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((update|reason=Several sections are still written as if the definition is yet to be decided e.g. references to "currently accepted" values since redefined|date=December 2023))

The [[Committee on Data for Science and Technology|scientific community]] examined several approaches to redefining the [[kilogram]] before deciding on a [[2019 redefinition of the SI base units|redefinition of the SI base units]] in November 2018. Each approach had advantages and disadvantages.

Prior to the redefinition, the kilogram and several other [[SI unit]]s based on the kilogram were defined by an artificial metal object called the [[international prototype of the kilogram]] (IPK).<ref name="vox"/> There was broad agreement that the older definition of the kilogram should be replaced.

[[File:Unit relations in the new SI.svg|thumb|upright=1.35|The [[International System of Units|SI system]] after the 2019 redefinition: the kilogram is now fixed in terms of the [[second]], the [[metre]] and the [[Planck constant]] ]]

The International Committee for Weights and Measures (CIPM) approved a redefinition of the SI base units in November 2018 that defines the kilogram by defining the [[Planck constant]] to be exactly ((val|6.62607015|e=−34|u=kg⋅m<sup>2</sup>⋅s<sup>−1</sup>)). This approach effectively defines the kilogram in terms of the second and the [[metre]], and took effect on 20 May 2019.<ref name="vox">((cite news |last1=Resnick |first1=Brian |title=The new kilogram just debuted. It's a massive achievement. |url=https://www.vox.com/science-and-health/2019/5/17/18627757/kilogram-redefined-world-metrology-day-explained |accessdate=23 May 2019 |publisher=vox.com |date=20 May 2019))</ref><ref name=draft-resolution-A>((citation
 |title=Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018)
 |url=https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf
 |access-date=2019-06-26
 |archive-date=2018-04-29
 |archive-url=https://web.archive.org/web/20180429025229/https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf
 |url-status=dead
 ))</ref><ref>[http://www.bipm.org/en/committees/cipm/meeting/105.html Decision CIPM/105-13 (October 2016)].  The day is the 144th anniversary of the [[Metre Convention]].</ref><ref>((cite news
|url= https://www.bbc.com/news/science-environment-46143399
|title= Kilogram gets a new definition
|author= Pallab Ghosh
|date= November 16, 2018
|journal= BBC News
|accessdate= November 16, 2018
))</ref>

In 1960, the metre, previously similarly having been defined with reference to a single platinum-iridium bar with two marks on it, was redefined in terms of an invariant physical constant (the wavelength of a particular emission of light emitted by [[krypton]],<ref>((SIbrochure8th|page=112))</ref> and later the [[speed of light]]) so that the standard can be independently reproduced in different laboratories by following a written specification.  

At the 94th Meeting of the [[International Committee for Weights and Measures]] (CIPM) in 2005, it was recommended that the same be done with the kilogram.<ref>((cite conference
 |url=https://www.bipm.org/cc/CIPM/Allowed/94/CIPM-Recom1CI-2005-EN.pdf
 |conference=94th meeting of the International Committee for Weights and Measures 
 |title=Recommendation 1: Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants 
 |date=October 2005 
 |page=233 
 |accessdate=February 7, 2018 
 |url-status=live 
 |archiveurl=https://web.archive.org/web/20070630011658/https://www.bipm.org/cc/CIPM/Allowed/94/CIPM-Recom1CI-2005-EN.pdf 
 |archivedate=June 30, 2007 
))</ref><!-- Original URL: http://www.bipm.org/utils/en/pdf/CIPM2005-EN.pdf -->

