再谈"流浪地球"——让地球脱离太阳系最少需要做多大的功?

从一部国产科幻大片《流浪地球》的一项宏大计划出发,针对该计划第二步——让地球脱离太阳系,利用动量守恒定律、动能定理和逃逸速度、有效反冲喷射速度概念,计算了在地球质量能够满足生命存在的需要的条件下,让它脱离太阳系所需的最少做功为2.72×1032焦耳,并从能源角度讨论让地球脱离太阳系的可能性问题.     

过渡金属掺杂在Bi2Te3体系中诱导产生的磁性

用从头计算方法研究了在Bi₂Te₃体系采用过渡金属掺杂从而诱导出磁性的可能性．用一个过渡金属原子置换一个Bi原子之后,可以在该体系中产生磁矩,这主要是由于过渡金属原子的3d轨道电子的自旋极化导致的．当一个Ti、V、Cr、Mn和Fe原子分别替代一个Bi原子时,体系显示的磁矩分别为0.92、1.97、2.97、4.04和4.98 μ_B．当引入两个过渡金属原子代替两个Bi原子的时候,交换耦合的特性取决于取代Bi原子的分布;代替的Bi原子的位置在Bi1和Bi5的位置时,这两个过渡金属原子之间的距离为11.52 ?, Bi_1.84TM_0.16Te₃体系能量最稳定并且表现出铁磁性耦合．     

固体潮相关的地球表面形变和涨落

在月球和太阳的引力作用下,地球的固体表面也发生与海水表面类似的周期性涨落,这种现象称为固体潮.固体潮的形成原因与海潮相同,但其计算问题远比后者复杂.本文用开尔文地球模型和比较简单的方法计算固体潮相关的地球表面方程和涨落幅度,并进行相关问题的讨论.     

阳离子空位和吸附氧的协同作用对Na0.5Bi0.5TiO3(100)表面磁性影响的第一性原理研究

The combination effect of cation vacancies and O₂ adsorption on ferromagnetism of Na_0.5Bi_0.5TiO₃(100) surface is studied by using density functional theory.An ideal Na_0.5Bi_0.5TiO₃(100) surface is non-magnetic and the cation vacancy could induce the magnetism.By comparing the formation energies for Na,Bi and Ti vacancy,the Na vacancy is more stable than the others.Therefore,we focus on the configuration and electric structure for the system of O₂ molecule adsorption on the Na_0.5Bi_0.5TiO₃(100) surface with a Na vacancy.Among the five physisorption configurations we considered,the most likely adsorption position is Na vacancy.The O₂ adsorption enhances the magnetism of the system.The contribution of spin polarization is mainly from the O 2p orbitals.The characteristics of exchange coupling are also calculated,which show that the ferromagnetic coupling is favorable.Compared with the previous calculation results,our calculations could explain the room-temperature ferromagnetism of Na_0.5Bi_0.5TiO₃ nanocrytalline powders more reasonably,because of taking into account adsorbed oxygen and cation vacancies.Moreover,our results also show that adsorption of O₂ molecule as well as introduction of cation vacancies may be a promising approach to improve multiferroic materials.     

过渡金属掺杂在Na0.5Bi0.5TiO3体系中诱导产生磁性的第一性原理研究

The origins of magnetism in transition-metal doped Na_0.5Bi_0.5TiO₃ system are investigated by ab initio calculations. The calculated results indicate that a transition-metal atom substitution for a Ti atom produces magnetic moments, which are due to the spin-polarization of transition-metal 3d electrons. The characteristics of exchange coupling are also calculated, which shows that in Cr-/Mn-/Fe-/Co-doped Na_0.5Bi_0.5TiO₃ system, the antiferromagnetic coupling is favorable. The results can successfully explain the experimental phenomenon that, in Mn-/Fe-doped Na_0.5Bi_0.5TiO₃ system, the ferromagnetism disappears at low temperature and the paramagnetic component becomes stronger with the increase of doping concentration of Mn/Fe/Co ions. Unexpectedly, we find the Na_0.5Bi_0.5Ti_0.67V_0.33iO₃ system with ferromagnetic coupling is favorable and produces a magnetic moment of 2.00 μB, which indicates that low temperature ferromagnetism materials could be made by introducing V atoms in Na_0.5Bi_0.5TiO₃. This may be a new way to produce low temperature multiferroic materials.     

太空液桥实验的理论研究——由太空课堂引起的又一教学案例

本文针对天宫课堂第二课中的液桥实验进行理论研究.基于液桥的对称性和体积不变性，根据最小势能原理，我们获得液桥形状的几何方程，据此探讨液桥形状随其长度的变化规律和最大长度.发现一个描述液桥形状的特征参数R,并揭示该参数与液桥内部压强的关系.