Uncertainty reevaluation in determining the volume of a silicon sphere by spherical harmonics in an Avogadro project

To determine the Avogadro constant with a target relative uncertainty of 2 x 10-s, the uncertainty component of the silicon sphere＇s volume introduced by the spherical harmonics method, which is usually used in determining the sphere＇s volume, is reevaluated. By means of representing the shape of the silicon sphere by an ellipsoid with Gaussian white noise in its diameters, the uncertainty of the current mapping methods based on the spherical harmonics theory can be estimated theoretically. It is evidenced that the uncertainty component attributed to the current mapping method is underestimated. To eliminate this effect as much as possible, the number of mapping points should be increased to more than before. Moreover, a new mapping method is proposed to accomplish the equal-area mapping with large number points on the silicon sphere.

Progress on accurate measurement of the Planck constant:Watt balance and counting atoms

The Planck constant h is one of the most significant constants in quantum physics. Recently, the precision measurement of the value of h has been a hot issue due to its important role for the establishment of both a new SI and a revised fundamental physical constant system. Up to date, two approaches, the watt balance and counting atoms, have been employed to determine the Planck constant at a level of several parts in 108. In this paper, the principle and progress on precision measurement of the Planck constant using watt balance and counting atoms at national metrology institutes are reviewed. Further improvement in determining the Planck constant and possible developments of a revised physical constant system in future are discussed.

Unity Formulas for the Coupling Constants and the Dimensionless Physical Constants

In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincare dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.

A Potentially Unifying Constant of Nature (Brief Note)

This brief note describes a method by which numerous empirically-determined quantum constants of nature can be substituted into Einstein’s field equation (EFE) for general relativity. This method involves treating the ratio G/ћ as an empirical constant of nature in its own right. This ratio is repre- sented by a new symbol, NT. It turns out that the value of NT (which is 6.32891937 × 1023 m⋅kg-2⋅s-1) is within 5% of Avogadro’s number NA, although the units are clearly different. Nevertheless, substitutions of NT or NA into the EFE, as shown, should yield an absolute value similar in magnitude to that calculated by the conventional EFE. The method described allows for quantum term EFE substitutions into Einstein’s gravitational constant κ. These terms include ћ, α, me, mp, R, kB, F, e, MU, and mU. More importantly, perhaps, one or more of the many new expressions given for κ may provide a more accurate result than κ incorporating G. If so, this may have important implications for additional forward progress towards unification. Whether any of these new expressions for Einstein’s field equation can move us closer to quantizing gravity remains to be determined.

“电解法制备Cu_(2)O及量气法测定阿伏加德罗常数”一体化实验及其实施结果与讨论——向全国不同层次高校的大一学生推荐一个微实验

基于向大一学生开设的“电解-量气法测定阿伏加德罗常数”实验,设计了Cu_(2)O的电化学合成及量气法测定阿伏加德罗常数一体化实验,该实验巧妙地融合了元素化学实验中有关Cu_(2)O的制备及性质实验内容。一次电解完成两个实验,节约电能,节省时间。Cu_(2)O的电化学合成及量气法测定阿伏加德罗常数一体化实验可作为一个微实验灵活穿插于大学基础化学实验教学中,对于培养大一学生的全方位思考的意识和多角度分析问题的能力以及经济、环保的理念有重要意义。

阿伏加德罗常数测量与千克重新定义

当千克用固定普朗克常数h的方法定义时,X射线晶体密度法(XRCD)即被用来定义和复现千克,它采用对浓缩28Si原子计数的方法来测量阿伏加德罗常数NA,已将NA和h的测量不确定度达到2×10-8,并反过来确定硅球的质量实现对千克的量值复现。阐述了晶格常数、同位素、浓缩硅、硅球直径及表面氧化层等阿伏加德罗常数测量的关键技术的研究进展。介绍了原子计数法千克定义及其量值复现方法,该方法将为国际单位制改制之后我国质量量值复现提供参考。

阿伏加德罗常数测量中单晶硅密度的绝对测量

基于改进型五幅算法,利用压力扫描原理设计出腔长可变式法-珀标准具和柔性铰链微位移平台,实现了标准具腔长和硅球表面与标准具之间的相移测量,建立了一套技术原理新颖、提高潜力较大的相移法精密测长系统。该测量系统对硅球直径的测量准确度优于3 nm,单晶硅密度的测量不确定度达到1×10-7。

实现质量量子基准的两种途径

基于基本物理常数定义新的国际单位制成为21世纪国际计量界研究的热点，然而目前一些常数的测定尚未达到所需的不确定度范围。质量量子标准研究更是目前计量领域研究的重点和难点。经过30多年的发展，硅球法和功率天平法取得了重大进展，但目前发表的测量结果之间尚存在10^-7量级的偏差。通过详细比较各国实现质量量子基准的两种途径，指出无论是依靠普朗克常数h还是阿佛伽德罗常数NA，在现阶段，取代国际千克原器尚有很长的一段路需要摸索。

