Kilogram In Terms Research Articles

A ‘Dynamic Kibble’ mass balance for the undergraduate physics teaching laboratory

Originally envisaged in 1975 to realise the SI unit of electrical current, the Ampere, the Kibble balance has since developed into a powerhouse of modern scientific measurement. By combining theoretical simplicity with precision of measurement, it has enabled the redefinition of Planck’s constant, and subsequently a practical method of defining the kilogram in terms of fundamental constants. This article introduces a novel version of this classic apparatus, the ‘Dynamic Kibble’ Balance. Dynamic in this case because the magnet velocity is now 3 orders of magnitude higher than the original, but the same theory applies. The apparatus is simple in approach, robust, easy to set up, and capable of a high level of precision using only electrical measurements (plus length and time). The importance of this measurement to metrology re-enforces the link between what is measured in the laboratory via calibration, measurement standards, and traceability. Using the apparatus and measurements described in this paper, the mass of the magnet assembly was measured as 19.4 ± 0.3 g, which lies within one SEM of the known value. This paper describes an uncomplicated method with a clear focus on the key physics and theory required. This experiment is intended for use in a first-year undergraduate physics laboratory. Further potential for both more advanced theory demonstration and experimental work is discussed.

A UME Kibble balance displacement measurement procedure

<p>The redefinition of the kilogram in terms of Planck constant came into effect on 20 May 2019. The National Metrology Institute of Turkey (UME) realised the new definition by means of the oscillating magnet Kibble balance. The novel dynamical measurement procedure developed for Kibble balance in Turkey has the advantage of being less sensitive to environmental disturbances compared to the traditional Kibble balance experiments. Precise displacement measurements are performed either with Michelson or Fabry-Perot interferometers in worldwide Kibble balances. Moreover, most of them operate in a global vacuum. A commercial Michelson interferometer has been used in UME’s Kibble balance experiment. In this article, we determine the contribution of ultra-small oscillations to the Planck constant by taking simultaneous displacement measurements on two back-to-back mirrors attached to the piezoelectric transducer, undergoing an oscillatory motion with the Michelson and Fabry-Perot interferometers. The following novel measurement procedure makes such measurements possible in a regular laboratory environment. Otherwise, the experiment needs to be performed in a global vacuum. This is why we were required to investigate the resolution performances of these devices in laboratory conditions. As the expected relative uncertainty in the redefinition of kilogram is above the resolution uncertainties of both interferometers, we may conclude that a commercial Michelson interferometer will serve our purposes in our route to the redefinition of a kilogram by means of local vacuum.</p>

External Magnetic Field Measurements in UME Kibble Balance

The new definition of kilogram in terms of the fixed value of Planck constant ensures the long-term stability of SI mass unit and enables traceability from more than one source. Kibble balance experiments offer an effective primary realization method for the new definition of kilogram. Kibble Balance apparatus operating at National Metrology Institute of Turkey is designed with a stationary coil and an oscillating magnet. In contradistinction to traditional moving coil Kibble balance experiments, external magnetic field brings an asymmetry between the Ampere’s law of force and the Faraday’s law of induction in moving magnet experiments. In this paper, we develop a method based on the external magnetic flux density difference measurements in vertical direction to take into account the effect of the external magnetic field on the realization of kilogram. The proposed model in this approach fits well with the data such that the kilogram realization requirement is met within the accuracy of the measuring instrument.

Journey of Kilogram from Physical Constant to Universal Physical Constant (h) via Artefact: A Brief Review

The redefinition of mass adopted in November 2018 and implemented from 20 May 2019, i.e. World Metrology Day, eliminated the artefact-based approach dependent upon the International Prototype of the Kilogram (IPK), in favour of realizing the kilogram in terms of the Planck constant h by fixing its value as 6.62607015 × 10−34 J s. In this paper, the authors present a general outline of the circumstances and related developments that paved the way for the new definition that replaced the IPK after a period of 130 years since it was formally sanctioned to define the kilogram in 1889. The new definition opens up fascinating developments in mass metrology which include different realization techniques, realizing the unit at values other than 1 kg, numerous sources for traceability can be envisaged etc.

