The momentum transfer in electron-energy-loss spectra ͑EELS͒ recorded in an electron microscope can be controlled in a manner akin to polarization-dependent soft-x-ray absorption spectroscopy, however with much greater spatial resolution. Here we report orientation-dependent EELS from fine-grained MgB 2 for both B K and Mg L 2,3 edges. Calculations based on an excited final state are used to suggest an anisotropic exciton for the peak at 55 eV at the Mg L 23 edge.Since the discovery of the superconductivity in layered metal MgB 2 at a superconducting transition temperature T c ϳ39 K, 1 much attention has been focused on understanding the superconductivity mechanism. Evidence of the B isotope shift of T c suggests a phonon-mediated BCS superconductivity. 2 Further evidence from high-resolution x-ray photoemission spectroscopy ͑XES͒ of multiple superconducting gaps in MgB 2 indicates a deviation from the conventional isotropic s-wave mechanism. 3 Band structure calculations show that the valence band of MgB 2 consists mainly of two distinct bands of two-dimensional covalent in-plane (B 2p x,y ) and three-dimensional metallic-type interlayer (B 2p z ). 4 -9 Anisotropic features of the density of states ͑DOS͒ approaching the Fermi energy in singe-crystal MgB 2 have been reported using angle-resolved XES. 10 Recently, the orientation-dependent B DOS has been reported, 11 but the results are different from our experiments and calculations. In addition, measurements of the orientation dependence of the unoccupied Mg DOS have not been reported. The grain size is generally less than a micron in sintered MgB 2 . Therefore spatially resolved spectroscopic methods become necessary for this anisotropic polycrystalline material.Electron-energy-loss spectroscopy ͑EELS͒ has also been used to study the orientation dependence of anisotropic single crystals. 12 When combined with a transmission electron microscope ͑TEM͒ this becomes a powerful technique to probe the electronic structure in the near atomic level and therefore to probe the anisotropic DOS in fine-grained solids.Here we report experimental EELS evidence for anisotropic features in both the B K and Mg L 23 edges. Under the assumption of the dipole selection rule ͑small momentum transfer, q•rӶ1), the B K and Mg L 23 edges approximately probe the unoccupied B p and Mg sϩd states, respectively. The orientation dependence of the B K edge reflects its anisotropic features in the DOS, which have been predicted by band structure calculations. However, the q dependence of the Mg DOS has not been reported before.In a one-electron approximation, EELS gives the fraction of beam electrons that, in traversing a thin slab, have lost energy E to the excitation of a core electron from an initial state to unoccupied final states. The transition probabilities can be calculated using Fermi's golden rule. For small angle scattering, the dipole approximation applies; therefore, the EELS intensities can be simplified as the product of the DOS and an atomic transition matrix: 13where ͉i͘ and...