摩尔新定义和准确测定的阿伏伽德罗常数

针对2019年国际SI单位新标准的实施,依据文献对阿伏伽德罗常数和摩尔物质量原理进行了简短的历史回顾。着重于摩尔新定义的概念和准确测定阿伏伽德罗常数的描述,突出了原子量精密测量技术、纳米量级精密测量技术以及材料制备和表征技术的发展。相对而言,摩尔新定义更能体现科学方法和科学思维同化学知识的关系,将会对无机化学、分析化学、物理化学等课程教学引起巨大的冲击波,并且会波及到每个化学专业本科生。本文内容可为提高本科生的科研思维和科研素质提供借鉴。

阿伏加德罗常数测量研究最新进展

综述了阿伏加德罗常数（NA）测量研究的最新进展。介绍了目前测NA准确度较高的方法-x射线晶体密度法，该方法通过测量单晶硅的摩尔质量、宏观密度和晶格常数得到NA。采用x射线晶体密度法有望实现NA相对测量不确定度达到2×10^-8。分析了当前限制NA测量准确度提高的关键研究内容：单晶硅摩尔质量、硅球直径和表面氧化层厚度的测量。并展望了NA测量未来的工作方向。

更新计量基本单位[kg]定义的研究现状

在国际单位制中 ,质量的基本单位 [kg]是以保存在巴黎国际计量局的千克原器定义的。现在 ,各国 [kg]基准的质量以平均每年约 0 .5 μg的增长率在变大 ,这种变化早已超过 [kg]国际比对的精度。从 2 0世纪五十年代开始 ,科学家们对更新 [kg]的定义进行了深入的探索与大量的研究 ,有望于 2 1世纪初将会有所突破 ,得以利用基本物理常数或原子的物理特性来建立量子化的 [kg]新定义。

阿伏加德罗常数测定实验探究

阿伏加德罗常数的测定是一个经典的基础化学实验。为了提升教学效果和增强学生实验技能,对该实验进行了讨论和探究。考察了阿伏加德罗常数测定的由来和进展,重点阐述和探讨了电解法测定该常数的实验原理和方法,并从电极、电源、实验结果分析等几个方面进行了论述,对测定方法和测定仪器提出了改进建议。通过改进,该实验在培养学生科学的思维方法和实验技能等方面可以发挥更好的作用。

阿伏加德罗常数测定的新进展

准确测定阿伏加德罗常数是实现用原子质量重新定义质量单位kg的有效途径。介绍了阿伏加德罗常数测定的历史、进展和前景。阿伏加德罗常数是联系宏观世界和微观世界的桥梁,是科学研究的前沿。测定阿伏加德罗常数利用了单晶硅晶体的结构周期性和完整性,促进了原子量精密测量技术、密度精密测量技术、纳米量级精密测量技术以及材料制备和表征技术的发展。

质量自然基准的研究进展及发展方向

质量单位千克是7个国际单位制基本单位之一,也是到目前为止唯一用实物复现的基本单位。几十年来围绕着实现质量自然基准,各国科学家进行了大量的研究,取得了巨大的进展。文中概述了科学工作者在这一领域的研究现状,实现质量自然基准的几种主要方法的基本原理及其研究进展,预测了质量自然基准研究的最终发展方向。

单晶硅球密度的绝对测量

单晶硅球密度的绝对测量是阿伏加德罗常数测量的关键技术。综述了单晶硅球密度测量的最新进展，包括硅球密度测量的技术原理、测量领域、影响因素、测量装置及最佳测量能力等等，分析了硅球密度测量的主要难点和关键技术，预测了相关研究的技术前景及发展趋势。

关于“阿伏伽德罗常数”的历史考量

从基本物理常数这个视角来看阿伏伽德罗常数会更易理解。最早测出阿伏伽德罗常数的人是法国科学家佩兰。阿伏伽德罗常数的测定历史长达百年，至今仍在继续。“阿伏伽德罗常数”与“物质的量”“摩尔”概念具有相同的历史源头，但是在不同学科领域发展着，最后又殊途同归。

阿伏伽德罗常数N_A的潜科学分析

针对阿伏伽德罗常数NA教学理念错位的常见现象,本文从潜—渐显—显—渐潜……的潜科学分析理念出发,分别探讨了阿伏伽德罗常数NA物理内涵和实验测量的系统进化过程.

布朗运动仿真实验的设计与实现

介绍了布朗运动仿真实验的设计与实现方法,利用"位置朗之万方程"的数值离散化,最大程度还原真实的布朗运动.通过对仿真实验数据的定量分析,并计算出了阿伏加德罗常量的近似值.

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry （SE） is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.

电流传感器构建原电池测定阿伏加德罗常数

阿伏伽德罗常数是一个重要的概念,为加深高一学生的理解从而在教学过程中引入测定阿伏伽德罗常数的实验。本文通过电流传感器构建原电池测定阿伏伽德罗常数,进而得出一种新的近似测定阿伏伽德罗常数的方法。同时,帮助学生理解概念,并体会各学科之间的紧密联系。