Line intensities and shapes

Figure 1.10 Effect of increasing microwave power on intensity and shape of an ESR line. Power increases from top to bottom of the figure. Units are relative values of Bx.

A method known as Rietveld analysis has been developed for solving crystal structures from powder diffraction data. The Rietveld method involves an interpretation of not only the line position but also of the line intensities, and because there is so much overlap of the reflections in the powder patterns, the method developed by Rietveld involves analysing the overall line profiles. Rietveld formulated a method of assigning each peak a gaussian shape and then allowing the gaussians to overlap so that an overall... 

INS spectroscopy avoids this problematic feedback effect, in the sense that it measures nuclear motion directly. This provides a simple relation between the amplitude of the motion, the cross section of the nuclei and the vibrational frequency to determine the intensity and shape of the spectral lines. The electron density is, of course, used to determine the potential energy surface that controls the nuclear motion but it is not involved in the calculation of the spectra. The combined use of INS spectroscopy, ab initio calculations and ACLIMAX can provide a good test of the molecular model, assessing the quality of structure and dynamics. 

Zero-field Mossbauer spectra of [LFeCl] and [LFe(p,-0)FeL] recorded at 80 K. Experimental data are provided by circles and simulations by lines. The intensities have been rescaled to visualize the differences in line widths and shapes. Courtesy of Prof Thorsten Glaser, University of Bielefeld. 

A Mossbauer spectrum is characterized by its total absorption area, the number, position, relative intensity, and shape of the various absorption lines. These features result from the various interactions between the Mossbauer nuclei and their surroundings, as well as any motion of the Mossbauer atoms (see the Appendix). 

High-resolution NMR provides spectra that consist of a number of lines and bands whose frequency, relative intensity and shape may be analysed to yield molecular parameters. The NMR parameters in questions are the nuclear shielding, a, which describes the shielding of the nucleus from the applied magnetic field by the surrounding electrons and gives rise to chemical shifts /, which relates to nuclear spin-spin coupling and depends upon relative nuclear orientations and the times and T2 which refer to the relaxation processes encountered by the nuclei excited in the NMR experiment. 

In the intrinsic part of the photoemission spectrum, that is, the elastic lines, there are basically three observables associated with each core-level or valence band peak line positions, line intensities, and line widths or line shapes. From these, different pieces of information can be gained. In core-level emission, the rough line positions reveal the elemental composition of the sample surface, whereas the exact positions are characteristic of the specific chemical environment of the atoms [6j. The intensities are determined not only by the atomic concentrations but also by the photoelectric cross sections and instrumental effects such as the photon flux and the transmission of the spectrometer. Finally, information on the many-body dynamics of the solid after the sudden creation of a photohole (the missing electron that has been ejected) is contained in the shape and width of the peak. In the simplest case, the line shape is Lorentzian and its width is a measure of... 

In the powder diffraction technique, a monochromatic (single-frequency) beam of x-rays is directed at a powdered sample spread on a support, and the diffraction intensity is measured as the detector is moved to different angles (Fig. 1). The pattern obtained is characteristic of the material in the sample, and it can be identified by comparison with a database of patterns. In effect, powder x-ray diffraction takes a fingerprint of the sample. It can also be used to identify the size and shape of the unit cell by measuring the spacing of the lines in the diffraction pattern. The central equation for analyzing the results of a powder diffraction experiment is the Bragg equation... 

LLNL AVLIS Laser. The first WFS measurements using a Na LGS were performed at LLNL (Max et al., 1994 Avicola et al., 1994). These experiments utilized an 1100 W dye laser, developed for atomic vapor laser isotope separation (AVLIS). The wavefront was better than 0.03 wave rms. The dye laser was pumped by 1500 W copper vapor lasers. They are not well suited as a pump for LGSs because of their 26 kHz pulse rate and 32 ns pulse length. The peak intensity at the Na layer, with an atmospheric transmission of 0.6 and a spot diameter of 2.0 m, is 25 W/cm, 4x the saturation. The laser linewidth and shape were tailored to match the D2 line. The power was varied from 7 to 1100 W on Na layer to study saturation. The spot size was measured to be 7 arcsec FWHM at 1100 W. It reduced to 4.6 arcsec after accounting for satura-... 

Fig. 12b). Since practically the same spectral shape is obtained at Q-band (35 GHz) (Fig. 12c), the commonly used criterion stating that the shape of an interaction spectrum is frequency-dependent fails to apply in this case. Actually, outer lines arising from the exchange interaction are visible on the spectrum calculated at Q-band (Fig. 12c), but these lines would be hardly detectable in an experimental spectrum, because of their weak intensity and to the small signal-to-noise ratio inherent in Q-band experiments. In these circumstances, spectra recorded at higher frequency would be needed to allow detection and study of the spin-spin interactions. 

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

Treating vibrational excitations in lattice systems of adsorbed molecules in terms of bound harmonic oscillators (as presented in Chapter III and also in Appendix 1) provides only a general notion of basic spectroscopic characteristics of an adsorbate, viz. spectral line frequencies and integral intensities. This approach, however, fails to account for line shapes and manipulates spectral lines as shapeless infinitely narrow and infinitely high images described by the Dirac -functions. In simplest cases, the shape of symmetric spectral lines can be characterized by their maximum positions and full width at half maximum (FWHM). These parameters are very sensitive to various perturbations and changes in temperature and can therefore provide additional evidence on the state of an adsorbate and its binding to a surface. 

A final remark about the line intensities in Fig. 5.10 (left) as the field is directed perpendicular to the y-beam, the situation corresponding to (p=9i)° in Table 5.4 applies and the line intensities from outward to inward are in the proportions of 3 4 1. One can also apply the external field parallel to the y-beam, with the result that the second and fifth lines of the sextet disappear from the spectra ( =0 in Table 5.4). Bpdker et al. [25] used this to simplify the spectrum of small iron particles and could in this way analyze the shape of the outer lines in more detail. 

The r-dependence of the spectra of PBLG- d2 is shown in Fig. 17. An increase in the pulse spacing r leads to a reduction of the spectral intensity and characteristic line shape changes. The remarkable r-dependence is observed around 40-60°C for both samples. These results show the presence of motions with rates as high as the QCC at the k and positions in this temperature region, and are consistent with the remarkable signal intensity loss around 50°C. 

---