In October 2010, the CIPM voted to submit a resolution for consideration at the [[General Conference on Weights and Measures]] (CGPM), to "take note of an intention" that the kilogram be defined in terms of the [[Planck constant]], ((math|''h'')) (which has dimensions of energy times time) together with other physical constants.<ref>((cite web|url=https://www.nist.gov/pml/wmd/20101026_si.cfm |title=NIST Backs Proposal for a Revamped System of Measurement Units |date=26 October 2010 |publisher=Nist.gov |accessdate=April 3, 2011))</ref><ref name="draft">((cite web
|url = http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf
|title = Draft Chapter 2 for SI Brochure, following redefinitions of the base units
|author = Ian Mills
|publisher = CCU
|date = September 29, 2010
|accessdate =January 1, 2011))</ref> This resolution was accepted by the 24th conference of the CGPM<ref>((cite conference
|url= http://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf
|title= Resolution 1 – On the possible future revision of the International System of Units, the SI
|conference= 24th meeting of the General Conference on Weights and Measures
| location = Sèvres, France
| date = October 17–21, 2011
| accessdate =October 25, 2011))</ref> in October 2011 and further discussed at the 25th conference in 2014.<ref name=":0">((Cite web|url=http://www.bipm.org/en/CGPM/db/25/1/|title=BIPM - Resolution 1 of the 25th CGPM|website=www.bipm.org|access-date=2017-03-27))</ref><ref>((cite press release
| url = http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf
| title = General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram.
| publisher = [[General Conference on Weights and Measures]]
| location = Sèvres, France
| date = October 23, 2011
| accessdate = October 25, 2011))</ref> Although the Committee recognised that significant progress had been made, they concluded that the data did not yet appear sufficiently robust to adopt the revised definition, and that work should continue to enable the adoption at the 26th meeting, scheduled for 2018.<ref name=":0" /> Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. The [[Kibble balance]] is one way do this.

As part of this project, a variety of very different technologies and approaches were considered and explored over many years. Some of these approaches were based on equipment and procedures that would have enabled the reproducible production of new, kilogram-mass prototypes on demand using measurement techniques and material properties that are ultimately based on, or traceable to, physical constants. Others were based on devices that measured either the acceleration or weight of hand-tuned kilogram test masses and which expressed their magnitudes in electrical terms via special components that permit traceability to physical constants. Such approaches depend on converting a weight measurement to a mass, and therefore require the precise measurement of the strength of [[gravity]] in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.

== Kibble balance ==
[[File:Watt balance, large view.jpg|thumb|upright=1.4|right|The [[National Institute of Standards and Technology|NIST]]'s [[Kibble balance]] is a project of the US government to develop an "electronic kilogram". The vacuum chamber dome, which lowers over the entire apparatus, is visible at top.]]
((main|Kibble balance))
The [[Kibble balance]] (known as a "watt balance" before 2016) is essentially a [[Mass versus weight#Types of scales and what they measure|single-pan]] [[weighing scale]] that measures the [[electric power]] necessary to oppose the weight of a kilogram test mass as it is pulled by Earth's gravity. It is a variation of an [[ampere balance]], with an extra calibration step that eliminates the effect of geometry. The [[electric potential]] in the Kibble balance is delineated by a [[Josephson effect|Josephson voltage standard]], which allows voltage to be linked to an invariant constant of nature with extremely high precision and stability. Its circuit [[Electrical resistance|resistance]] is calibrated against a [[quantum Hall effect]] [[Resistor#Resistance standards|resistance standard]].

The Kibble balance requires extremely precise measurement of the local gravitational acceleration ''g'' in the laboratory, using a [[gravimeter]]. For instance when the elevation of the centre of the gravimeter differs from that of the nearby test mass in the Kibble balance, the NIST compensates for Earth's gravity gradient of 309((nbsp))[[Gal (unit)|μGal]] per metre, which affects the weight of a one-kilogram test mass by about 316((nbsp))μg/m.

In April 2007, the [[National Institute of Standards and Technology|NIST's]] implementation of the Kibble balance demonstrated a combined relative standard uncertainty (CRSU) of 36((nbsp))μg.<ref name="IEEESteiner">((cite journal|last1=Steiner|first1=Richard L.|last2=Williams|first2=Edwin R.|last3=Liu|first3=Ruimin|last4=Newell|first4=David B.|title=Uncertainty Improvements of the NIST Electronic Kilogram|journal=IEEE Transactions on Instrumentation and Measurement|volume=56|issue=2|year=2007|pages=592–596|issn=0018-9456|doi=10.1109/TIM.2007.890590|bibcode=2007ITIM...56..592S |s2cid=33637678 |url=https://zenodo.org/record/1232237))</ref><ref group="Note">The combined relative standard uncertainty (CRSU) of these measurements, as with all other tolerances and uncertainties in this article unless otherwise noted, are at one standard deviation (1''σ''), which equates to a confidence level of about 68%; that is to say, 68% of the measurements fall within the stated tolerance.</ref> The UK's [[National Physical Laboratory, UK|National Physical Laboratory's]] Kibble balance demonstrated a CRSU of 70.3((nbsp))μg in 2007.<ref>"An initial measurement of Planck's constant using the NPL Mark II watt balance", I.A. Robinson ''et al.'', ''Metrologia'' '''44''' (2007), ((nowrap|427–440;))<br>NPL: ''[http://www.npl.co.uk/science-technology/mass-and-force/research/npl-kibble-balance NPL Kibble Balance]''</ref> That Kibble balance was disassembled and shipped in 2009 to Canada's Institute for National Measurement Standards (part of the [[National Research Council (Canada)|National Research Council]]), where research and development with the device could continue.

