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The kilogram or kilogramme (symbol: kg) is
the base unit of mass in the International System of Units (SI). Until 20 May 2019, it
remains defined by a platinum alloy cylinder, the International Prototype Kilogram (informally
Le Grand K or IPK), manufactured in 1889, and carefully stored in Saint-Cloud, a suburb
of Paris. After 20 May, it will be defined in terms of fundamental physical constants.
The kilogram was originally defined as the mass of a litre (cubic decimetre) of water.
That was an inconvenient quantity to precisely replicate, so in 1799 a platinum artefact
was fashioned to define the kilogram. That artefact, and the later IPK, have been the
standard of the unit of mass for the metric system ever since.
In spite of best efforts to maintain it, the IPK has diverged from its replicas by approximately
50 micrograms since their manufacture late in the 19th century. This led to efforts to
develop measurement technology precise enough to allow replacing the kilogram artifact with
a definition based directly on physical phenomena, a process which is scheduled to finally take
place in 2019. The new definition is based on invariant constants
of nature, in particular the Planck constant which will change to being defined rather
than measured, thereby fixing the value of the kilogram in terms of the second and the
metre, and eliminating the need for the IPK. The new definition was approved by the General
Conference on Weights and Measures (CGPM) on 16 November 2018. The Planck constant relates
a light particle’s energy, and hence mass, to its frequency. The new definition only
became possible when instruments were devised to measure the Planck constant with sufficient
accuracy based on the IPK definition of the kilogram.==Definition==
The gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimetre
of water at the melting point of ice. The final kilogram, manufactured as a prototype
in 1799 and from which the International Prototype Kilogram (IPK) was derived in 1875, had a
mass equal to the mass of 1 dm3 of water under atmospheric pressure and at the temperature
of its maximum density, which is approximately 4 °C.
The kilogram is the only named SI unit with an SI prefix (kilo) as part of its name. Until
the 2019 redefinition of SI base units, it was also the last SI unit that was still directly
defined by an artefact rather than a fundamental physical property that could be independently
reproduced in different laboratories. Three other base units (cd, A, mol) and 17 derived
units (N, Pa, J, W, C, V, F, Ω, S, Wb, T, H, kat, Gy, Sv, lm, lx) in the SI system are
defined in relation to the kilogram, and thus its stability is important. The definitions
of only eight other named SI units do not depend on the kilogram: those of temperature
(K, °C), time and frequency (s, Hz, Bq), length (m), and angle (rad, sr).The IPK is
rarely used or handled. Copies of the IPK kept by national metrology laboratories around
the world were compared with the IPK in 1889, 1948, and 1989 to provide traceability of
measurements of mass anywhere in the world back to the IPK.
The International Prototype Kilogram was commissioned by the General Conference on Weights and Measures
(CGPM) under the authority of the Metre Convention (1875), and in the custody of the International
Bureau of Weights and Measures (BIPM) who hold it on behalf of the CGPM. After the International
Prototype Kilogram had been found to vary in mass over time relative to its reproductions,
the International Committee for Weights and Measures (CIPM) recommended in 2005 that the
kilogram be redefined in terms of a fundamental constant of nature. At its 2011 meeting, the
CGPM agreed in principle that the kilogram should be redefined in terms of the Planck
constant, h. The decision was originally deferred until 2014; in 2014 it was deferred again
until the next meeting. CIPM has proposed revised definitions of the SI base units,
for consideration at the 26th CGPM. The formal vote, which took place on 16 November 2018,
approved the change, with the new definitions coming into force on 20 May 2019. The accepted
redefinition defines the Planck Constant as exactly 6.62607015×10−34 kg⋅m2⋅s−1,
thereby defining the kilogram in terms of the second and the metre. Since the metre
is defined as a time fraction of the speed of light in vacuum, then the kilogram is defined
in terms of the time only. The avoirdupois (or international) pound,
used in both the imperial and US customary systems, is now defined in terms of the kilogram.
