Kilogramkg redirects here. For other uses, see KG.The kilogram
or kilogramme (SI unit symbol: kg), isthe base unit of mass in the
International System of Units(SI) (the Metric system) and is dened
as being equal tothe mass of the International Prototype of the
Kilogram(IPK).[2]The gram, 1/1000th of a kilogram, was originally
denedin 1795 as the mass of one cubic centimeter of water atthe
melting point of water.[3] The original prototype kilo-gram,
manufactured in 1799 and from which the IPK isderived, had a mass
equal to the mass of 1.000025 litersof water at 4 C.The kilogram is
the only SI base unit with an SI prex(kilo, symbol k) as part of
its name. It is also the onlySI unit that is still directly dened
by an artifact ratherthan a fundamental physical property that can
be repro-duced in dierent laboratories. Three other base units
inthe SI system are dened relative to the kilogram, so itsstability
is important.The International Prototype Kilogramwas commissionedby
the General Conference on Weights and Measures(CGPM) under the
authority of the Metre Convention(1875),and is in the custody of
the International Bu-reau of Weights and Measures (BIPM) who hold
it onbehalf of the CGPM. After the International PrototypeKilogram
had been found to vary in mass over time,the International
Committee for Weights and Measures(CIPM) recommended in 2005 that
the kilogram be re-dened in terms of a fundamental constant of
nature. Atits 2011 meeting, the CGPM agreed in principle that
thekilogram should be redened in terms of the Planck con-stant. The
decision was originally deferred until 2014; in2014 it was deferred
again until the next meeting.[4]TheInternational
PrototypeKilogram(IPK)israrelyused or handled. Copies of the IPK
kept by nationalmetrology laboratories around the world were
comparedwiththe IPKin1889, 1948, and1989toprovidetraceability of
measurements of mass anywhere in theworld back to the IPK.The
avoirdupois (or international) pound, used in boththe Imperial
system and U.S. customary units, is denedas exactly 0.45359237 kg,
making one kilogram approx-imately equal to 2.2046 avoirdupois
pounds. Other tra-ditional units of weight and mass around the
world arealso dened in terms of the kilogram, making the
IPKtheprimary standard for virtually all units of mass on Earth.1
Name and terminologyThe wordkilogramme orkilogram is derived from
theFrench kilogramme,[5] which itself was a learned coinage,prexing
the Greek stem of khilioi a thousand togramma, a Late Latin term
for a small weight, itselffrom Greek .[6] The word kilogramme was
writ-ten into French law in 1795, in the Decree of 18 Germi-nal,[7]
which revised the older system of units introducedby the French
National Convention in 1793, where thegravet had been dened as
weight (poids) of a cubic cen-timetre of water, equal to 1/1000th
of a grave.[8] In thedecree of 1795, the term gramme thus replaced
gravet,and kilogramme replaced grave.The French spelling was
adopted in the United Kingdomwhen the word was used for the rst
time in English in1797,[5] with the spelling kilogram being adopted
in theUnited States. In the United Kingdom both spellings areused,
with kilogram having become by far the morecommon.[9][Note 3] UK
law regulating the units to be usedwhen trading by weight or
measure does not prevent theuse of either spelling.[10]In the 19th
century the French word kilo, a shorteningof kilogramme, was
imported into the English languagewhere it has been used to mean
both kilogram[11] andkilometer.[12] While kilo is acceptable in
many generalisttexts, for example The Economist,[13] its use is
typicallyconsidered inappropriate in certain applications
includ-ing scientic, technical and legal writing, where
authorsshould adhere strictly to SI nomenclature.[14][15] Whenthe
United States Congress gave the metric system legalstatus in 1866,
it permitted the use of the word kilo as analternative to the word
kilogram,[16] but in 1990 revokedthe status of the word
kilo.[17]During the 19th century, the standard system of
metricunits was the centimetregramsecond system of units,treating
the gram as the fundamental unit of mass andthe kilogram simply as
a derived unit. In 1901, however,following the discoveries by James
Clerk Maxwell to theeect that electric measurements could not be
explainedin terms of the three fundamental units of length, massand
time, Giovanni Giorgi proposed a new standard sys-tem which would
include a fourth fundamental unit tomeasure quantities in
electromagnetism.[18] In 1935 thiswas adopted by the IEC as the
Giorgi system, now alsoknown as MKS system,[19] and in 1946 the
CIPM ap-proved a proposal to adopt the ampere as the
electromag-netic unit of the MKSA system.[20] In 1948 the
CGPMcommissioned the CIPM to make recommendations for12 3
KILOGRAMME DES ARCHIVESa single practical system of units of
measurement, suit-able for adoption by all countries adhering to
the MetreConvention.[21] This led to the launch of SI in 1960
andthe subsequent publication of the SI Brochure, whichstated that
It is not permissible to use abbreviations forunit symbols or unit
names ....[22][Note 4] The CGS andMKS systems co-existed during
much of the early-to-mid 20th century, but as a result of the
decision to adoptthe Giorgi system as the international system of
unitsin 1960, the kilogram is now the SI base unit for mass,while
the denition of the gram is derived from that ofthe kilogram.2
Nature of massMeasurement of weight gravitational attraction of
themeasurand causes a distortion of the springMeasurement ofmass
