Band widths temperature effects

The damping behavior of polymers can be altered to optimize either the temperature span covered or the damping effectiveness for particular temperatures. The area under the loss modulus temperature curve tends to be constant for some polymer combination, which has been expressed by the empirical "temperature band width law" of Oberst (2) ... 

The band contour depends not only on the temperature but also on Hund s coupling cases. Jungen (1980) has pointed out that the rotational structure becomes narrower as n increases due to a change from Hund s case (b) to case (d). This envelope-narrowing effect must not be construed as a variation of autoionization widths with effective quantum number n. Fortunately, doubleresonance techniques in the vacuum ultraviolet region are now able to isolate... 

It might be expected, in terms of ligand field theory, that dr-d transitions would be very sharp. The actual situation is illustrated in Figure I. Such absorption bands may sharpen somewhat and develop indications of vibrational structure at very low temperature, but the effect is typically not very dramatic [there are exceptions, as with Cr(CN) (8, 9)]. Ligand field theory does not specifically treat the matter of band width. It has been ascribed in a general way to perturbations of an electronic nature (such as Jahn-Teller effects) (2). 

Band intensities spectral, 249 selection rules, 244 Band widths spectral, 246 temperature effects, 248 Barium, pentakis(diacetamide)-stereochemistry, 99 Bathocuproine absorptiometry, 550 Bathophenanthroline absorptiometry, 550... 

Teliurium(rV) complexes liquid-liquid extraction, 546 Temperature effects spectra band widths, 248 Ten-coordinate compounds stereochemistry, 98... 

Fig. 47. Schematic quasiparticle density of states N (s) as obtained from the mean-field dispersion, eq. (112). They lead to a hybridization gap centered around , = and two peaks in N e) whose width and separation is also of order The Fermi level (0) is pinned in this region. The temperature dependence of the effective hybridization K, given by the function fl T) = rJ(T)/rJ(0, N = 2) as shown in the inset (Coleman 1987). IF is a slightly renormalized band width [a square DOS of width W has been used for the bare A/,(e)].

Here i/ (z) = d In T(z) /dz is the digamma function and W is the band width of the Lorentzian conduction electron density of states. Furthermore, T) is the effective temperature-dependent coupling strength of the longitudinal sound waves to quasiparticles. It may be written as... 

When vibrations of free and hydrogen bonded species are overlapped (most often due to rather high band width) the position of the maximum for the resulting envelope band depends on the equilibrium shift (like in NMR spectroscopy) as was observed e.g. for (triphos)Re(CO)2H HA ° or (triphos)Ru(CO)H2 HA. Otherwise, the proton donor concentration and temperature effect only the intensity ratio of and bands... 

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