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Harmonic lattice dynamics calculations have been performed for the antiferroelectric P213 ordered phase of α-carbon monoxide and for two related structures with a different head–tail ordering of the CO molecules. The potential used is an ab initio CO–CO potential with its anisotropy expanded in spherical harmonics, as well as a site–site model fitted to this ab initio potential. Good agreement with experiment is obtained for the structure, the cohesion energy, and the phonon frequencies without any adjustment of the potential. Head–tail reordering of the molecules is energetically almost neutral if it is accompanied by a translational displacement along the bond axes, which is symmetric with respect to the inversion centers of the average Pa3 structure. This displacement is induced in particular by the strong head–tail anisotropy in the short-range repulsion. Translation–rotation coupling is found to be important; it affects especially the frequency of the lowest optical mode.

Low-energy electron energy loss (LE-EELS) spectra have been calculated by a generalization of R-matrix methods to solid state systems. The scattering processes involved in LE-EELS can be explained by an atomic model. The contribution of exchange scattering in the calculated loss spectra is important over a large energy range of incident electron energies and is comparable in strength with direct scattering. The ratio of spin-flip to nonflip intensity in LE-EELS depends on the magnetic structure of the target, the type of transition involved (triplet-triplet or triplet-singlet), and the scattering geometry. [S0031-9007 (97)02868-8] PACS numbers: 82.80.PvIn this Letter we describe the use of theoretical techniques from atomic physics to study the inelastic scattering of low-energy electrons from NiO, involving the atomic 3d-3d excitations on the Ni 21 ions. In the experiments, electrons with an energy of typically 20-100 eV are reflected off the solid in LEED geometry [1][2][3][4]. Dipoleforbidden transitions, and transitions that are not allowed because of spin selection rules, can be measured in this way and the experiments show a wealth of angle-, spinpolarization-, and energy-dependent structure. Attempts have been made to understand this behavior of the spectral weight, both for the case of localized 3d-3d excitations in transition metal compounds such as NiO and CoO [1-4] and for the even more localized 4f-4f excitations in rare earth metals like Gd [5][6][7][8]. As far as the loss energies are concerned, the data from low-energy electronenergy-loss spectroscopy (LE-EELS) experiments and theoretical studies show satisfactory agreement [4,9]. Turning to the behavior of the peak intensities, no theoretical models exist that can give a quantitative estimate of direct and exchange scattering in LE-EELS-for incident electron energies smaller than 150 eV-and explain the complex behavior of the localized excitations as a function of the scattering parameters (energy, geometry, spin polarization). This makes the interpretation of the experimental results a difficult task, especially if one recognizes the following complications: first, it is not easy to separate the scattering events into those that involve one single inelastic scattering and those that are a combination of both inelastic and elastic scattering (either single or multiple). Second, multiplicity-changing (triplet-singlet) transitions in LE-EELS have strong overlap with the triplet-triplet transitions, and, finally, spin-dependent LE-EELS measurements using sputtered NiO samples have a large defect state contribution [2].For the theoretical description of localized excitations in LE-EELS, we rely on a technique from atomic physics, R-matrix theory [10,11], and generalize this to the context of solid state systems. This is a multichannel version of scattering theory taking into account inelastic processes corresponding to excitations of the scattering center. It thus provides a way of generalizing scattering methods like Korringa-Kohn-Rostoker which only...

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