Analysis of the effects of seismic interference on the measurement results of gravitational acceleration by ballistic laser gravimeters

The article is devoted to analysis of the effect of seismic interference on the measurement uncertainty of gravitational acceleration (GA) by ballistic laser gravimeters (BLG), which employ either symmetric or asymmetric measurement techniques. Carrying out such an analysis is currently an urgent metrological problem aimed at improving designs of BLGs and methods of signal processing which they implement. In particular, precise determination of the GA is indispensable to definition of the kilogram in terms of Planck’s constant as it was done in the revised version of the International System of Units (SI), which came into force on May 20, 2019.The article uses the model of the BLG mechanical system that takes into account the elasticity of ground base on which the BLG foundation is installed, as well as the reference reflector (RR) suspension elasticity of the interferometer with respect to the foundation.There are two main types of seismic interference, namely the external interference caused by soil micro-oscillations and auto seismic interference caused by oscillations in the BLG mechanical part due to the push or drop of the test body (TB). These interferences have different causes, different characteristics and lead to different measurement uncertainties: external seismic interference leads to the type A uncertainty, while auto seismic one is responsible for the type B uncertainty.One of the most important characteristics of any BLG with respect to external seismic interference is its effective noise band. The article for the first time analyzes the dependence of the effective noise band both on the BLG data processing method and on the period of proper oscillations of the RR suspension system. It is established that when the period of proper oscillations of the RR suspension system exceeds significantly the observation time, the BLG effective noise band is determined by the RR suspension system.It has been shown by simulation that asymmetric gravimeters provide a much smaller (by an order of magnitude and more) auto seismic uncertainty (ASU) of the GA measurement compared to symmetric gravimeters. Due to the elastic suspension of the RR of interferometer, the ASU of the GA measurement for all types of ballistic gravimeters can be reduced significantly.It is concluded that the use of a weighted least squares method for processing data in ballistic gravimeters can provide better interference immunity rates than the conventional method of least squares.

Boltzmann and Planck constants remeasured

NIST has announced more accurate measurements of the Boltzmann and Planck constants. The new values will contribute to an international effort to move away from defining basic units using physical objects and instead, starting in 2019, derive them from seven fundamental constants of nature. The kelvin, for example, is currently defined by measuring the triple point of water in a sealed glass cell. Going forward, metrologists want to define the kelvin in terms of the Boltzmann constant, which NIST researchers determined to be 1.3806410 × 10–23 J/K by measuring the degree of random motion of electrons in a resistor (Metrologia 2017, DOI: 10.1088/1681-7575/aa7b3f). Meanwhile, the kilogram is currently defined as the mass of a plum-sized cylinder of platinum-iridium alloy. Instead, metrologists want to define the kilogram in terms of the Planck constant. NIST scientists have now measured that constant’s value as 6.626069934 × 10–34 kg·m2/second by using a Kibble balance,

A brief history of the unit of mass: continuity of successive definitions of the kilogram

The very first definition of the kilogram was in terms of a constant of nature, although this idea could not be fully realized at the end of the 18th century. Instead the kilogram was defined by an artefact whose mass was made to approximate as closely as possible a physical constant with unit kg m−3—the maximum density of distilled water at atmospheric pressure. For the next two centuries, mass comparators improved greatly as did the materials from which artefacts could be constructed. These improvements put tighter constraints on the realization of a non-artefact definition of the kilogram. However, it is now expected that the goal of redefining the kilogram in terms of fundamental constants will be achieved in 2018. We present a history of the kilogram with emphasis on continuity of this unit of mass each time it has been redefined and the stability of a unit defined by the mass of an artefact.

Redefine the Kilogram in Terms of the Carbon-12 Atom and an Exact Value of the Avogadro Constant

We report on a method for redefinition of the kilogram by 12C, which ideally joins the atomic and the macroscopic mass units in a natural way. The kilogram artifact will be composed of a number of concentric shells around C-60 and that this is sometimes referred to as a “carbon onion”. A 135887620-layer carbon onion containing 50184508751575328771368200 atoms of 12C falls in the acceptable range for the redefinition of kilogram and is closest to the recent experimental results. An Avogadro constant is thus derived to be 602214105018903945256418.4. A perfect carbon onion is ideal for kilogram redefinition and determination of the Avogadro constant because it is expected to exhibit characteristics of central symmetry, high stability, high strength, high sphericity, low roughness, weak inter-planar force and strong in-plane bonding, easy atomic counting, and these are important for technical feasibility in further experiments.

