Fundamental lines

Fundamental lines of pharmaeeutieal analysis development in Ukraine are as follows ... 

The eompensation of the voltage error amplifier should be a single-pole rolloff with a unity gain frequeney of 38 Hz. This is required to rejeet the fundamental line frequeneies of 50 and 60 Hz. The feedbaek eapaeitor around the voltage error amplifier beeomes... 

We note that the formalism presented here plays a major role in infrared spectroscopy. The process that gives rise to a fundamental line in the infrared spectrum of a molecule is the absorption of a photon whose frequency corresponds to that of one of the normal modes, and the simultaneous transition of this mode from the ground state (n = 0) to the first excited state. 

Anharmonicity leads to deviations of two kinds. At higher quantum numbers, AE becomes smaller, and the selection rule is not rigorously followed as a result, transitions of A 2 or 3 are observed. Such transformations are responsible for the appearance of overtone lines at frequencies approximately two or three times that of the fundamental line the intensity of overtone absorption is frequently low, and the peaks may not be observed. Vibrational spectra are further comphcated by the fact that two different vibrations in a molecule can interact to give absorption peaks with frequencies that are approximately the sums or differences of their fundamental frequencies. Again, the intensities of combination and difference peaks are generally low. 

The theory and instrumentation of Fourier transform mass spectrometry (FTMS) have been discussed extensively in this book and elsewhere [21-23]. All experiments were performed on a Nicolet prototype FTMS-1000 Fourier transform mass spectrometer previously described in detail [24] and equipped with a 5.2 cm cubic trapping cell situated between the poles of a Varian 15 in. electromagnet maintained at 0.85 T. The cell was constructed in our laboratory and utilizes two 80 transmittance stainless steel screens as the transmitter plates. This permits irradiation with a 2.5 kW Hg-Xe arc lamp, used in conjunction with a Schoeffel 0.25 m monochromator set for 10 nm resolution. Metal ions are generated by focusing the beam of a Quanta Ray Nd YAG laser (either the fundamental line at 1064 nm or the frequency doubled line at 532 nm) into the center-drilled hole (1 mm) of a high-purity rod of the appropriate metal supported on the transmitter screen nearest to the laser. The laser ionization technique for generating metal ions has been outlined elsewhere [25]-... 

The terms with L = 0,1,2,3 are called S, P, D, F these letters were adapted from the pre-1900 labeling of spectroscopic transitions as giving "sharp," "principal," "diffuse", and "fundamental" lines. 

Now that the fundamental line to be taken with regard to the practical final solution of the Jewish question has been determined and the authorities involved are in complete agreement, I would ask you [...] ... 

Comparing these equations with Eqs. (13-1), we note that only the superlattice lines are affected. But the effect is a strong one, because the intensity of a superlattice line is proportional to F and therefore to S. For example, a decrease in order from S = l.(X) to 5 = 0.84 decreases the intensity of a superlattice line by about 30 percent. The weakening of superlattice lines by partial disorder is illustrated in Fig, 13-3. By comparing the integrated intensity ratio of a superlattice and fundamental line, we can determine S experimentally. 

In other words, there are fundamental lines, those for which (/i + fc + /) is even, which are unchanged in intensity whether the alloy is ordered or not. And there are superlattice lines, those for which (h + k + 1) is odd, which are present only in the pattern of an alloy exhibiting some degree of order, and then with an intensity which depends on the degree of order present. 

We have already seen that the intensity of a superlattice line from an ordered solid solution is much lower than that of a fundamental line. Will it ever be so low that the line cannot be detected We can make an approximate estimate by ignoring the variation in multiplicity factor and Lorentz-polarization factor from line to line, and assuming that the relative integrated intensities of a superlattice and fundamental line are given by their relative F values. For fully ordered AuCus, for example, we find from Eqs. (13-1) that... 

Superlattice lines are therefore only about one-tenth as strong as fundamental lines, but they can still be detected without any difficulty, as shown by Fig. 13-3. 

Calculate the ratio of the integrated intensity of the 100 superlattice line to that of the 110 fundamental line for fully ordered -brass, if Cu Ka radiation is used. Estimate the corrections to the atomic scattering factors from Fig. 13-8. The lattice parameter of iff-brass (CuZn) is 2.95 A. 

The f block refers to the rare earth elements. The label f originally stood for the fundamental lines in the spectrum. 

The two techniques detect the same modes as long as there is no center of symmetry in the molecule. In general, if there is a center of symmetry, there will be no fundamental lines in common in the two spectra. 

In absorption, a value of 0.184meV (l.48cm 1) has been measured for the FWHM of the P line at LHeT in CZnatSi. In 30Si, the energies of the fundamental lines are found to increase by about 0.8 meV [97],... 

The rms value of the fundamental line current is 392.26 amps. Therefore its peak value is 392.26 2 = 554.74 amps which corresponds to b having a value of 1.1026. The peak values of the harmonic components of the line current are given below in Table 15.5. 

The approach may be fast in generating partial and approximate answers for existing equipment when the absorbent composition has to be modified, for example, yet will probably not withstand progress in the knowledge of the hydrodynamics of two-phase flow, which will increase the accuracy of and the confidence in the design along the fundamental lines discussed in the preceding chapters and sections. 

Fleming, M., and Mooradian, A., "Fundamental line broadening of single-mode (GeiAl)As diode lasers," Appl. Phys. Lett. 38 511 (1981). 

F = (/au + 3/cu) when hkl are unmixed, but when hkl are mixed then F instead of being zero it is F = (/au — /cu)- Therefore, so far as the diffraction lines are concerned, there exists one extra line for the reflection hkl mixed (odd and even) only when the structure is perfectly ordered, otherwise it remains as zero. This extra line is the manifestation of ordered structure and is known as super lattice line even though they are weaker than fundamental lines. 

The selection rule for Raman intensities (b) discussed in the previous section requires that the vibrational quantum number changes by +1 for the Stokes lines in the Raman spectra. This is, however, true for the fundamental lines, corresponding to transition 0->l, and for the "hot bands" related to transitions of the type l->2, 2->3, etc. These appear at the same frequency in the spectra as the fundamental bands. Thus, the frequencies associated with fundamental and "hot band" transitions are hardly discernible. All such transitions contribute to the intensity of a Raman band. A summation over all vibrational quantum numbers Vj from zero to infinity is needed to account for all contributions to the intensity I,. Following the considerations given in Section 1.1 [Eqs. (1.31) and (1.39)], the expression is obtained... 

According to the haimonic oscillator selection rule, as briefly discussed in Section 8.1, fundamental transitions are only allowed in Raman spectra. In practice, it means that the fundamental lines will appear with higher intensity than the overtone and combination lines. In this section the relationship between molecular symmetiy and the intensity of the Raman line will be considered. 

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