The virtue of electronic realisations like the Kibble balance is that the definition and dissemination of the kilogram no longer depends upon the stability of kilogram prototypes, which must be very carefully handled and stored. It frees physicists from the need to rely on assumptions about the stability of those prototypes. Instead, hand-tuned, close-approximation mass standards can simply be weighed and documented as being equal to one kilogram plus an offset value. With the Kibble balance, while the kilogram is ''delineated'' in electrical and gravity terms, all of which are traceable to invariants of nature; it is ''defined'' in a manner that is directly traceable to three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the metre. By fixing the Planck constant, the ''definition'' of the kilogram depends in addition only on the ''definitions'' of the second and the metre. The definition of the second depends on a single defined physical constant: the ground state hyperfine splitting frequency of the caesium-133 atom ((math|Δ''ν''(<sup>133</sup>Cs)<sub>hfs</sub>)). The metre depends on the second and on an additional defined physical constant: the [[speed of light]] ((math|''c'')). With the kilogram  redefined in this manner, physical objects such as the IPK are no longer part of the definition, but instead become ''transfer standards''.

Scales like the Kibble balance also permit more flexibility in choosing materials with especially desirable properties for mass standards. For instance, Pt((nbhyph))10Ir could continue to be used so that the specific gravity of newly produced mass standards would be the same as existing national primary and check standards (≈21.55((nbsp))g/ml). This would reduce the relative uncertainty when making [[Mass versus weight#Buoyancy_effects_of_air_on_measurement|mass comparisons in air]]. Alternatively, entirely different materials and constructions could be explored with the objective of producing mass standards with greater stability. For instance, [[osmium]]-iridium alloys could be investigated if platinum's propensity to absorb hydrogen (due to catalysis of VOCs and hydrocarbon-based cleaning solvents) and atmospheric [[Mercury (element)|mercury]] proved to be sources of instability. Also, vapor-deposited, protective ceramic coatings like [[Titanium nitride|nitrides]] could be investigated for their suitability for chemically isolating these new alloys.

The challenge with Kibble balances is not only in reducing their uncertainty, but also in making them truly ''practical'' realisations of the kilogram. Nearly every aspect of Kibble balances and their support equipment requires such extraordinarily precise and accurate, state-of-the-art technology that—unlike a device like an atomic clock—few countries would currently choose to fund their operation. For instance, the NIST's Kibble balance used four resistance standards in 2007, each of which was rotated through the Kibble balance every two to six weeks after being calibrated in a different part of [[NIST#Organization|NIST headquarters]] facility in [[Gaithersburg, Maryland]]. It was found that simply moving the resistance standards down the hall to the Kibble balance after calibration altered their values 10((nbsp))[[Parts per billion|ppb]] (equivalent to 10((nbsp))μg) or more.<ref>R. Steiner, ''No FG-5?'', NIST, Nov 30, 2007. "We rotate between about 4 resistance standards, transferring from the calibration lab to my lab every 2–6 weeks. Resistors do not transfer well, and sometimes shift at each transfer by 10&nbsp;ppb or more."</ref> Present-day technology is insufficient to permit stable operation of Kibble balances between even biannual calibrations. When the new definition takes effect, it is likely there will only be a few—at most—Kibble balances initially operating in the world.

==Other approaches==
((hatnote|In the concise form, such as ((val|1.85487|(14)|e=13)), the digits between the parentheses denote the [[uncertainty]] at one [[standard deviation]] (1''σ'', the 68% confidence level) in the same number of least significant digits of the [[significand]].))
Several alternative approaches to redefining the kilogram that were fundamentally different from the Kibble balance were explored to varying degrees, with some abandoned. The Avogadro project, in particular, was important for the 2018 redefinition decision because it provided an accurate measurement of the Planck constant that was consistent with and independent of the Kibble balance method.<ref>((cite news |url=https://www.nytimes.com/2018/11/16/science/kilogram-physics-measurement.html |title=The Kilogram Is Dead. Long Live the Kilogram! |first=XiaoZhi |last=Lim |work=The New York Times |date=November 16, 2018 |quote=Avogadro's constant and the Planck constant are intertwined in the laws of physics. Having measured Avogadro's constant, Dr. Bettin could derive the Planck constant. And with a precise measure of the Planck constant, he could validate the results of Dr. Kibble's work, and vice versa.))</ref> The alternative approaches included:

=== Atom-counting approaches ===

==== Avogadro project ====
((More citations needed section|date=May 2022))
((Anchor|Avogadro project)) 
<!--IMAGE & CAPTION-->
[[File:Silicon sphere for Avogadro project.jpg|thumb|right|[[Achim Leistner]] at the [[Australian Centre for Precision Optics]] (ACPO) holds a 1((nbsp))kg, single-crystal silicon sphere for the Avogadro project. Among the roundest man-made objects in the world, the sphere scaled to the size of Earth would have a high point of only 2.4&nbsp;metres above "sea level".<!--
FOOTNOTE TO IMAGE CAPTION--><ref group="Note">The sphere shown in the photograph has an out-of-roundness value (peak to valley on the radius) of 50((nbsp))nm. According to ACPO, they improved on that with an out-of-roundness of 35((nbsp))nm. On the 93.6((nbsp))mm diameter sphere, an out-of-roundness of 35((nbsp))nm (deviation of ±17.5((nbsp))nm from the average) is a fractional roundness ((nowrap|(∆''r''/''r'') ((=)) ((val|3.7|e=-7)))).  Scaled to the size of Earth, this is equivalent to a maximum deviation from sea level of only 2.4((nbsp))m. The roundness of that ACPO sphere is exceeded only by two of the four [[Fused quartz|fused-quartz]] gyroscope rotors flown on [[Gravity Probe B|Gravity Probe((nbsp))B]], which were manufactured in the late 1990s and given their final figure at the [http://hepl.stanford.edu/ W.W. Hansen Experimental Physics Lab] at [[Stanford University]]. Particularly, "Gyro 4" is recorded in the [[Guinness World Records|Guinness]] database of world records (their database, not in their book) as ''the'' world's roundest man-made object. According to a published report ([http://aa.stanford.edu/aeroastro/posters2007/Polhode_Motion.pdf 221((nbsp))kB PDF, here] ((Webarchive|url=https://web.archive.org/web/20080227031301/http://aa.stanford.edu/aeroastro/posters2007/Polhode_Motion.pdf |date=2008-02-27 )) <!-- Indeterminate link! --><span style="margin-left:0.2em">)</span> and the GP((nbhyph))B public affairs coordinator at Stanford University, of the four gyroscopes onboard the probe, Gyro((nbsp))4 has a maximum surface undulation from a perfect sphere of 3.4((nbsp))±0.4((nbsp))nm on the 38.1((nbsp))mm diameter sphere, which is a ((nowrap|∆''r''/''r'' ((=)) ((val|1.8|e=-7)).)) Scaled to the size of Earth, this is equivalent to a deviation the size of North America rising slowly up out of the sea (in molecular-layer terraces 11.9((nbsp))cm high), reaching a maximum elevation of 1.14((nbsp))±0.13((nbsp))m in Nebraska, and then gradually sloping back down to sea level on the other side of the continent.</ref>]]
<!--END of  FOOTNOTE-->
Another Avogadro constant-based approach, known as the [[International Avogadro Coordination]]'s ''Avogadro project'', would define and delineate the kilogram as a 93.6((nbsp))mm diameter sphere of [[silicon]] atoms. Silicon was chosen because a commercial infrastructure with [[mature technology]] for creating defect-free, ultra-pure monocrystalline silicon already exists, the [[Czochralski process]], to service the [[semiconductor]] industry. 

To make a practical realisation of the kilogram, a silicon [[Boule (crystal)|boule]] (a rod-like, single-crystal ingot) would be produced. Its [[isotope|isotopic]] composition would be measured with a [[Mass spectrometry|mass spectrometer]] to determine its average relative atomic mass. The boule would be cut, ground, and polished into spheres. The size of a select sphere would be measured using optical [[interferometry]] to an uncertainty of about 0.3((nbsp))nm on the radius—roughly a single atomic layer. The precise lattice spacing between the atoms in its crystal structure (≈((nbsp))192((nbsp))pm) would be measured using a scanning [[X-ray interferometer]]. This permits its atomic spacing to be determined with an uncertainty of only three parts per billion. With the size of the sphere, its average atomic mass, and its atomic spacing known, the required sphere diameter can be calculated with sufficient precision and low uncertainty to enable it to be finish-polished to a target mass of one kilogram.