the gravitational force on themeasurand is balanced against the
gravitational force onthe weights.See also: Mass versus weightThe
kilogram is a unit of mass, a property which corre-sponds to the
common perception of how heavy an ob-ject is. Mass is an inertial
property; that is, it is related tothe tendency of an object at
rest to remain at rest, or if inmotion to remain in motion at a
constant velocity, unlessacted upon by a force. According to
"Newtons laws ofmotion" and the equation F = ma, (second lawof
motion)when acted upon by a force F of one newton, an objectwith
mass m of one kilogram will accelerate a at the rateof one meter
per second per second (1 m/s2)about one-tenth the acceleration due
to Earths gravity[Note 5]While theweightof an object is dependent
upon thestrength of the local gravitational eld, the mass of an
ob-ject is independent of gravity, as mass is a measure of howmuch
matter an object contains.[Note 6] Accordingly, forastronauts in
microgravity, no eort is required to holdobjects o the cabin oor;
they are weightless. How-ever, since objects in microgravity still
retain their massand inertia, an astronaut must exert ten times as
muchforce to accelerate a 10kilogram object at the same rateas a
1kilogram object.Because at any given point on Earth the weight of
an ob-ject is proportional to its mass, the mass of an object
inkilograms is usually measured by comparing its weight tothe
weight of a standard mass, whose mass is known inkilograms, using a
device called a weighing scale. Theratio of the force of gravity on
the two objects, measuredby the scale, is equal to the ratio of
their masses.3 Kilogramme des ArchivesFor more on the history of
the kilogram, see grave (unit).On April 7, 1795, the gram was
decreed in France to beTheAragokilogram, anexact
copyoftheKilogrammedesArchives commissioned in 1821 by the US under
supervision ofFrench physicist Franois Arago that served as the USs
rst kilo-gram standard of mass until 1889, when the US converted
toprimary metric standards and received its current kilogram
pro-totypes, K4 and K20.the absolute weight of a volume of pure
water equal tothe cube of the hundredth part of the metre, and at
thetemperature of melting ice.[23] The concept of using aunit
volume of water to dene a unit measure of mass wasproposed by the
English philosopher John Wilkins in his1668 essay as a means of
linking mass and length.[24][25]Since trade and commerce typically
involve items signif-icantly more massive than one gram, and since
a massstandard made of water would be inconvenient and un-stable,
the regulation of commerce necessitated the
man-ufactureofapractical realizationofthewater-baseddenition of
mass. Accordingly, a provisional mass stan-dard was made as a
single-piece,metallic artifact onethousand times as massive as the
gramthe kilogram.At the same time, work was commissioned to
preciselydeterminethemass ofacubicdecimeter (oneliter)of
water.[Note 7][23]Although the decreed denition of4.1 Copies of the
international prototype kilogram 3the kilogram specied water at 0
Cits highly stabletemperature pointthe French chemist Louis
Lefvre-Gineau and the Italian naturalist Giovanni Fabbroni af-ter
several years of research chose to redene the stan-dard in 1799 to
waters most stabledensity point: thetemperature at which water
reaches maximum density,which was measured at the time as 4 C.[Note
8][26] Theyconcluded that one cubic decimeter of water at its
max-imum density was equal to 99.9265% of the target massof the
provisionalkilogram standard made four yearsearlier.[Note 9][27]
That same year, 1799, an all-platinumkilogram prototype was
fabricated with the objective thatit would equal, as close as was
scientically feasible forthe day, the mass of one cubic decimeter
of water at 4C. The prototype was presented to the Archives of
theRepublic in June and on December 10, 1799, the proto-type was
formally ratied as the kilogramme des Archives(Kilogram of the
Archives) and the kilogram was denedas being equal to its mass.
This standard stood for thenext 90 years.4 International prototype
kilo-gramACGIoftheinternational prototypekilogram(theinchruleris
for scale). The prototype is manufactured from a platinumiridium
alloy and is 39.17 mm in both diameter and height, itsedges have a
four-angle (22.5, 45, 67.5 and 79) chamfer tominimize wear.Since
1889 the magnitude of the kilogram has been de-ned as the mass of
an object called theinternationalprototypekilogram,[28]often
referred to in the profes-sional metrology world as the IPK. The
IPK is madeof a platinum alloy known as Pt10Ir, which is
90%platinum and 10% iridium (by mass) and is machinedinto a
right-circular cylinder (height = diameter) of 39.17millimeters to
minimize its surface area.[29] The additionof 10%iridiumimproved
upon the all-platinumKilogramof the Archives by greatly increasing
hardness while stillretaining platinums many virtues: extreme
resistance tooxidation, extremely high density (almost twice as
denseas lead and more than 21 times as dense as water),
sat-isfactory electrical and thermal conductivities, and
lowmagnetic susceptibility. The IPK and its six sister copiesare
stored at the International Bureau of Weights andMeasures (known by
its French-language initials BIPM)in an environmentally monitored
safe in the lower vaultlocated in the basement of the BIPMs
Pavillon de Bre-teuil in Svres on the outskirts of Paris
(seeExternalimages, below, for photographs). Three
independentlycontrolled keys are required to open the vault.
