Characteristic temperature

Experimental data of the effective transverse relaxation time are plotted in Fig. 17 as a function of the reciprocal temperature for different polymers. The molecular weight dependence for M Mc is due to free-volume effects. We will come back to this sort of molecular weight effect later in the review. 

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TPD Temperature-programmed desorption [171, 172] The surface is heated and chemisorbed species desorb at characteristic temperatures Characterization of surface sites and desorption kinetics... 

High-tempemture behaviour. Consider T much higher than a characteristic temperature like 0q or 0g. Since P /)co is then small compared to 1, one can expand the exponential to obtain... 

Alkali Metal Perchlorates. The anhydrous salts of the Group 1 (lA) or alkah metal perchlorates are isomorphous with one another as well as with ammonium perchlorate. Crystal stmctures have been determined by optical and x-ray methods (38). With the exception of lithium perchlorate, the compounds all exhibit dimorphism when undergoing transitions from rhombic to cubic forms at characteristic temperatures (33,34). Potassium perchlorate [7778-74-7] KCIO, the first such compound discovered, is used in pyrotechnics (qv) and has the highest percentage of oxygen (60.1%). 

Factors Affecting Performance. There are many factors that affect both the choice of a particular thermal treatment and its performance. Chief among these are waste characteristics, temperature, residence time, mixing or turbulence, and air supply. 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

These heat capacity approximations take no account of the quantal nature of atomic vibrations as discussed by Einstein and Debye. The Debye equation proposed a relationship for the heat capacity, the temperature dependence of which is related to a characteristic temperature, Oy, by a universal expression by making a simplified approximation to the vibrational spectimii of die... 

On the other hand, it is clear that in the classical regime, T> (T i is the crossover temperature for stepwise transfer), the transition should be step-wise and occur through one of the saddle points. Therefore, there should exist another characteristic temperature. r 2> above which there exist two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points atlT = T i. The existence of the second crossover temperature, 7, 2, for two-proton transfer has been noted by Dakhnovskii and Semenov [1989]. 

Boiling Point at 1 atm - Defined as the characteristic temperature of a liquid when its vapor pressure is 1 atm. As an example, when water is heated to 100°C (212°F), its vapor pressure rises to 1 atm and the liquid boils. The boiling point at 1 atm indicates whether the liquid will boil and become a gas at any particular temperature and at sea-level atmospheric pressure. 

Creep characteristics temperature range-creep apparent modulus... 

The characteristic temperatures of the martensitic transformation, as well as the (Af -Mf) temperature range were strongly influenced by the microstructure of the alloy. Applied predeformation lowered both and temperature range of transformation while the ageing at 510 K that followed decreased the width of the transformation. 

Returning now to proton transfers in methanol solution, we see that the family of curves in Fig. 44, calculated with S = 185.4 is very similar to those for aqueous solution. The curve for a = 0.0 passes through its maximum at the characteristic temperature 185.4°K. We now find that we can interpret the experimental results recorded in Table 16 for we see in Fig. 44 that curves drawn for values of a between —3 and —4 pass through zero near room temperature. The row of circles give values of... 

Deuteron Transfers in D20. As shown in Table 1 the characteristic temperature d for the dielectric constant of D20 is almost the same as for H20. The values of the dielectric constant of D20 are given with... 

Figure 12-11. Thickness dependence of the electron only j(V) characteristics at L=0.22, 0.31, and 0.37 pm. Solid lines have been calculated for an exponential distribution of electron traps of the total density 101 cnTJ and a characteristic temperature T,.= 1500 K (Ref. [41[).

Here, is the total density of traps and 7o is a characteristic temperature that accounts for the slope of the distribution. Results are gathered in Table 14-4. L both materials, a comparable characteristic temperature was found, while the total density of traps was ten times higher in 6T than in DH6T. 

Here, is an effective overlap parameter that characterizes the tunneling of chaiges from one site to the other (it has the same meaning as a in Eq. (14.60)). T0 is the characteristic temperature of the exponential distribution and a0 and Be are adjustable parameters connected to the percolation theory. Bc is the critical number of bonds reached at percolation onset. For a three-dimensional amorphous system, Bc rs 2.8. Note that the model predicts a power law dependence of the mobility with gate voltage. 

These ideas are best learned by using them yourself. Let us take an example from your own laboratory work. You have observed the heating of a variety of solid materials sulfur, wax, tin, lead, silver chloride, and copper. Each melts at a characteristic temperature. This fact led us to the generalization A solid melts to a liquid at a characteristic temperature. Your confidence in the generalization was bolstered by the additional information (communicated to you, not experienced) that this applies to hundreds of thousands of substances. ... 

Recent space-probe and earth-based spectroscopic studies of the planet Venus suggest how much remains to be learned about the other planets. Earlier estimates of the surface temperature of Venus placed it near 60°C. The more detailed studies show, however, that two characteristic temperatures can be identified, —40°C and 430°C. The lower temperature is attributed to light emitted front high altitude cloud tops. The higher temperature is likely to be the average surface temperature. 

Mention of the approach given by van Krevelen et al. [529,530] has already been made. Other methods based on points of inflection have been described but in some treatments it would seem probable that the integration constant has been omitted [559]. Doyle s treatment [533] avoids this error by using a characteristic temperature, 0 = T— Tm, where Tm is the temperature at which the reaction rate reaches a maximum. Doyle writes... 

Reactant Kinetic characteristics Temperature range (K) E (kj mole-1 Ref. l)... 

Early discussions, by Tammann and by Hedvall, considered the possible existence of a common characteristic (approximate) temperature for a solid at which chemical interactions with other reactants became detectable. For example [111], such a characteristic temperature for CaO, measured in various reactions with CuS04, Co3(P04)2, MgC03, and MnSi03, was found to be 788—838 K. Similarly, the onset of reaction of BaO with the sulphates of Mg, Ca, Sr, Co, Cu, and Zn occurred between 601 and 645 K. In the latter example, it has been shown that the fusion of Ba(OH)2 (an impurity not easily excluded from BaO) could contribute to the initiation of reaction. Eutectic formation during the reactions of BaCl2 with alkali metal sulphates... 

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