Experiments are being performed on the Avogadro Project's silicon spheres to determine whether their masses are most stable when stored in a vacuum, a partial vacuum, or ambient pressure. However, no technical means currently exist to prove a long-term stability any better than that of the IPK's, because the most sensitive and accurate measurements of mass are made with [[Mass versus weight#Types of scales and what they measure|dual-pan]] [[Beam balance|balances]] like the BIPM's FB((nbhyph))2 flexure-strip balance (see ''((section link||External links))'', below). Balances can only compare the mass of a silicon sphere to that of a reference mass. Given the latest understanding of the lack of long-term mass stability with the IPK and its replicas, there is no known, perfectly stable mass artefact to compare against. [[Mass versus weight#Types of scales and what they measure|Single-pan]] [[Weighing scale|scale]]s, which measure weight relative to an invariant of nature, are not precise to the necessary long-term uncertainty of 10–20 parts per billion. Another issue to be overcome is that silicon oxidises and forms a thin layer (equivalent to ((nowrap|5–20)) silicon atoms deep) of [[silicon dioxide]] ([[quartz]]) and [[silicon monoxide]]. This layer slightly increases the mass of the sphere, an effect that must be accounted for when polishing the sphere to its finished size.  Oxidation is not an issue with platinum and iridium, both of which are [[noble metal]]s that are roughly as [[Galvanic series|cathodic]] as oxygen and therefore don't oxidise unless coaxed to do so in the laboratory. The presence of the thin oxide layer on a silicon-sphere mass prototype places additional restrictions on the procedures that might be suitable to clean it to avoid changing the layer's thickness or oxide [[stoichiometry]].

All silicon-based approaches would fix the Avogadro constant but vary in the details of the definition of the kilogram. One approach would use silicon with all three of its natural isotopes present. About 7.78% of silicon comprises the two heavier isotopes: <sup>29</sup>Si and <sup>30</sup>Si. As described in ''((section link||Carbon-12))'' below, this method would ''define'' the magnitude of the kilogram in terms of a certain number of <sup>12</sup>C atoms by fixing the Avogadro constant; the silicon sphere would be the ''practical realisation''. This approach could accurately delineate the magnitude of the kilogram because the masses of the three silicon [[nuclide]]s relative to <sup>12</sup>C are known with great precision (relative uncertainties of 1((nbsp))[[Parts per billion|ppb]] or better). An alternative method for creating a silicon sphere-based kilogram proposes to use [[Isotope separation|isotopic separation]] techniques to enrich the silicon until it is nearly pure <sup>28</sup>Si, which has a relative atomic mass of ((val|27.9769265325|(19))).<ref name=AvogadroNature>((cite journal|last=Brumfiel|first=Geoff|title=Elemental shift for kilo|journal=Nature|date=October 21, 2010|volume=467|issue=7318|pages=892|url=http://www.nature.com/news/2010/101019/pdf/467892a.pdf|doi=10.1038/467892a|pmid=20962811|doi-access=free))</ref> With this approach, the Avogadro constant would not only be fixed, but so too would the atomic mass of <sup>28</sup>Si. As such, the definition of the kilogram would be decoupled from <sup>12</sup>C and the kilogram would instead be defined as ((nowrap|((sfrac|1000|((val|27.9769265325)))) ⋅ ((val|6.02214179|e=23)))) atoms of <sup>28</sup>Si (≈ ((val|35.74374043)) fixed moles of <sup>28</sup>Si atoms). Physicists could elect to define the kilogram in terms of <sup>28</sup>Si even when kilogram prototypes are made of natural silicon (all three isotopes present). Even with a kilogram definition based on theoretically pure <sup>28</sup>Si, a silicon-sphere prototype made of only nearly pure <sup>28</sup>Si would necessarily deviate slightly from the defined number of moles of silicon to compensate for various chemical and isotopic impurities as well as the effect of surface oxides.<ref>NPL: ''[http://www.npl.co.uk/science-technology/mass-and-force/research/avogadro-project Avogadro Project]''; Australian National Measurement Institute: ''[<!-- http://www.measurement.gov.au/index.cfm?event=object.showContent&objectID=7CBA5E62-BCD6-81AC-15017BE81748EF4B --> Redefining the kilogram through the Avogadro constant]''; and Australian Centre for Precision Optics: ''[http://www.acpo.csiro.au/avogadro.htm The Avogadro Project] ((Webarchive|url=https://web.archive.org/web/20140407015811/http://www.acpo.csiro.au/avogadro.htm|date=2014-04-07))''</ref>((Dead link|date=November 2023))