Ocialcopies of the IPK were made available to other nationsto serve
as their national standards. These are comparedto the IPK roughly
every 40 years, thereby providingtraceability of local measurements
back to the IPK.[30]The Metre Convention was signed on May 20, 1875
andfurther formalized the metric system (a predecessor tothe SI),
quickly leading to the production of the IPK. TheIPK is one of
three cylinders made in 1879 by JohnsonMatthey, which continues to
manufacture nearly all ofthe national prototypes today.[31][32] In
1883, the massof the IPK was found to be indistinguishable from
thatof the Kilogramme des Archives made eighty-four yearsprior, and
was formally ratied as the kilogram by the 1stCGPM in
1889.[29]Modern measurements of Vienna Standard Mean OceanWater,
which is pure distilled water with an isotopiccomposition
representative of the average of the worldsoceans,show it has a
density of 0.999975 0.000001kg/L at its point of maximum density
(3.984 C) underone standard atmosphere (760 torr) of pressure.[33]
Thus,a cubic decimeter of water at its point of maximum den-sity is
only 25 parts per million less massive than the IPK;that is to say,
the 25 milligram dierence shows that thescientists over 216 years
ago managed to make the massof the Kilogram of the Archives equal
that of a cubicdecimeter of water at 4 C, with a margin of error at
mostwithin the mass of a single excess grain of rice.4.1
Copiesoftheinternational prototypekilogramThe various copies of the
international prototype kilo-gram are given the following
designations in the litera-ture:The IPK itself. Located in Svres,
France.Six sister copies, numbered: K1, 7, 8(41),[Note 10]32, 43
and 47.[34] Located in Svres, France.Three unocial copies,
numbered: 25, 88 and 91(numbers 9 and 31 were used before 2004 but
werereplacedby88and91[35]). LocatedinSvres,France.National
prototypes, stored in[36][37][38][39] Australia(44 and 87),Austria
(49),Belgium (28 and 37),4 4 INTERNATIONAL PROTOTYPE
KILOGRAMNational prototype kilogram K20, one of two prototypes
storedat theUSNational
InstituteofStandardsandTechnologyinGaithersburg, Maryland, which
serve as primary standards fordening all units of mass and weight
in the United States. This isa replica for public display, shown as
it is normally stored, undertwo bell jars.Brazil (66), Canada (50
and 74), China (60 and64; 75 in Hong Kong), Czech Republic
(67),Denmark (48), Egypt (58), Finland (23), France(35),
Germany(52, 55and70), Hungary(16),India (57), Indonesia (46),
Israel (71), Italy (5 and76), Japan (6 and 94), Kazakhstan, Kenya
(95),Mexico (21, 90 and 96), Netherlands (53), NorthKorea (68),
Norway (36), Pakistan (93), Poland(51), Portugal (69), Romania (2),
Russia (12 and26[40]), Singapore (83), Slovakia (41 and 65),
SouthAfrica (56), South Korea (39, 72 and 84), Spain(24 and 3),
Sweden (86), Switzerland (38 and 89),Taiwan (78), Thailand (80),
Turkey (54[41]), UnitedKingdom (18,[42] 81 and 82) and the United
States(20,[43] 4, 79, 85 and 92).Some additional copies held by
non-national organi-zations, such as the French Academy of Sciences
inParis (34) and the Istituto di Metrologia G. Colon-netti in Turin
(62).[36]4.2 Stability of the international prototypekilogramBy
denition, the error in the measured value of the IPK'smass is
exactly zero; the IPK is the kilogram.However,any changes in the
IPKs mass over time can be deducedby comparing its mass to that of
its ocial copies storedthroughout the world, a rarely undertaken
process calledperiodic verication. The only three verications
oc-curred in 1889, 1948, and 1989. For instance, the U.S.owns four
90% platinum / 10% iridium (Pt10Ir) kilo-gram standards, two of
which, K4 and K20, are fromthe original batch of 40 replicas
delivered in 1884.[Note 11]The K20 prototype was designated as the
primary na-tional standard of mass for the U.S. Both of these, as
wellas those from other nations, are periodically returned tothe
BIPM for verication.[Note 12]Note that none of the replicas has a
mass precisely equalto that of the IPK; their masses are calibrated
and doc-umented as oset values. For instance, K20, the USsprimary
standard, originally had an ocial mass of 1 kg 39 micrograms (g) in
1889; that is to say, K20 was 39g less than the IPK. A verication
performed in 1948showed a mass of 1 kg 19 g. The latest
vericationperformed in 1989 shows a mass precisely identical toits
original 1889 value.Quite unlike transient variationssuch as this,
the USs check standard, K4, has persistentlydeclined in mass
relative to the IPKand for an identi-able reason. Check standards
are used much more of-ten than primary standards and are prone to
scratches andother wear. K4 was originally delivered with an
ocialmass of 1 kg 75 g in 1889, but as of 1989 was o-cially
calibrated at 1 kg 106 g and ten years later was1 kg 116 g. Over a
period of 110 years, K4 lost 41 grelative to the IPK.[44]Mass drift
over time of national prototypes K21K40, plus two ofthe IPKs sister
copies: K32 and K8(41).[Note 10]All mass changesare relative to the
IPK. The initial 1889 starting-value osets rel-ative to the IPK
have been nulled.[36]The above are all relativemeasurements; no
historical mass-measurement data is availableto determine which of
the prototypes has been most stable relativeto an invariant of
nature. There is the distinct possibility that allthe prototypes
gained mass over 100 years and that K21, K35,K40, and the IPK
simply gained less than the others.4.3 Dependency of the SI on the
IPK 5Beyond the simple wear that check standards can experi-ence,
the mass of even the carefully stored national pro-totypes can
drift relative to the IPK for a variety of rea-sons, some known and
some unknown. Since the IPKand its replicas are stored in air
(albeit under two ormore nested bell jars), they gain mass through
adsorptionof atmospheric contamination onto their surfaces.
