The Instrument Resolution

In principle all the X-ray emission methods can give chemical state information from small shifts and line shape changes (cf, XPS and AES in Chapter 5). Though done for molecular studies to derive electronic structure information, this type of work is rarely done for materials analysis. The reasons are the instrumental resolution of commercial systems is not adequate and the emission lines routinely used for elemental analysis are often not those most useftil for chemical shift meas-ure-ments. The latter generally involve shallower levels (narrower natural line widths), meaning longer wavelength (softer) X-ray emission. 

A perturbative approach to Eq. (12) has recently been developed by Gomez-Monivas et al. [37]. For a dielectric film on top of a flat metallic surface, these authors find that the electrostatic force is a convolution of the instrumental resolution with an effective profile... 

The most intense 826-cm band is broader than the other bands. The broadened band suggests a frequency distribution in the observed portion of the surface. Indeed, the symmetric peak in the imaginary part of the spectrum is fitted with a Gaussian function rather than with a Lorenz function. The bandwidth was estimated to be 56 cm by considering the instrumental resolution, 15 cm in this particular spectrum. This number is larger than the intrinsic bandwidth of the bulk modes [50]. 

Due to the convolution with the instrumental resolution, an accurate determination of the spectral shape is not possible. Therefore, the value of has to be determined by other methods or from coherent scattering measurements. 

In the vacuum ultraviolet absorption bands in the region 1280 to 1600 A correspond to the fourth positive system A1 n-X L+. The absorption cross sections of this system are given in Fig. V-7. Since the widths of the CO rotational lines are much smaller than the instrumental resolution ( 10 cm" 1), it is not possible to obtain the absorption cross section of each rotational line [see Section 1-8 for details]. Thus, the cross sections shown in Fig. V-7 are much less than the true cross sections. An estimate of the integrated absorption coefficient of the (0,0) band is 1.7 x 104cm-latm-1 (899). Various electronic states and transitions are given in Fig. V-8. 

As well as the general shape of the spectrometer function, a simpler but also important characteristic feature of an electron spectrometer is its full-width-at-half-maximum (fwhm) value A sp (see Fig. 1.14). This quantity determines the instrumental resolution given usually as the relative value R ... 

Note that such convolutions are commutative, associative, and distributive.) If these photoelectrons, created with the distribution function Fs( kin, kin) in the source region, are detected with an energy analyser, a further convolution is necessary to account for the instrumental resolution as described by the spectrometer functions Gsp( kin, pass), equ. (1.48). The convolution yields the distribution function fexp( pass, kin), or equivalently Fexp(Usp, l/°p), of photoelectrons observed at a preselected pass-energy pass or, equivalently, at a given spectrometer voltage Gsp. One has (see equ. (10.54b))... 

Since the full photoelectron line is detected with the large-scale channelplate detector, each photoelectron contributes to the single counting rate /t which, therefore, becomes independent of the instrumental resolution and is given by... 

The instrument repeatability, evaluated by replicating five times each measurement in three runs carried out in different days The instrument resolution... 

In the present example the instrument resolution and the uncertainty of the gas mixtures compositions give the highest contributions to uncertainty, which is anyhow one order of magnitude lower than with a two-point calibration. 

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