Solids line broadening

Before going into some detail on the applied techniques, we shall first summarise the causes of line broadening in the spectra of solids. Line broadening in 13C NMR spectra of solids will be discussed below. 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

Stress in crystalline solids produces small shifts, typically a few wavenumbers, in the Raman lines that sometimes are accompanied by a small amount of line broadening. Measurement of a series of Raman spectra in high-pressure equipment under static or uniaxial pressure allows the line shifts to be calibrated in terms of stress level. This information can be used to characterize built-in stress in thin films, along grain boundaries, and in thermally stressed materials. Microfocus spectra can be obtained from crack tips in ceramic material and by a careful spatial mapping along and across the crack estimates can be obtained of the stress fields around the crack. ... 

Most surface area measurements are based on the interpretation of the low temperature equilibrium adsorption of nitrogen or of krypton on the solid using the BET theory [33,269,276—278]. There is an extensive literature devoted to area determinations from gas adsorption data. Estimates of surfaces may also be obtained from electron micrographs, X-ray diffraction line broadening [279] and changes in the catalytic activity of the solid phase [ 280]. 

The ESR spectra of a large variety of sulfonyl radicals have been obtained photolytically in liquid phase over a wide range of temperature. Some selected data are summarized in Table 2. The magnitudes of hyperfine splittings and the observations of line broadening resulting from restricted rotation about the C—S bond have been used successfully in conjunction with INDO SCF MO calculations to elucidate both structure and conformational properties. Thus the spin distribution in these species is typical of (T-radicals with a pyramidal center at sulfur and in accord with the solid-state ESR data. 

Fig. 4.5. The broadening of the P-R doublet (Atc = n/2, V2f = n/8) in the integral non-Markovian theory (solid line) and in the Markovian approximation (dotted line).

A higher-MHz NMR spectrometer is always a better choice, since the sensitivity of the experiment is proportional to the frequency of measurement. Moreover, with highly concentrated solutions, the presence of some solid particles can cause an increase in T) (FID will be short) and line broadening of the NMR signals will result. Therefore, an optimum concentration (say, 25-50 millimolar solution) is recommended. Of course, H-NMR spectra can be readily measured at much lower concentrations, though higher concentrations are necessary for recording - C-NMR spectra. 

The chemical analyses of the samples are reported in Table 2. The X-ray diffraction spectra of these solids do not show the presence of any Cu oxide phase with size larger than 3-4 nm, excepted in the cases of Cu(3)Si02 and Cu(4)Zr02 on one side, Cu(146)Na(6)FAU-10 and Cu(146)Na(28)MFI-15 on the other side, where the lines characteristic of CuO do appear with a line broadening corresponding to a particle size of about 4 nm. 

Fig. 40.32. Deconvolution (result in solid line) of a Gaussian peak (dashed line) for peak broadening ((M i/,)prf/(H vi)G = 1). (a) Without noise, (b) With coloured noise (A((0,1%), Tx = 1.5) inverse filter in combination with a low-pass filter, (c) With coloured noise (A (0,1 %), Ta = 1.5) inverse filter without low-pass filter.

Another issue of concern is the amplitude of magnetic field gradients required for solids imaging. For spectra up to a few kHz wide, standard frequency encoding schemes can be used to obtain reasonable spatial resolution. This will not work for broader lines, but it is well known that phase encoding is much more tolerant to line broadening and can be used for spectral widths in excess of 100 kHz with no major loss in spatial resolution. 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

We have referred to the various interactions which can cause line broadening in the solid state. One of these, which is normally not a problem in liquid state NMR, is due to the fact that the chemical shift itself is a tensor, i.e. in a coordinate system with orthogonal axes x, y and z its values along these axes can be very different. This anisotropy of the chemical shift is proportional to the magnetic field of the spectrometer (one reason why ultra-high field spectrometers are not so useful), and can lead in solid state spectra to the presence of a series of spinning sidebands, as shown in the spectra of solid polycrystalline powdered triphenylphosphine which follows (Fig. 49). In the absence of spinning, the linewidth of this sample would be around 75 ppm ... 

The anisotropies that lead to line broadening in isotropic ESR spectra influence solid-state spectra more directly. Accordingly a more complex spin Hamiltonian is required to interpret such spectra ... 

The majority of double-resonance solid-state NMR experiments involving spin-1/2 nuclei use transfer of nuclear polarization via dipolar cross polarization (CP) to enhance polarization of the diluted spins S with small gyromagnetic ratio ys and significant longitudinal relaxation time T at the expense of abundant spins I with large y, and short 7 [215]. Typically, CP is used in combination with MAS, to eliminate the line broadening due to CS A, as well as with heteronuclear decoupling. To achieve the / S CP transfer, a (n/2)y pulse is applied at the I spin frequency,... 

Table 4.1. Various processes contributing to the spectral line broadening for local vibrations. Frequencies of collectivized local vibrations QK (solid arrows) are supposed to exceed phonon frequencies oiRq (dashed arrows) Ok > max oncq. For an extremely narrow band of local vibrations, diagrams A and B respectively refer to relaxation and dephasing processes, whereas diagrams C account for the case realizable only at the nonzero band width for local vibrations.

P and 19F NMR spectroscopy), and attempts to record a CP/MAS solid-state NMR spectrum (19F, 31P, 23Na) failed because of the large line-broadening by the 23Na ions (I = 3/2) and strong spin-spin coupling. 

The examples illustrate the strong points of XRD for catalyst studies XRD identifies crystallographic phases, if desired under in situ conditions, and can be used to monitor the kinetics of solid state reactions such as reduction, oxidation, sulfidation, carburization or nitridation that are used in the activation of catalysts. In addition, careful analysis of diffraction line shapes or - more common but less accurate-simple determination of the line broadening gives information on particle size. 

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