Ac-cordingly, they are cleaned in a process the BIPM de-veloped
between 1939 and 1946 known as the BIPMcleaning method[45] that
comprises rmly rubbing witha chamois soaked in equal parts ether
and ethanol, fol-lowed by steam cleaning with bi-distilled water,
and al-lowingtheprototypestosettlefor710daysbeforeverication.[Note
13] Cleaning the prototypes removes be-tween 5 and 60 g of
contamination depending largely onthe time elapsed since the last
cleaning. Further, a secondcleaning can remove up to 10 g more.
After cleaningeven when they are stored under their bell jarsthe
IPKand its replicas immediately begin gaining mass again.The BIPM
even developed a model of this gain and con-cluded that it averaged
1.11 g per month for the rst3 months after cleaning and then
decreased to an aver-age of about 1 g per year thereafter. Since
check stan-dards like K4 are not cleaned for routine calibrations
ofother mass standardsa precaution to minimize the po-tential for
wear and handling damagethe BIPMs modelof time-dependent mass gain
has been used as an aftercleaning correction factor.Because the rst
forty ocial copies are made of thesamealloyas
theIPKandarestoredunder similarconditions,periodic verications
using a large numberof replicasespecially the national primary
standards,which are rarely usedcan convincingly demonstrate
thestability of the IPK. What has become clear after thethird
periodic verication performed between 1988 and1992 is that masses
of the entire worldwide ensembleof prototypes have been slowly but
inexorably diverg-ing from each other. It is also clear that the
mass ofthe IPK lost perhaps 50 g over the last century,andpossibly
signicantly more, in comparison to its ocialcopies.[36][46] The
reason for this drift has eluded physi-cists who have dedicated
their careers to the SI unit ofmass. No plausible mechanism has
been proposed to ex-plain either a steady decrease in the mass of
the IPK, oran increase in that of its replicas dispersed throughout
theworld.[Note 14][47][48][49] This relative nature of the
changesamongst the worlds kilogram prototypes is often misre-ported
in the popular press, and even some notable sci-entic magazines,
which often state that the IPK simplylost 50 g and omit the very
important caveat of "incomparison to its ocial copies".[Note 15]
Moreover, thereare no technical means available to determine
whetheror not the entire worldwide ensemble of prototypes suf-fers
fromeven greater long-termtrends upwards or down-wards because
their mass relative to an invariant of na-ture is unknown at a
level below 1000 g over a period of100 or even 50 years.[46] Given
the lack of data identi-fying which of the worlds kilogram
prototypes has beenmost stable in absolute terms, it is equally
valid to statethat the rst batch of replicas has, as a group,
gained anaverage of about 25 g over one hundred years in
com-parison to the IPK.[Note 16]What is known specically about the
IPK is that it ex-hibits a short-terminstability of about 30 g over
a periodof about a month in its after-cleaned mass.[50] The
precisereason for this short-terminstability is not understood
butis thought to entail surface eects: microscopic dier-ences
between the prototypes polished surfaces, possi-bly aggravated by
hydrogen absorption due to catalysis ofthe volatile organic
compounds that slowly deposit ontothe prototypes as well as the
hydrocarbon-based solventsused to clean them.[49][51]It has been
possible to rule out many explanations of theobserved divergences
in the masses of the worlds proto-types proposed by scientists and
the general public. TheBIPMs FAQexplains, for example, that the
divergence isdependent on the amount of time elapsed between
mea-surements and not dependent on the number of times theartifacts
have been cleaned or possible changes in grav-ity or
environment.[52] Reports published in 2013 by Pe-ter Cumpson of
Newcastle University based on the X-rayphotoelectron spectroscopy
of samples that were storedalongside various prototype kilograms
suggested that onesource of the divergence between the various
prototypescould be traced to mercury that had been absorbed by
theprototypes being in the proximity of mercury-based in-struments.
