Inner shell vacancy

For atoms having an atomic number greater than 10, the electron filling the inner shell vacancy may come from one of several possible subshells, each at a different energy, resulting in families of characteristic X-ray energies, e.g., the Ka, P family, the La, P, y family, etc. 

The complete description of the number of Auger electrons that are detected in the energy distribution of electrons coming from a surface under bombardment by a primary electron beam contains many factors. They can be separated into contributions from four basic processes, the creation of inner shell vacancies in atoms of the sample, the emission of electrons as a result of Auger processes resulting from these inner shell vacancies, the transport of those electrons out of the sample, and the detection and measurement of the energy distribution of the electrons coming from the sample. 

Once an inner shell vacancy is created in an atom the atom may then remrn toward its ground state via emission of a characteristic X ray or through a radiationless Auger transition. The probability of X-ray emission is called the fluorescence yield. 

The Auger effect is the phenomenon involving electron-hole recombination in an inner-shell vacancy causing the emission of another electron. 

In this case, an M electron is emitted as an Auger electron. The Auger process is termed a radiationless transition. The probability that an inner shell vacancy... 

Three analytical techniques which differ in how the primary vacancies are created share the use of such X-rays to identify the elements present. In X-ray fluorescence, the solid sample is irradiated by an X-ray beam (called the primary beam), which interacts with the atoms in the solid to create inner shell vacancies, which then de-excite via the emission of secondary or fluorescent X-rays - hence the name of the technique. The second uses a beam of electrons to create the initial vacancies, giving rise to the family of techniques known collectively as electron microscopy. The third and most recently developed instrumentation uses (usually) a proton beam to cause the initial vacancies, and is known as particle- (or proton-) induced X-ray emission (PIXE). 

As noted above, there are several ways of creating an inner shell vacancy which may de-excite via the emission of a characteristic X-ray. XRF uses a primary beam of X-rays, but suffers from the fact that the characteristic X-ray spectrum recorded from a solid sample contains a scattered version of the primary spectrum, increasing the background signal and therefore degrading analytical sensitivity. The use of an electron beam to create inner shell... 

This chapter discusses the range of analytical methods which use the properties of X-rays to identify composition. The methods fall into two distinct groups those which study X-rays produced by the atoms to chemically identify the elements present, and X-ray diffraction (XRD), which uses X-rays of known wavelengths to determine the spacing in crystalline structures and therefore identify chemical compounds. The first group includes a variety of methods to identify the elements present, all of which examine the X-rays produced when vacancies in the inner electron shells are filled. These methods vary in how the primary vacancies in the inner electron shell are created. X-ray fluorescence (XRF) uses an X-ray beam to create inner shell vacancies analytical electron microscopy uses electrons, and particle (or proton) induced X-ray emission (PIXE) uses a proton beam. More detailed information on the techniques described here can be found in Ewing (1985, 1997) and Fifield and Kealey (2000). 

Figure 5.1 The X-ray emission and Auger processes (Pollard and Heron 1996 37). An inner shell vacancy is created in the K shell by the photoelectric process (emitted photoelectron not shown), (a) shows the X-ray emission process, where an L shell electron drops down to fill the vacancy, and the excess energy (EK - EL) is carried away as an X-ray photon. In (b), an L shell electron drops down, but the excess energy is carried away by an Auger electron emitted from the M shell, with kinetic energy approximately equal to EK - EL — EM. Reproduced by permission of the Royal Society of Chemistry.

The probability that the inner shell vacancy will de-excite by one or other of these processes depends on the energy level of the initial vacancy and the atomic weight of the atom. The fluorescent yield, co, is defined as the number of X-ray photons emitted per unit vacancy, and is a measure of the... 

Some incident electrons will create inner shell vacancies as described above. The electrons ejected by the primary beam (photoelectrons) can be used analytically (in XPS) but are generally ignored in electron microscopy. The inner shell vacancy can de-excite via the Auger process (Auger electrons are also generally neglected in this application) or via the emission of characteristic X-rays, which are detected and which form the basis of the analytical operation of the electron microscope. 

