The heat capacity of small metallic grains studied by the random matrices theory

The random matrices theory is applied to a study of the heat capacity of small metallic grains. The numerical calculations indicate that the level distribution and the difference between the particles respectively with an even and an odd numbers of electrons are important for the heat capacity of the small metallic grains at a low temperature and the level correlation mainly affects the heat capacity at a high temperature.     

Random matrices applied to superconductivity in nano-particles

In this paper we introduce an approach in which the random matrices are applied to superconducting nano-particles, and obtain the effects of enhancement and attenuation simultaneously. We also explore the influence of magnetic fields on the superconductivity and the condensation energies in nano-particles. Comparisons with other models and some experimental results are given.     

超小金属微粒超导电性的能级统计

用平均场理论的自洽方程计算了随机矩阵理论中三种系综(Gauss Orthogonal Ensemble;Gauss Unitary Ensemble;Gauss Symplectic Ensemble)所对应的电子能级的奇/偶电子数分布对临界电子能级间距的影响,得到了在不同的自旋-轨道耦合和磁场中奇/偶电子数分布的临界电子能级间距的定量关系以及奇电子数的Δ((0)随平均能间距o>的变化. 关键词：     

LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS

In this paper we have calculated the variations of the gap Δ'(0,d) and transition temperature T'_c in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical d_c, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'_c decreases and Δ'(0,d)/k_BT'_c≤πe_-γ in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes Δ'(0,d)/k_B T'_c>πe_-γ in even numbers of electrons.     

超硬B-C-N材料的电子结构、硬度和光学性质的第一性原理计算

本文基于密度泛函理论(DFT)的第一性原理平面波超软赝势方法计算了z-BC₂N和z-B₂CN的4种晶体结构的电子结构、硬度和光学性质。结果表明，z-BC₂N(2)为直接带隙半导体，其禁带宽度2.449 eV,z-BC₂N(1)为间接宽带隙半导体，其禁带宽度为3.381 eV,而z-B₂CN(1)和z-B₂CN(2)为导体；硬度结果显示z-BC₂N(1)、z-BC₂N(2)和z-B₂CN(1)为超硬材料。最后通过计算z-BC₂N基本光学函数与光子能量的关系表征了其光学性质。分析结果表明，z-BC₂N结构可以用作良好的耐磨材料和窗口耐热材料。     

纳米量级超导Al粒子在磁场中的Zeeman分裂

用随机矩阵理论对BCS理论中的自洽方程进行修正.由此得到的新自洽方程能合理地描述纳米量级Al粒子的超导电性.更进一步论证在外磁场作用下,s>0态由于Zeeman效应得出了实验中已观测到的超导增强效应. 关键词： 纳米粒子 超导电性 Zeeman分裂     

超小金属粒子的热力学性质

超小金属粒子系综的热力学性质受到分离电子能级分布和能级关联的影响。在考虑能级统计后，数值计算了含有奇数或偶数个电子的超小金属粒子正则系综的电子比热和自旋磁化率，并讨论了其低温和高温特征。作为例子，本文数值纳米铝粒子的电子比热和自旋磁化率。     

IVB族过渡金属氮化物弹性与光学性质研究

基于密度泛函理论平面波方法研究了IVB族过渡金属氮化物TiN, ZrN, HfN的电子结构、 弹性性质和光学性质. 研究表明, IVB族过渡金属氮化物晶格的电子结构分别体现了共价性、 离子性和金属性, 且基态下体系呈金属性. 各晶格在坐标基矢方向上的杨氏模量的数值与体对角线方向上的差距明显, 体现出典型的弹性性质各向异性, 这导致了实验研究在制备其薄膜时不可避免地产生晶格畸变与微裂纹. 伴随着态密度中赝隙的红移, TiN, ZrN, HfN的金属性依次增强, 使得材料在力学性能方面脆性减弱, 单晶的各向异性程度提升, 以及光学性质方面电子跃迁机理由带内跃迁到带间跃迁转变所需入射光子能量的蓝移和光谱选择性能的下降. 因此, 通过降低IVB族过渡金属氮化物中自由电子的组分以加强材料的共价性, 有利于提高材料弹性性质的各向同性, 改善材料的光谱选择性能. 关键词： 第一性原理 弹性性质 光学性质     

金属小粒子不同自旋态超导电性统计系综研究

用统计系综理论对遵从高斯正交系综的所有金属小粒子的不同自旋态Sz=0,12,1,32,2,52,…进行了研究.发现以上各态均存在临界能间距dcΔ(0)=1381,185,081,050,036,028,…随粒子尺寸的减小,其超导电性终究会消失;金属小粒子的自旋态越高,临界能间距dc越小.对自旋S=0的态,确实存在超导增强效应. 关键词： 金属小粒子 超导电性 无规矩阵     

Anisotropy of elasticity and minimum thermal conductivity of monocrystal M4AlC3 （M = Ti,Zr, Hf）

The elastic constants, elastic anisotropy index, and anisotropic fractional ratios of Ti4AlC3, Zr4AlC3, and Hf4AlC3 are studied by using a plane wave method based on density functional theory. All compounds are characterized by the elastic anisotropy index. The bond length, population, and hardness of the three compounds are calculated. The degrees of hardness are then compared. The minimum thermal conductivity at high temperature limitation in the propagation direction of [0001](0001) is calculated by the acoustic wave velocity, which indicates that the thermal conductivity is also anisotropic. Finally, the electronic structures of the compounds are analyzed numerically. We show that the bonding of the M4AlC3 lattice exhibits mixed properties of covalent bonding, ionic bonding, and metallic bonding. Moreover, no energy gap is observed at the Fermi level, indicating that various compounds exhibit metallic conductivity at the ground state.