PHYSICAL REVIE%' 8 VOLUME 34, NUMBER 3 1 AUGUST 1986 White lines in the L2 3 electron-energy-loss and x-ray absorption spectra of 3d transition metals %. G. %'addington' Department of Metallurgy and Science of Materials, Uniuersity of Oxford, Parks Road, Oxford OXI 3PH England P. Rex~ Center for Solid State Science and Department of Physics, Arizona State Uniuersity, Ternpe, Arizona 85287 I. P. Grant Department of Theoretical Chemistry, Uniuersity of Oxford, South Parks Road, Oxford OXI 3PH England C. J. Humphreys~ Department of Metallurgy and Science of Materials, Uniuersity of Oxford, Parks Road, Oxford OXI 3PH England (Received 28 January 1986j In the electron-energy-loss or x-ray-absorption spectra of the 3d transition metals the onset of the L2 3 edge (2p excitation) is marked by two sharp peaks often called white lines. The peaks are attri- buted to the excitation of the 2@3/2 and 2@i/2 subshells to unoccupied d levels but the observed ratio of their areas is not the statistical 2:1 ratio expected from initial-state occupation. In this paper we report the results of multiconfiguration Dirac-Fock calculations of the transition rates which should include atomic many-electron effects. %e compare our results with experimental energy-loss mea- surements from a number of sources. There is good agreement for the ratio of the two components although the detailed shape can show additional solid-state effects. In particular, the L3-L2 ratio is very sensitive to the charge state for elements in the middle of the period such as Mn and Cr. This effect can therefore be used to measure ionicity in energy-loss microanaiysis in the electron micro- scope. INraaDUCIION Sharp peaks at the thresholds of absorption edges were first observed by x-ray absorption for the L edges of heavy elements such as Pt. As early observations were made photographically, the peaks were seen as white lines on the photographic plate. The name has remained even though photographic recording has been superceded by electronic data-acquisition systems (see Refs. 1 and 2 for general review of white-line observations). White lines in the 2p spectra from the transition metals were first ob- served by Cauchois and Honnelle ' by x-ray absorption. For small scattering angles the energy-loss spectrum of high-energy ( — 100 kV) electrons transmitted through thin specimens in an electron microscope is identical to the x-ray-absorption spectrum. The energy-loss experi- ments of Leapman and Grunes ' showed that the ratio of the two spin-orbit components from the 2p3/z and 2pi/z transitions did not follow the statistical 2:1 ratio expected from the ratio for the initial states. Various nonrelativis- tic band calculations failed to reproduce the observed ef- fect and other "many-electron" explanations were pro- posed. The electron-energy-loss results were confirmed by synchrotron-radiation x-ray-absorption studies for calci- um, scandium, and titanium by Barth et a/. , who be- lieved that the results could be explained using an atomic theory without solid-state effa:ts. There have been other synchrotron results for calcium and copper in copper ox- ide. Similar white-line effects have been observed in the 3d absorption spectra of rare-earth elements, initially by x-ray-absorption spectroscopy and later by electron- energy-loss spectroscopy (EELS). The ratios of the M& (3 d s/2 ) and Mq (3 d 3/2 ) spin-orbit components do not equal the initial-state 3:2 ratio. Atomic multiplet calcula- tions, in which the transition rates are calculated by per- turbation theory on a nonrelativistic Schrodinger equa- tion' ' gave reasonable agreement with the white-line structure at the ends of the rare-earth-metal period. The most recent example of this approach is a full multiplet calculation for all the rare-earth elements. ' An alternative to the atomic multiplet approach has been the relativistic linear combination of atomic orbitals (LCAO) band calculation of Mattheis and Deitz. '6 They leave the number of holes in the two bands associated with the spin-orbit components as a parameter which can be determined by accurate band calculations or experi- ment. This has been used recently to explain magnetic or- dering in amorphous metals. ' Other recent experimental work has concentrated on energy-loss measurements of various 3d transition metals in different compounds showing different degrees of ionicity. ' In this paper we apply an atomic multiconfiguration Dirac-Fock (MCDF) program to the 2p excitation. '9 The program handles both elo:trostatic and spin-orbit effects automatically as part of the Dirac formalism. The more familiar atomic multiplet method of calculation — for ex- ample, in the work of Sugar' — treats the spin-orbit in- teraction as a perturbation of an essentially nonrelativistic problem. It is also customary in these calculations to scale down the electrostatic and exchange parameters by 1986 The American Physical Society