Shape broadening

Emission band near 11 jim associated with carbon stars Shape broadened vibrational modes in SiC... 

Applications to Biological Samples. - Methods of distance measurements were compared for four doubly spin-labelled derivatives of human carbonic anhydrase.53 The distances between the spin labels were obtained from continuous wave spectra by analysis of the relative intensity of the half-field transition, Fourier deconvolution of the line-shape broadening, and computer simulation of line-shape changes. For variants with interspin distances greater than 18 A, the DEER method also was used. For each variant, at least two methods were applicable and reasonable agreement between distances obtained by different methods was obtained. The useful distance ranges for the techniques employed at X-band with natural isotope abundance spin labels were estimated to be half-field transition (5-10 A), line-shape simulation (up to 15 A), Fourier deconvolution (8 - 20 A), and four-pulse DEER (> 18 A).53... 

Haeberlin (5) expressed the prevailing attitude of the spectroscopist in 1976 with the statement, "Narrow is beautiful." Although this attitude still prevails, it has long been recognized that a wealth of information is contained in NMR line shapes broadened by specific interactions in solids. Extracting that information has been difficult, since a variety of mechanisms contribute to the line shape, and each must be selectively removed from the others to decipher the... 

The rate theory, on the other hand, describes the migration of molecules in a column. This includes band shape, broadening, and the diffusion of a solute. Rate theory follows the van Deemter equation, which is the most appropriate for prediction of dispersion in liquid chromatography colunms. It does this by taking into account the various pathways that a sample must travel through a column. Using the... 

Ns laser photolysis measurements on (1-pyrenyl) - (CH2 ) (p-N,N-dimethylaminophenyl) (abbreviated as P-(CH2)n"D) were performed in some solvents (18). Their absorption spectra are reproduced by the superposition of bands of the donor cation and the acceptor anion. Only the bandwidth is dependent upon solvent polarity and the number of CH2 groups, which is reduced to the relative geometrical structure of the donor and the acceptor. Exciplex formation dynamics of these compounds has been established by ps transient absorption spectroscopy (19). The absorption spectrum of P-CH2-D in 2-propanol is almost independent of the delay time. On the other hand, P-(0112)3-0 gives a similar spectrum at about 1 ns after excitation, and its spectral shape broadens with a time-constant of 1.2 ns. 

In order to avoid divergences in the density of states we make the substitution e=e+ix (x=0.03 eV). This substitution introduces a Lorenzian shaped broadening of the true eigenstates corresponding to the Hamiltonian in Eq. 1,... 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

Harde H, Katzenellenbogen N and Grischkowsky D 1995 Line-shape transition of collision broadened lines Phys. Rev. Lett. 74 1307-10... 

Kleier D A and Binsch G 1970 General theory of exchange-broadened NMR line shapes. II. Exploitation of invariance properties J. Magn. Reson. 3 146-60... 

The interfacial fluctuations broaden laterally averaged profiles. Within the convolution approximation ( B3.6.15) one obtains a profile with the shape of the erfc fimction [49] ... 

Wlrile tire Bms fonnula can be used to locate tire spectral position of tire excitonic state, tliere is no equivalent a priori description of the spectral widtli of tliis state. These bandwidtlis have been attributed to a combination of effects, including inlromogeneous broadening arising from size dispersion, optical dephasing from exciton-surface and exciton-phonon scattering, and fast lifetimes resulting from surface localization 1167, 168, 170, 1711. Due to tire complex nature of tliese line shapes, tliere have been few quantitative calculations of absorjDtion spectra. This situation is in contrast witli tliat of metal nanoparticles, where a more quantitative level of prediction is possible. 

Figure 2.5 shows, for a sample in the gas phase, a typical absorption line with a HWHM (half-width at half-maximum) of Av and a characteristic line shape. The line is not infinitely narrow even if we assume that the instmment used for observation has not imposed any broadening of its own. We shall consider three important factors that may contribute to the line width and shape. 

Equation (2.27) illustrates what is called the natural line broadening. Since each atom or molecule behaves identically in this respect it is an example of homogeneous line broadening, which results in a characteristic lorentzian line shape. 

The spectrum of the alloy in Figure 8.19 shows pronounced differences. The shape of the Fermi edge is different from that of Cu or Pd and proves to be sensitive to the constitution of the alloy. The peak due to formation of the 3/2 core state of Cu is shifted by 0.94 eV in the alloy and broadened slightly. The two Pd peaks are also shifted, but only slightly, and are narrowed to almost 50 per cent of their width in Pd itself... 

Finally, instmmental broadening results from resolution limitations of the equipment. Resolution is often expressed as resolving power, v/Av, where Av is the probe linewidth or instmmental bandpass at frequency V. Unless Av is significantly smaller than the spectral width of the transition, the observed line is broadened, and its shape is the convolution of the instrumental line shape (apparatus function) and the tme transition profile. 

The discussion of diffraction so far has made no reference to the size of the 2D grating. It has been assumed that the grating is infinite. In analogy with optical or X-ray diffraction, finite sizes of the ordered regions on the surface (finite-sized gratings) broaden the diffracted beams. From an analysis of the diffracted-beam shapes, the types of structural disorder in the surface region can be identified and quantified. - ... 

The analogy of a crystal surface as a diffraction grating also suggests how surface defects can be probed. Recall that for a diffraction grating the width of a diffracted peak will decrease as the number of lines in the grating is increased. This observation can be used in interpreting the shape of RHEED spots. Defects on a crystal surfr.ee can limit the number of atomic rows that scatter coherendy, thereby broadening RHEED features. 

Because defects limit the order on a surface, they will alter the dif action pattern, primarily by broadening diffracted beams. Methods have been developed, mostly in the LEED literature, to analyze the shape of diffracted beams to gain information on step distributions on surfaces. These methods apply equally well to RHEED. 

One of the great advantages of Modulation Spectroscopy is its ability to fit the line shapes of sharp, localized structures, as illustrated in the lower part of Figure 1. These fits yield important relevant parameters, such as the value of the energy gap and the broadening parameter. 

Figure 4 Raman spectra of a series of strontium titanates showing typicai iine shapes and information avaiiabie for fingerprinting. The broadening of the high-wavenumber lines is related to the polar character of the TiOs octahadra that occur in all of these structures.

Figure 3 Characteristic solid state NMR line shapes, dominated by the chemical shift anisotropy. The spatial distribution of the chemical shift is assumed to be spherically symmetric (a), axially symmetric (b), and completely asymmetric (c). The top trace shows theoretical line shapes, while the bottom trace shows rear spectra influenced by broadening effects due to dipole-dipole couplings.

In numerous applications of polymeric materials multilayers of films are used. This practice is found in microelectronic, aeronautical, and biomedical applications to name a few. Developing good adhesion between these layers requires interdiffusion of the molecules at the interfaces between the layers over size scales comparable to the molecular diameter (tens of nm). In addition, these interfaces are buried within the specimen. Aside from this practical aspect, interdififlision over short distances holds the key for critically evaluating current theories of polymer difllision. Theories of polymer interdiffusion predict specific shapes for the concentration profile of segments across the interface as a function of time. Interdiffiision studies on bilayered specimen comprised of a layer of polystyrene (PS) on a layer of perdeuterated (PS) d-PS, can be used as a model system that will capture the fundamental physics of the problem. Initially, the bilayer will have a sharp interface, which upon annealing will broaden with time. 

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