The IPK has been stored within centimetersof a mercury thermometer
since at least as far back asthe late 1980s.[53] In this Newcastle
University work sixplatinum weights made in the nineteenth century
were allfound to have mercury at the surface, the most
contami-nated of which had the equivalent of 250 g of mercurywhen
scaled to the surface area of a kilogram prototype.Scientists are
seeing far greater variability in the proto-types than previously
believed. The increasing diver-gence in the masses of the worlds
prototypes and theshort-term instability in the IPK has prompted
researchinto improved methods to obtain a smooth surface nishusing
diamond turning on newly manufactured replicasand has intensied the
search for a new denition of thekilogram. See Proposed future
denitions, below.[54]4.3 Dependency of the SI on the IPKThe
stability of the IPK is crucial because the kilogramunderpins much
of the SI system of measurement as itis currently dened and
structured. For instance, thenewton is dened as the force necessary
to accelerate onekilogram at one meter per second squared. If the
mass ofthe IPK were to change slightly, so too must the newtonby a
proportional degree. In turn, the pascal, the SI unitof pressure,
is dened in terms of the newton. This chainof dependency follows to
many other SI units of measure.For instance, the joule, the SI unit
of energy, is dened as6 5 PROPOSED FUTURE DEFINITIONSA cdkgs mK
molThe magnitude of many of the units comprising the SI system
ofmeasurement, including most of those used in the measurementof
electricity and light, are highly dependent upon the stability ofa
136-year-old, golf-ball-sized cylinder of metal stored in a vaultin
France.that expended when a force of one newton acts throughone
meter. Next to be aected is the SI unit of power,the watt, which is
one joule per second. The ampere toois dened relative to the
newton, and ultimately, the kilo-gram.With the magnitude of the
primary units of electricitythus determined by the kilogram, so too
followmany oth-ers, namely the coulomb, volt, tesla, and weber.
Evenunits used in the measure of light would be aected;
thecandelafollowing the change in the wattwould in turnaect the
lumen and lux.Because the magnitude of many of the units
compris-ing the SI system of measurement is ultimately denedby the
mass of a 136-year-old, golf-ball-sized piece ofmetal, the quality
of the IPK must be diligently protectedto preserve the integrity of
the SI system. Yet, despite thebest stewardship, the average mass
of the worldwide en-semble of prototypes and the mass of the IPK
have likelydiverged another 6.1 g since the third periodic
veri-cation 26 years ago.[Note 17] Further, the worlds
nationalmetrology laboratories must wait for the fourth
periodicverication to conrm whether the historical
trendsper-sisted.Fortunately, denitions of the SI units are quite
dierentfrom their practical realizations. For instance, the meteris
dened as the distance light travels in a vacuum duringa time
interval of1,, of a second. However, themeters practical
realization typically takes the form of aheliumneon laser, and the
meters length is delineatednot denedas 1579800.298728 wavelengths
of lightfrom this laser. Now suppose that the ocial measure-ment of
the second was found to have drifted by a fewparts per billion (it
is actually extremely stable with a re-producibility of a few parts
in 1015).[55] There would beno automatic eect on the meter because
the secondand thus the meters lengthis abstracted via the
lasercomprising the meters practical realization.
Scientistsperforming meter calibrations would simply continue
tomeasure out the same number of laser wavelengths un-til an
agreement was reached to do otherwise. The sameis true with regard
to the real-world dependency on thekilogram: if the mass of the IPK
was found to havechanged slightly, there would be no automatic eect
uponthe other units of measure because their practical
realiza-tions provide an insulating layer of abstraction. Any
dis-crepancy would eventually have to be reconciled though,because
the virtue of the SI system is its precise math-ematical and
logical harmony amongst its units. If theIPKs value were denitively
proven to have changed, onesolution would be to simply redene the
kilogram as be-ing equal to the mass of the IPK plus an oset value,
sim-ilarly to what is currently done with its replicas; e.g.,
thekilogram is equal to the mass of the IPK + 42 parts perbillion"
(equivalent to 42 g).The long-term solution to this problem,
however, is toliberate the SI systems dependency on the IPK by
devel-oping a practical realization of the kilogram that can
bereproduced in dierent laboratories by following a writ-ten
specication.The units of measure in such a practi-cal realization
would have their magnitudes precisely de-ned and expressed in terms
of fundamental physical con-stants. While major portions of the SI
system would stillbe based on the kilogram, the kilogram would in
turn bebased on invariant, universal constants of nature. Muchwork
towards that end is ongoing, though no alternativehas yet achieved
the uncertainty of 20 parts per billion(~20 g) required to improve
upon the IPK. However,as of April 2007,the USs National Institute
of Stan-dards and Technology (NIST) had an implementation ofthe
watt balance that was approaching this goal, with ademonstrated
uncertainty of 36 g.[56] See Watt balancebelow.The avoirdupois
pound, used in both the imperial sys-temandU.S. customaryunits, is
denedas exactly0.45359237 kg,[57] making one kilogram
approximatelyequal to 2.2046 avoirdupois pounds.5 Proposed future
denitionsSee also: New SI denitionsInthe following sections,
wherever numericequalities areshownin'conciseform'suchas