Other traditional units of weight and mass around the world are now also defined in terms
of the kilogram, making the kilogram the primary standard for virtually all units of mass on
Earth.==Name and terminology==
The word kilogramme or kilogram is derived from the French kilogramme, which itself was
a learned coinage, prefixing the Greek stem of χίλιοι khilioi “a thousand” to gramma,
a Late Latin term for “a small weight”, itself from Greek γράμμα.
The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal,
which revised the older system of units introduced by the French National Convention in 1793,
where the gravet had been defined as weight (poids) of a cubic centimetre of water, equal
to 1/1000 of a grave. In the decree of 1795, the term gramme thus replaced gravet, and
kilogramme replaced grave. The French spelling was adopted in Great Britain
when the word was used for the first time in English in 1795, with the spelling kilogram
being adopted in the United States. In the United Kingdom both spellings are used, with
“kilogram” having become by far the more common. UK law regulating the units to be used when
trading by weight or measure does not prevent the use of either spelling.In the 19th century
the French word kilo, a shortening of kilogramme, was imported into the English language where
it has been used to mean both kilogram and kilometre. While kilo is acceptable in many
generalist texts, for example The Economist, its use is typically considered inappropriate
in certain applications including scientific, technical and legal writing, where authors
should adhere strictly to SI nomenclature. When the United States Congress gave the metric
system legal status in 1866, it permitted the use of the word kilo as an alternative
to the word kilogram, but in 1990 revoked the status of the word kilo.During the 19th
century, the standard system of metric units was the centimetre–gram–second system
of units, treating the gram as the fundamental unit of mass and the kilogram simply as a
derived unit. In 1901, however, following the discoveries
by James Clerk Maxwell to the effect that electric measurements could not be explained
in terms of the three fundamental units of length, mass and time, Giovanni Giorgi proposed
a new standard system that would include a fourth fundamental unit to measure quantities
in electromagnetism. In 1935 this was adopted by the IEC as the
Giorgi system, now also known as MKS system, and in 1946 the CIPM approved a proposal to
adopt the ampere as the electromagnetic unit of the “MKSA system”.
In 1948 the CGPM commissioned the CIPM “to make recommendations for a single practical
system of units of measurement, suitable for adoption by all countries adhering to the
Metre Convention”. This led to the launch of SI in 1960 and the subsequent publication
of the “SI Brochure”, which stated that “It is not permissible to use abbreviations for
unit symbols or unit names …”. The CGS and MKS systems co-existed during
much of the early-to-mid 20th century, but as a result of the decision to adopt the “Giorgi
system” as the international system of units in 1960, the kilogram is now the SI base unit
for mass, while the definition of the gram is derived from that of the kilogram.==Mass and weight==The kilogram is a unit of mass, a property
corresponding to the common perception of how “heavy” an object is. Mass is an inertial
property; that is, it is related to the tendency of an object at rest to remain at rest, or
if in motion to remain in motion at a constant velocity, unless acted upon by a force.
While the weight of an object is dependent on the strength of the local gravitational
field, the mass of an object is independent of gravity, as mass is a measure of the quantity
of matter. Accordingly, for astronauts in microgravity, no effort is required to hold
objects off the cabin floor; they are “weightless”. However, since objects in microgravity still
retain their mass and inertia, an astronaut must exert ten times as much force to accelerate
a 10‑kilogram object at the same rate as a 1‑kilogram object.
Because at any given point on Earth the weight of an object is proportional to its mass,
the mass of an object in kilograms is usually measured by comparing its weight to the weight
of a standard mass, whose mass is known in kilograms, using a device called a weighing
scale. The ratio of the force of gravity on the two objects, measured by the scale, is
equal to the ratio of their masses.==Kilogramme des Archives==On April 7, 1795, the gram was decreed in
France to be “the absolute weight of a volume of pure water equal to the cube of the hundredth
part of the metre, and at the temperature of melting ice”.
Since trade and commerce typically involve items significantly more massive than one
gram, and since a mass standard made of water would be inconvenient and unstable, the regulation
of commerce necessitated the manufacture of a practical realization of the water-based
definition of mass. Accordingly, a provisional mass standard was made as a single-piece,
metallic artifact one thousand times as massive as the gram—the kilogram.
