等离子体色散函数的计算方法

本文推出了复宗量ξ=x+iy的误差函数的级数表达式。在这一基础上,对0≤y≤1,|x|≤10宗量区,给出了较高精度的等离子体色散函数Z及其微商Z'的计算方法。进而,对复平面ξ的各个区域,系统地研完了等离子体色散函数和相应的计算方法;在VAX—11/750计算机上得到了满意的结果,文章对这些结果,所用方法及其精度作了讨论;分别对y≥0和y<0,描述了Z和Z'的基本行为。     

W22[a,b]空间中的最佳Hermite插值算子

本文介绍具有再生核的函数Hilbere空间W₂²给出了W₂²空间再生核的有限表达式,利用它构造出最佳Hilbere插值逼近算子(H_2nu)(x)的真体表达式,当节点系无限加密时,能够保证(H_2nu)(x)一致收敛于u(x),(H_2nu)(y)一致收敛于u'(x),且每增加一个节点,误差在Sobolev范数意义下单调下降。     

奇摄动拟线性弱耦合系统解的估计

本文研究奇摄动拟线性系统边值问题#br#εY"=F(t,y,ε)Y'+g(t,y,ε),(0≤t < 1)#br#Y(0,ε)=A(ε),Y(1,ε)=B(ε)#br#其中,Y,g,A,B都是n维向量,F(t,Y,ε)是n×n阶对角短阵,Y',Y"是关于变量t的导数。     

多点边值问题的插值矩阵法及误差分析

插值矩阵法是求解多点边值问题的数值法。本文给出的该法的误差分析,论证了插值矩阵法解得的y(x),y'(x),…,y^(m)(x)有相同的精度,并对二阶方程,给出该法的稳定性证明和收敛阶。     

NiMgn(n=1—12)团簇的第一性原理研究

采用基于密度泛函理论(DFT)中的广义梯度近似 (GGA),在考虑自旋多重度的情况下,对NiMg_n(n=1—12)团簇进行了构型优化,频率分析和电子性质计算.结果表明：n=1,2时,体系的基态为自旋三重态,n≥3时,为单重态;Ni原子掺杂使主团簇结构发生了明显变化. n≤8时,三角双锥,四角双锥结构主导着NiMg_n基态团簇的生长行为; n在9—12之间时,主团簇Mg_n+1(n=1—12)的基于三棱柱构型的基态演化行为发生了一定程度的改变;n≥6时,Ni原子陷入了主团簇内部;掺杂使体系的平均结合能增大,能隙减小;n=4,6,10是团簇的幻数;不同尺寸团簇的s, p, d轨道杂化中,Ni原子3d, 4p成分所起作用不同; NiMg₆基态结构具有很高的对称性(O_h),很好的稳定性和化学活性,能隙仅为0.25eV. 关键词： n团簇')" href="#">NiMg_n团簇 几何结构 稳定性 化学活性     

La0.1Bi0.9-xEuxFeO3化合物的结构与性能研究

利用固相反应烧结技术制备La_0.1Bi_0.9-xEu_xFeO₃系列化合物. 利用X射线粉末衍射进行物相鉴定和结构分析,确定了材料的相关系：x≤0.05,材料为R3c结构相;0.08≤x≤0.12,材料为赝R3c结构相;x≥0.15是Pbnm相,其中0.15≤x≤0.20区域Pbnm相存在畸变. 磁测量结果表明,材料具有弱铁磁性,对于x≤0.20材料,磁矩在x=0.12成分存在极值. 利用阻抗分析仪测量了室温介电常数随成分的变化关系.讨论了材料的结构与弱铁磁性和室温介电常数间的关系. 关键词： 0.1Bi_0.9-xEu_xFeO₃')" href="#">La_0.1Bi_0.9-xEu_xFeO₃ X射线衍射 磁性 介电常数     

单母体遗传算法优化(H2O)n(n≤14)的结构

在传统遗传算法的基础上提出了单母体遗传算法(single-parent genetic algorithm, SPGA)，通过对母体团簇实施两种不同的变异操作对结构进行优化，给出了分子团簇结构优化的算法实现. 结合TIP3P模型势函数，研究了水分子团簇(H₂O)_n(n≤14)的稳定结构. 优化结构和已有理论及实验结果一致. 计算结果表明当n<8时，平均结合能随n增加较快；当n≥8时有小的起伏. n=4,8,10,12的团簇结构具有较高对称性，比较稳定. 关键词： 单母体遗传算法 水分子团簇 结构优化     

