Absorption of X-ray photons

As illustrated in Fig. 7.15, the electromagnetic radiation measured in an XRF experiment is the result of one or more valence electrons filling the vacancy created by an initial photoionization where a core electron was ejected upon absorption of x-ray photons. The quantity of radiation from a certain level will be dependent on the relative efficiency of the radiationless and radiative deactivation processes, with this relative efficiency being denoted at the fluorescent yield. The fluorescent yield is defined as the number of x-ray photons emitted within a given series divided by the number of vacancies formed in the associated level within the same time period. 

The absorption of x-ray photons frequently results in photoelectron emission (Figure 7.13) these electrons when not scattered by other atoms leave the material, according to the photoelectric effect, with a kinetic energy equal to the difference between the photon energy and that needed to remove it from the target atom, which is the binding energy or work function ... 

In X-ray photoelectron spectroscopy (XPS) (see above) the experimental information is obtained by analyzing the kinetic energy of the photoelectrons generated by the absorption of photons of fixed energy. In X-ray absorption spectroscopy the absorption of X-ray photons is measured as a function of photon energy. Accordingly, the technique requires a tunable X-ray source and can only be carried out at an electron synchrotron. 

The basis of XRE analysis is the photoelectric absorption and the subsequent emission of X-ray photons characteristic of the fingerprints of analyte atoms in the sample. Element composition can be quantified by the relative intensities of the indivi-... 

Figure 4.10. Absorption of X-rays as a function of photon energy E = hv by a free atom and by atoms in a lattice. The fine structure, due to the interference of waves...

The relationship of the dependent variables for diffraction and absorption, I,/Io and n, is considered here. The transmitted intensity of X-ray photons is equal to their incident intensity minus the intensity of photoelectrons of wavelength X emitted ( scattered ) at all angles, z/,... 

In the experiment, the transmission intensities for the excited and the dark sample are determined by the number of x-ray photons (/t) recorded on the detector behind the sample, and we typically accumulate for several pump-probe shots. In the absence of external noise sources the accuracy of such a measurement is governed by the shot noise distribution, which is given by Poisson statistics of the transmitted pulse intensity. Indeed, we have demonstrated that we can suppress the majority of electronic noise in experiment, which validates this rather idealistic treatment [13,14]. Applying the error propagation formula to eq. (1) then delivers the experimental noise of the measurement, and we can thus calculate the signal-to-noise ratio S/N as a function of the input parameters. Most important is hereby the sample concentration nsam at the chosen sample thickness d. Via the occasionally very different absorption cross sections in the optical (pump) and the x-ray (probe) domains it will determine the fraction of excited state species as a function of laser fluence. 

Fig. 10.16. Absorption of X-rays as a function of photon energy h by a free atom and by an atom in a lattice. The spherical electron wave from the central atom is scattered back by the neighbouring atoms, which leads to interference, which is constructive or destructive depending on the wavelength of the electron wave (or the kinetic energy of the electron) and the distance between the atoms. As a result, the X-ray absorption probability is modulated and the spectrum shows fine structure which represents the EXAFS spectrum [37],...

To correct for matrix effects the absorption of X-rays by the matrix must be calculated. If 6 is the angle of the axis of the spectrometer to the surface of the sample, a photon created at a mass depth pr has a probability of [1 - exp (-p/p.p.r. cosec 0)] of being absorbed (p/p is the mass absorption coefficient of the sample for the radiation under consideration, p is the density of the material crossed and z is the thickness crossed). 

This is reasonable because absorption of x-rays is proportional to the probability of a photon to encounter an atom when passing through matter. This probability is directly proportional to the number of atoms in the unit volume, i.e. to the density of the material. 

An important characteristic of any detector is how efficiently it collects x-ray photons and then converts them into a measurable signal. Detector efficiency is determined by first, a fi-action of x-ray photons that pass through the detector window (the higher, the better) and second, a fraction of photons that are absorbed by the detector and thus result in a series of detectable events (again, the higher, the better). The product of the two fractions, which is known as the absorption or quantum efficiency, should usually be between 0.5 and 1. 

The correctness of the scale factor is dependent on many parameters. The most critical are the photon flux in the incident beam remains identical during measurements at any Bragg angle the volume of the material producing scattered intensity is constant the number of crystallites approaches infinity and their orientations are completely random the background is accounted precisely the absorption of x-rays (when relevant) is accounted. 

The probability for absorption of an X-ray photon by an electron of an inner shell is dcperuleni on the initial and final states of tire excited electron. The initial stale is dial of the core electron, while the final Male is more difficult to describe. The absorption of X-ray radiation generates an electron... 

The X-rays enter the analysis chamber typically through a thin window made of 50-100nm thick membranes of Al, Si, or SijN4. Such windows have high transmission (e.g., the transmission of the 100 nm Al window varies from 70% to 90% for photon energies between 400 and 1000 eV) and prevent gases from entering the X-ray source (synchrotron beamline or anode), which needs to be operated in vacuum. The window must be placed as close as possible to the sample to minimize the absorption of X-rays by the gas phase inside the reaction chamber. 

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