Definition and classification of core edges

Colliex, C.

doi:10.1107/97809553602060000593

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 404-406

Section 4.3.4.4.1. Definition and classification of core edges

C. Colliex^a

4.3.4.4.1. Definition and classification of core edges

| top | pdf |

As for any core-electron spectroscopy, EELS spectroscopy at higher energy losses mostly deals with the excitation of well defined atomic electrons. When considering solid specimens, both initial and final states in the transition are actually eigenstates in the solid state. However, the initial wavefunction can be considered as purely atomic for core excitations. As a first consequence, one can classify these transitions as a function of the parameters of atomic physics: Z is the atomic number of the element; n, l, and j = l + s are the quantum numbers describing the subshells from which the electron has been excited. The spectroscopy notation used is shown in Fig. 4.3.4.21 . The list of major transitions is displayed as a function of Z and [E_c] in Fig. 4.3.4.22 .

Figure 4.3.4.21| top | pdf |

Definition of electron shells and transitions involved in core-loss spectroscopy [from Ahn & Krivanek (1982)].

Figure 4.3.4.22| top | pdf |

Chart of edges encountered in the 50 eV up to 3 keV energy-loss range with symbols identifying the types of shapes [see Ahn & Krivanek (1982) for further comments].

Core excitations appear as edges superimposed, from the threshold energy [E_c] upwards, above a regularly decreasing background. As explained below, the basic matrix element governing the probability of transition is similar for optical absorption spectroscopy and for small-angle-scattering EELS spectroscopy . Consequently, selection rules for dipole transitions define the dominant transitions to be observed, i.e. $[l'-l=\Delta l=\pm 1\quad {\rm and}\quad j'-j=\Delta j=0,\pm1. \eqno (4.3.4.37)]$ This major rule has important consequences for the edge shapes to be observed: approximate behaviours are also shown in Fig. 4.3.4.22. A very useful library of core edges can be found in the EELS atlas (Ahn & Krivanek, 1982), from which we have selected the family of edges gathered in Fig. 4.3.4.23 . They display the following typical profiles:

(i) K edges for low-Z elements $[(3\le Z\le 14)]$ . The carbon K edge occurring at 284 eV is a nice example with a clear hydrogenic or saw-tooth profile and fine structures on threshold depending on the local environment (amorphous, graphite, diamond, organic molecules, $[\ldots]$ ); see Isaacson (1972a,b).

Figure 4.3.4.23| top | pdf |

A selection of typical profiles (K, L_2,3, M_4,5, and N_2,3) illustrating the most important behaviours encountered on major edges through the Periodic Table. A few edges are displayed prior to and others after background stripping. [Data extracted from Ahn & Krivanek (1982).]

(ii) $[L_{\it 2,3}]$ edges for medium-Z elements $[(11\,\lesssim\, Z\,\lesssim\,45)]$ . The $[L_{2,3}]$ edges exhibit different shapes when the outer occupied shell changes in nature: a delayed profile is observed as long as the first vacant d states are located, along the energy scale, rather above the Fermi level (sulfur case). When these d states coincide with the first accessible levels, sharp peaks, generally known as `white lines', appear at threshold (this is the case for transition elements with the Fermi level inside the d band). These lines are generally split by the spin-orbit term on the initial level into $[2p^{3/2}]$ and $[2p^{1/2}]$ (or and ) terms. For higher-Z elements, the bound d levels are fully occupied, and no longer contribute as host orbitals for the excited 2p electrons. One finds again a more traditional hydrogenic profile (such as for the germanium case ).
(iii) $[M_{\it 4,5}]$ edges for heavier-Z elements $[(37\,\lesssim\, Z\, \lesssim\,83)]$ . A sequence of $[M_{4,5}]$ edge profiles, rather similar to $[L_{2,3}]$ edges, is observed, the difference being that one then investigates the density of the final f states. White lines can also be detected when the f levels lie in the neighbourhood of the Fermi level, e.g. for rare-earth elements.

The deeper accessible signals, for incident electrons in the range of 100–400 kV primary voltage, lie between 2500 and 3000 eV, which corresponds roughly to the middle of the second row of transition elements (Mo–Ru) for the $[L_{2,3}]$ edge and to the very heavy metals (Pb–Bi) for the $[M_{4,5}]$ edge.
(iv) A final example in Fig. 4.3.4.23 concerns one of these resonant peaks associated with the excitation of levels just below the conduction band. These are features with high intensity of the same order or even superior to that of plasmons of conduction band electrons previously described in Subsection 4.3.4.3. It occurs with the $[M_{2,3}]$ level for the first transition series, with the $[N_{2,3}]$ level for the second series (for example, strontium in Fig. 4.3.4.23) or with the $[O_{2,3}]$ level for the third series, including the rare-earth elements. The shape varies gradually from a plasmon-like peak with a short lifetime to an asymmetric Fano-type profile, a consequence of the coupling between discrete and continuum final states of the same energy (Fano, 1961).

References

Ahn, C. C. & Krivanek, O. L. (1982). An EELS atlas. Available from Center for Solid State Science, Arizona State University, Tempe, Arizona 85287, USA.Google Scholar

Fano, U. (1961). Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1966–1978.Google Scholar

Isaacson, M. (1972a). Interaction of 24 keV electrons with the nucleic acid bases, adenine, thymine and uracil. I. Outer shell excitation. J. Chem. Phys. 56, 1803–1812.Google Scholar

Isaacson, M. (1972b). Interaction of 25 keV electrons with the nucleic acid bases, adenine, thymine and uracil. II. Inner shell excitation and inelastic scattering cross section. J. Chem. Phys. 56, 1813–1818.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 404-406