An analysis and design of the mechanical characteristics of the knife edges used in the NPL watt balance

Of the seven base units of the international system of units, the SI, only the kilogram is still defined in terms of a material artefact. The watt balance is an experimental approach which supports a new definition of the kilogram in terms of constants of nature. Some watt balances, such as the NPL Mk II watt balance, use knives and flats for the balance pivots as they have the advantages of greater robustness over flexure pivots in this particular application. However, hysteresis in the knives can produce errors in the weighing through systematic shifts in the equilibrium point of the balance and it is desirable to investigate this effect as an aid to its elimination. This paper analyses the hysteresis mechanism using both finite element techniques and direct measurement. It was found that the cause of hysteresis is not normal stress but shear stress and that the deformation of the flat, rather than that of the knife, is an important factor. Problems that could not be analysed in a two-dimensional finite element model were investigated using a simplified stand-alone balance. The combined results from the finite element analysis and the stand-alone balance suggest that material properties and tip radius are more important than friction coefficient and tip angle. At loads where knife and flat distortion are low the straightness of the knife and the roughness of the surfaces can have a significant effect.

Instrumental neutron activation analysis of an enriched 28Si single-crystal

The determination of the Avogadro constant plays a key role in the redefinition of the kilogram in terms of a fundamental constant. The present experiment makes use of a silicon single-crystal highly enriched in 28Si that must have a total impurity mass fraction smaller than a few parts in 109. To verify this requirement, we previously developed a relative analytical method based on neutron activation for the elemental characterization of a sample of the precursor natural silicon crystal WASO 04. The method is now extended to fifty-nine elements and applied to a monoisotopic 28Si single-crystal that was grown to test the achievable enrichment. Since this crystal was likely contaminated, this measurement tested also the detection capabilities of the analysis. The results quantified contaminations by Ge, Ga, As, Tm, Lu, Ta, W and Ir and, for a number of the detectable elements, demonstrated that we can already reach the targeted 1 ng/g detection limit.

The Avogadro constant and a new definition of the kilogram

The Avogadro constant, the number of entities in the amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach for the determination of the Avogadro constant by “counting” the atoms in 1kg single-crystal spheres, which are highly enriched with the 28Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA=6.02214084(18)×1023mol−1, is now the most accurate input datum for a new definition of the kilogram.

Determination of the Atomic Weight of 28Si-Enriched Silicon for a Revised Estimate of the Avogadro Constant

The much anticipated overhaul of the International System of Units (SI) will result in new definitions of base units in terms of fundamental constants. However, redefinition of the kilogram in terms of the Planck constant (h) cannot proceed without consistency between the Avogadro and Planck constants, which are both related through the Rydberg constant. In this work, an independent assessment of the atomic weight of silicon in a highly enriched (28)Si crystal supplied by the International Avogadro Coordination (IAC) was performed. This recent analytical approach, based on dissolution with NaOH and its isotopic characterization by multicollector inductively coupled plasma mass spectrometry, is critically evaluated. The resultant atomic weight A(r)(Si) = 27.976 968 39(24)(k=1) differs significantly from the most recent value of A(r)(Si) = 27.976 970 27(23)(k=1). Using the results generated herein for A(r)(Si) along with other IAC measurement results for mass, volume, and the lattice spacing, the estimate of the Avogadro constant becomes N(A) = 6.022 140 40(19) × 10(23) mol(-1).

Towards the redefinition of the kilogram: a measurement of the Planck constant using the NPL Mark II watt balance

After the elimination of significant mechanical problems, the NPL Mark II moving-coil watt balance made an initial series of measurements in the period from October 2006 to March 2007. Incremental improvements were made to the apparatus in the period from June 2007 to November 2008 and measurements of the Planck constant h were made up to June 2009, with the aim of providing further information to the ongoing efforts to redefine the SI kilogram in terms of a fixed value of the Planck constant. The apparatus was sold to NRC-INMS in early 2009 and was dismantled and shipped to Canada in the period between June and August 2009.In June 2009, just prior to the shipment, a possible source of significant type-B uncertainty in the mass/force exchange was discovered. There was insufficient time to fully investigate and correct the effect so a component has been added to the uncertainty budget to account for its estimated magnitude. The standard uncertainty of the apparatus, without allowance for the mass/force exchange problem, is estimated to be 36 nW W−1, which represents an improvement of almost a factor of two from the previously reported uncertainty of 66 nW W−1, but, allowing for the problem, the uncertainty increases to 200 nW W−1. Further work, once the apparatus is rebuilt in Canada, should eliminate the source of the added uncertainty. The value of h calculated from the measurements made from 2006 to 2009 is 6.626 071 23(133) × 10−34 J s, which represents a change of 43 nW W−1 from the value reported in 2007. The corresponding value of the Avogadro constant, NA, is 6.022 139 78(120) × 1023 mol−1.

