有重位点阵关系两相的复合点阵(Ⅱ) 两相空间点阵及其点阵平面的重合系数

本文用数论分析方法,给出有重位点阵关系两相空间点阵及其点阵平面重合系数求法的普遍而简便的公式。空间点阵的重合系数α_2~(3)=1/C~(1),点阵平面的重合系数α_2~(h)= (H~(2)C~(1)/C~(1),C~(1)为重位点阵基矢对应矩阵,H~(2)=[h_1~(2)h_2~(2)h_3~(2)].在C~(1)未知的情况下,空间点阵及其点阵平面的重合系数可以通过两相基矢有理对应矩阵φ及重合系数矩阵C来求,这时α_2~(3)=k_1~(2)k_2~(2)/d~3,α_2~(h)=(CH~(2),dk_1~(2))/d~2.求矩阵C比求矩阵C~(1)要方便得多。     

位错点阵投影的三维数字成像

提出一种基于位错点阵投影的三维数字成像方法。该方法以二维点阵结构光顺序照明参考平面和被测物体表面,通过分析分别投影在参考平面和物体上的点阵的成像过程,建立投射在参考平面和被测物体表面上的点阵中同一点在成像面上横向位置错动与被测物体深度之间的数学模型。依据此模型,通过计算相对应点在成像平面上的横向位移。可计算出物体的深度图像。二维点阵可以在垂直于光轴的平面内做横向和纵向的两维移动,以填补由于离散而丢失的其他空间点的深度信息,获得高空间分辨率。实验验证了该方法的可行性,此方法对于拓扑复杂的表面和大梯度表面有较强的适应性。     

带电粒子在四电荷点阵中的运动

本文讨论了带电粒子在四电荷点阵平面中所受的作用力以及不同初始条件下的运动。     

衍射轴棱锥产生光学点阵的理论和实验

提出一种利用衍射轴棱锥产生三维光格的方法.由广义的惠更斯一菲涅耳衍射积分理论出发.分析准直单色平面光波大角度斜入射轴棱锥形成的光学点阵的特性.数值模拟光束在不同入射角入射轴棱锥情况下,随轴向距离变化的纵向光强分布以及同一轴向距离处的横向光强分布光斑图.结果指出,随着入射轴棱锥角度的增大,在最大无衍射距离内会形成有规则的光学点阵,这种光学点阵与三维光子晶体的结构相近,实验结果与数值模拟相吻合.     

有重位点阵关系两相的复合点阵(Ⅱ)——两相空间点阵及其点阵平面的重合系数

本文用数论分析方法,给出有重位点阵关系两相空间点阵及其点阵平面重合系数求法的普遍而简便的公式。空间点阵的重合系数α₂⁽³⁾=1/|C⁽¹⁾|,点阵平面的重合系数α₂^(h)= (H⁽²⁾C⁽¹⁾/|C⁽¹⁾|, C⁽¹⁾为重位点阵基矢对应矩阵,H⁽²⁾=[h₁⁽²⁾h₂⁽²⁾h₃⁽²⁾].在C⁽¹⁾未知的情况下,空间点阵及其点阵平面的重合系数可以通过两相基矢有理对应矩阵φ及重合系数矩阵C来求,这时α₂⁽³⁾= k₁⁽²⁾k₂⁽²⁾/d³, α₂^(h)=(CH⁽²⁾,dk₁⁽²⁾)/d².求矩阵C比求矩阵C⁽¹⁾要方便得多。 关键词：     

约化胞与电子衍射谱的标定

对应于14种布喇菲点阵有44种约化胞,不但约化矢的选法是唯一的,而且可以根据约化矢标量积矩阵(a·a b·b c·c b·c c·a a·b)的不同形式,确定布喇菲点阵类型。在晶体点阵已知的情况下,从点阵参数计算出倒易点阵中的平面约化胞,并与试验得到的电子衍射谱对比以标定衍射斑点的指数。在晶体点阵未知的情况下,从已知转角的两个电子衍射谱中选三个接近中心的衍射斑点,相当于三个低指数倒易矢量。由它们构成倒易点阵的一个初基胞,变换成正点阵的初基胞后,经过约化得出约化胞和相应的布喇菲单胞的类型和参数,同时标定衍射斑点的指数。这些标定计算已编成电子计算机程序,可以用来直接确定晶体点阵类型和进行物相分析。     