At the same time, work was commissioned to precisely determine the mass of a cubic decimetre
(one litre) of water. Although the decreed definition of the kilogram specified water
at 0 °C—its highly stable temperature point—the French chemist Louis Lefèvre-Gineau and the
Italian naturalist Giovanni Fabbroni after several years of research chose to redefine
the standard in 1799 to water’s most stable density point: the temperature at which water
reaches maximum density, which was measured at the time as 4 °C.
They concluded that one cubic decimetre of water at its maximum density was equal to
99.9265% of the target mass of the provisional kilogram standard made four years earlier.
That same year, 1799, an all-platinum kilogram prototype was fabricated with the objective
that it would equal, as close as was scientifically feasible for the day, the mass of one cubic
decimetre of water at 4 °C. The prototype was presented to the Archives of the Republic
in June and on December 10, 1799, the prototype was formally ratified as the kilogramme des
Archives (Kilogram of the Archives) and the kilogram was defined as being equal to its
mass. This standard stood for the next 90 years.==International Prototype of the Kilogram
==Since 1889 the magnitude of the kilogram has
been defined as the mass of an object called the International Prototype of the Kilogram,
often referred to in the professional metrology world as the “IPK”. The IPK is made of a platinum
alloy known as “Pt‑10Ir”, which is 90% platinum and 10% iridium (by mass) and is machined
into a right-circular cylinder (height=diameter) of about 39 millimetres to minimize its surface
area. The addition of 10% iridium improved upon the all-platinum Kilogram of the Archives
by greatly increasing hardness while still retaining platinum’s many virtues: extreme
resistance to oxidation, extremely high density (almost twice as dense as lead and more than
21 times as dense as water), satisfactory electrical and thermal conductivities, and
low magnetic susceptibility. The IPK and its six sister copies are stored at the International
Bureau of Weights and Measures (known by its French-language initials BIPM) in an environmentally
monitored safe in the lower vault located in the basement of the BIPM’s Pavillon de
Breteuil in Saint-Cloud on the outskirts of Paris (see External images, below, for photographs).
Three independently controlled keys are required to open the vault. Official copies of the
IPK were made available to other nations to serve as their national standards. These are
compared to the IPK roughly every 40 years, thereby providing traceability of local measurements
back to the IPK. The Metre Convention was signed on May 20,
1875 and further formalized the metric system (a predecessor to the SI), quickly leading
to the production of the IPK. The IPK is one of three cylinders made in 1879 by Johnson
Matthey, which continues to manufacture nearly all of the national prototypes today. In 1883,
the mass of the IPK was found to be indistinguishable from that of the Kilogramme des Archives made
eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPM in
1889.Modern measurements of Vienna Standard Mean Ocean Water, which is pure distilled
water with an isotopic composition representative of the average of the world’s oceans, show
that it has a density of 0.999975 ±0.000001 kg/L at its point of maximum density (3.984
°C) under one standard atmosphere (101 325 Pa or 760 torr) of pressure. Thus, a cubic
decimetre of water at its point of maximum density is only 25 parts per million less
massive than the IPK; that is to say, the 25 milligram difference shows that the scientists
over 219 years ago managed to make the mass of the Kilogram of the Archives equal that
of a cubic decimetre of water at 4 °C, with a margin of error at most within the mass
of a single excess grain of rice.===Copies of the international prototype
kilogram===The various copies of the international prototype
kilogram are given the following designations in the literature: The IPK itself, stored in the BIPM’s vault
in Saint-Cloud, France. Six sister copies: K1, 7, 8(41), 32, 43 and
47. Stored in the same vault at the BIPM. Ten working copies: eight (9, 31, 42′, 63,
77, 88, 91, and 650) for routine use and two (25 and 73) for special use. Kept in the BIPM’s
calibration laboratory in Saint-Cloud, France. National prototypes, stored in Argentina (30),
Australia (44 and 87), Austria (49), Belgium (28 and 37), Brazil (66), Canada (50 and 74),
China (60 and 64; 75 in Hong Kong), Czech Republic (67), Denmark (48), Egypt (58), Finland
(23), France (35), Germany (52, 55 and 70), Hungary (16), India (57), Indonesia (46),
Israel (71), Italy (5 and 76), Japan (6, 30, 94 and E59), Kazakhstan, Kenya (95), Mexico
(21, 90 and 96), Netherlands (53), North Korea (68), Norway (36), Pakistan (93), Poland (51),
Portugal (69), Romania (2), Russia (12 and 26), Serbia (11 and 29), Singapore (83), Slovakia
(41 and 65), South Africa (56), South Korea (39, 72 and 84), Spain (24 and 3), Sweden
(40 and 86), Switzerland (38 and 89), Taiwan (78), Thailand (80), Turkey (54), United Kingdom
(18, 81 and 82), and the United States (20, 4, 79, 85 and 92).
