Absorption cross sections calculation

The effective absorption cross sections calculated from these data for the two isotopes with and without overlap terms are shown in Table II. 

Figure 8 Absorption cross sections calculated from the autocorrelation functions displayed in Figure 7. n and k denote the NO stretching and the XNO bending quantum numbers, respectively. Reprinted, with permission of the American Chemical Society, from Ref. 45...

As a second example of the application of ion-beam analysis techniques to semiconductors, we take the calibration of IR absorption measurements of the hydrogen content of sputtered amorphous silicon and silicon nitride. In early measurements, the hydrogen content of glow-discharge a-Si H deduced from IR absorption measurements, using ablsinitio calculations of the absorption cross section of the Si—H IR absorption bands, was com-... 

Finally, the molecular absorption cross-section capture area of a molecule. Operationally, it can be calculated as the (Napierian) absorption coefficient divided by the number N of molecular entities contained in a unit volume of the absorbing medium along the light path ... 

The molecular absorption cross-section can then be calculated from the experimental value of e using the following relation ... 

Colorless or light yellow metal at ordinary temperatures it occurs in hexagonal close-packed crystalline form, known as alpha-gadolinium alpha form transforms to a body-centered cubic allotropic form, beta-gadolinium upon heating at 1,262°C density 7.90 g/cm melting point 1,313°C vaporizes at 3,266°C vapor pressure 9.0 torr at 1,800°C (calculated) electrical resistivity 134.0 microhm-cm at 25°C Poisson ratio 0.259 modulus of elasticity 8.15x106 psi thermal neutron absorption cross section 46,000 barns insoluble in water dissolves in acid (reacts). 

Silvery-gray metal slowly tarnishes in moist air crystallizes in hexagonal close-packed structure density 11.49 g/cm (calculated) melts at 2,172°C vaporizes at 4,265°C Young s (elastic) modulus 3.76 x 10 kg/cm Poisson s ratio 0.293 thermal neutron absorption cross-section 22 barns superconductor below 11°K insoluble in water and hydrochloric acid dissolves in nitric acid, concentrated sulfuric acid and aqua regia. 

Most commercial spectrometers report absorbance, as defined in Eq. (Q), versus wavelength. This is very important to recognize, since as we will see later, calculations of the rate of light absorption in the atmosphere require the use of absorption coefficients to the base e rather than to the base 10. While the recent atmospheric chemistry literature reports absorption cross sections to the base e, most measurements of absorption coefficients reported in the general chemical literature are to the base 10. If these are to be used in calculating photolysis rates in the atmosphere, the factor of 2.303 must be taken into account. 

Only reaction (7) leads to the removal of NOz via photochemistry and hence the quantum yield for reaction (7) is needed to calculate the photolysis rate. Data on both primary quantum yields and absorption cross section [Pg.80]

It must again be stressed that the absorption cross sections, a (A), used to calculate photolysis rates are to the base e, not base 10, even though the latter is what has often been measured and reported in the literature in the past. 

Because the actinic flux data are reported as averages over certain wavelength intervals, rather than integrating over Eq. (OO) in a continuous manner, in practice one calculates the sum of the product discrete wavelength intervals AA. The intervals are chosen to match the available flux data for example, in Table 3.7, actinic fluxes are reported as averages over 2-nm intervals from 290 to 320 nm, which is important for the 03 absorption, 5-nm intervals from 320 to 420 nm, 10-nm intervals from 420 to 580 nm, and 20-nm intervals from 580 to 700 nm. Since the primary quantum yield, ( A), and the absorption cross section, a(A), are not normally reported over identical intervals, representative averages of these parameters over the same intervals for which the actinic flux data are reported must be calculated from the literature data. 

Experimentally, while the determination of absorption cross sections is fairly straightforward, measuring primary quantum yields is not, due to interference from rapid secondary reactions. As a result, in cases where quantum yield data are not available, calculations of maximum rates of photolysis are often carried out in which it is assumed that (A) = 1.0. It should be emphasized in such cases that this represents only a maximum rate constant for photolysis the true rate constant may be much smaller, even zero, if photophysical fates of the excited molecule such as fluorescence or quenching predominate. 

