Wavenumber depth-dependent

Lanz and Com [51] proposed a 20-nm thick space charge layer on the Ti02 surface. When the fourth-order response with our TMA-covered surface is generated in the space charge layer, the broad width of the 826-cm band is understood as a depth-dependent wavenumber of the lattice vibration. 

From this equation it can be seen that the depth of penetration depends on the angle of incidence of the infrared radiation, the refractive indices of the ATR element and the sample, and the wavelength of the radiation. As a consequence of lower penetration at higher wavenumber (shorter wavelength), bands are relatively weaker compared to a transmission spectrum, but surface specificity is higher. It has to be kept in mind that the refractive index of a medium may change in the vicinity of an absorption band. This is especially the case for strong bands for which this variation (anomalous dispersion) can distort the band shape and shift the peak maxima, but mathematical models can be applied that correct for this effect, and these are made available as software commands by some instrument manufacturers. 

The wavenumber dependence of the penetration depth for a KRS-5 optical element (a mixed salt of thallium bromide and iodide) (kj = 2.5) and a sample with 2 = 1 -5 is shown in Figure 3.13(c). 

Figure 13,3 Wavenumber dependence of the depth of penetration, (a) IRE, synthetic diamond angle of incidence, 45° (b) IRE, synthetic diamond angle of incidence, 60° (c) IRE, Ce angle of Incidence, 45° and (d) IRE, Ce angle of incidence, 60°. The refractive index of the sample Is assumed to be 1.5. The Ce IRE Is practically usable over the region of 4000-600cm ...

In many commercially available FT-IR spectrometer systems, software (called the ATR correction) for correcting the band intensities of an observed ATR spectrum for the wavelength-dependent depth of penetration expressed in Equation (13.4) is installed, in order to make the observed ATR spectrum more closely resemble a transmission spectrum. In ATR spectra, peak positions, particularly those of intense bands, tend to have wavenumbers lower than those in corresponding transmission spectra. As described earlier, this is related to the anomalous dispersion of the refractive index in the vicinity of the absorption band. The effect has been discussed and software for correcting ATR spectra to take account of this effect is available [9]. The software for this purpose is also installed in some commercially available FT-IR spectrometers. Input data necessary for this software are the refractive index of the sample and the IRE, the angle of incidence, and the number of internal reflections. 

The bottom spectrum in Figure 4.50 is the DRIFTS spectrum of sucrose the depth the infrared beam penetrated into the sample did not depend upon wavenumber, and the dashed line shows that the peak heights at high and low W are about the same. The top spectrum in Figure 4.50 shows the ATR spectrum of sucrose, and the dashed line shows that the peaks near 1000 cm" are much bigger than the peaks around 3300 cm. Note that the peak positions in the two spectra are similar and the relative intensities of the peaks are different. 

The entire measurement process for the spectrum in Figure 4.57, including scanning, took less than one minute. Note the high SNR in the spectrum, and how the peaks at low wavenumber are significantly smaller than the peaks at high wavenumber—a result of the depth of penetration s dependence on wavenumber as discussed above. 

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