Some additional copies held by non-national organizations, such as the French Academy
of Sciences in Paris (34) and the Istituto di Metrologia G. Colonnetti in Turin (62).===Stability of the international prototype
kilogram===By definition, the error in the measured value
of the IPK’s mass is exactly zero; the mass of the IPK is the kilogram. However, any changes
in the IPK’s mass over time can be deduced by comparing its mass to that of its official
copies stored throughout the world, a rarely undertaken process called “periodic verification”.
The only three verifications occurred in 1889, 1948, and 1989. For instance, the US owns
four 90% platinum / 10% iridium (Pt‑10Ir) kilogram standards, two of which, K4 and K20,
are from the original batch of 40 replicas delivered in 1884. The K20 prototype was designated
as the primary national standard of mass for the US. Both of these, as well as those from
other nations, are periodically returned to the BIPM for verification. Great care is exercised
when transporting prototypes. In 1984, the K4 and K20 prototypes were hand-carried in
the passenger section of separate commercial airliners.
Note that none of the replicas has a mass precisely equal to that of the IPK; their
masses are calibrated and documented as offset values. For instance, K20, the US’s primary
standard, originally had an official mass of 1 kg − 39 μg (micrograms) in 1889; that
is to say, K20 was 39 μg less than the IPK. A verification performed in 1948 showed a
mass of 1 kg − 19 μg. The latest verification performed in 1989 shows a mass precisely identical
to its original 1889 value. Quite unlike transient variations such as this, the US’s check standard,
K4, has persistently declined in mass relative to the IPK—and for an identifiable reason:
check standards are used much more often than primary standards and are prone to scratches
and other wear. K4 was originally delivered with an official mass of 1 kg − 75 μg in
1889, but as of 1989 was officially calibrated at 1 kg − 106 μg and ten years later was
1 kg − 116 μg. Over a period of 110 years, K4 lost 41 μg relative to the IPK. Beyond the simple wear that check standards
can experience, the mass of even the carefully stored national prototypes can drift relative
to the IPK for a variety of reasons, some known and some unknown. Since the IPK and
its replicas are stored in air (albeit under two or more nested bell jars), they gain mass
through adsorption of atmospheric contamination onto their surfaces. Accordingly, they are
cleaned in a process the BIPM developed between 1939 and 1946 known as “the BIPM cleaning
method” that comprises firmly rubbing with a chamois soaked in equal parts ether and
ethanol, followed by steam cleaning with bi-distilled water, and allowing the prototypes to settle
for 7–10 days before verification. Before the BIPM’s published report in 1994 detailing
the relative change in mass of the prototypes, different standard bodies used different techniques
to clean their prototypes. The NIST’s practice before then was to soak and rinse its two
prototypes first in benzene, then in ethanol, and to then clean them with a jet of bi-distilled
water steam. Cleaning the prototypes removes between 5 and 60 μg of contamination depending
largely on the time elapsed since the last cleaning. Further, a second cleaning can remove
up to 10 μg more. After cleaning—even when they are stored under their bell jars—the
IPK and its replicas immediately begin gaining mass again. The BIPM even developed a model
of this gain and concluded that it averaged 1.11 μg per month for the first 3 months
after cleaning and then decreased to an average of about 1 μg per year thereafter. Since
check standards like K4 are not cleaned for routine calibrations of other mass standards—a
precaution to minimize the potential for wear and handling damage—the BIPM’s model of
time-dependent mass gain has been used as an “after cleaning” correction factor.