非晶Ni-P合金晶化过程中生成的六角亚稳相

本文利用透射电镜中的双倾台绕c^{*轴旋转晶体,唯一地确定了Ni-P非晶膜晶化后生成成分约为Ni_2.2P的针状亚稳相具有六角点阵,a=6.73?,c=9.42?。堆垛类型为AA…。(001)平面的高分辨点阵象以及衍射斑点沿c*方向拉长成条纹均表明晶体存在一维无序错排。 关键词：}     

反铁磁Ising自旋S=1三角格子上的基态研究

本文采用文献[1]中提出的费米变换方法,研究了与三态点阵气体模型等价的三角点阵上的近邻相互作用的具有五个参数的最一般的 S=1 lsing 反铁磁体,严格地求得了它的基态能量和丰富而复杂的零温相图.同时还利用四相点方程,将 k,l 平面分成25个小区域,它们分别对应于各个拓扑不等价的基态相图.     

格点规范理论(Ⅰ)

本文介绍了由Wilson等人发展起来的处理粒子间强相互作用的格点规范理论。由于这个理论是建立在点阵上的规范理论,故首先讨论了点阵上体系的场论性质和统计物理性质之间的联系,介绍了处理粒子禁闭问题的Wilson判据,点阵的哈密顿形式。然后讨论了各种具体模型的计算方法,如规范场的点阵模型、紧致QED模型、费米子模型、阿贝尔Higgs模型等。在此基础上,总结出Wilson定理。本文也讨论了格点规范理论中的实空间重正化群方法,介绍了Heisenberg平面模型的重正化群分析,一维的二维的复现关系及Migdal近似。最后评介了近年来对于Wilson回路算子的一些研究,内容包括’t Hooft代数和Wilson回路算子方程等。     

格点规范理论(Ⅰ)

本文介绍了由Wilson等人发展起来的处理粒子间强相互作用的格点规范理论。由于这个理论是建立在点阵上的规范理论,故首先讨论了点阵上体系的场论性质和统计物理性质之间的联系,介绍了处理粒子禁闭问题的Wilson判据,点阵的哈密顿形式。然后讨论了各种具体模型的计算方法,如规范场的点阵模型、紧致QED模型、费米子模型、阿贝尔Higgs模型等。在此基础上,总结出Wilson定理。本文也讨论了格点规范理论中的实空间重正化群方法,介绍了Heisenberg平面模型的重正化群分析,一维的二维的复现关系及Migdal近似。最后评介了近年来对于Wilson回路算子的一些研究,内容包括’t Hooft代数和Wilson回路算子方程等。     

Graphite格子光子晶体带隙的数值模拟

采用平面波展开法模拟计算了由锗圆柱构成的Graphite格子二维光子晶体的带隙结构,发现由空气背景中的介质柱构成的二维Graphite格子结构的光子晶体具有完全光子带隙,并得到了使完全带隙最大化的结构参数。数值计算结果表明,Graphite结构二维光子晶体在填充比从f=0.058到f=0.605连续变化的很大范围内都有完全带隙出现,在低能区出现了Δ=0.053(ωa/2πc)的较大带隙。     

Dimers Belonging to Three Orientations on Plane Honeycomb Lattices

It is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice, and in each type all dimers are mutually parallel. Based on a previous result, we can compute the partition function of the dimer problem of the plane (free boundary) honeycomb lattices with three different activities by using the number of its pure dimer coverings (perfect matchings). The explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way (for a shape of plane honeycomb lattices, the procedure that the size goes to infinite, corresponds to a way that the honeycomb lattice goes to infinite). From these results, an interesting phenomena is observed. In the case of the regions of the plane honeycomb lattice has zero entropy per dimer—when its size goes to infinite—though in the thermodynamic limit, there is no freedom in placing a dimer at all, but if we distinguish three types of dimers with nonzero activities, then its free energy per dimer is nonzero. Furthermore, a sufficient condition for the plane honeycomb lattice with zero entropy per dimer (when the three activities are equal to 1) is obtained. Finally, the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed.     

