计算透射电镜薄样品中面状特征迹线转动角的新公式

鉴于现有文献中关于面状特征迹线转动角的计算公式(简称pp公式)与实验测量结果相差较大,笔者模拟薄晶体样品位向调整时的双倾操作过程,推导出计算面状特征迹线方向随样品倾转而变化的新公式。通过与实验测量值及pp公式计算结果相比较,证实本公式给出的计算值与实验结果相符,并再次反映出pp公式的不适用性。     

关于“离子选择电极标准加入法 研究Ⅲ.二次标准加入误差规律探讨”一文的商榷

编辑同志: 本刊在1986年2期81页上刊登了题示谭新民同志的文章,该文导出的误差公式实际上与所引文的误差公式完全一致的,且文中表1所列文公式算值是错误的,应与该文公式算值相同,其原因可能是作者未把文的△E_2(E_2-E_1)搞清楚。为更客观的说明问题,下面把谭文和文的误差公式作一比较。     

无机含氧酸的强度与結构的关系

1.提出计算无机含氧酸的pK值的经验公式。计算结果与实验值极为接近。 2.由于公式中包含有各项结构因素如电负性值、配键、双键、OH基、已电离的OH基等。讨论了各项因素对酸性强度的影响,并计算出其影响的大小。 3.还计算了一般在前人无法计算的OH,H_2O,H_2O_2,H_2S_2O_3,H_2N_2O_2,H_2CrO_4,HSO_3Cl的pK值。 4.提供计算3价金属离子水解及其氢氧化物酸式电离的pK值的经验公式,计算结果与实验值非常接近。也讨论了结构因素对酸性强度的影响。     

恒温式量热计冷却校正公式的进一步研究

通过对参数“α”影响热值误差的理论分析,剖析了研究新的最佳冷却校正公式的途径和方向。据此,在前文提出两个新公式的基础上,进一步提出了一个改进的“α”值计算模型,并由电算求解列出“α”值计算表。从大量数据验证来看,它可能成为迄今为止国内外所见到的近似冷却校正公式中的优秀者,它兼具操作最简便,准确度仅次于最准确的Regnault-Pfaundler 公式的两个特点。     

粉煤表面的动电位

本文考察了pH 值、表面活性剂、电解质、煤中矿物质及氧化等因素对九种不同煤化程度煤的动电位的影响并进行了讨论。提出了无烟煤及烟煤的动电位(ξ)与pH 值之间的关系,可用ξ=ae~(bx)经验公式关联起来,并对国外有关文献中的数据进行了验算,动电位的测定值与公式计算值均是显著相关的。     

无机含氧酸电离常数的计算

本文提出了一个计算无机含氧酸 pK 值经验公式。对于 MO_n(OH)_m 酸,比式(2)多引一个电负性参数。对于 M(OH)_m 酸,比式(2)多引一个电负性和一个原子价参数。形式是简单的。用这公式计算的结果表明较以前的工作有所改进。67个含氧酸的 pK 值平均偏差是0.56。本文还提出了多中心原子含氧酸 pK 值的计算方法。另外,说明了公式(4)的各项意义。对一些争议之处也作了简单的讨论。     

油脂氢化的动力学模型

给出了油脂氢化反应中活化态氢与甘三酯分子反应的动力学模型。H_2吸附在催化剂上形成活化态氢。它分别与甘三酯中的三烯酸(酯)、二烯酸(酯)、单烯酸(酯)发生反应。采取类似Ridel-Langmuir的方法, 导出了油酯氢化动力学方程式。对该公式进行了验证, 理论值与实验值相当一致。本文公式可概括半经验的Albright公式、Allen公式和Moharir公式。     

Cu-Zr二元系非晶合金的玻璃形成能力预测

按照无序固溶模型和线性化合物自由能模型, 对Cu-Zr二元系合金过冷熔体的结晶驱动力采用Turnbull和Thompson-Spaepen (TS)两种近似公式进行了计算. 以连续形核理论为基础, 利用Davies-Uhlmann公式计算了八种成分合金的两组温度-时间转变(TTT)曲线和临界冷却速度. 计算结果表明, 关于玻璃形成能力的两组计算值与实验值都比较吻合, 利用TS公式计算得到的临界冷却速率更接近实验值, 说明该方法能更好地预测Cu-Zr二元体系的玻璃形成能力.     

取代苯乙酮羰基17O-NMR化学位移的规律

提出计算取代苯乙酮羰基17O-NMR化学位移的公式δcal=550.0+△o+△m+△p,通过线性回归法确定了12种取代基参数.以44种取代苯乙酮为样本点作回归检验表明该公式的置信度为99.5%,计算值与实验值的偏差△δ在5.0(相对误差约0.5%)以内的羰基17O-NMR化学位移的计算值在90%左右.     