Because the first forty official copies are made of the same alloy as the IPK and are
stored under similar conditions, periodic verifications using a large number of replicas—especially
the national primary standards, which are rarely used—can convincingly demonstrate
the stability of the IPK. What has become clear after the third periodic verification
performed between 1988 and 1992 is that masses of the entire worldwide ensemble of prototypes
have been slowly but inexorably diverging from each other. It is also clear that the
mass of the IPK lost perhaps 50 μg over the last century, and possibly significantly more,
in comparison to its official copies. The reason for this drift has eluded physicists
who have dedicated their careers to the SI unit of mass. No plausible mechanism has been
proposed to explain either a steady decrease in the mass of the IPK, or an increase in
that of its replicas dispersed throughout the world. Moreover, there are no technical
means available to determine whether or not the entire worldwide ensemble of prototypes
suffers from even greater long-term trends upwards or downwards because their mass “relative
to an invariant of nature is unknown at a level below 1000 μg over a period of 100
or even 50 years”. Given the lack of data identifying which of the world’s kilogram
prototypes has been most stable in absolute terms, it is equally valid to state that the
first batch of replicas has, as a group, gained an average of about 25 μg over one hundred
years in comparison to the IPK.What is known specifically about the IPK is that it exhibits
a short-term instability of about 30 μg over a period of about a month in its after-cleaned
mass. The precise reason for this short-term instability is not understood but is thought
to entail surface effects: microscopic differences between the prototypes’ polished surfaces,
possibly aggravated by hydrogen absorption due to catalysis of the volatile organic compounds
that slowly deposit onto the prototypes as well as the hydrocarbon-based solvents used
to clean them.It has been possible to rule out many explanations of the observed divergences
in the masses of the world’s prototypes proposed by scientists and the general public. The
BIPM’s FAQ explains, for example, that the divergence is dependent on the amount of time
elapsed between measurements and not dependent on the number of times the prototype or its
copies have been cleaned or possible changes in gravity or environment. Reports published
in 2013 by Peter Cumpson of Newcastle University based on the X-ray photoelectron spectroscopy
of samples that were stored alongside various prototype kilograms suggested that one source
of the divergence between the various prototypes could be traced to mercury that had been absorbed
by the prototypes being in the proximity of mercury-based instruments. The IPK has been
stored within centimetres of a mercury thermometer since at least as far back as the late 1980s.
In this Newcastle University work six platinum weights made in the nineteenth century were
all found to have mercury at the surface, the most contaminated of which had the equivalent
of 250 μg of mercury when scaled to the surface area of a kilogram prototype.
Scientists are seeing far greater variability in the prototypes than previously believed.
The increasing divergence in the masses of the world’s prototypes and the short-term
instability in the IPK has prompted research into improved methods to obtain a smooth surface
finish using diamond turning on newly manufactured replicas and was one of the reasons that led
to the redefinition of the Kilogram. See § Redefinition agreed on 16 November 2018, below.===Dependency of the SI on the IPK===The stability of the IPK is crucial because
the kilogram underpins much of the SI system of measurement as it is currently defined
and structured. For instance, the newton is defined as the force necessary to accelerate
one kilogram at one metre per second squared. If the mass of the IPK were to change slightly
then the newton would also change proportionally. In turn, the pascal, the SI unit of pressure,
is defined in terms of the newton. This chain of dependency follows to many other SI units
of measure. For instance, the joule, the SI unit of energy, is defined as that expended
when a force of one newton acts through one metre. Next to be affected is the SI unit
of power, the watt, which is one joule per second. The ampere too is defined relative
to the newton. With the magnitude of the primary units of
electricity thus determined by the kilogram, so too follow many others, namely the coulomb,
volt, tesla, and weber. Even units used in the measure of light would be affected; the
candela—following the change in the watt—would in turn affect the lumen and lux.
