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scientific community The scientific community is a diverse network of interacting scientists. It includes many " sub-communities" working on particular scientific fields, and within particular institutions; interdisciplinary and cross-institutional activities are als ...
examined several approaches to redefining the
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
before deciding on a 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 The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
s based on the kilogram, were defined by an artificial metal object called the
international prototype of the kilogram The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used t ...
(IPK). There was broad agreement that the older definition of the kilogram should be replaced. 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 The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
to be exactly . This approach effectively defines the kilogram in terms of the second and the
metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
, and took effect on 20 May 2019. 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 Krypton (from grc, κρυπτός, translit=kryptos 'the hidden one') is a chemical element with the symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace amounts in the atmosphere and is often ...
, and later the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
) 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 The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(CIPM) in 2005, it was recommended that the same be done with the kilogram. In October 2010, the CIPM voted to submit a resolution for consideration at the
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(CGPM), to "take note of an intention" that the kilogram be defined in terms of the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
, (which has dimensions of energy times time) together with other physical constants. This resolution was accepted by the 24th conference of the CGPM in October 2011 and further discussed at the 25th conference in 2014. 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. 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 A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize t ...
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 physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.


Kibble balance

The
Kibble balance A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize t ...
(known as a "watt balance" before 2016) is essentially a single-pan
weighing scale A scale or balance is a device used to measure weight or mass. These are also known as mass scales, weight scales, mass balances, and weight balances. The traditional scale consists of two plates or bowls suspended at equal distances from a ...
that measures the
electric power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions o ...
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 The ampere balance (also current balance or Kelvin balance) is an electromechanical apparatus used for the precise measurement of the SI unit of electric current, the ampere. It was invented by William Thomson, 1st Baron Kelvin. The curre ...
, with an extra calibration step that eliminates the effect of geometry. The
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
in the Kibble balance is delineated by a
Josephson voltage standard A Josephson voltage standard is a complex system that uses a superconducting integrated circuit chip operating at a temperature of 4 K to generate stable voltages that depend only on an applied frequency and fundamental constants. It is an int ...
, which allows voltage to be linked to an invariant constant of nature with extremely high precision and stability. Its circuit resistance is calibrated against a
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
resistance standard. The Kibble balance requires extremely precise measurement of the local gravitational acceleration ''g'' in the laboratory, using a
gravimeter Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. Units of measurement Gr ...
. 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 μGal per metre, which affects the weight of a one-kilogram test mass by about 316μg/m. In April 2007, the NIST's implementation of the Kibble balance demonstrated a combined relative standard uncertainty (CRSU) of 36μg.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. The UK's National Physical Laboratory's Kibble balance demonstrated a CRSU of 70.3μg in 2007. That Kibble balance was disassembled and shipped in 2009 to Canada's Institute for National Measurement Standards (part of the
National Research Council National Research Council may refer to: * National Research Council (Canada), sponsoring research and development * National Research Council (Italy), scientific and technological research, Rome * National Research Council (United States), part of ...
), where research and development with the device could continue. Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration ''g'', are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, ''g'' varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see ''
Earth's gravity The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity ...
''). There are also slight seasonal variations in ''g'' at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape caused by the Moon and the Sun. Although ''g'' would not be a term in the ''definition'' of the kilogram, it would be crucial in the process of measurement of the kilogram when relating energy to power. Accordingly, ''g'' must be measured with at least as much precision and accuracy as are the other terms, so measurements of ''g'' must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, ''g'' is measured using dropping-mass absolute gravimeters that contain an iodine-stabilised
helium–neon laser A helium–neon laser or He-Ne laser, is a type of gas laser whose high energetic medium gain medium consists of a mixture of 10:1 ratio of helium and neon at a total pressure of about 1 torr inside of a small electrical discharge. The best ...
interferometer Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber op ...
. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium
atomic clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8 ppb of . 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 . The metre depends on the second and on an additional defined physical constant: the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. 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, Pt10Ir 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 (≈21.55g/ml). This would reduce the relative uncertainty when making 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 Osmium (from Greek grc, ὀσμή, osme, smell, label=none) is a chemical element with the symbol Os and atomic number 76. It is a hard, brittle, bluish-white transition metal in the platinum group that is found as a trace element in alloys, mos ...
-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 Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
proved to be sources of instability. Also, vapor-deposited, protective ceramic coatings like
nitrides In chemistry, a nitride is an inorganic compound of nitrogen. The "nitride" anion, N3- ion, is very elusive but compounds of nitride are numerous, although rarely naturally occuring. Some nitrides have a find applications, such as wear-resistant ...
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 headquarters facility in
Gaithersburg, Maryland Gaithersburg ( ), officially the City of Gaithersburg, is a city in Montgomery County, Maryland, Montgomery County, Maryland, United States. At the time of the 2020 United States Census, 2020 U.S. Census, Gaithersburg had a population of 69,657, ...
. It was found that simply moving the resistance standards down the hall to the Kibble balance after calibration altered their values 10 ppb (equivalent to 10μg) or more. 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.


