Vacancy state

Interatomic Coulombic decay (ICD) is an electronic decay process that is particularly important for those inner-shell or inner-subshell vacancies that are not energetic enough to give rise to Auger decay. Typical examples include inner-valence-ionized states of rare gas atoms. In isolated systems, such vacancy states are bound to decay radiatively on the nanosecond timescale. A rather different scenario is realized whenever such a low-energy inner-shell-ionized species is let to interact with an environment, for example, in a cluster. In such a case, the existence of the doubly ionized states with positive charges residing on two different cluster units leads to an interatomic (or intermolecular) decay process in which the recombination part of the two-electron transition takes part on one unit, whereas the ionization occurs on another one. ICD [73-75] is mediated by electronic correlation between two atoms (or molecules). In clusters of various sizes and compositions, ICD occurs on the timescale from hundreds of femtoseconds [18] down to several femtoseconds [76-79]. 

In the periodic cluster approach, the size of the supercell influences the number of orbitals and thus the discrete representation of the band structure. Using this model to describe localized defects such as vacancies introduces an additional difficulty because now the spatial extent of the vacancy wavefunction must be related to the size of the supercell. A 64-atom supercell was found to be too small to adequately describe the vacancy wavefunction, the amplitude of the wave function of a monovacancy at the cell boundary is still V4 of the maximum value. This means that the wavefunction has a considerable overlap with the vacancy wavefunctions of the neighboring cells. This artificial defect-defect interaction leads to a dispersion of about 0.8 eV for the vacancy states. When a 216-atom supercell is considered, the wavefunction amplitude at the cell boundary is only Vs of the maximum value and the dispersion is less than 0.2 A supercell of at... 

Since the rate of decay of a vacancy state is the sum of radiative and nonradiative transition rates, the ratios of the intensities of individual X-ray lines are proportional to the ratio of the rates for the corresponding transitions. The fractional emission rates Fij (where i is the munber of subshell and j is the transition e.g.. For L we take Fsa) is defined as ... 

The ZrC calculations by the APW-CPA method of Ivashchenko, Lisenko and Zhurakovsky (1983) were more refined. Although they do not reproduce the characteristic two-peak fine strueture of the density of vacancy states, they correctly reproduce the increases of the DOSs at the Fermi level and p, as the vacancy concentration increases. 

In a conclusion, we mention the CPA calculations of DOSs of nonstoichiometric MoC c (x = 1,0.83, and 0.67) with NaCl- and WC-type structures (Kolpachev, 1988). As was found for hexagonal MoC, the energy of the vacancy LDOS coincides with the energy of an intensive dxz,yz maximum near the Fermi energy, and the density of vacancy states is much lower for the hexagonal structure modification than for the cubic one. 

Among the band calculations, there were two attempts, by Ivashchenko (1984) and Schalder and Monnier (1989), to study the influence of structural defects on the electronic structure of solid solutions. Ivashchenko used the APW-LCAO-CPA method for analysis of the DOS distribution in the ZrC jN D (x + y + z = 1) alloy. It was found that metallization of the alloy takes place as z increases. Some Hf carbonitrides with a variable number of p atoms and cation and anion vacancies were studied by Schalder and Monnier (1989) making use of the relativistic KKR-GF method. Reasonable agreement was obtained between the calculated and experimental photoelectron spectra. It was shown that the presence of defects in the solid solutions leads to the formation of additional vacancy states (Fig. 5.12), which are typical for binary phases (Chapter 4), and to partial charge polarisation towards metallic centres. The latter effect is more pronounced for C vacancies (see Table 5.1). One of the most interesting conclusions of this paper was the establishment of the nonmonotonic variation of the N(Ep) in the series HfC HfCj,Nj HfN (Table 5.1). 

These peculiarities in the distribution of the impurity states are defined primarily by the nearest neighbourhood of M or C vacancies. The electronic states of these atoms interact strongly with outer orbitals of the Be atoms, which fill these vacancies in the soUd solution. As follows from Chapter 4, the vacancy states of C defects in TiC and NbC produce intensive DOS peaks near the Fermi level and result in an increase of the electron density along the M-M bonds near the defect. The shape of these states is determined by the admixtures of Be2p functions. Similar features are seen in the LDOS of Be in position (2) and M defects, revealing the dominant hybridisation of the impurity states and C2p-orbitals. 

The origin for this systematic discrepancy is the configuration interaction betYggn the inner-shell vacancy state and the Auger continuum ... 

Due to Cl at least the following configurations in the ground state and the initial vacancy state are mixed (passive closed shells have been omitted) ... 

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