Because the magnitude of many of the units comprising the SI system of measurement is
ultimately defined by the mass of a 139-year-old, golf-ball-sized piece of metal, the quality
of the IPK must be diligently protected to preserve the integrity of the SI system. Yet,
despite the best stewardship, the average mass of the worldwide ensemble of prototypes
and the mass of the IPK have likely diverged another 6.9 μg since the third periodic verification
29 years ago. Further, the world’s national metrology laboratories must wait for the fourth
periodic verification to confirm whether the historical trends persisted.
Fortunately, definitions of the SI units are quite different from their practical realizations.
For instance, the metre is defined as the distance light travels in a vacuum during
a time interval of ​1⁄299,792,458 of a second. However, the metre’s practical realization
typically takes the form of a helium–neon laser, and the metre’s length is delineated—not
defined—as 1579800.298728 wavelengths of light from this laser. Now suppose that the
official measurement of the second was found to have drifted by a few parts per billion
(it is actually extremely stable with a reproducibility of a few parts in 1015).
There would be no automatic effect on the metre because the second—and thus the metre’s
length—is abstracted via the laser comprising the metre’s practical realization. Scientists
performing metre calibrations would simply continue to measure out the same number of
laser wavelengths until an agreement was reached to do otherwise.
The same is true with regard to the real-world dependency on the kilogram: if the mass of
the IPK was found to have changed slightly, there would be no automatic effect upon the
other units of measure because their practical realizations provide an insulating layer of
abstraction. Any discrepancy would eventually have to be reconciled though, because the
virtue of the SI system is its precise mathematical and logical harmony amongst its units. If
the IPK’s value were definitively proven to have changed, one solution would be to simply
redefine the kilogram as being equal to the mass of the IPK plus an offset value, similarly
to what is currently done with its replicas; e.g., “the kilogram is equal to the mass of
the IPK + 42 parts per billion” (equivalent to 42 μg).
The long-term solution to this problem, however, is to liberate the SI system’s dependency
on the IPK by developing a practical realization of the kilogram that can be reproduced in
different laboratories by following a written specification. The units of measure in such
a practical realization would have their magnitudes precisely defined and expressed in terms of
fundamental physical constants. While major portions of the SI system would still be based
on the kilogram, the kilogram would in turn be based on invariant, universal constants
of nature.==Redefinition agreed on 16 November 2018
==The International Committee for Weights and
Measures (CIPM) approved a proposed redefinition of SI base units in November 2018 that defines
the kilogram by defining the Planck constant to be exactly 6.62607015×10−34 kg⋅m2⋅s−1.
This approach effectively defines the kilogram in terms of the second and the metre, and
will take effect in 2019.===History of redefinition===
Prior to the redefinition the kilogram, and several other SI units based on the kilogram,
were defined by a man-made metal artefact: the Kilogram des Archives from 1799 to 1889,
and the International Prototype Kilogram from 1889 onward.
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, 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.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, h (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 (discussed below) 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. They too are covered below. Some of these now-abandoned
approaches were based on equipment and procedures that would have enabled the reproducible production
of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) 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. All 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===The Kibble balance (known as a “watt balance”
before 2016) is essentially a 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
voltage standard, 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 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 μGal per metre, which affects the weight of a one-kilogram test mass by about
316 μg/m. In April 2007, the NIST’s implementation of
the Kibble balance demonstrated a combined relative standard uncertainty (CRSU) of 36
μg. The UK’s National Physical Laboratory’s Kibble balance demonstrated a CRSU of 70.3
μg 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), 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).
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-stabilized helium–neon laser interferometer. The fringe-signal,
frequency-sweep output from the interferometer is measured with a rubidium atomic clock.