Alternative approaches to redefining the kilogram

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. The alternative approaches included:


Atom-counting approaches


Avogadro project

Another Avogadro constant-based approach, known as the
International Avogadro Coordination The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining co ...
's ''Avogadro project'', would define and delineate the kilogram as a 93.6mm diameter sphere of
silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
atoms. Silicon was chosen because a commercial infrastructure with
mature technology A mature technology is a technology that has been in use for long enough that most of its initial faults and inherent problems have been removed or reduced by further development. In some contexts, it may also refer to technology that has not se ...
for creating defect-free, ultra-pure monocrystalline silicon already exists, the Czochralski process, to service the
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
industry. To make a practical realisation of the kilogram, a silicon boule (a rod-like, single-crystal ingot) would be produced. Its isotopic composition would be measured with a
mass spectrometer Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is used ...
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 Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
to an uncertainty of about 0.3nm on the radius—roughly a single atomic layer. The precise lattice spacing between the atoms in its crystal structure (≈192pm) 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 dual-pan balances like the BIPM's FB2 flexure-strip balance (see ', 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. Single-pan scales, 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 silicon atoms deep) of
silicon dioxide Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
(
quartz Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...
) and
silicon monoxide Silicon monoxide is the chemical compound with the formula SiO where silicon is present in the oxidation state +2. In the vapour phase, it is a diatomic molecule. It has been detected in stellar objects and has been described as the most common o ...
. 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 A noble metal is ordinarily regarded as a metallic chemical element that is generally resistant to corrosion and is usually found in nature in its raw form. Gold, platinum, and the other platinum group metals (ruthenium, rhodium, palladium, o ...
s that are roughly as
cathodic A cathode is the electrode from which a conventional current leaves a polarized electrical device. This definition can be recalled by using the mnemonic ''CCD'' for ''Cathode Current Departs''. A conventional current describes the direction in whi ...
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 Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
. 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: 29Si and 30Si. As described in ' below, this method would ''define'' the magnitude of the kilogram in terms of a certain number of 12C 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 A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was coined by Truman ...
s relative to 12C are known with great precision (relative uncertainties of 1 ppb or better). An alternative method for creating a silicon sphere-based kilogram proposes to use
isotopic separation Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes. The use of the nuclides produced is varied. The largest variety is used in research (e.g. in chemistry where atoms of "marker" n ...
techniques to enrich the silicon until it is nearly pure 28Si, which has a relative atomic mass of . With this approach, the Avogadro constant would not only be fixed, but so too would the atomic mass of 28Si. As such, the definition of the kilogram would be decoupled from 12C and the kilogram would instead be defined as atoms of 28Si (≈ fixed moles of 28Si atoms). Physicists could elect to define the kilogram in terms of 28Si even when kilogram prototypes are made of natural silicon (all three isotopes present). Even with a kilogram definition based on theoretically pure 28Si, a silicon-sphere prototype made of only nearly pure 28Si 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.


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 carbon12 atoms. Carbon12 (12C) is an
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) ...
of carbon. The
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
is currently defined as "the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon12". Thus, the current definition of the mole requires that moles ( mol) of 12C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...
, is experimentally determined, and the current best estimate of its value is This new definition of the kilogram proposed to fix the Avogadro constant at precisely with the kilogram being defined as "the mass equal to that of atoms of 12C". The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
. That relative standard uncertainty has been 50parts 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 12C atom—and the magnitude of the kilogram—could be no better than the current 50ppb 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 ', below), which would precisely fix the Planck constant, would continue to allow moles of 12C 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 12C-based definition proposes to define the Avogadro constant as being precisely 3 (≈) atoms. An imaginary realisation of a 12-gram mass prototype would be a cube of 12C atoms measuring precisely atoms across on a side. With this proposal, the kilogram would be defined as "the mass equal to 3× atoms of 12C."