The new SI based on fundamental constants

The papers in this Discussion Meeting Issue of Philosophical Transactions A are based on the presentations given at a Discussion Meeting held at the Royal Society in London on 24 and 25 January 2011 entitled ‘The new SI: units of measurement based on fundamental constants’. The meeting was

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

The Avogadro constant, the number of entities in an amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant--the product of the Planck constant and the Avogadro constant--is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach to determine the Avogadro constant from the number of atoms in 1 kg single-crystal spheres that are highly enriched with the (28)Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, N(A)=6.022 140 82(18)×10(23) mol(-1), is now the most accurate input datum for a new definition of the kilogram.

Evaluation of equipment and procedures for the transfer and storage of mass standards in inert gas

This paper reports on work to improve mass stability when transferring platinum/iridium, stainless steel and silicon artefacts between air and vacuum using inert gas (argon) as a transfer/storage medium. Work is underway to redefine the kilogram in terms of a fundamental constant of nature and this will involve realizing a kilogram in vacuum. The development of an effective traceability link to this kilogram in vacuum is therefore essential for dissemination of the mass scale in the future. The work reported here investigates the effect of cycling artefacts between air and vacuum compared with cycling artefacts between argon and vacuum. Additionally, the effect of transferring artefacts between short-term storage in air compared with short term-storage in argon is investigated. The results presented demonstrate improved stability in the artefacts that are transferred between storage in argon and vacuum compared with those that are transferred between storage in air and vacuum.

Alignment Procedure Used in the BIPM Watt Balance

The Bureau International des Poids et Mesures (BIPM) is developing a watt balance to measure accurately the Planck constant h by linking it to the kilogram. The kilogram is currently the only base unit of the International System of Units still defined by a material artifact. A fixed numerical value of h could be the basis for the expected future redefinition of the kilogram in terms of fundamental constants. One main concern of the watt balance experiment is the alignment of the involved vectors. In particular, the electromagnetic force exerted on the watt balance coil needs to be carefully aligned parallel to the gravitational force exerted on the test mass. To address this requirement, we have developed an original experimental procedure that has been validated with a test coil which is a prototype for the ultimate watt balance coil. The result is accurate enough to enable a determination of the Planck constant with a relative uncertainty of about 1·10-8 , which is the ultimate goal of the BIPM watt balance.

Determination of the Avogadro Constant by Counting the Atoms in aSi28Crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

Towards a natural system of units for physics and metrology

A few years ago it was proposed by Mills et al.,2005 to redefine the kilogram in terms of values of certainnatural constants. It is expected that the consequences of thisredefinition will include some disadvantages in mass measurementsand advantages in the electric measurements and in some other areas.To achieve the best possible balance between gains and losses it iscrucial to create such a version of the SI, in which electricmeasurements in SI units are possible with the highest accuracy.This can be only done with a simultaneous redefinition of the kilogramand ampere and we consider various details of such a scenario.Further consideration involves a suggestion on a redefinition of thekelvin and mole, which we also consider. Besides, we discuss variousgeneral issues of the natural units ranging from fundamental topractical.

The atomic units, the kilogram and the other proposed changes to the SI

The close relationship between the SI units incorporating the proposed changes of Mills et al and the atomic system of units is discussed. It is shown that when the definition of the second is taken into account, a definition of the kilogram in terms of the mass of a photon of specified frequency results in a kilogram that implicitly depends on α4me and other dimensionless constants, where α is the fine structure constant and me is the electron rest mass. Thus the choice of definitions proposed by Mills et al implicitly yields a kilogram that depends either essentially on α4me or on the unified atomic mass unit, mu. Consequently, the kilogram could be regarded as implicitly retaining its present status as an independently defined SI base unit with either definition. The α-dependence of the kilogram and many other SI quantities would, of course, be affected by future changes in the definition of the second.