La2-xNdxCuO4+δ(0.1≤x≤1.2)体系中滞弹性弛豫与相变内耗研究

通过对La_2-xNd_xCuO_4+δ(0.1≤x≤1.2)体系中滞弹性弛豫与相变内耗性能的研究发现,当0.1≤x≤1.0时,在250K左右存在一个与间隙氧有关的弛豫内耗峰,并且当0.1≤x≤0.4时,弛豫内耗峰峰高随着x值的增大而升高,此时体系为正交结构;当0.5≤x≤1.0时,体系在宏观上呈现四方结构,此时内耗峰峰高随着x< 关键词： 2-xNd_<i>xCuO_4+δ')" href="#">La_2-xNd_<i>xCuO_4+δ 间隙氧 弛豫内耗峰 相变内耗峰     

合金团簇(FeCr)n中的非共线磁序和自旋轨道耦合效应

利用密度泛函理论对合金团簇(FeCr)_n (n≤6)的几何结构、稳定性和磁性进行了系统的研究. 研究结果表明, 对n≤3的合金团簇, 其基态具有共线的反铁磁序; 而对于n≥4 的合金团簇, 其基态具有非共线磁序, 因此在n=4时体系发生了共线磁序向非共线磁序的“相变”. 此外, 虽然3d过渡金属原子中电子的自旋轨道耦合效应比较弱, 但计算结果表明对于某些小尺寸的合金团簇其轨道磁矩不能忽略. 对非共线磁性团簇的成键性质以及产生磁序“相变”的物理起源进行了详细讨论. 关键词： n合金团簇')" href="#">(FeCr)_n合金团簇 密度泛函理论 非共线磁序 自旋轨道耦合效应     

杂多阴离子的NMR和ESR研究——P-V-W Keggin阴离子的31P、51V、17O-NMR谱

本文合成了六种含有P-V-W和V-V-W Keggin结构的杂多阴离子,并研究了它们的³¹P、⁵¹V、¹⁷O-NMR谱,对于PV_xW_12-xO₄₀^(x+3)-(x=1~4)阴离子,当x=1时,³¹P和⁵¹V-NMR谱只有一条线,并且此线化学位移和pH无关。当x ≥ 2时,谱线数目随着x迅速增加,其原因是几何异构体的数目和类型迅速增加。它们的化学位移δ_p,和δ_v。依赖于溶液的酸性和x,即δ_p,随pH值和x增加而减少,而δ_v,却随pH和x的增加而增加。最后简短讨论了桥氧上质子化的影响。     

The angular intensity correlation functions C(1) and C(10) for the scattering of light from randomly rough dielectric and metal surfaces

We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S(q|k) on the angular intensity correlation function C(q,k|q',k')=〈I(q|k)I(q'|k')〉-〈I(q|k)〉〈I(q'|k')〉, where the intensity I(q|k) is defined in terms of S(q|k) by I(q|k)=L^-1₁(ω/c)|S(q|k)|², with L₁ the length of the x₁ axis covered by the random surface. We focus our attention on the C⁽¹⁾ and C⁽¹⁰⁾ correlation functions, which are the contributions to C(q,k|q',k') proportional to δ(q-k-q'+k') and δ(q-k+q'-k'), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C⁽¹⁰⁾ correlation function are determined by exactly the same statistical moment of S(q|k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C⁽¹⁰⁾ correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.     

The role of polarization of Xe by di- and monovalent cations in Xe NMR studies in zeolite A

We consider the role of polarization in the adsorption of Xe in zeolites of type A by direct comparative analysis of the adsorption isotherms, distributions of occupancies, and ¹²⁹Xe NMR chemical shifts of Xe_n in cages containing Ca_xNa_{12 −2x} ions per alpha cage (x = 0, 1, 2, 3, 5). We find that the qualitative trends in the adsorption isotherms, and in the progressions of Xe_n chemical shifts (for n = 0–8 in cages with x = 0, 1 Ca²⁺ ions and for n = 0–5 in cages with x = 2, 3 Ca²⁺ ions) upon increasing the level of Ca²⁺ ion for Na⁺ ion substitution could only be accounted for by including polarization of the Xe atom by the zeolite framework and its ions. This system, which permits observation of individual Xe_n peaks and of directly comparable adsorption isotherms in several cage types, provides a good model system for the interpretation of the more general case in which only the overall average ¹²⁹Xe NMR chemical shift is observed in open network zeolites, arising from free exchange of Xe among cavities of variable occupancy and variable cation distribution.     