Once the actinic fluxes, quantum yields, and absorption cross sections have been summarized as in Table 3.19, the individual products < .,v(A)wavelength interval can be calculated and summed to give kp. Note that the individual reaction channels (9a) and (9b) are calculated separately and then added to get the total photolysis rate constant for the photolysis of acetaldehyde. However, the rate constants for the individual channels are also useful in that (9a) produces free radicals that will participate directly in the NO to N02 conversion and hence in the formation of 03, etc., while (9b) produces relatively unreactive stable products. 

The absolute values of the absorption cross sections of HCHO have been somewhat controversial. This appears to be due to a lack of sufficient resolution in some studies as discussed in Chapter 3.B.2, if the spectral resolution is too low relative to the bandwidth, nonlinear Beer-Lambert plots result. The strongly banded structure means that calculations of the photolysis rate constant require actinic flux data that have much finer resolution than the 2- to 5-nm intervals for which these flux data are given in Chapter 3 or, alternatively, that the measured absorption cross sections must be appropriately averaged. One significant advantage of the highly structured absorption of HCHO is that it can be used to measure low concentrations of this important aldehyde in the atmosphere by UV absorption (see Sections A.ld and A.4f in Chapter 11.). 

Gierczak et al. (1998) have also measured the temperature dependence for the absorption cross sections in addition to the quantum yields as a function of pressure and temperature. They have used these data, combined with the kinetics of the OH-acetone reaction, which is the other major removal process, to calculate the contributions of the OH reactions and of photolysis to the loss of acetone in the atmosphere as a function of altitude. Figure 4.31 shows that photolysis is a significant, but not the major, contributor at the... 

Barnes et al. (1998) have measured the yield of OH from HOC1 photolysis and find, in addition to the strong absorption shown in Fig. 4.39, a weak absorption feature at 380 nm due to excitation to the lowest triplet state. Although the absorption cross section of this weak absorption is only 4 X 10 21 cm2 molecule-1, its contribution lowers the calculated stratospheric lifetime of HOC1 by 10-20%. 

A major advantage of this approach is that the fundamental spectroscopic parameters for OH, including the absorption cross sections for various transitions, are well known (e.g., see Mount, 1992 Dorn et al., 1995b), so that absolute concentrations of OH can be calculated based solely on the absorption spectra. Another major advantage is that the laser beams are expanded so that generation of OH in the beam itself by photolysis of ozone is not the problem that it has been in LIF measurements (vide infra). 

As is the case for LIF, calibration to obtain absolute concentrations is a challenge. In the instrument shown in Fig. 11.45, a calibration source based on the photolysis of water at 185 nm is installed in the inlet. From the absorption cross section of HzO gas at 185 nm, its concentration, the light intensity, and the sample flow rate, the concentration of OH generated by the photolysis can be calculated. However, not only is there significant uncertainty in the absorption cross section for HzO at 185 nm (e.g., see Lazendorf et al., 1997 Hofzumahaus et al., 1997, 1998 and Tanner et al., 1997), but the measured calibration factor was highly variable from day to day, by as much as a factor of two (Tanner et al., 1997). 

Crowley et al. (1994) have measured the absorption cross sections of CH3OCl and calculate a lifetime with respect to photolysis under stratospheric conditions of 4 h at a solar zenith angle of 80°. The rate of the heterogeneous reaction (38) is not known. 

The entanglement time and area depend on the thickness of nonhnear crystal, the type of nonlinear interaction, and piunping conditions. Their chosen values are close to those used in [73]. Together, they yield the critical flux density of 0c = 3 x 10 cm. This results in the entangled photon absorption cross-section = 2.95 x 10 cm. The latter estimate falls between the values obtained earlier from quantum-mechanical calculations for Na (6.0 X 10-3° K2CsSb (2.6 x lO cm ) [73]. 

In the experiment, the transmission intensities for the excited and the dark sample are determined by the number of x-ray photons (/t) recorded on the detector behind the sample, and we typically accumulate for several pump-probe shots. In the absence of external noise sources the accuracy of such a measurement is governed by the shot noise distribution, which is given by Poisson statistics of the transmitted pulse intensity. Indeed, we have demonstrated that we can suppress the majority of electronic noise in experiment, which validates this rather idealistic treatment [13,14]. Applying the error propagation formula to eq. (1) then delivers the experimental noise of the measurement, and we can thus calculate the signal-to-noise ratio S/N as a function of the input parameters. Most important is hereby the sample concentration nsam at the chosen sample thickness d. Via the occasionally very different absorption cross sections in the optical (pump) and the x-ray (probe) domains it will determine the fraction of excited state species as a function of laser fluence. 

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