(L2, L3), (M4, M5)…spectra

EELS spectra associated with electronic excitation from the L₂ and L₃ levels of elements or the M₄ and M₅ levels to the conduction band. Two similar-shaped spectra appear with an energy difference between the L₂ and L₃ levels. The spectra set is called (L₂ and L₃) spectra. For example, the energy difference between the L₂ and L₃ levels of the 3d transition metals is about 5 to 20 eV. The M₄ and M₅ spectra show a similar feature to (L₂ and L₃) spectra.
Due to the spin-orbit coupling, the 2p and 3d inner-shell levels split into two levels. That is, the 2p split levels are expressed as L₂(2p_1/2) and L₃(2p_3/2), and the 3d split levels are expressed as M₄(3d_3/2) and M₅(3d_5/2) (). L₂ and L₃ spectra are caused by the transition respectively from the levels L₂(2p_1/2) and L₃(2p_3/2) to the 3s and 3d components of the conduction band. M₄ and M₅ spectra are caused by the transition respectively from the levels M₄(3d_3/2) and M₅(3d_5/2) to p and f components of the conduction band. Since the final states of the unoccupied states are the same for both transitions, L₂ and L₃ (M₄ and M₅) spectra appear as spectra of similar shape separated by the energy difference between the levels L₂ and L₃ (M₄ and M₅).

The intensity ratio of the L₂ and L₃ spectra is expected to be 1:2 from the occupation ratio of the inner-shell L₂ and L₃ levels. However, the ratio experimentally observed is different from the expected ratio because the density of states of 3d electron in the conduction band is modified and the selection rule for electron transitions becomes different due to the core-hole interaction, the spin orbit coupling at the final state and the Coulomb repulsion of 3d electrons. Utilizing the phenomenon in which the intensity ratio deviates from 1:2, information on the valence of the 3d transition metal can be obtained.

Fig. 1(a) shows L₂ and L₃ (absorption edge) spectra of copper oxide (CuO). Two peaks of L₂ and L₃ spectra are separated by about 20 eV. The intensity ratio of L₂ and L₃ deviates from 1:2. Fig. 1(b) illustrates the electronic energy state of CuO. The L₂ and L₃ levels have an energy difference of approximately 20 eV due to spin orbit coupling. The observed spectra are interpreted as those from the inner-shell L₂ and L₃ levels to 3d unoccupied narrow states which is formed at the bottom of the conduction band. The electron configuration of Cu²⁺ in CuO is [3d⁹, 4s⁰] and one hole exists at 3d_5/2. The transition selection rule in this case is not determined by the orbital angular momentum change  but by the total angular momentum change  due to the spin-orbit coupling. Thus, the transition from 2p_3/2(L₃) to 3d_5/2 is allowed, but the transition from 2p_1/2(L₂) to 3d_5/2 is forbidden. This indicates that the L₃ peak should be observed, but the L₂ peak should not be observed. However, a weak L₂ peak is observed in the experiment as shown in Fig. 1(a). This is because there exist holes at the 3d_3/2 orbital component, which are caused by a weak covalent bonding between Cu and O.

Fig. 1 (a) L₂ and L₃ (absorption edge) spectra of copper oxide (CuO). The L₃ transition peak appears at 932 eV and the L₂ transition peak appears at 952 eV. The intensity ratio between the L₂ and L₃ spectra clearly deviates from 1:2. (b) Schematic electronic energy state of CuO and the process of L₂ and L₃ transitions. V.B. represents the valence band and C.B. represents the conduction band. The red and the pink parts respectively show the occupied and the unoccupied states of the Cu-3d orbit. The Cu-4s orbital component exists over a relatively broad energy range in C.B. and its density of states is small. Thus, the transition spectra to the 4s orbital component are observed as the broad background.

The difference of the M₄ and M₅ energy levels of sixth-period elements is 10 to 120 eV. Two spectra with similar shape successively appear with the energy difference in the EELS spectrum. The intensity ratio of the M₄ and M₅ spectra is expected to be 2:3 from the occupation ratio of the inner-shell 3d electron levels.
Fig. 2(a) shows M₄ and M₅ (absorption edge) spectra of Ba in barium titanate (BaTiO₃). Two peaks of M₄ and M₅ levels are seen with an energy difference of approximately 15 eV. The intensity ratio of M₄ and M₅ is approximately 2:3 as expected. Fig. 2(b) illustrates the electronic energy state of BaTiO₃. The M₄ and M₅ levels for Ba have the energy difference of approximately 15 eV due to spin-orbit coupling. The unoccupied narrow state of Ba-4f component is formed in the conduction band. Thus, transition spectra from the inner-shell M₄ and M₅ levels to the 4f unoccupied state are observed.
The L₂ and L₃ absorption edges of barium are reported to be 5247 eV and 5624 eV. Usually, as EELS measurements are performed up to about 1000 eV, it is difficult to observe the L₂ and L₃ spectra of barium.

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