Line peak width effects

Table XI. An example of the effect of line peak width, i.e., the number of diodes summed for peak area calculation, on the measurement accuracy.

The resolution of overlapping spectral peaks depends on their separations, intensities, and widths. Whereas separation and intensity are predominantly functions of the sample, peak width is strongly influenced by the instrument s design. The observed line is a convolution of the natural line, a function characteristic of inelastically scattered electrons that produces a skewed base line, and the instrument function. The instrument function is, in turn, the convolution of the x-ray excitation line shape, the broadening inherent in the electron energy analyzer, and the effect of electrical filtering. This description is summarized in Table I. 

A general model for electronic relaxation of the Gd3+ S = 7/2 ion in various complexes in solution was presented by Rast el al. [86]. Contrary to the usual assumption, the electronic relaxation in their model is not only due to the effects of the transient zero field splitting, but is also strongly influenced by the static crystal field effect which is modulated by the random Brownian rotation of the complex. Experimental peak-to-peak widths of three gadolinium complexes could be well interpreted as a function of temperature and frequency using three static and one transient crystal field parameters. Moreover, their interpretation of experimental data did not require the addition of any field independent contribution to the line width like the spin-rotation mechanism. 

The line-shape of a true (undistorted) EPR spectrum should be independent of the acquisition parameters, and therefore to assess spectral distortion one can compare spectra acquired with different parameters. Figure 15.6 illustrates the effect of modulation amplitude on EPR line-shape. The central line-width (peak-to-peak width AHpp = 1.6 G) remains unchanged when the modulation amplitude is increased from 0.5 to 1 G while at a modulation amplitude of 10 G, distortion and line-broadening (AHpp = 6.4 G) can be clearly observed. The main sources of spectral distortions are modulation amplitude, microwave power, and scanning rate (speed). These are discussed in the following sections. 

As we saw in Section 3.5, the line width (peak width at half height) of a Lorentzian line is determined by the reciprocal of the effective spin-spin relaxation time (7 ). For small organic... 

Ideally, a Bragg diffraction peak is a line without width as shown in Figure 2.19b. In reality, diffraction from a crystal specimen produces a peak with a certain width as shown in Figure 2.19a. The peak width can result from instrumental factors and the size effect of the crystals. Small crystals cause the peak to be widened due to incompletely destructive interference. This phenomenon can be understood by examining the case illustrated in Figure 2.20. 

The effect of saturation works out to a contribution of —43 kHz. On a line of width Av — 200 kHz, typical for those operating conditions, that would be about 5% rms sum addition to the linewidth. This example serves to illustrate the tradeoff between Q, source power, pressure and hence linewidth, in the choice of operating conditions. In the example given, this contribution to line broadening would hardly be noticeable. For quantitative work where spectral peak area is measured, the effect of power saturation will be less apparent than if height were the measurand. 

In Fig. 4.15.1 we reproduce the electron spin resonance spectrum of monoprotonated / -benzosemiquinone in tetrahydrofuran at — 63°C, a spectrum which shows most of the features discussed above. The spectrum has been analysed in terms of four hyperfine splitting constants, as shown in Fig. 4.15.1, since the asymmetric disposition of the —OH group causes the protons meta to the site of protonation to be non-equivalent. The four splitting constants are readily obtained by measuring distances from the first line of the spectrum the g-value may of course be obtained by simultaneous measurement of microwave frequency and magnetic field at the centre of the spectrum. Readers unfamiliar with line-width effects may care to compute the expected relative intensities of the lines and compare the results with the experimental amplitudes of the first derivative trace. In such a presentation the peak-to-peak amplitude, for a Lorentzian line, is proportional to the reciprocal of the square... 

Dependence of the peak area A, peak height H, and peak width Won the effective thickness of the absorber (ta). F is the natural line width and fs is the Mossbauer-Lamb factor of the source... 

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