Determination of total x-ray absorption coefficient using non-resonant x-ray emission

Abstract

An alternative measure of x-ray absorption spectroscopy (XAS) called inverse partial fluorescence yield (IPFY) has recently been developed that is both bulk sensitive and free of saturation effects. Here we show that the angle dependence of IPFY can provide a measure directly proportional to the total x-ray absorption coefficient, µ(E). In contrast, fluorescence yield (FY) and electron yield (EY) spectra are offset and/or distorted from µ(E) by an unknown and difficult to measure amount. Moreover, our measurement can determine µ(E) in absolute units with no free parameters by scaling to µ(E) at the non-resonant emission energy. We demonstrate this technique with measurements on NiO and NdGaO(3). Determining µ(E) across edge-steps enables the use of XAS as a non-destructive measure of material composition. In NdGaO(3), we also demonstrate the utility of IPFY for insulating samples, where neither EY or FY provide reliable spectra due to sample charging and self-absorption effects, respectively.

Figure 1. Energy sensitive fluorescence yield of NiO.

(a) Normalized x-ray fluorescence of NiO as the incident photon energy is scanned through the Ni L₃ and L₂ edges.(b) The emission spectra in the pre- and post-edge regions at incident photon energies of 845 eV and 880 eV taken in 1-eV windows. Emissions corresponding to the resonant Ni 3d to 2p and 3s to 2p () and non-resonant (normal) O 2p to 1s (K_α) processes are observed. (c) The Ni L and O K partial fluorescence yield extracted from panel a in 150-eV wide energy windows centered on the respective emissions. The resonant Ni L PFY shows strong distortions resulting from saturation effects. The normal O K PFY dips as the absorption increases through the Ni L_3,2 absorption edges. (d) The IPFY is the inverse of the O K PFY shown in panel c. The NiO IPFY is in good agreement with total electron yield data from Ref. which has been scaled and offset to match the IPFY.

Figure 2. Angle dependence of PFY and IPFY.

(a) The Ni L PFY for various experimental geometries.The spectra are distorted by strong self-absorption effects that depend on the angle of incidence (α) and angle of emission (β). (b) The IPFY extracted from the O K PFY for the same experimental geometries as panel a. The spectra are offset by a geometry dependent constant, but are otherwise not distorted. The inset plots the IPFY at E_i = 845 eV (red circles) as a function of sin α/ sin β, which varies linearly as predicted by Eq. (1). (c) The linear absorption coefficient, µ(E_i), obtained from IPFY spectra. As described in the text, the offsets in the IPFY spectra are subtracted, collapsing the IPFY spectra onto a single curve proportional to µ(E_i). The spectra shown here have been scaled using a single tabulated value for µ(E_f) and plotted against the tabulated (green) and calculated (red squares) absorption coefficients.

Figure 3. Wide energy range IPFY of NdGaO₃.

(a) IPFY of NdGaO₃ for several measurement geometries.The IPFY is measured using the O K emission in a 150 eV window centred about 524 eV. The measurements at different geometries exhibit different sloping backgrounds due to the energy dependence of µ_OK(E_i) and the quantum efficiency of the I₀ measurement, ν(E_i). (b) S(E_i) calculated using Eq. (3) with the different measurement geometries depicted in the legend of panel a. The black line is a linear fit to S(E_i). (c) The IPFY/S(E_i) spectra are rigidly offset by B. (d) The total absorption coefficient, µ(E_i), determined using Eq. (5) (the data are scaled to µ(524 eV) from Ref. 14). The spectra measured with different geometries collapse onto a single curve over the entire energy range.

Figure 4. Normalized IPFY compared to atomic calculations.

The absorption coefficient of NdGaO₃ extracted from the O K IPFY and corrected for the energy dependence of the O K absorption and the quantum efficiency of the I₀ measurement.The incident photon energy was scanned across the Nd M₅ and M₄ edges. The data agrees well with calculated XAS over a wide energy range.

Figure 5. XAS of NdGaO₃.

(a) The TEY of NdGaO₃ exhibits an anomalous negative edge-jump across the Nd M_5,4 edges (red curve).A spectrum collected with the incident photon energy scanned in the negative direction (blue curve) soon after has positive edgejumps. This difference is attributed to a charge up of the sample surface, affecting the TEY measurement. Neither spectrum matches well with TEY on pure metallic Nd from Ref. . (b) The partial fluorescence yield from the Nd emission of NdGaO₃ is strongly distorted by saturation effects. (c) The IPFY extracted from the O K PFY of NdGaO₃ agrees remarkably well with the TEY of pure Nd from Ref. which is scaled and offset to match the IPFY.