Nickel shows some activity at low temperatures approximately equivalent to the activity of rhodium, but normal catalytic behavior with a constant activation energy is observed only at substantially higher temperatures similar to those necessary for activity with palladium. [Pg.259]

Eq. (9.4) is a low temperature approximation but is easily modified to include the Fermi distribution of the electrons. [Pg.323]

We follow this with a low temperature approximation to the integral over the well s phase space population. The resulting equilibrium constant is [Pg.203]

Line spectrum calculated in the low temperature approximation, valid at both 4 °K and 1.2 °K. There are no free parameters the lack of sharp lines in the observed spectra is attributed to spin relaxation (After Lang and Marshall, Ref. 103)) [Pg.16]

Fig. 4.1 The zero point energy or low temperature approximation As temperature drops and u increases above u 4 the harmonic oscillator partition function Q (Harm. Osc.) is better and better approximated by the zero point energy term, exp(—u/2). For a typical CH stretching frequency, v = 3000 cm-1, u 4 at 1050 K and it is reasonable to use the ZPE approximation for that frequency at temperatures below 1000 k |

We once again carry out the integral in the low temperature approximation and find [Pg.208]

Thus a plot of C /r vs. should yield a straight line in the low-temperature approximation. [Pg.138]

Sulfur ylides containing only alkyl, vinyl or aryl groups are very unstable and must generally be generated and used at low temperatures (approximately -70°C). On the other hand, ylides containing carbonyl, cyano, nitro or sulfonyl [Pg.187]

In the limit that g —> 1, the equilibrium distributions are more delocalized and the low temperature approximation may not be well justified. [Pg.203]

An alternate approach to the analysis of isotope effects at large values of u is the low temperature approximation. As the temperature tends to zero, the function (Equation 1) approaches [Pg.197]

Hydrothermal synthesis of a-alumina has been well studied. Since the hydro-thermal reaction of aluminum compound yields boehmite at relatively low temperatures (approximately 200°C), transformation of boehmite was examined and it was reported that more than 10 hours is required for complete conversion into a-alumina, even with a reaction at 445°C in a 0.1 N NaOH solution and in the presence of seed crystals. On the other hand, under glycothermal conditions, a-alumina is formed at 285°C for 4 h. The equilibrium point between diaspore (another polymorph of AlOOH) and a-alumina under the saturated vapor pressure of water was determined to be 360°C. However, near the equilibrium point, the transformation rate is very sluggish, and only a small conversion of diaspore is observed. Therefore complete conversion of diaspore into a-alumina requires a much higher temperature. Since boehmite is slightly less stable than diaspore, the hypothetical equilibrium point between boehmite and a-alumina would be lower than that for diaspore-alumina. However, a-alumina would not be formed by a hydrothermal reaction at such a low temperature as has been achieved in the glycothermal reaction. [Pg.303]

The time independent product of exponentials in Eq. (A2.70) becomes the exponential of a sum over all modes. Thus Eq. (A2.57) becomes for the individual normal mode, excited to its n harmonic, in its low temperature approximation. [Pg.557]

The Debye-Waller factor always decreases the observed intensity in neutron spectroscopy and significant experimental efforts are made to reduce its impact. To follow this more closely we retrace our steps and, from Eq. (A2.70), write the full expression for 2W, instead of the low temperature approximation used in Eq.(A2.80). [Pg.559]

© 2019 chempedia.info