Outer-shell vacancies

Kr outer-shell vacancies present in the final state, f). Physically, this means that the three-electron transition consists of virtual two-electron recombination on krypton cations followed by ionization of X (see Figure 6.6). The corresponding recombination matrix element entering Eq. (21) is... 

In contrast to the DV-Xa ground-state discussion, outer-shell vacancies are now created through a two-step mechanism In a first step they are accommodated with proximately equal probabilities in both e resonance levels of a mixed F and Zn character. Then, in the course of the relaxation occurring in response to stronger binding due to vacancies, the two resonance states again separate and are transformed back into F 2p and Zn 3d (cf. left part of Fig. 4) and, in effect, the e vacancies are transferred either to F or Zn (from lowest and highest e, respectively). 

Figure Bl.24.14. A schematic diagram of x-ray generation by energetic particle excitation, (a) A beam of energetic ions is used to eject inner-shell electrons from atoms in a sample, (b) These vacancies are filled by outer-shell electrons and the electrons make a transition in energy in moving from one level to another this energy is released in the fomi of characteristic x-rays, the energy of which identifies that particular atom. The x-rays that are emitted from the sample are measured witli an energy dispersive detector.

The transitions involved in Auger emission are illustrated in Fig. 10. The primary process is the ionization of an inner shell by bombardment with electrons. The vacancy is then filled by an electron from an outer shell, and the energy released can either appear as an X-ray quantum, or... 

Exposure of elements to a broad spectrum of X-rays results in the ejection of electrons from their inner shells. Electrons from outer shells falling into these vacancies emit radiation of specific wavelengths (see Figure 14.13). Analysis of this radiation, referred to as X-ray fluorescence (XRF), allows for the identification of the element from which the photon is emitted. Instruments for carrying out this analysis can be either laboratory sized or can be handheld... 

In Auger transitions, incident electrons interact with the inner shell electrons E of the sample. The vacancy created by an ejected inner shell electron is filled by an outer shell electron (Ei), and a second outer shell electron ( 2) is ejected leaving the atom in a doubly ionized state. The electrons ejected from the outer shells are called Auger electrons, named after the Frenchman Pierre Auger, who discovered the effect. Thus, AES measures the energies of the Auger electrons ( a) emitted from the first 10 A of a sample surface. The energy equation is expressed as... 

X-ray fluorescence (XRF). The sample is irradiated with monochromatic X-rays that eject electrons from the inner shells of the elements. When an electron from an outer shell of the ion drops into the vacancy, it emits characteristic X-rays whose wavelength is used to identify the element and whose intensity is related to the amount present. XRF is used primarily for elements heavier than magnesium because of the weak fluorescence of lighter elements and absorption of the X-rays within the particles. The combination of transmission or scanning electron microscopy (TEM/SEM) with X-ray fluorescence, also known as energy-dispersive spectrometry (EDS), was discussed in Section B.2b. 

PIXE is a technique that uses a MeV proton beam to induce inner-shell electrons to be ejected from atoms in the sample. As outer-shell electrons fill the vacancies, characteristic X-rays are emitted and can be used to determine the elemental composition of a sample. Only elements heavier than fluorine can be detected due to absorption of lower-energy X-rays in the window between the sample chamber and the X-ray detector. An advantage of PIXE over electron beam techniques is that there is less charging of the sample from the incoming beam and less emission of secondary and auger electrons from the sample. Another is the speed of analysis and the fact that samples can be analyzed without special preparation. A disadvantage for cosmochemistry is that the technique is not as well quantified as electron beam techniques. PIXE has not been widely used in cosmochemistry. 

Metallic bonding is the attraction of all the atomic nuclei in a crystal for the outer shell electrons rhat are shared in a delocalized manner among all available orbitals. Metal atoms characteristically protide more orbital vacancies than electrons for sharing with other atoms. 

Lines, corresponding to different transitions from initial states with vacancy in the shells with the same n, compose a series of spectra, e.g. K-, L-, M-series etc. Main diagram lines correspond to electric dipole ( 1) transitions between shells with different n. The lines of 2-transitions also belong to diagram lines. Selection rules of 1-radiation as well as the one-particle character of the energy levels of atoms with closed shells and one inner vacancy cause, as a rule, a doublet nature of the spectra, similar to optical spectra of alkaline elements. X-ray spectra are even simpler than optical spectra because their series consist of small numbers of lines, smaller than the number of shells in an atom. The main lines of the X-ray radiation spectrum, corresponding to transitions in inner shells, preserve their character also for the case of an atom with open outer shells, because the outer shells hardly influence the properties of inner shells. 

X-ray fluorescence spectrometry (XRF) is a non-destructive method of elemental analysis. XRF is based on the principle that each element emits its own characteristic X-ray line spectrum. When an X-ray beam impinges on a target element, orbital electrons are ejected. The resulting vacancies or holes in the inner shells are filled by outer shell electrons. During this process, energy is released in the form of secondary X-rays known as fluorescence. The energy of the emitted X-ray photon is dependent upon the distribution of electrons in the excited atom. Since every element has a unique electron distribution, every element produces... 

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... 

Electrons can move between the various levels—and between different materials so long as their levels and bands overlap to create a tunnel —but there are two requirements they need a boost of energy to reach a higher energy band, and a vacant slot in the band they enter. The outer shells of metallic conductors have several of these vacancies, along with electrons that are loosely held, and it is these slots that those free electrons head for when voltage—the energy, the electromotive force derived from an... 

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). 

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