Electronic Band Structure of Graphene Based on the Rectangular 4-Atom Unit Cell

The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.

三维四向复合材料微观模型的研究现状及展望

三维四向复合材料是一种新结构形式的复合材料,具有优良的力学性能、抗冲击损伤性能及耐烧蚀性能,受到各国学者的重视。在讨论目前较为成功的"米"字型、"六面体截面"交织型、"双扭线"型等单胞微观模型的基础上,提出了"贝塞尔"单胞模型。该模型较好地模拟了三维四向复合材料纤维的走向与微观结构,为下一步深入研究打下了基础。

四步法矩形组合截面三维编织物的细观结构

采用控制体积法研究了以四步法编织矩形组合截面三维编织物的特殊细观结构。根据三维编织原理,得到编织物内各区域携纱器的运动规律。从中看出,除了常规矩形截面三维编织物所具有的内部、棱(外)角和表面区域外,矩形交接区域的内部、内角和表面具有特殊的细观结构。分析了矩形组合截面三维编织物所特有的矩形交接区域以及交接内部、交接内角和交接表面的细观结构,建立了这三个区域的单胞模型。结果表明,交接区域的内部单胞外形为立方体,交接区域的内角单胞外形为七棱柱体,交接区域的表面单胞为五棱柱体。与常规矩形截面的单胞相比,矩形组合截面在交接区域中,纱线的空间形态和编织角均存在明显不同。