三核自旋偶合体系的磁化率公式

对多核自旋偶合体系的研究是设计分子基铁磁体的基础犤１犦。在多核自旋偶合体系中，磁交换参数Jij值的评估对研究多核间的磁交换机理和研究多核自旋偶合体系的磁－构相关性是至关重要的。多核间的磁交换参数Jij值不能从实验直接得到，理论计算又有很大的困难和不准确性。目前，Jij值主要是通过多核自旋偶合体系的变温磁化率公式拟合实验数据来评估。因此，磁化率公式在磁化学研究中具有重要的理论和实际意义。通常，磁化率公式是通过求解多核自旋偶合体系的自旋交换Hamiltonian算符的本征方程，求出体系的能量本征值，然后用Boltzmann分…     

Asymptotics of distribution functions in wedge-shaped film

Asymptotic formulas are derived for one- and two-particle distribution functions in a liquid wedge-shaped film. These formulas are valid at fairly large distances from the solid walls that confine the film. Along with the dependence on distances to solid walls, these formulas also determine the dependence on the opening angle of the wedge-shaped pore. In the limit of a straight angle, formulas are transformed into asymptotic formulas for the plane surface layer; in the limit of small angles, they are transformed into corresponding formulas for the plane film.     

计算单向复合材料弹性模量的新公式

根据复合材料单层的实际构造，提出了串并联组合模型，采用微观力学与宏观力学相结合的方法，推导出一组计算单向复合材料弹性模量的新公式。其优点是：Ｅ１和ｖ（１２）、Ｅ２和Ｇ（１２）的计算式形式对称，结构简单，计算容易，物理意义明确。我们把由世界上许多著名学者提出的多组预测公式和本文导出式计算所得的结果与国内外已发表的硼／环氧、碳／环氧、玻璃／环氧复合材料的实验数据相比较，结果表明：导出式比其他公式精确、更有价值，可供二程设计使用。     

The calculation of matrix elements for valence bond functions

Pauling's formulas for the calculation of matrix elements for valence bond functions are derived using a simple substitutional process. The results generalize and simplify the formulas. In particular, the formulas do not depend upon orthogonality of atomic orbitals nor upon the nature of the choice of bond structures (canonical or not). The results are particularly adaptable to automatic computation.     

结构相角二阶代数式的应用：Ⅱ.正交空间群二阶式及其应用

以作者在前文中提出的单相角二阶代数式的推导方法为依据,在完成三斜、单斜空间群推导结果的基础上,进而又完成了正交晶系59个空间群二阶式的推导,从而提供了低级晶系(三斜、单斜和正交)全部74个空间群的简明、完备的二阶代数式运算用表。对三个晶体结构进行了相角估算,结果较好。文中提出了代数法应用的新特点,即“一种类型相角可用多种二阶式求得,多种类型相角也可用一种二阶式求算”。     

On the Accuracy of Measuring Small Contact Angles by the Sessile Drop Method

The errors arising in measuring the contact angles of a sessile drop by the mirror method are analyzed. The formulas are derived enabling one to take into account the distortions of a visible image and enhance the accuracy of measuring contact angles. The derived formulas are experimentally verified.     

An investigation of gas chromatography with atomic emission detection for the determination of empirical formulas

The atomic emission detector (AED) is a valuable tool for the identification of unknowns in complex mixtures. To the extent that elemental response factors are independent of compound structure, gas chromatographic results allow calculation of atomic ratios for unknown compounds. In favorable cases, empirical formulas can be found. An algorithm for automated calculation of empirical formulas for all the peaks in a chromatogram has been developed. When finite accuracy prevents an exact determination of empirical formulas, the algorithm gives a list of all formulas for each compound which are compatible with the user-defined limits. Examples are given of calculations for fatty acid methyl esters, substituted phenols, and pesticides. Analyses of volatile pollutants and polychlorinated biphenyls reveal a nonlinearity for hydrogen response, and an interference of chlorine on hydrogen. A lubricating oil analysis is used to illustrate the identification of unknowns.     

Analytical second derivatives of molecular electronic energy integrals obtained by spherical gaussian orbital

In this research, the complete general formulas for the analytical second derivative of the molecular integrals for spherical gaussian orbitals of electronic energy are presented. Formulas were given for the second derivative for orbital exponent, orbital and nuclear cartesian coordinates and coefficients of contracted gaussians. In order to save computational time, the formulas for the second derivative are written in terms of the original integrals. Although the formulas were presented in general for any type of application, the Floating Spherical Gaussian Orbital (FSGO) method is applied to some molecules such as LiH, H₂O and CH₂ (singlet) to check the formulas. The results were compared with the results of the finite difference method. Besides the accuracy of the analytical derivative, the saving in computational time is significant.     

Computing upper and lower bounds using Monte Carlo methods

We computed lower bounds for some ground and excited states of the helium atom using variational Monte Carlo and the Weinstein, Temple, and Stevenson formulas. For these systems, the Temple and Stevenson bounds are approximately the same and have similar standard deviations. The Weinstein bounds are much further from the actual energies and have much larger standard deviations. We also investigated the reliability of these lower bound formulas when nonorthogonal wave functions are used. The Temple formula has been shown to produce an accurate lower bound even under such circumstances, while the Weinstein and Stevenson formulas are shown to yield incorrect results. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Matrix elements between spin-bonded functions in a hole-particle formalism

Closed formulas are given for Hamiltonian matrix elements between spin-bonded functions in a holeparticle formalism. The derivation is based on Wick's theorem and the use of Jucys diagrams. The final formulas are only slightly more complicated than those for bonded functions in a particle formalism.     

Evaluation of some trigonometric series occurring in infinite chain polymer calculations

Closed formulas are presented for a number of trigonometric series whose summands contain inverse powers of one or two quadratic forms. It is shown how to arrange the formulas to remove apparent numerical instabilities, and useful numerical approximations are identified together with the range of their validity.