==== Carbon-12 ====
Though not offering a practical realisation, this definition would precisely define the magnitude of the kilogram in terms of a certain number of [[carbon-12|carbon((nbhyph))12]] atoms. Carbon((nbhyph))12 (<sup>12</sup>C) is an [[isotope]] of carbon. The [[mole (unit)|mole]] is currently defined as "the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon((nbhyph))12". Thus, the current definition of the mole requires that ((sfrac|1000|12)) moles (((sfrac|83|1|3))&nbsp;mol) of <sup>12</sup>C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the [[Avogadro constant]], is experimentally determined, and the current best estimate of its value is ((physconst|NA|unit=no|after= &nbsp;entities per mole.)) This new definition of the kilogram proposed to fix the Avogadro constant at precisely ((val|6.02214|end=X|e=23|u=mol-1)) with the kilogram being defined as "the mass equal to that of ((nowrap|((sfrac|1000|12)) ⋅ ((val|6.02214|end=X|e=23)))) atoms of <sup>12</sup>C".

The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the [[Planck constant]]. That relative standard uncertainty has been 50((nbsp))parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposal would be that the uncertainty in the mass of a <sup>12</sup>C atom—and the magnitude of the kilogram—could be no better than the current 50((nbsp))ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram would be subject to future refinement as improved measurements of the value of the Planck constant become available; electronic realisations of the kilogram would be recalibrated as required. Conversely, an electronic ''definition'' of the kilogram (see ''((section link||Electronic approaches))'', below), which would precisely fix the Planck constant, would continue to allow ((sfrac|83|1|3)) moles of <sup>12</sup>C to have a mass of precisely one kilogram but the number of atoms comprising a mole (the Avogadro constant) would continue to be subject to future refinement.

A variation on a <sup>12</sup>C-based definition proposes to define the Avogadro constant as being precisely ((val|84446889))<sup>3</sup> (≈((nbsp))((val|6.02214162|e=23))) atoms. An imaginary realisation of a 12-gram mass prototype would be a cube of <sup>12</sup>C atoms measuring precisely ((val|84446889)) atoms across on a side. With this proposal, the kilogram would be defined as "the mass equal to ((val|84446889))<sup>3</sup>((nbsp))× ((sfrac|83|1|3)) atoms of <sup>12</sup>C."<ref> ((cite journal|last=Hill|first=Theodore P |author2=Miller, Jack |author3=Censullo, Albert C|title=Towards a better definition of the kilogram|journal=Metrologia|date=June 1, 2011|volume=48|issue=3|pages=83–86|doi=10.1088/0026-1394/48/3/002|bibcode = 2011Metro..48...83H |arxiv = 1005.5139 |s2cid=1847580 ))</ref>((refn|The proposal originally was to redefine the kilogram as the mass of ((val|84446886))<sup>3</sup> carbon-12 atoms.<ref>Georgia Tech, ''[http://gtresearchnews.gatech.edu/definition-kilogram/ "A Better Definition for the Kilogram?"]'' September 21, 2007 (press release).</ref> The value ((val|84446886)) had been chosen because it has a special property; its cube (the proposed new value for the Avogadro constant) is divisible by twelve. Thus with that definition of the kilogram, there would have been an integer number of atoms in one gram of <sup>12</sup>C: ((val|50184508190229061679538)) atoms. The uncertainty in the Avogadro constant has narrowed considerably since this proposal was first submitted to ''[[American Scientist]]'' for publication. The 2014 CODATA value for the Avogadro constant (((val|6.022140857|(74)|e=23))) has a relative standard uncertainty of 12 parts per billion and the cube root of this number is ((val|84446885.41|(35))), i.e. there are no integers within the range of uncertainty.|group=Note))