由面心立方（111）面间距谈几何晶体学的几个基本概念

通过对面心立方晶体（111）面间距的计算,对几何晶体学中几个基本概念进行了全面的辨析;在此基础上,给出了晶面指数和密勒指数之间的转换矩阵．     

诊断LiF单晶弹性变形的瞬态X射线衍射

利用瞬态X射线衍射技术对LiF单晶沿晶向[100]方向冲击加载的晶格变形进行了诊断研究。实验在神光Ⅱ装置的球形靶上进行,北四路激光驱动Cu靶获得的类He线作为X射线背光源,第九路为加载光源,对大小为7mm×7mm、厚300μm的受激光加载的LiF单晶衍射,实验获得了LiF单晶晶面(200)压缩和未压缩状态的衍射信号。实验结果表明:LiF单晶在激光沿[100]方向冲击加载下,晶格发生了弹性变形,(200)晶面间距变小,衍射线上移,晶格压缩量为11%;该瞬态X射线衍射技术可用于冲击加载下的微观动态响应特性测量。     

Synchronized family dynamics in globally coupled maps

The dynamics of a globally coupled, logistic map lattice is explored over a parameter plane consisting of the coupling strength, varepsilon, and the map parameter, a. By considering simple periodic orbits of relatively small lattices, and then an extensive set of initial-value calculations, the phenomenology of solutions over the parameter plane is broadly classified. The lattice possesses many stable solutions, except for sufficiently large coupling strengths, where the lattice elements always synchronize, and for small map parameter, where only simple fixed points are found. For smaller varepsilon and larger a, there is a portion of the parameter plane in which chaotic, asynchronous lattices are found. Over much of the parameter plane, lattices converge to states in which the maps are partitioned into a number of synchronized families. The dynamics and stability of two-family states (solutions partitioned into two families) are explored in detail. (c) 1999 American Institute of Physics.     

Spectral element modeling for extended Timoshenko beams

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.     

MOVING NONLINEAR LOCALIZED MODES FOR ONE-DIMENSIONAL KLEIN－GORDON DIATOMIC LATTICE

We study analytically the moving nonlinear localized vibrational modes (discrete breathers) for a one-dimensional Klein－Gordon diatomic lattice in the whole ω(q) plane of the system by means of a semi- discrete approximation, in which the carrier wave of the modes is treated explicitly while the envelope is described in the continuum approximation. We find that both pulse and kink envelope moving modes for this lattice system can occur with certain carrier wave vectors and vibrational frequencies in separate regions of the ω(q) plane. However, the kink envelope moving modes have not been reported previously for this lattice system.     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

Quantitative analysis of defects and domain boundaries in mesoporous SBA-16 films

Some quantitative structural analyses on defects and domain boundaries observed in SBA-16 films were performed using the lattice concept and geometric phase method. These analyses show that there exist low angle, high angle and translational anti-phase domain boundaries in SBA-16 films. While some of the domain boundaries bear analogue to those found in normal solid crystals, others are similar to that found in the liquid crystals. In particular near Sigma11 and Sigma13b high angle boundaries were observed. On the one hand the Sigma11 boundaries were found to exist with or without steps (ledge) associated with them depending on whether or not the boundary plane is parallel to the densely packed lattice plane. On the other hand segments of the boundary plane in the Sigma13b boundary were found being always associated with densely packed lattice plane, with the {011} type of lattice plane in one domain being parallel to the {112} type of plane in the other domain. The translational domain boundary was observed to have a translation vector having a projected component of (1/2) <110> on the (111) plane. The bending deformation similar to that found in the nematics liquid crystal was also observed and quantitatively analyzed using the geometric phase method, and rotational field associated with the deformation was identified.     

Upper bound to the charge-transfer energy on a 2D Wigner lattice in high-Tc cuprates

Assuming that the energy of a 2D Wigner lattice, which has been frequently observed on the CuO₂ plane in layered high-T_c cuprates, is composed of Coulomb energy, kinetic energy, and charge-transfer energy which is necessary to transfer electrons or holes onto the CuO₂ plane (the magnitude of the energy is expected to be of the order of the work function of the compound constituting the plane from which the electrons are transferred, if the CuO₂ plane easily accepts the electrons or holes, as if the CuO₂ plane were crystal surface), we find in the mean-field approximation, that the total energy for a unit lattice, E₀, can be given by a function of the charge-transfer energy E_φ as E₀= (E_φ−E_φ⁰+O((E_φ−E_φ⁰)₂)(>0), where the value of E_φ⁰(1.5 in the ground state, for example) is independent of the lattice configuration. This relation implies that the upper bound to the charge-transfer energy is given by E_φ⁰. The smallness of E_φ⁰, compared with the work function of ordinary metals and alloys (with the work function around 4 eV), is necessary for the realization of the 2D Wigner lattice in many layered high-T_c cuprates.