Ion accumulation

Another Avogadro-based approach,
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
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 Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...
or
bismuth Bismuth is a chemical element with the Symbol (chemistry), symbol Bi and atomic number 83. It is a post-transition metal and one of the pnictogens, with chemical properties resembling its lighter group 15 siblings arsenic and antimony. Elemental ...
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s (atoms stripped of an electron) and counting them by measuring the electric current required to neutralise the ions. Gold (197Au) and bismuth (209Bi) were chosen because they can be safely handled and have the two highest
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nbs ...
es among the
mononuclidic elements A mononuclidic element or monotopic element is one of the 21 chemical elements that is found naturally on Earth essentially as a single nuclide (which may, or may not, be a stable nuclide). This single nuclide will have a characteristic atomic m ...
that are stable (gold) or effectively so (bismuth).In 2003, the same year the first gold-deposition experiments were conducted, physicists found that the only naturally occurring isotope of bismuth, 209Bi, is actually very slightly
radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
, with the longest known radioactive
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
of any naturally occurring element that decays via
alpha radiation Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atom ...
—a half-life of . As this is 1.4 billion times the age of the universe, 209Bi is considered a stable isotope for most practical applications (those unrelated to such disciplines as
nucleocosmochronology Nucleocosmochronology or nuclear cosmochronology is a technique used to determine timescales for astrophysical objects and events. It compares the observed ratios of abundances of heavy radioactive and stable nuclides to the primordial ratios pred ...
and
geochronology Geochronology is the science of determining the age of rocks, fossils, and sediments using signatures inherent in the rocks themselves. Absolute geochronology can be accomplished through radioactive isotopes, whereas relative geochronology is pr ...
). In other terms, of the bismuth that existed on Earth 4.567 billion years ago still exists today. Only two mononuclidic elements are heavier than bismuth and only one approaches its stability:
thorium Thorium is a weakly radioactive metallic chemical element with the symbol Th and atomic number 90. Thorium is silvery and tarnishes black when it is exposed to air, forming thorium dioxide; it is moderately soft and malleable and has a high me ...
. Long considered a possible replacement for uranium in nuclear reactors, thorium can cause cancer when inhaled because it is over 1.2billion times more radioactive than bismuth. It also has such a strong tendency to oxidise that its powders are
pyrophoric A substance is pyrophoric (from grc-gre, πυροφόρος, , 'fire-bearing') if it ignites spontaneously in air at or below (for gases) or within 5 minutes after coming into contact with air (for liquids and solids). Examples are organolith ...
. These characteristics make thorium unsuitable in ion-deposition experiments. See also ''
Isotopes of bismuth Bismuth (83Bi) has 41 known isotopes, ranging from 184Bi to 224Bi. Bismuth has no stable isotopes, but does have one very long-lived isotope; thus, the standard atomic weight can be given as . Although bismuth-209 is now known to be unstable, it ...
'', ''
Isotopes of gold Gold (79Au) has one stable isotope, 197Au, and 36 radioisotopes, with 195Au being the most stable with a half-life of 186 days. Gold is currently considered the heaviest monoisotopic element. Bismuth formerly held that distinction until alpha-deca ...
'' and ''
Isotopes of thorium Thorium (90Th) has seven naturally occurring isotopes but none are stable. One isotope, 232Th, is ''relatively'' stable, with a half-life of 1.405×1010 years, considerably longer than the age of the Earth, and even slightly longer than the gene ...
''.
See also ''
Table of nuclides A table or chart of nuclides is a two-dimensional graph of isotopes of the elements, in which one axis represents the number of neutrons (symbol ''N'') and the other represents the number of protons (atomic number, symbol ''Z'') in the atomic nu ...
''. With a gold-based definition of the kilogram for instance, the relative atomic mass of gold could have been fixed as precisely , from the current value of . As with a definition based upon carbon12, the Avogadro constant would also have been fixed. The kilogram would then have been defined as "the mass equal to that of precisely atoms of gold" (precisely 3,057,443,620,887,933,963,384,315 atoms of gold or about fixed moles). In 2003, German experiments with gold at a current of only demonstrated a relative uncertainty of 1.5%.The German national metrology institute, known as the Physikalisch-Technische Bundesanstalt (PTB)
Working group 1.24, Ion Accumulation
/ref> Follow-on experiments using bismuth ions and a current of 30mA were expected to accumulate a mass of 30g in six days and to have a relative uncertainty of better than 1 ppm. Ultimately, ionaccumulation 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. 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 In physics, sputtering is a phenomenon in which microscopic particles of a solid material are ejected from its surface, after the material is itself bombarded by energetic particles of a plasma or gas. It occurs naturally in outer space, and can ...
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 (<1km/s for gold). 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 The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
(''e''), likely to (from the currently recommended value of ). Doing so would have effectively defined the
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
as a flow of 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. Beyond the slowness of making a new mass standard and the poor reproducibility, there were other intrinsic shortcomings to the ionaccumulation 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 A noble metal is ordinarily regarded as a metallic chemical element that is generally resistant to corrosion and is usually found in nature in its raw form. Gold, platinum, and the other platinum group metals (ruthenium, rhodium, palladium, o ...
(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

This approach would define the kilogram as "the mass which would be accelerated at precisely 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 elementary charges per second". Effectively, this would define the kilogram as a derivative of the
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
rather than the present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would specify
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
(''e'') as precisely
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
rather than the current recommended value of 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
superconducting Superconductivity is a set of physical properties observed in certain materials where Electrical resistance and conductance, electrical resistance vanishes and magnetic field, magnetic flux fields are expelled from the material. Any material e ...
, 30g mass supported by
diamagnetic Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted ...
levitation never achieved an uncertainty better than ten parts per million.
Magnetic hysteresis Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become '' ...
was one of the limiting issues. Other groups performed similar research that used different techniques to levitate the mass.


Notes


References

{{reflist SI base units Units of mass