电性、磁性、机械性能的各向异性

于2.0eV低于c轴。为了理解这个不同，返回看图3。c的吸收完
全是由于pz态的价电子分布在c轴线上。 pz这个光跃迁是，电子 从X范围也附近跃迁到导带底部。 By contrast the ab-absorption
spectrum, which originates from the light polarized along the in-plane direction, correspond to electron-hole pairs with px+py character Figs. 3a And 3c. This kind of excitations, like that occurring at Γ (or Z),are
张恺琪
In this paper we aim to explore the electronic and optical properties of the C4 phase by means of hybrid density functional theory. Our results provide evidence for the presence of strong electronic and optical anisotropy. Due to the well known difficulties of standard density functional theory(DFT) in predicting the band gaps of semiconductors and insulators, in the present work we employ a hybrid density functional method based on the Heyd–Scuseria–Ernzerhof HSE scheme as implemented in the Vienna ab initio simulation package VASP. Within the HSE method, the many body
Although both C4 and diamond represent a fourfold coordination scheme of a sp3-type hybrid, the
squared-like bonding scheme in C4
is associated with a substantially stronger electronic hybridization, as
附： 根据原子轨道最大重叠原理，成键时轨道之间可有两种不 同的重叠方式，从而形成两种类型的共价键——σ键和π键。 σ键--以“头碰头” 方式进行重叠，轨道的重叠部分沿键轴 呈圆柱形对称分布，原子轨道间以重叠方式形成的共价键。 π键--原子轨道中两个互相平行的轨道如py或pz 以“肩并肩” 方式进行重叠，轨道的重叠部分垂直于键轴并呈镜面反对称分 布（原子轨道在镜面两边波的瓣符号相反），而形成的共价键。
exchange x and correlation c functional is constructed by a proper mixing of
the Hartree–Fock(HF) and Perdew–Burke–Ernzerhof exchange
密度泛函理论
密度泛函理论是一种研究多电子体系电子结构的量子力学方法,主 要目标是用电子密度取代波函数做为研究的 基本量。因为多电子波函数
合材料中某一组分在另一组分中分布的特殊性造成的。(2)按照各 向异性性质分类, 有电学各向异性、磁学各向异性、热学各向异
性、光学各向异性和力学各向异性等。(3)从观察的角度出发又有
宏观各向异性和微观各向异性之分。
体心四方C4（bct C4）的结构和石墨、金刚石
相似。 1.石墨→ bct C4：通过一个垂直的压力，保持
结论：计算表明超强度的C4型碳有高的各向异性。我们发现 各向异性和C4型的特殊的键和形式（两个定向的C-C键和不
同的键距）有密切关系，这引起了价带顶分布的电子的各向
异性，并最终影响了电学、光学和机械性质。
谢谢！
有 3N 个变量（N 为电子数，每个电子包含三个空间变量），而电子密
度仅是三个变量的函数，无论在概念上还是实际上都更方便处理。
杂化密度泛函
在LDA（GGA）泛函中加入精确的交换项，构成杂化泛函。在杂化 泛函里面,体系的交换能是通过Hartree-Fock方法和密度泛函理论方法两 种方法的线性组合来计算得到。这种方法得到杂化泛函在实际计算中比 单纯的密度泛函理论方法准确很多，因此得到了广泛的研究和利用。
各向异性
材料的各向异性是指在相同的外在条件(如温度、压力、场 等)下, 材料的某些性能沿不同的方向存在差异的性质。
各向异性材料的分类主要有以下3 种:(1)按照材料产生各向
异性的原因可分为结构型和复合型两类。结构型各向异性材料的 产生是由材料本身内部原子的排列、晶格结构类型的差异造成的。
而复合型各向异性材料的产生是由2 种或2 种以上组分组成的复
In contrast, the C4 p states [Fig.(2b)] are split into an inplane doubly degenerate
C (px,py) component and a vertical C pz orbital, both strongly hybridized with the C-s states.
APPLIED PHYSICS LETTERS 97, 061910 2010
Anisotropy in electronic, optical, and mechanical properties of superhard body-centered tetragonal C4 phase of carbon
AB与CD平行，适度弯曲使碳原子共面。
2.石墨→金刚石：垂直压力使AB与CD段逆向 滑动。 3.C4 →金刚石：通过(001)(100)方向的滑移。 C4结构的特点是，碳原子有很强的共价键。通 过往正方形引入四个之字形碳链沿着c轴方向。 面内和面外的C-C键距分别是1.561 Å 和1.505 Å。金刚石的结构中C-C键距是1.54 Å。 图1 (a)石墨结构 (b)体心四方C4 结构 (c)金刚石结构 在C4结构中，AB和CD间的σ键成对形成。在金 刚石结构中，只有BC方向上的σ键。
晶体的光学各向异性
晶体结构表现出一定的空间周期性和对称性。这种结构特点导 致了晶体的宏观量的振动方向总是与光的传播方向垂直的，即光矢量的横向
振动状态，相对于传播方向不具有对称性，这种光矢量的振动相对 于传播方向的不对称性称为光的偏振性。
通过比较c轴线和ab面光偏振的吸收光谱(图4) ，发现光谱的 形状和强度都不相同。由于不同的偏振机制，ab面的吸收开始
fully confined in the ab-plane.
Our calculations revealed that the C4 phase possesses an indirect optical gap of 3.75 eV, 40% smaller than the band gap of diamond, in very good agreement with the previous value obtained by the Green’s function GW approach 3.78 eV. This indirect gap is opened between the top of the valence band at Z and the conduction band minimum along the Γ Q direction and therefore it is exclusively correlated with the in-plane px+pz states and the corresponding in-plane C–C distance. One would expect that by elongating the in-plane C–C bonds, the band gap will be reduced because the covalency of the C–C bond decreases. We have already mentioned that the C4 is obtained upon vertical compression of metallic graphite; indeed, by reverting the process, namely, increasing the C–C in-plane distance in the C4 phase, the C4 phase is progressively transformed back to graphite and it eventually becomes metallic due to the breaking of the σ -type covalent bonds and the formation of π–type hybrids.
P. Y. Wei, Y. Sun, X.-Q. Chen,a D. Z. Li, and Y. Y. Li Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China (Received 7 June 2010; accepted 25 July 2010; published online 11 August 2010)