Electronic Structure, Charge Transfer and Bonding in Intermetallics Using EELS and Density Functional Theory
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pseudopotentials, etc) has enabled these methods to be faster and more reliable, when combined with the greatly increased power of workstations, so that these computer codes can now be executed on workstations and even on fast personal computers. We have used the LMTO method with the local density approximation for exchange and correlation. The LMTO calculations were run selfconsistently and EELS spectra were calculated by combining the computed density of states (DOS) with the matrix elements for the transition from initial to final states (see below). This treatment is based on the single-particle approximation of the EELS spectrum (see, for example [2]). We have also calculated spectra based on the more computationally demanding Korringa-Kohn-Rostoker (KKR) non-linear method for comparison (agreement is very good for the systems studied). ELECTRON ENERGY LOSS SPECTROSCOPY (EELS) In EELS, the fast incident electron excites electrons in the crystal from bound to unoccupied states (that is, states above the Fermi level). If the initial state has angular momentum L then the final states must have angular momentum L+ 1 or L- 1. Hence if the initial state is a p state, the final state must be d or s. The EELS intensity for a transition from an initial state with angular momentum L to a final unoccupied state with angular momentum L+1 is: I 0CIML+12 PL*PL+,
(1)
where PL and PL+I are the density of the initial states and the density of unoccupied final states, respectively, and * denotes convolution of the initial and final density of states. For excitations from inner shells the density of initial states, PL, is a delta function to a good approximation, hence I oc IML+I12 PL+1
(2)
Thus the intensity of EELS spectra is proportional to the density of unoccupied final states. This is an important result. The matrix element ML+l is given by ML+l=JWqL*(r)HWL+l(r)dr
(3)
where VL(r) and wVL+(r) are the initial and final state wavefunctions and H represents the electronelectron interaction. For non-zero ML+l then 'g and 4VL+1 must overlap, hence if 1YL is a localised core state, 4lL+1 must be local to the same atomic volume, hence EELS probes the local density of states. For intermetallics based on transition metal elements (eg NiAl) we are particularly interested in the nature of the 3d band, hence in the transitions from initial 2p states to unoccupied 3d states. The 2p state is split into 2p312 and 2pi12 initial states (spin-orbit coupled) hence the transition from 2p to 3d gives rise to two distinct sets of peaks, separated in energy (the 2 p'i2 --ý 3d transition gives rise to the L 2 peak and the 2p3/2 --- 3d transition to the lower energy L 3 peak). The L2 and L3 peaks are known as white lines since they originally appeared on x-ray absorption spectra as white lines on a dark background. Ni AND NiAI: THE BONDING COMPARED Figure 1 shows experimental EELS spectra for the Ni L2-3 edges from fcc Ni and from NiAl. It is immediately apparent that EELS is sensitive to the bonding changes which occur when Ni goes from meta
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