We should note that the photoelectric effect often leaves an inner shell vacancy in the atom that previously contained the ejected electron. This vacancy will be filled by an atomic transition, called fluorescence, and generally produces an X-ray photon. In an interesting twist of fate, the X-ray photon will have an energy that is just below the sharp rise in the attenuation coefficient due to conservation of momentum and can often escape from the absorber. Recall that the direction of the fluorescence photon will be uncorrelated with the direction of the incident photon and a fraction will be emitted backwards from the absorber. The absorber will thus emit its own characteristic X-rays when it is irradiated with high-energy photons. 

In summary, the dynamics of the electronic decay of inner-shell vacancies in a charged environment, such as created by interaction of a cluster with a high intensity FEL radiation, can be qualitatively different from the one induced by a low-intensity source. If the emitted electrons are slow enough to be trapped by the neighboring charges, the familiar exponential decay will be suppressed by quantum beats between the initial state and the quasi-continuum of discrete final states. Physically, the predicted oscillations correspond to creation of the initial vacancy due to the reflections of the emitted electron by the charged cluster potential and the subsequent inverse Auger transition. 

Figure 6.6 Schematic representation of collective interatomic decay of two inner-shell vacancies, see Eq. (20).

Some qualitative understanding of the CICD can be gained by means of Wentzel-type theory that treats the initial and final states of the decay as single Slater determinants taking electronic repulsion responsible for the transitions as a perturbation. The collective decay of two inner-shell vacancies (see Figure 6.6) is a three-electron transition mediated by two-electron interaction. Thus, the process is forbidden in the first-order perturbation theory, and its rate cannot be calculated by the first-order expressions, such as (1). Going to the second-order perturbation theory, the expression for the collective decay width can be written as... 

Relativistic Hartree-Slater values of the X-ray emission rates for the filling of K- and L-shell vacancies in berkelium have been tabulated (78). X-ray emission rates for the filling of all possible single inner-shell vacancies in berkelium by electric dipole transitions have been calculated, using nonrelativistic Hartree-Slater wavefunctions (79). 

As the matter of fact, 1(a) of empty orbitals can be defined as the sum of the electron affinity and A (a, a). This problem also occurs in X-ray emission involving the loosest bound electrons jumping down in an inner vacancy. As we already discussed after Eq. (7) the last term of Eq. (20) is essentially (r r) of the outer electron being attracted as if (23) the element had the subsequent atomic number (Z -f 1). In metals, the bottom of the partly occupied conduction band tails off toward more negative energies than in the groundstate without inner-shell vacancies (this problem seen from the point of view of the relaxation of the surrounding electron density by photo-ionization of a metal is discussed by Watson and Perlman in this volume) and in compounds, transitions from filled penultimate... 

The x-ray emission process in atoms and molecules is considered in three steps. In the first step (t = — oo), all the electrons are in their lowest energy states, the ground state (GS). Then an inner-shell vacancy is created at t = 0 in the second step. This state can be called the initial state (Init). After a certain period between this step and the next step, the vacancy in the inner shell moves to an outer shell accompanying x-ray emission. In the final step, the vacancy is assumed to remain in the outer shell (t = oo). Let us call this state the final state (Fin). 

When the nuclear charge changes due to radioactive decay and/or an inner-shell vacancy is produced, the bound electrons in the same atom or molecule experience the sudden change in the central potential and have a small but finite probability to be excited to an unoccupied bound state (shakeup) or ejected to the continuum (shakeoff). We calculated the shakeup-plu.s-shakeoff probabilities accompanying PI and EC using the method of Carlson and Nestor [45]. 

Further extension of methodological discussion seems quite pointless here. Instead, the usefulness of the SW method should be exemplified by a brief review of some of its applications to environmental effects on nucleus-shell interactions and the processes of creation and decay of inner-shell vacancies. 

Creation and decay of highly excited atom states carrying inner-shell vacancies... 

Fig. 2 Schematic illustration of the valence electron structure of light and heavy Si-bearing molecules (a) and the Si 1-type valence charge fiactions in dependence on inner-shell vacancy configuration (b) cf. [36].

The Auger electrons and characteristic X-rays are emitted from initial states with one inner-shell vacancy or sometimes with several vacancies in inner-and outer-shells, where the initial states are formed by ionization and excitation of inner- and outer-shell electrons. In ionization of the isolated atom, constituents of all the atomic orbitals except for an ionized electron remain unchanged after... 

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