Translational line

If both AEa and A b equal zero, we have a purely translational line of the supermolecule. These can be found at frequencies comparable to the width Av, that is in the microwave and far-infrared regions of the spectrum. 

Molecular systems. Translational spectra like the ones shown for rare gas mixtures exist also for molecular gases and mixtures involving molecular gases. However, in that case, the rotational induced band will in general affect the appearance of the translational line since it appears generally at nearly the same frequencies. 

Molecules rotate. As a consequence, the induced dipole p(t) as function of time is likely to show a modulation by the rotational frequencies which, when Fourier transformed, leads to the appearance of induced rotational lines or bands. These occur at low frequencies in the microwave and far infrared region and are in general superimposed with the translational line, especially at higher temperatures. Only molecules that have a large rotational constant, e.g., H2 (Bo 60 cm-1), reveal substantial parts of the translational spectra, see Figs. 3.10 and 3.12, pp. 82 and 85, as examples. 

Similar results were also obtained for argon-krypton mixtures [252]. Apart from the low-frequency region of the intercollisional dip, the variation of the translational line shape is rather subtle reduced absorption profiles of a number of rare gas mixtures at near-liquid densities (up to 750 amagat) have been proposed which ignore these variations totally [252],... 

A translational line like the one seen above in rare gas mixtures is relatively weak but discernible in pure hydrogen at low frequencies (<230 cm-1), Fig. 3.10. However, if a(v)/[l —exp (—hcv/kT)] is plotted instead of a(v), the line at zero frequency is prominent, Fig. 3.11 the 6o(l) line that corresponds to an orientational transition of ortho-H2. Other absorption lines are prominent, Fig. 3.10. Especially at low temperatures, strong but diffuse So(0) and So(l) lines appear near the rotational transition frequencies at 354 and 587 cm-1, respectively. These rotational transitions of H2 are, of course, well known from Raman studies and correspond to J = 0 -> 2 and J = 1 — 3 transitions J designates the rotational quantum number. These transitions are infrared inactive in the isolated molecule. At higher temperatures, rotational lines So(J) with J > 1 are also discernible these may be seen more clearly in mixtures of hydrogen with the heavier rare gases, see for example Fig. 3.14 below. 

A rotation of the H2 molecule through 180° creates an identical electric field. In other words, for every full rotation of a H2 molecule, the dipole induced in the collisional partner X oscillates twice through the full cycle. Quadrupole induced lines occur, therefore, at twice the (classical) rotation frequencies, or with selection rules J — J + 2, like rotational Raman lines of linear molecules. Orientational transitions (J — J AM 0) occur at zero frequency and make up the translational line. Besides multipole induction of the lowest-order multipole moments consistent with... 

The binary spectra of hydrogen-helium mixtures, Fig. 3.12, differ from the spectra of pure hydrogen, Fig. 3.10, especially by the translational line (familiar from the spectra of rare gas mixtures) whose intensity increases strongly with increasing temperature. Moreover, the rotational line intensities when normalized by the product of helium and hydrogen... 

The H2-He spectra may also be decomposed into translational and rotational line profiles, Fig. 3.13, similarly as this was sketched above for hydrogen, Fig. 3.11. In contrast to the decomposition for H2-H2 pairs, for the translational line of H2-He we must assume different profiles for the translational profile on the one hand, and the rotational profiles on the other [123]. The translational line of H2-He arises mainly from overlap induction which is of a much shorter range than the quadrupolar induction which shapes the rotational lines. As a consequence, at any given temperature, the translational line is much broader than the rotational lines. In the case of H2-He, it is also much more intense. 

Measurements of enhancement spectra exist for several gases and mixtures. Figure 3.14 shows the collision-induced absorption spectra of H2-X pairs, with X = He, Ne, Ar, Kr, Xe [213]. The translational lines were omitted for technical reasons. Because the spectra are recorded at room temperature, the So(J) lines of H2 are quite diffuse. Most prominent is the So(l) line at 587 cm-1, but lines at other rotational transition frequencies of H2 are also discernible, for example So(0) at 354 cm-1, So(2) at 815 cm-1, and So(3) at 1035 cm-1, especially for the massive pairs. 

Figure A3.4.5. Simple models for effeetive eollision eross seetions a hard sphere without tlireshold (dotted line) hard sphere with tlireshold (dashed line) and hyperbolie threshold (full eiirve). is the (translational) eollision energy and is the threshold energy. Oq is the hard sphere eollision eross seetion. The dashed-dotted eurve is of the generalized type E > q) Oq (1 - q/ j) exp[(l - j/ q)/(<3 q)] with the parameter...

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

This result, when substituted into the expressions for C(t), yields expressions identieal to those given for the three eases treated above with one modifieation. The translational motion average need no longer be eonsidered in eaeh C(t) instead, the earlier expressions for C(t) must eaeh be multiplied by a faetor exp(- co2t2kT/(2me2)) that embodies the translationally averaged Doppler shift. The speetral line shape funetion I(co) ean then be obtained for eaeh C(t) by simply Fourier transforming ... 

The reaction path shows how Xe and Clj react with electrons initially to form Xe cations. These react with Clj or Cl- to give electronically excited-state molecules XeCl, which emit light to return to ground-state XeCI. The latter are not stable and immediately dissociate to give xenon and chlorine. In such gas lasers, translational motion of the excited-state XeCl gives rise to some Doppler shifting in the laser light, so the emission line is not as sharp as it is in solid-state lasers. 

In plotting on WeibuU paper, a downward concave plot implies a non2ero minimum life. Values for S < can be selected by trial and error. When they are subtracted from each /, a relatively straight line is produced. This essentially translates the three-parameter WeibuU distribution back to a two-parameter distribution. 

Values extracted and in some cases rounded off from ttose cited in RaLinovict (ed.), Theimophysical Propeities of Neon, Ai gon, Kiypton and Xenon, Standards Press, Moscow, 1976. Ttis source contains values for tte compressed state for pressures up to 1000 bar, etc. t = triple point. Above tbe sobd line tbe condensed phase is solid below it, it is liquid. Tbe notation 5.646. signifies 5.646 X 10 . At 83.8 K, tbe viscosity of tbe saturated liquid is 2.93 X 10 Pa-s = 0.000293 Ns/ui . Tbis book was published in English translation by Hemisphere, New York, 1988 (604 pp.). 

The presence of errors within the underlying database fudher degrades the accuracy and precision of the parameter e.stimate. If the database contains bias, this will translate into bias in the parameter estimates. In the flash example referenced above, including reasonable database uncertainty in the phase equilibria increases me 95 percent confidence interval to 14. As the database uncertainty increases, the uncertainty in the resultant parameter estimate increases as shown by the trend line represented in Fig. 30-24. Failure to account for the database uncertainty results in poor extrapolations to other operating conditions. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

Fig. 4. The relation between the fundamental symmetry vector R = p3] -1- qa2 and the two vectors of the tubule unit cell for a carbon nanotube specified by (n,m) which, in turn, determine the chiral vector C, and the translation vector T. The projection of R on the C, and T axes, respectively, yield (or x) and t (see text). After N/d) translations, R reaches a lattice point B". The dashed vertical lines denote normals to the vector C/, at distances of L/d, IL/d, 3L/d,..., L from the origin.

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