The Avogadro constant: determining the number of atoms in a single-crystal
            <sup>28</sup>
            Si sphere

Becker, Peter; Bettin, H.

doi:10.1098/rsta.2011.0222

Cited by 33 publications

(23 citation statements)

References 22 publications

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“…In practice, it is more convenient for all frequency and time measurements to be traceable to the SI definition of the second. From Becker & Bettin [11],…”

Section: Resultsmentioning

confidence: 99%

“…It is up to the skill and ingenuity of scientists to devise appropriate experiments to yield a highly accurate value for R h /f in the case of the Planck constant (see Stock [10] for an example of the watt balance) or R N in the case of the Avogadro constant (see Becker & Bettin [11] for an example of the silicon-crystal method). Nor can dimensional analysis give us any insight into the importance of these constants to physics.…”

Section: Generalization Of Equation (24) To Measure Fundamental Consmentioning

confidence: 99%

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The role of the international prototype of the kilogram after redefinition of the International System of Units

Davis

2011

Phil. Trans. R. Soc. A.

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Since 1889, the international prototype of the kilogram has served to define the unit of mass in what is now known as the International System of Units (SI). This definition, which continues to serve mass metrology well, is an anachronism for twenty-first century physics. Indeed, the kilogram will no doubt be redefined in terms of a physical constant, such as the Planck constant. As a practical matter, linking the quantum world to the macroscopic world of mass metrology has, and remains, challenging although great progress has been made. The international prototype or, more likely, a modern ensemble of reference standards, may yet have a role to play for some time after redefinition, as described in this paper.

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“…In practice, it is more convenient for all frequency and time measurements to be traceable to the SI definition of the second. From Becker & Bettin [11],…”

Section: Resultsmentioning

confidence: 99%

Section: Generalization Of Equation (24) To Measure Fundamental Consmentioning

confidence: 99%

The role of the international prototype of the kilogram after redefinition of the International System of Units

Davis

2011

Phil. Trans. R. Soc. A.

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“…Although defining the kilogram by fixing the value of the Planck constant is conceptually more complex than, for example, defining the kilogram in terms of the mass of the electron or a specified atom, the other advantages of fixing the value of the Planck constant make this the preferable definition. See also the paper by Bordé [13], as well as those of Becker & Bettin [14], Stock [15] and Davis [16] in this issue.…”

Section: Choosing the Fundamental Constants To Be Used In The Definitmentioning

confidence: 99%

Adapting the International System of Units to the twenty-first century

Mills

Mohr

Quinn

et al. 2011

Phil. Trans. R. Soc. A.

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We review the proposal of the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), currently being considered by the General Conference on Weights and Measures (Conférences Générales des Poids et Mesures, CGPM), to revise the International System of Units (Le Système International d'Unitès, SI). The proposal includes new definitions for four of the seven base units of the SI, and a new form of words to present the definitions of all the units. The objective of the proposed changes is to adopt definitions referenced to constants of nature, taken in the widest sense, so that the definitions may be based on what are believed to be true invariants. In particular, whereas in the current SI the kilogram, ampere, kelvin and mole are linked to exact numerical values of the mass of the international prototype of the kilogram, the magnetic constant (permeability of vacuum), the triple-point temperature of water and the molar mass of carbon-12, respectively, in the new SI these units are linked to exact numerical values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant, respectively. The new wording used expresses the definitions in a simple and unambiguous manner without the need for the distinction between base and derived units. The importance of relations among the fundamental constants to the definitions, and the importance of establishing a mise en pratique for the realization of each definition, are also discussed.

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Phase-shifting interferometry to determine the absolute diameter of a silicon sphere using a frequency-tunable diode laser

Wei

et al. 2013

2013 Conference on Lasers &Amp; Electro-Optics Europe &Amp; International Quantum Electronics Conference CLEO EUROPE/IQEC

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In order to redefine the kilogram, the Avogadro constant is determined by means of the X-ray crystal density method, where the lattice constant, density and mean molar mass of a single crystal silicon sphere are absolutely measured [1]. The density of the silicon sphere, whose diameter and mass are approximately 93.6 mm and 1 kg respectively, is obtained by the accurate diameter and mass. To measure the absolute diameter, laser interferometry is the most promising method with nanometer resolutions and traceable measurement results. However, the 2π ambiguity range limits the measurement range. In this contribution, a chain of temporal synthetic wavelengths, generated by use of a frequency-tunable diode laser calibrated by an optical frequency comb, is used to measure the absolute diameter with an accuracy of 3 nm in air, where the fractional interference phase is measured by phase-shifting interferometry.As shown in Fig. 1 (a), the diameter of the silicon sphere D can be expressed as D=L-(d 1 +d 2 ), where the length of the etalon L and the two gaps between the surface of the etalon and the adjacent of the sphere d 1 and d 2 are measured by analysing the interference fringes, respectively. The reference plates are fixed at the outside surface of the etalon, made of ultralow expansion glass, by optical wringing. The two surfaces of each reference plate have a wedge of 42 minutes of arc to eliminate the spurious reflection. The angle between the reference surfaces is better than 10 second of arc corresponding to a diameter measurement error of ~0.1 nm. The nominal diameter and the length of the etalon are 93.62 μm and 108.01 μm, respectively, measured by a coordinate measuring machine. To achieve an accuracy of nanometer level, laser interferometry is used to measure the interference phase.To extend the unambiguous range and determine the absolute distance using interferometry, methods based on generating synthetic wavelengths larger than the laser wavelength are presented [2]. In multiple wavelength interferometry, the absolute distance is expressed as L=λ s (ΔN +Δε)/2, where λ s =λ i λ j /(λ i -λ j ) is the temporal synthetic wavelength generated by single wavelengths of λ i and λ j , ΔN and Δε are the variations of the normalized integral and fractional phases, respectively. Thus, using an effective variable synthetic wavelength, the measurement range is proportional to λ s and the accuracy is relevant to the single laser wavelength and the accuracy of the interference phase measurement. To enhance the phase measurement accuracy in phase-shifting interferometry, a frequency-tunable diode laser (ECDL) calibrated by an optical frequency comb (OFC) is used to produce accurate phase steps by changing the laser frequency, as shown in Fig. 1 (b) [3]. With this technique, phase measurement uncertainties from the laser frequency and phase steps are negligible. Fig. 1 (b) Schematic of the diameter determination interferometer. (a) Schematic of the arbitrary single optical frequency synthesizer.

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The Avogadro constant: determining the number of atoms in a single-crystal ²⁸ Si sphere

Cited by 33 publications

References 22 publications

The role of the international prototype of the kilogram after redefinition of the International System of Units

The role of the international prototype of the kilogram after redefinition of the International System of Units

Adapting the International System of Units to the twenty-first century

Phase-shifting interferometry to determine the absolute diameter of a silicon sphere using a frequency-tunable diode laser

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The Avogadro constant: determining the number of atoms in a single-crystal 28 Si sphere

Cited by 33 publications

References 22 publications

The role of the international prototype of the kilogram after redefinition of the International System of Units

The role of the international prototype of the kilogram after redefinition of the International System of Units

Adapting the International System of Units to the twenty-first century

Phase-shifting interferometry to determine the absolute diameter of a silicon sphere using a frequency-tunable diode laser

Contact Info

Product

Resources

About

The Avogadro constant: determining the number of atoms in a single-crystal ²⁸ Si sphere