1.85487(14)1013the two digits betweentheparentheses
denotetheuncertaintyat 1standarddeviation(68%condencelevel)inthe
two least signicant digits of the signicand.5.1 The watt balance 7A
nal X in a proposed denition denotes digitsyet to be agreed on.As
of 2014 the kilogram was the only SI unit still de-ned by an
artifact. In 1960 the meter, having previ-ously also been dened by
reference to an artifact (a sin-gle platinum-iridium bar with two
marks on it) was re-dened in terms of invariant, fundamental
physical con-stants (the wavelength of a particular emission of
lightemitted by krypton,[58] and later the speed of light) sothat
the standard can be reproduced in dierent labora-tories by
following a written specication. At the 94thMeeting of the
International Committee for Weights andMeasures (2005)[59] it was
recommended that the samebe done with the kilogram.In October 2010,
the International Committee forWeights and Measures (known by its
French-languageinitials CIPM) voted to submit a resolution for
considera-tion at the General Conference on Weights and
Measures(CGPM), to take note of an intention that the kilogrambe
dened in terms of the Planck constant, h (which hasdimensions of
energy times time) together with other fun-damental units.[60][61]
This resolution was accepted by the24th conference of the CGPM[62]
in October 2011 andin addition the date of the 25th conference was
movedforward from 2014 to 2015.[63] Such a denition
wouldtheoretically permit any apparatus that was capable of
de-lineating the kilogram in terms of the Planck constant tobe used
as long as it possessed sucient precision, ac-curacy and stability.
The watt balance (discussed below)may be able to do this.In the
project to replace the last artifact that underpinsmuch of the
International System of Units (SI), a vari-ety of other very
dierent technologies and approacheswere considered and explored
over many years. Theytoo are covered below. Some of these
now-abandonedapproacheswerebasedonequipment andproceduresthat would
have enabled the reproducible production ofnew, kilogram-mass
prototypes on demand (albeit withextraordinary eort) using
measurement techniques andmaterial properties that are ultimately
based on, or trace-able to, fundamental constants. Others were
based ondevices that measured either the acceleration or weightof
hand-tuned kilogram test masses and which expressedtheir magnitudes
in electrical terms via special compo-nents that permit
traceability to fundamental constants.All approaches depend on
converting a weight measure-ment to a mass, and therefore require
the precise mea-surement of the strength of gravity in
laboratories. Allapproaches would have precisely xed one or more
con-stants of nature at a dened value.5.1 The watt balanceMain
article: Watt balanceThe NISTs watt balance is a project of the US
Government todevelop an electronic kilogram. The vacuum chamber
dome,which lowers over the entire apparatus, is visible at top.The
watt balance is essentially a single-pan weighing scalethat
measures the electric power necessary to oppose theweight of a
kilogram test mass as it is pulled by Earthsgravity. It is a
variation of an ampere balance in thatit employs an extra
calibration step that nulls the eectof geometry. The electric
potential in the watt balanceis delineated by a Josephson voltage
standard, which al-lows voltage to be linked to an invariant
constant of na-ture with extremely high precision and stability.
Its circuitresistance is calibrated against a quantum Hall
resistancestandard.The watt balance requires exquisitely precise
measure-ment of the local gravitational acceleration g in the
labo-ratory, using a gravimeter. (See FG5 absolute gravime-ter in
External images, below). For instance, the NISTcompensates for
Earths gravity gradient of 309 Gal permeter when the elevation of
the center of the gravimeterdiers from that of the nearby test mass
in the watt bal-ance; a change in the weight of a one-kilogram test
massthat equates to about 316 g/m.In April 2007, the NISTs
implementation of the wattbalance demonstrated a combined relative
standard un-certainty (CRSU) of 36 g and a short-term resolutionof
1015 g.[56][Note 18] The UKs National Physical Lab-oratorys watt
balance demonstrated a CRSU of 70.3g in 2007.[64] That watt balance
was disassembled andshipped in 2009 to Canadas Institute for
National Mea-surement Standards (part of the National Research
Coun-cil), where research and development with the devicecould
continue.If the CGPM adopts the new proposal and the new de-nition
of the kilogram becomes part of the SI, the valuein SI units of the
Planck constant (h), which is a mea-sure that relates the energy of
photons to their frequency,would be precisely xed (the currently
accepted valueof 6.62606957(29)1034 J s[65] has an uncertainty of 8
5 PROPOSED FUTURE DEFINITIONSabout 1 in 23 million).[Note 19] Once
agreed upon interna-tionally, the kilogram would no longer be dened
as themass of the IPK. All the remaining units in the
Interna-tional System of Units (the SI) that today have
depen-dencies upon the kilogram and the joule would also fallin
place, their magnitudes ultimately dened, in part, interms of
photon oscillations rather than the IPK.The local gravitational
accelerationg is measured with excep-tional
precisionwiththehelpofalaserinterferometer. Thelasers pattern of
interference fringesthe dark and light bandsaboveblooms at an ever
faster rate as a free-falling cornerreector drops inside an
absolute gravimeter. The patterns fre-quency sweep is timed by an
atomic clock.Gravity and the nature of the watt balance, which
os-cillates test masses up and down against the local
grav-itational acceleration g, are exploited so that
