine field. On homolytic reactions of diaziridines there are only a few observations. 

A similar expansion can be written in the vicinity of Q = 0. Path integration amounts to the Gaussian integration over the Q , whereas the integration over the unstable mode Qq is understood as described in section 3.3. In that section we also justified the correction factor (f) = T /T = X l2n which should multiply the Im F result in order to reproduce the correct high-temperature behavior. Direct use of the Im F formula finally yields... 

Fig. 11. High-temperature behavior of the solubility s of hydrogen in silicon and of its diffusion coefficient D. Squares are from the measurements of Van Wieringen and Warmholtz (1956) on H2, fitted by the full lines (80) and (81), respectively. Crosses are measurements of s using 3H2, by Ichimiya and Furuichi (1968), fitted by the dotted line(82). 

Pezzotti, G., Tanaka, I., Okamoto, T., Si3N4/SiC-whisker composites without sintering aids III, High-temperature behavior, J. Am. Ceram. Soc., 74(2), 1991, 326-332. 

Since relatively little is known about the high-temperature behavior of the rare-earth sulfates, a summary covering all of them is given first, followed by information about the individual salts. 

Fig. 11. Temperature dependence of A S° for liquids (1) n-propane, (2) n-butane, (3) i-butane, (4) pentane, (5) hexane, (6) cyclohexane, (7) benzene, (8) toluene, and (9) ethylbenzene. High temperature behavior of heat capacity change described by exponential scaling [see Eq. (15) and p. 216].

The formation of benzyne from chlorobenzene at 690° is further substantiated by the presence of a small amount, 0 5 on the same scale, of biphenylene among the products. The high-temperature behavior of chlorobenzene thus parallels somewhat its behavior at ordinary tempera-... 

Plasticized sulfur is a hot-melt adhesive and fulfills more of these requirements than any presently available, commercial glue. However, modified sulfur cannot be applied with present production equipment, and sulfur lacks many important, frequently required qualifications, among them fire resistance and resistance to heat. Thus, substantially more work would be necessary to make elemental sulfur a viable commercial bulk glue. However, we found that elemental sulfur can be polymerized in situ with formaldehyde resins (5,33), and this yields bonds which have good mechanical properties, moisture resistance, and promising high-temperature behavior. Such glues can be handled with presently available equipment and presently common process conditions (35,36). These materials are described separately (33). 

Figure 49. The mobility of the excess electrons in various SnCh samples determined by means of the Hall effect and conductivity. The high temperature behavior points to acoustic phonon scattering. Both samples differ in purity. According to Ref..155. (Reprinted from H. J. van Daal, Polar Optical-Mode Scattering of Electrons in SnC>2. , Solid State Commun. 6, 5-9. Copyright 1968 with permission from Elsevier.)...

Now let us discuss the applicability of the results obtained for other models of semiflexible macromolecules. It is clear that the qualitative form of the phase diagram does not depend on the model adopted. The low-temperature behavior of the phase diagram is independent of the flexibility distribution along the chain contour as well, since at low temperatures the two coexisting phases are very dilute, nearly ideal solution and the dense phase composed of practically completely stretched chains. The high temperature behavior is also universal (see Sect. 3.2). So, some unessential dependence of the parameters of the phase diagram on the chosen polymer chain model (with the same p) can be expected only in the intermediate temperature range, i.e. in the vicinity of the triple point. 

The high temperature behaviors of Ba7MnFe6F34 (Fig. 4) and Ba7FeFe6F34 are extremely similar in the high temperature limit, both follow a Curie-Weiss law % = C/ T — 8) with Curie constants of 30.5 and 31.9, and 8 parameters of —152.0 and —163.5 K respectively. Their xT=i T) curves show around 60 K the minimum expected for ferrimagnetic systems and, at lower temperatures, a divergence when approaching Tc-... 

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