Examples a spectrum

Thermal stability. The presence of side chains, cross-linking, and benzene rings in the polymer s "backbone increase the melting temperatures. For example, a spectrum of polymers with increasing melting temperatures would be polyethylene, polypropylene, polystyrene, nylon, and polyimide. 

The improvement in the signal-to-noise ratio (S/N) is proportional to the square root of the ratio of the number of scans. For example, a spectrum acquired with 64 scans will have an improved S/N of 7(64/16) = v4 = 2 over one acquired with 16 scans. 

Once the qualification results such as those in Table 10.5 are in hand, validation of instrumental accuracy should be conducted periodically. In the current example, a spectrum of the calcium ascorbate standard might be obtained each day, and stored in an archive. These spectra provide an immediate check on the position of the 767 and 1582 cm bands and may be accessed at a future date. If a particular sample spectrum comes into question, the calcium ascorbate spectrum for that day may be examined for any discrepancies. As noted earlier, a particular validation procedure will depend on the application, but a possible daily routine might include ... 

The most dramatic effect of collisions is to induce mixing between nearby excited states of the atom, whose presence would not normally manifest itself. Consider for example a spectrum in which a regular Ryd-... 

To transform the abstract factors determined in the first step into interpretable factors, rotation methods are applied. If definite target vectors can be assumed to be contained in the data, for example, a spectrum under a spectrochromatogram, the rotation of data is performed by using a target. This technique is known as target-transform factor analysis TTFA, c Example 5.6). 

However, a truly surprising result was a remarkable insensitivity to space charge for mass spectra obtained by axial injection from Q3/2. in 2D-trap mass spectrometer mode. For example, a spectrum of the [M-i-H]+ ions of reserpine (miz 609) obtained using us a collision cell and in 2D-trap MS mode at an ion... 

One problem with multivariate data is that its sheer volume may make it difficult to see patterns and relationships. For example, a spectrum would normally be characterized by several hundred intensity measurements rather than just four as in Table 8.1 and in this case the correlation matrix would contain hundreds of values. Thus the aim of many methods of multivariate analysis is data reduction. Quite frequently there is some correlation between the variables, as there is for the data in Table 8.1, and so some of the information is redundant. Principal component analysis (PCA) is a technique for reducing the amount of data when there is correlation present. It is worth stressing that it is not a useful technique if the variables are uncorrelated. 

Sometimes it is necessary to record broadband proton decoupled spectra without any NOE. The NOE may be undesirable either because quantitative information is needed about the relative number of atoms contributing to each peak in, for example, a spectrum, or because the nucleus being studied has a negative NOE (e.g., N or Si). Such spectra are also used as controls when measuring NOE values. In other instances coupled spectra with NOE are used as a means of improving sensitivity. 

Such power levels can be quite adequate for Doppler-free saturation spectroscopy, as demonstrated in a series of recent studies of ultraviolet transitions of neutral helium in our laboratory at Stanford. (35-37) Fig. 5 shows as an example a spectrum of the 2 S - 5 P transition of He near 294.5 nm, recorded by intermodulated fluorescence spectroscopy. The ultraviolet radiation was generated by a yellow cw ring cavity dye laser with cavity-enhanced external ADA (ammonium dihydrogen arsenate) frequency doubler. The absorbing metastable He atoms were produced by electron impact excitation of He gas at about 0.04 torr. The spectrum shows a cluster of resolved line components which could be assigned after the fine and hyperfine Hamiltonian had been diagonalized in an uncoupled representation. We were surprised to learn that the hyperfine structure of the 5 P state of this simple 3-body system had been neither measured nor calculated before. 

The more localized Tamm surface states show less dispersion, and the angular resolution is less important. As an example, a spectrum and the corresponding fit for the M Tamm state on Cu(lOO) is shown Figure 6.19a [108]. The state shows a narrow intrinsic linewidth of T = 7 meV even at an energy of — 1.8 eV below the Fermi energy. This is attributed to the localized character of the d states and the small overlap with the sp bands, which provide the main decay channel for inelastic decay. 

These equations indicate that the energy of the scattered ions is sensitive to the mass of the scattering atom s in the surface. By scanning the energy of the scattered ions, one obtains a kind of mass spectrometric analysis of the surface composition. Figure VIII-12 shows an example of such a spectrum. Neutral, that is, molecular, as well as ion beams may be used, although for the former a velocity selector is now needed to define ,. ... 

The spectral frequency range covered by the central lobe of this sinc fiinction increases as the piilselength decreases. For a spectrum to be undistorted it should really be confined to the middle portion of this central lobe (figure B 1.12.2). There are a number of examples in the literature of solid-state NMR where the resonances are in fact broader than the central lobe so that the spectrum reported is only effectively providing infonnation about the RF-irradiation envelope, not the shape of the signal from the sample itself... 

For example, a metastable peak appeared at 147.9 mass units in a mass spectrum with prominent peaks at 65, 91, 92, 107, 108, 155, 172, and 200 mass units. Try all possible combinations in the above expression. The fit is given by... 

With the availability of computerized data acquisition and storage it is possible to build database libraries of standard reference spectra. When a spectrum of an unknown compound is obtained, its identity can often be determined by searching through a library of reference spectra. This process is known as spectral searching. Comparisons are made by an algorithm that calculates the cumulative difference between the absorbances of the sample and reference spectra. For example, one simple algorithm uses the following equation... 

Special isotope ratio mass spectrometers are needed to measure the small variations, which are too small to be read off from a spectrum obtained on a routine mass spectrometer. Ratios of isotopes measured very accurately (usually as 0/00, i.e., as parts per 1000 [mil] rather than parts per 100 [percent]) give information on, for example, reaction mechanisms, dating of historic samples, or testing for drugs in metabolic systems. Such uses are illustrated in the main text. 

A beam of charged particles (an ion beam) with an energy from a few hundred keV to several MeV is produced in an accelerator and bombards a sample. Nuclear reactions with low-Z nuclei in the sample are induced by this ion beam. Products of these reactions (typically p, d, t, He, a particles, and y rays) are detected, producing a spectrum of particle yield versus energy. Many (p, a) reactions have energies that are too low for efficient detection. In these cases, the associated y rays are detected instead. Important examples are ... 

An example of a spectrum with a chemical shift is that of the tin 3d peaks in Eig. 2.8. A thin layer of oxide on the metallic tin surface enables photoelectrons from both the underlying metal and the oxide to appear together. Resolution of the doublet 3 ds/2, 3 dii2 into the components from the metal (Sn ) and from the oxide Sn " is shown in Eig. 2.8 B. The shift in this instance is 1.6-1.7 eV. Curve resolution is an operation that can be performed routinely by data processing systems associated with photoelectron spectrometers. 

Fig. 2.8. Example of a chemical shift in the Sn 3d peak for a very thin layer of Sn oxide in Sn metal. (A) spectrum after linear background subtraction, (B) spectrum resolved into its respective components. (a) Sn, (b) Sn .

---