==== Ion accumulation ====
Another Avogadro-based approach, [[ion]] accumulation, since abandoned, would have defined and delineated the kilogram by precisely creating new metal prototypes on demand. It would have done so by accumulating [[gold]] or [[bismuth]] [[ion]]s (atoms stripped of an electron) and counting them by measuring the electric current required to neutralise the ions. Gold (<sup>197</sup>Au) and bismuth (<sup>209</sup>Bi) were chosen because they can be safely handled and have the two highest [[atomic mass]]es among the [[mononuclidic elements]] that are stable (gold) or effectively so (bismuth).<ref group="Note">In 2003, the same year the first gold-deposition experiments were conducted, physicists found that the only naturally occurring isotope of bismuth, <sup>209</sup>Bi, is actually very slightly [[Radioactive decay|radioactive]], with the longest known radioactive [[half-life]] of any naturally occurring element that decays via [[Alpha particle|alpha radiation]]—a half-life of ((val|19|2|e=18|u=years)). As this is 1.4&nbsp;billion times the age of the universe, <sup>209</sup>Bi is considered a stable isotope for most practical applications (those unrelated to such disciplines as [[nucleocosmochronology]] and [[geochronology]]). In other terms, ((val|99.999999983|u=%)) of the bismuth that existed on Earth 4.567&nbsp;billion years ago still exists today. Only two mononuclidic elements are heavier than bismuth and only one approaches its stability: [[thorium]]. Long considered a possible replacement for uranium in nuclear reactors, thorium can cause cancer when inhaled because it is over 1.2((nbsp))billion times more radioactive than bismuth. It also has such a strong tendency to oxidise that its powders are [[pyrophoric]]. These characteristics make thorium unsuitable in ion-deposition experiments. See also ''[[Isotopes of bismuth]]'', ''[[Isotopes of gold]]'' and ''[[Isotopes of thorium]]''.</ref>  See also ''[[Table of nuclides]]''.

With a gold-based definition of the kilogram for instance, the relative atomic mass of gold could have been fixed as precisely ((val|196.9665687)), from the current value of ((val|196.9665687|(6))). As with a definition based upon carbon((nbhyph))12, the Avogadro constant would also have been fixed. The kilogram would then have been defined as "the mass equal to that of precisely ((nowrap|((sfrac|1000|((val|196.9665687)))) ⋅ ((val|6.02214179|e=23)))) atoms of gold" (precisely 3,057,443,620,887,933,963,384,315 atoms of gold or about ((val|5.07700371)) fixed moles).

In 2003, German experiments with gold at a current of only ((val|10|u=μA)) demonstrated a relative uncertainty of 1.5%.<ref name="PTB">The German national metrology institute, known as the Physikalisch-Technische Bundesanstalt (PTB): [http://www.ptb.de/en/org/1/12/124/ionenex.htm Working group 1.24, Ion Accumulation]</ref> Follow-on experiments using bismuth ions and a current of 30((nbsp))mA were expected to accumulate a mass of 30((nbsp))g in six days and to have a relative uncertainty of better than 1&nbsp;ppm.<ref>[http://www.bipm.org/utils/en/zip/CGPM22.zip ''General Conference on Weights and Measures, 22nd Meeting, October 2003''] (3.2((nbsp))MB ZIP file).</ref> Ultimately, ion((nbhyph))accumulation approaches proved to be unsuitable. Measurements required months and the data proved too erratic for the technique to be considered a viable future replacement to the IPK.<ref>Bowers, Mary, ''[[The Caravan (magazine)|The Caravan]]'', September 1–15, 2009: [https://web.archive.org/web/20110322075220/http://www.marybowers.org.uk/18_The%20Caravan%20September%201-15.pdf "Why the World is Losing Weight"]</ref>

Among the many technical challenges of the ion-deposition apparatus was obtaining a sufficiently high ion current (mass deposition rate) while simultaneously decelerating the ions so they could all deposit onto a target electrode embedded in a balance pan. Experiments with gold showed the ions had to be decelerated to very low energies to avoid [[sputtering]] effects—a phenomenon whereby ions that had already been counted ricochet off the target electrode or even dislodged atoms that had already been deposited. The deposited mass fraction in the 2003 German experiments only approached very close to 100% at ion energies of less than around ((val|1|ul=eV)) (<((nbsp))1((nbsp))km/s for gold).<ref name="PTB" />