mechanicalpower is compared against electrical power, which is
thesquare of voltage divided by electrical resistance. How-ever, g
varies signicantlyby nearly 1%depending onwhere on the Earths
surface the measurement is made(see Earths gravity). There are also
slight seasonal vari-ations in g due to changes in underground
water tables,and larger semimonthly and diurnal changes due to
tidaldistortions in the Earths shape caused by the Moon. Al-though
g would not be a term in the denition of the kilo-gram, it would be
crucial in the delineation of the kilo-gramwhen relating energy to
power. Accordingly, g mustbe measured with at least as much
precision and accuracyas are the other terms, so measurements of g
must alsobe traceable to fundamental constants of nature. For
themost precise work in mass metrology, g is measured us-ing
dropping-mass absolute gravimeters that contain aniodine-stabilized
heliumneon laser interferometer.Thefringe-signal, frequency-sweep
output from the interfer-ometer is measured with a rubidium atomic
clock. Sincethis type of dropping-mass gravimeter derives its
accu-racy and stability from the constancy of the speed of lightas
well as the innate properties of helium, neon, and ru-bidium atoms,
the 'gravity' term in the delineation of anall-electronic kilogram
is also measured in terms of in-variants of natureand with very
high precision. For in-stance, in the basement of the NISTs
Gaithersburg fa-cility in 2009, when measuring the gravity acting
uponPt10Ir test masses (which are denser, smaller, and havea
slightly lower center of gravity inside the watt balancethan
stainless steel masses), the measured value was typ-ically within 8
ppb of 9.80101644 m/s2.[66]The virtue of electronic realizations
like the watt balanceis that the denition and dissemination of the
kilogramwould no longer be dependent upon the stability of
kilo-gram prototypes, which must be very carefully handledand
stored. It would free physicists from the need to relyon
assumptions about the stability of those prototypes.Instead,
hand-tuned, close-approximation mass standardswould simply be
weighed and documented as being equalto one kilogram plus an oset
value.With the watt bal-ance, while the kilogram would be
delineated in electricaland gravity terms, all of which are
traceable to invariantsof nature; it would be dened in a manner
that is directlytraceable to just three fundamental constants of
nature.The Planck constant denes the kilogram in terms of thesecond
and the meter. By xing the Planck constant, thedenition of the
kilogram would depend only on the de-nitions of the second and the
meter. The denition of thesecond depends on a single dened physical
constant: theground state hyperne splitting frequency of the
caesium133 atom(133Cs). The meter depends on the secondand on an
additional dened physical constant: the speedof light c. If the
kilogram is redened in this manner,mass artifactsphysical objects
calibrated in a watt bal-ance, including the IPKwould no longer be
part of thedenition, but would instead become transfer
standards.Scales like the watt balance also permit more exibilityin
choosing materials with especially desirable propertiesfor mass
standards. For instance, Pt10Ir could continueto be used so that
the specic gravity of newly producedmass standards would be the
same as existing nationalprimary and check standards (21.55 g/ml).
This wouldreduce the relative uncertainty when making mass
com-parisons in air. Alternatively, entirely dierent materialsand
constructions could be explored with the objectiveof producing mass
standards with greater stability. Forinstance, osmium-iridium
alloys could be investigated ifplatinums propensity to absorb
hydrogen (due to catalysisof VOCs and hydrocarbon-based cleaning
solvents) andatmospheric mercury proved to be sources of
instability.Also, vapor-deposited, protective ceramic coatings
likenitrides could be investigated for their suitability to
iso-late these new alloys.The challenge with watt balances is not
only in reducingtheir uncertainty, but also in making them truly
practicalrealizations of the kilogram. Nearly every aspect of
wattbalances and their support equipment requires such
ex-traordinarily precise and accurate, state-of-the-art tech-nology
thatunlike a device like an atomic clockfewcountries would
currently choose to fund their operation.For instance, the NISTs
watt balance used four resistancestandards in 2007, each of which
was rotated throughthe watt balance every two to six weeks after
being cali-5.2 Atom-counting approaches 9brated in a dierent part
of NIST headquarters facility inGaithersburg, Maryland. It was
found that simply movingthe resistance standards down the hall to
the watt balanceafter calibration altered their values 10 ppb
(equivalentto 10 g) or more.[67] Present-day technology is
insu-cient to permit stable operation of watt balances betweeneven
biannual calibrations. If the kilogram is dened interms of the
Planck constant, it is likely there will only bea fewat mostwatt
balances initially operating in theworld.Alternative approaches to
redening the kilogram thatwere fundamentally dierent from the watt
balance wereexplored to varying degrees with some abandoned, as
fol-lows:5.2 Atom-counting approaches5.2.1 Carbon-12Though not
oering a practical realization, this deni-tion would precisely dene
the magnitude of the kilo-gram in terms of a certain number of
carbon12 atoms.Carbon12 (12C) is an isotope of carbon. The mole
iscurrently dened as the quantity of entities (elementaryparticles
like atoms or molecules) equal to the number ofatoms in 12 grams of
carbon12. Thus, the current def-inition of the mole requires
that100012 (83) moles of12Chas a mass of precisely one kilogram.
