Ion-beam shadowing effects have been measured for keV secondary electrons induced by protons, deuterons, and alpha particles in the energy range of 5.3-8.35 MeV/u, under various channeling conditions in Si, GaAs, and MgO crystals. From a comparison of the electron yields for protons and for the other projectiles of equal velocity, we have determined averaged numbers of the interstitial target electrons that suffer no shadowing effect. This method is useful for investigating the bond-electron distribution in a crystal lattice. Furthermore, the results for deuterons and alpha particles indicate that the quantum-mechanical diffraction of ions disappears in a series of small-angle scatterings by the aligned atoms, even when the Coulomb-scattering parameter has a nonclassical value (kappa=1.1).

We show that the Mizoguchi structure is energetically stabilized over the Verwey structure for magnetite by electron hopping on the B sublattice. We use the one-band Cullen-Callen model Hamiltonian for the electronic band structure taking the nearest-neighbor and the second-neighbor Coulomb interactions, U1 and U2, into account. There is a competition between the Coulomb and the band-structure energies. The Coulomb energy tends to favor the Verwey structure while the band-structure energy tends to favor the Mizoguchi structure. We find that for U1 less than or similar to 0.25 eV, the kinetic-energy (band-structure energy) term dominates making the Mizoguchi structure energetically favorable over the Verwey structure. For a larger value of U1, the band-structure effect alone is insufficient, making it necessary to invoke other mechanisms such as the electron-phonon coupling earlier proposed by other authors, to stabilize the Mizoguchi structure. The energy of a single ''reversed-ring'' excitation in the Mizoguchi structure is calculated to be of the order of a few meV. The small energy is consistent with Cullen's explanation of the absence of cell doubling in the C(a) plane as observed in diffraction experiments. The Mizoguchi order is unstable with respect to the formation of reversed-ring excitations if only U1 is present, but is stabilized by a small value of U2.

We argue that the analysis of Reimers et al. [Phys. Rev. B 45, 7295 (1992)] of their Monte Carlo data on the Heisenberg pyrochlore antiferromagnet, which suggests a new universality class, is not conclusive. By reanalysis of their data, we demonstrate asymptotic volume dependence in some thermodynamic quantities, which suggests the possibility that the transition may be first order.