WmBn(m+n≤7)团簇结构与稳定性的密度泛函理论研究

采用密度泛函理论(DFT)中的B3LYP方法,在LANL2DZ基组水平上优化W_mB_n(m+n≤7)团簇的几何结构,得到它们的基态构型,并对基态构型的平均结合能、二阶能量差分、能隙及WIB键级进行计算.结果表明:WB_n团簇的基态构型均是平面结构;当m≥2且m+n≥4时,除W₃B团簇外,其余团簇的基态结构均为立体结构;团簇的热力学稳定性随W原子个数的增加越来越好,W-W键的强度明显高于W-B和B-B键,W原子对团簇的稳定性起主导作用;W₂B₂和W₃B团簇最稳定.     

密度泛函理论研究BeSin(n=1-12)团簇的结构、稳定性与电子性质

运用密度泛函理论(DFT),考虑多种初始构型下的自旋多重态,在B3LYP/6-311G基组水平上研究BeSi_n(n=1-12)团簇的平衡几何结构、电子性质、振动光谱与极化率.结果表明:BeSi_n团簇在基态附近有许多能量非常接近的同分异构体,且BeSi_n团簇的基态结构绝大多数为立体结构.n=1时,体系的基态为自旋三重态,n≥2时,则为单重态.铍原子的掺入使得主团簇的电子性质发生了明显的变化,掺杂使得体系的化学稳定性降低.BeSi₃,BeSi₅,BeSi₇与BeSi₉是幻数结构.团簇中原子间的成键相互作用随n的增大而增强.     

Current-induced step bunching at vicinal surfaces during crystal sublimation

The limits of the applicability of the generalized BCF model of electromigration-affected sublimation are discussed in detail. Only in surface-diffusion limited sublimation are the steps boundaries, effectively separating the transport processes at neighbouring terraces. In the opposite case of high surface mobility and slow exchange between the 2D gas of mobile adatoms and the crystal, many atoms simply cross the steps, spending some time in an intermediate state of adsorption at the step edge, but never becoming “crystal atoms”. In this regime of sublimation the steps are no longer boundaries. Therefore, one cannot analyze diffusion and desorption on one separate terrace (as in the generalized BCF model) since the coupling between the adatom concentration fields on neighbouring terraces cannot be neglected. A relevant model for this regime of electromigration-affected sublimation is proposed in this paper. This model manifests step buching at the step-up direction of the adatom electromigration. The central result of the mathematical treatment is the formula (x₂−x₁)^{n + 2}=(4kT/F) l^{n + 1}₀, relating the interstep distance x₂−x₁ in a stable pair of steps with the electromigration inducing force F. Here n and l₀ determine the form and the magnitude of the step-step interaction. The formula obtained for x₂−x₁ provides a gound to evaluate n and l₀ from a set of experimental data on sublimation by combined DC and radiative heating.     

Defect structure of quenched γ-BICOVOX by combined X-ray and neutron powder diffraction

A detailed investigation of the defect structure of the Co doped BIMEVOX solid electrolyte, Bi₂V_{1 − x}Co_xO_{5.5 − 3x/2} (x = 0.1 and x = 0.2), quenched from high temperature, has been carried out using X-ray and neutron powder diffraction data measured at room temperature. The structure is built up from alternating layers of [Bi₂O₂]_n²ⁿ⁺ and [V_{1 − x}Co_xO_{3.5 − 3x/2}]_n²ⁿ⁻ with disorder limited to the vanadate layer. The ideal V/Co co-ordination is octahedral with corner sharing of equatorial oxygens. The refinements show that the true structure is distorted, with disorder in both apical and equatorial oxygens and oxygen vacancies concentrated in the equatorial positions. Detailed analysis of the oxygen site occupancies reveals two main types of V/Co co-ordination viz. distorted octahedral and distorted tetrahedral. The majority of the sites in both compositions are tetrahedral.     

原子轨道强耦合方法研究He2+-H-碰撞的电荷转移过程

应用双中心原子轨道强耦合方法研究He²⁺-H^-碰撞的单次电荷转移过程.计算中,对入射粒子He²⁺,包含n=1~7的所有束缚态,计算的能量本征值与NIST标准数据在百分之几的精度内符合很好;对靶H^-,包括一个束缚态1s和五个连续态ns(n=2~6),束缚态能量与他人理论结果一致.在4~400 keV的入射粒子能量范围,计算单电子俘获过程的总截面及到各个壳层上的态选择截面.发现在较低的入射粒子能量,电子主要俘获到He⁺离子主量子数n=3~5的壳层,高能区俘获到n=2的壳层为主;对同一主量子数n,在低能区俘获到高角动量态(l=n-1,n-2)的电荷转移截面相对较大,在高能区主要俘获到l=1的p壳层.同时还计算入射粒子能量分别为4 keV和400 keV时,电子俘获到激发态辐射退激发产生的电荷转移发射光谱,并发现cascade效应的影响很大.