Chapter 5.16. Normalization of XANES spectra

Normalization of the XANES spectrum by this method is typically broken up into two parts: (i) fitting of the pre-edge baseline region and (ii) fitting of the post-edge region to create a unit step height. This process has been described in detail in several excellent publications (Hayes & Boyce, 1983; Sayers & Bunker, 1988; Teo, 1986) and the conventional standards have been discussed by the International Committee on Standards and Criteria in EXAFS (Lytle et al., 1989). In general, if the raw spectrum μ is being normalized, and μ₀ is the fit to the background pre-edge and μ₁ is the fit to the post-edge region, the normalization follows the form

Fitting of the pre-edge baseline μ₀ is normally performed using a polynomial function, with the intent of obtaining a flat baseline close to zero. The most used function is a simple linear polynomial of the form A + BE, where E is the incident X-ray energy (Fig. 1a). For transmission data, the Victoreen function of the form CE⁻³ − DE⁻⁴ may also be used (Fig. 1b), which more closely matches the slope of the theoretical absorption coefficient (Teo, 1986). These forms work best when the pre-edge region is approximately linear in nature. However, when using energy-discriminating detectors, such as germanium and silicon detectors, at low concentrations of the element of interest, the elastic scatter of the incident beam by both the sample and air can provide a large source of additional signal in the region of interest (Fig. 1c). The effect of scatter in these cases is a nonlinear background that increases in intensity at lower energies, where the scatter is closer to the region of interest in energy as defined by the fluorescence window. In such a case, fitting this region with the tail of a Gaussian peak function can approximate the pre-edge background.

Figure 1 Examples of pre-edge baseline fitting for XANES. (a) The linear polynomial used in fluorescence data. (b) The Victoreen function for transmission data. (c) The Gaussian tail used to fit scattering contributions in dilute fluorescence samples collected with germanium or silicon energy-discriminating detectors.

The ideal post-edge normalization μ₁ is performed in order to create a unit step across the absorption edge. Normalization strategies may include (i) normalizing to a single point, such as the maximum peak of the spectrum (i.e. the white line), (ii) normalization to the mean value of the spectrum over a specified range or (iii) normalizing using a linear or quadratic polynomial function across a specified range. Examples are shown in Fig. 2. Generally, the first two options mentioned here have substantial issues that can arise with their use depending on the experimental conditions and the form of the data. In this approach, the latter case of using polynomial functions for the data set is generally the most common. The specified range is typically 40–100 eV after the absorption edge to the end of the spectrum. Adjustments to the fitting range can be made to avoid particular regions of structure in the edge region that may adversely affect the polynomial fit in the near-edge region. Care should be taken to collect data points in the spectrum that go well beyond the XANES region in order to achieve proper normalization (Calvin, 2013). In cases where the data range is truncated, it may difficult for the polynomial fit to achieve a uniform process, particularly if the purpose of the data is to compare spectra with different XANES features (Fig. 3). In these cases, one may often choose to try several background fits to examine the effects that the various fit parameters may have on the resulting normalization and that may propagate into the next fitting steps. This is the most common case where it is necessary to fall back on the suboptimal normalization steps mentioned above. Of course, the best-practice strategy is to ensure that the data are collected over a sufficiently large energy range after the edge to perform a more ideal normalization.

Figure 2 Examples of post-edge fitting to obtain normalized unit step-height spectra. (a) Post-edge normalization using quadratic polynomial fitting to the post-edge region. (b) Post-edge normalization to set the maximum of the white line at the edge to 1. (c) Post-edge normalization to average the range of values after the edge. (d) Comparison of normalization results.

Figure 3 XANES spectra with a shortened data-collection range can present problems with accurately normalizing the data. Although a normalized spectrum can be obtained, it may difficult to compare with other model compounds.

Later analysis of XANES data can be strongly dependent on the quality of the normalization process, and the comparison of spectra with different backgrounds (i.e. data collected in fluorescence versus transmission) can require different techniques in the pre-edge/post-edge methods. The above­mentioned methods require judgement from the experimenter of which background and normalization functions are ideal, and can introduce unintentional `user error' into the results. As shown in Figs. 2(d) and 3, poor or inconsistent choices can lead to spectra with a poor quality of normalization when following the conventional approaches. An approach was developed by Weng et al. (2005) which provides an automated and objective solution to this process.

The MBACK method fits a single, continuous background function over both the pre-edge and post-edge regions of the spectrum (Weng et al., 2005). To avoid complications with the edge region, the background is not fitted over the range from ∼20 eV below the edge to 80 eV above the edge. The background function and a scale factor are adjusted during the fit to find the best agreement with tabulated X-ray absorption cross sections, thus minimizingwhere μ is the raw spectrum, μ_back is the background function and μ_tab is the tabulated X-ray absorption coefficient, s is the scale factor and n₁ and n₂ are the points in the raw spectrum that correspond to the fitting-range limits above. The background μ_back is given as the sum of two components. The first is a complementary error function to accommodate elastic scatter centred at the energy of the X-ray emission line of the absorbing element (E_m) with a fitted width (ξ) and amplitude (A). The second component is a set of Legendre polynomials that are centred at the X-ray absorption edge of order m = 2–3, with a final form of

This overall method was found to be more reliable for comparing data from different data sources and produced white-line heights and pre-edge features that were more consistent than conventional methods (Weng et al., 2005). An example of the MBACK algorithm, as applied to the data set used for the conventional method, is shown in Fig. 4. Note that since the spectrum is normalized to the tabulated value of the X-ray absorption coefficient, the post-edge will not necessarily be flat, nor will it be equal to 1.

Figure 4 XANES spectrum normalized using the MBACK procedure. Note that the post-edge region matches the tabulated values for the X-ray coefficient (manganese, Z = 25).