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 Pt‑10Ir 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 9.80101644 m/s2.The virtue of electronic realizations
like the Kibble balance is that the definition and dissemination of the kilogram would no
longer be dependent upon the stability of kilogram prototypes, which must be very carefully
handled and stored. It would free physicists from the need to rely on assumptions about
the stability of those prototypes. Instead, hand-tuned, close-approximation mass standards
would simply be weighed and documented as being equal to one kilogram plus an offset
value. With the Kibble balance, while the kilogram would be delineated in electrical
and gravity terms, all of which are traceable to invariants of nature; it would be 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 would in addition depend 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
Δν(133Cs)hfs. The metre depends on the second and on an additional defined physical constant:
the speed of light c. Once the kilogram is redefined in this manner, physical objects
such as the IPK will no longer be part of the definition, but will 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‑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 g/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-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 proved to be sources
of instability. Also, vapor-deposited, protective ceramic coatings like 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 realizations 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. 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
10 μg) 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’s Avogadro project, would define and delineate
the kilogram as a 93.6 mm diameter sphere of silicon atoms. Silicon was chosen because
a commercial infrastructure with mature processes for creating defect-free, ultra-pure monocrystalline
silicon already exists to service the semiconductor industry. To make a practical realization
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 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 nm on the radius—roughly a single atomic layer. The precise lattice spacing
between the atoms in its crystal structure (≈ 192 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 dual-pan balances like the BIPM’s FB‑2
flexure-strip balance (see § 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. 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 oxidizes and forms a thin
layer (equivalent to 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 metals that are roughly as cathodic
as oxygen and therefore don’t oxidize 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: 29Si and 30Si. As described in § Carbon-12 above, 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 realization.
This approach could accurately delineate the magnitude of the kilogram because the masses
of the three silicon nuclides 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 techniques to enrich the silicon until it
is nearly pure 28Si, which has a relative atomic mass of 27.9769265325(19). 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 ​1000⁄27.9769265325 ⋅ 6.02214179×1023 atoms of 28Si (≈ 35.74374043
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 realization, this definition would precisely define the
magnitude of the kilogram in terms of a certain number of carbon‑12 atoms. Carbon‑12 (12C)
is an isotope of carbon. The 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‑12”.
Thus, the current definition of the mole requires that ​1000⁄12 moles (​83 1⁄3 mol)
of 12C 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 6.022140857(74)×1023 entities per mole. This new definition of the kilogram
proposed to fix the Avogadro constant at precisely 6.02214X×1023 mol−1 with the kilogram being
defined as “the mass equal to that of ​1000⁄12 ⋅ 6.02214X×1023 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. That relative standard uncertainty
has been 50 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 12C
atom—and the magnitude of the kilogram—could be no better than the current 50 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 realizations of the kilogram would be recalibrated as required.
Conversely, an electronic definition of the kilogram (see § Electronic approaches, below),
which would precisely fix the Planck constant, would continue to allow ​83 1⁄3 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
844468893 (≈ 6.02214162×1023) atoms. An imaginary realization of a 12-gram mass prototype
would be a cube of 12C atoms measuring precisely 84446889 atoms across on a side. With this
proposal, the kilogram would be defined as “the mass equal to 844468893 × ​83 1⁄3
atoms of 12C.”====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 ions (atoms stripped of an electron) and counting them
by measuring the electric current required to neutralize the ions. Gold (197Au) and bismuth
(209Bi) were chosen because they can be safely handled and have the two highest atomic masses
among the mononuclidic elements that are stable (gold) or effectively so (bismuth). 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 196.9665687,
from the current value of 196.9665687(6). As with a definition based upon carbon‑12,
the Avogadro constant would also have been fixed. The kilogram would then have been defined
as “the mass equal to that of precisely ​1000⁄196.9665687 ⋅ 6.02214179×1023 atoms of gold” (precisely
3,057,443,620,887,933,963,384,315 atoms of gold or about 5.07700371 fixed moles).
In 2003, German experiments with gold at a current of only 10 μA demonstrated a relative
uncertainty of 1.5%. Follow-on experiments using bismuth ions and a current of 30 mA
were expected to accumulate a mass of 30 g in six days and to have a relative uncertainty
of better than 1 ppm. Ultimately, ion‑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.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 1 eV (

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