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In this paper, the exact solutions of Dirac electronic states of graphene in Coulomb and magnetic fields are acquired. The Coulomb field not only causes the splitting of Landau levels in gapless graphene but also leads to the variation of the energy level ordering in gapped graphene. The dependence of the binding energies on the gap and the magnetic field is discussed. Furthermore, the valley degree of freedom and the valley splitting spacing can be controlled by the Coulomb and magnetic fields in gapped graphene. The intervalley mixing of graphene is estimated and calculated in the direct sum spaces of the two valleys. The results obtained help us to understand the behaviors of the planar Dirac electron in electromagnetic fields and can be applied to the controlling of the electron's behaviors in graphene.

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Halo evolution of an Al-17.5Si alloy surface after treatment with increasing pulse numbers of a high-current pulsed electron beam (HCPEB) was investigated. A halo is a ring microstructure resembling a bull’s eye. SEM results indicate that the nanocrystallization of halo induced by HCPEB treatment leads to gradual diffusion of the Si phase. Multiple pulses numbers cause the Si phase to be significantly refined and uniformly distributed. In addition, nanosilicon particles with a grain size of 30~100 nm were formed after HCPEB treatment, as shown by TEM observation. XRD results indicate that Si diffraction peaks broadened after HCPEB treatment. The microhardness tests demonstrate that the microhardness at the midpoint from the halo edge to center decreased sharply from 9770.7 MPa at 5 pulses to 2664.14 MPa at 25 pulses. The relative wear resistance of a 15-pulse sample is effectively improved by a factor of 6.5, exhibiting optimal wear resistance.