If the kilogram had been defined as a precise quantity of gold or bismuth atoms deposited with an electric current, not only would the Avogadro constant and the atomic mass of gold or bismuth have to have been precisely fixed, but also the value of the [[elementary charge]] (''e''), likely to ((val|1.60217|end=X|e=-19|ul=C)) (from the currently recommended value of ((physconst|e))). Doing so would have effectively defined the [[ampere]] as a flow of ((sfrac|1|((val|1.60217|end=X|e=-19)))) electrons per second past a fixed point in an electric circuit. The SI unit of mass would have been fully defined by having precisely fixed the values of the Avogadro constant and elementary charge, and by exploiting the fact that the atomic masses of bismuth and gold atoms are invariant, universal constants of nature.<!-- Should it be mentioned that fixing both the elementary charge and the mass of some atom would "unfix" the magnetic constant of vacuum? -->

Beyond the slowness of making a new mass standard and the poor reproducibility, there were other intrinsic shortcomings to the ion((nbhyph))accumulation approach that proved to be formidable obstacles to ion-accumulation-based techniques becoming a practical realisation. The apparatus necessarily required that the deposition chamber have an integral balance system to enable the convenient calibration of a reasonable quantity of transfer standards relative to any single internal ion-deposited prototype. Furthermore, the mass prototypes produced by ion deposition techniques would have been nothing like the freestanding platinum-iridium prototypes currently in use; they would have been deposited onto—and become part of—an electrode imbedded into one pan of a special balance integrated into the device. Moreover, the ion-deposited mass wouldn't have had a hard, highly polished surface that can be vigorously cleaned like those of current prototypes. Gold, while dense and a [[noble metal]] (resistant to oxidation and the formation of other compounds), is extremely soft so an internal gold prototype would have to be kept well isolated and scrupulously clean to avoid contamination and the potential of wear from having to remove the contamination. Bismuth, which is an inexpensive metal used in low-temperature solders, slowly oxidises when exposed to room-temperature air and forms other chemical compounds and so would not have produced stable reference masses unless it was continually maintained in a vacuum or inert atmosphere.

=== Ampere-based force ===
[[File:Meissner effect p1390048.jpg|thumb|right|A magnet floating above a superconductor bathed in liquid nitrogen demonstrates [[Superdiamagnetism|perfect diamagnetic]] levitation via the [[Meissner effect]]. Experiments with an ampere-based definition of the kilogram flipped this arrangement upside-down: an electric field accelerated a superconducting test mass supported by fixed magnets.]]

This approach would define the kilogram as "the mass which would be accelerated at precisely ((val|2|e=-7|u=m/s<sup>2</sup>)) when subjected to the per-metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed one metre apart in vacuum, through which flow a constant current of ((sfrac|((gaps|1.602|17|e=-19)))) elementary charges per second".

Effectively, this would define the kilogram as a derivative of the [[ampere]] rather than the present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would specify [[elementary charge]] (''e'') as precisely ((gaps|1.602|17|e=-19)) [[coulomb]] rather than the current recommended value of ((physconst|e|after=.)) It would necessarily follow that the ampere (one coulomb per second) would also become an electric current of this precise quantity of elementary charges per second passing a given point in an electric circuit.
The virtue of a practical realisation based upon this definition is that unlike the Kibble balance and other scale-based methods, all of which require the careful characterisation of gravity in the laboratory, this method delineates the magnitude of the kilogram directly in the very terms that define the nature of mass: acceleration due to an applied force. Unfortunately, it is extremely difficult to develop a practical realisation based upon accelerating masses. Experiments over a period of years in Japan with a [[Superconductivity|superconducting]], 30((nbsp))g mass supported by [[Diamagnetism|diamagnetic]] levitation never achieved an uncertainty better than ten parts per million. [[Magnetic hysteresis]] was one of the limiting issues. Other groups performed similar research that used different techniques to levitate the mass.<ref>((cite press release |publisher=NIST |archiveurl=https://web.archive.org/web/20080522131052/https://www.nist.gov/public_affairs/newsfromnist_beyond_the_kilogram.htm|archivedate=May 22, 2008|url=https://www.nist.gov/public_affairs/newsfromnist_beyond_the_kilogram.htm |title=Beyond the kilogram: redefining the International System of Units))</ref><ref>((cite journal |author=Robinson, I.A. |title=Toward a Final Result From the NPL Mark II Watt Balance |journal=IEEE Transactions on Instrumentation and Measurement |date=April 2009 |volume=58 |issue=4 |pages=936–941 |doi=10.1109/TIM.2008.2008090 |bibcode=2009ITIM...58..936R |s2cid=36038698 ))</ref>

== Notes ==
((reflist|group=Note))
==References==
((reflist))
[[Category:SI base units]]
[[Category:Units of mass]]

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