The number ofatoms in a mole, a quantity known as the Avogadro
con-stant, is experimentally determined, and the current
bestestimate of its value is 6.02214129(27)1023entities
permole.[68] This new denition of the kilogram proposedto x the
Avogadro constant at precisely 6.02214X1023with the kilogrambeing
dened as the mass equal to thatof100012 6.02214X1023atoms of12C.The
accuracy of the measured value of the Avogadro con-stant is
currently limited by the uncertainty in the valueof the Planck
constanta measure relating the energy ofphotons to their frequency.
That relative standard uncer-tainty has been 50 parts per billion
(ppb) since 2006. Byxing the Avogadro constant, the practical eect
of thisproposal would be that the uncertainty in the mass of a12C
atomand the magnitude of the kilogramcouldbe no better than the
current 50 ppb uncertainty in thePlanck constant. Under this
proposal, the magnitude ofthe kilogram would be subject to future
renement asimproved measurements of the value of the Planck
con-stant become available; electronic realizations of the
kilo-gram would be recalibrated as required. Conversely,
anelectronic denition of the kilogram (see Electronic ap-proaches,
below), which would precisely x the Planckconstant, would continue
to allow 83 moles of12C tohave a mass of precisely one kilogram but
the number ofatoms comprising a mole (the Avogadro constant)
wouldcontinue to be subject to future renement.A variation on
a12C-based denition proposes to denethe Avogadro constant as being
precisely 84,446,8893( 6.022141621023) atoms. An imaginary
realizationof a 12-gram mass prototype would be a cube of12Catoms
measuring precisely 84,446,889 atoms across ona side. With this
proposal, the kilogram would be de-ned as the mass equal to
84,446,8893 83 atoms of12C.[69][Note 20]5.2.2 Avogadro
projectAchimLeistnerat theAustralianCentreforPrecisionOptics(ACPO)
is holding a 1 kg,single-crystal silicon sphere for theAvogadro
project. These spheres are among the roundest
man-madeobjectsintheworld. Ifthebest ofthesesphereswerescaled to
the size of Earth, its high pointa continent-size
areawouldrisetoamaximumelevationof2.4metersabovesealevel.[Note
21]Another Avogadro constant-based approach, known asthe
International Avogadro Coordination's Avogadroproject, would dene
and delineate the kilogram as asoftball-size (93.6 mm diameter)
sphere of silicon atoms.Silicon was chosen because a commercial
infrastructurewithmatureprocessesfor creatingdefect-free,
ultra-pure monocrystalline silicon already exists to service
thesemiconductor industry.To make a practical realizationof the
kilogram, a silicon boule (a rod-like, single-crystalingot) would
be produced. Its isotopic composition wouldbe measured with a mass
spectrometer to determine itsaverage relative atomic mass. The
boule would be cut,ground, and polished into spheres. The size of a
selectsphere would be measured using optical interferometryto an
uncertainty of about 0.3 nm on the radiusroughly10 5 PROPOSED
FUTURE DEFINITIONSa single atomic layer. The precise lattice
spacing betweenthe atoms in its crystal structure (192 pm) would
bemeasured using a scanning X-ray interferometer. Thispermits its
atomic spacing to be determined with an un-certainty of only three
parts per billion. With the size ofthe sphere, its average atomic
mass, and its atomic spac-ing known, the required sphere diameter
can be calcu-lated with sucient precision and low uncertainty to
en-able it to be nish-polished to a target mass of one
kilo-gram.Experiments are being performed on the AvogadroProjects
silicon spheres to determine whether theirmasses are most stable
when stored in a vacuum, a par-tial vacuum, or ambient pressure.
However, no techni-cal means currently exist to prove a long-term
stabilityany better than that of the IPKs because the most
sen-sitive and accurate measurements of mass are made withdual-pan
balances like the BIPMs FB2 exure-strip bal-ance (see External
links, below). Balances can only com-pare the mass of a silicon
sphere to that of a referencemass. Given the latest understanding
of the lack of long-term mass stability with the IPK and its
replicas, thereis no known, perfectly stable mass artifact to
compareagainst. Single-pan scales, which measure weight rela-tive
to an invariant of nature, are not precise to the nec-essary
long-term uncertainty of 1020 parts per billion.Another issue to be
overcome is that silicon oxidizes andforms a thin layer (equivalent
to 520 silicon atoms) ofsilicon dioxide (quartz) and silicon
monoxide. This layerslightly increases the mass of the sphere, an
eect whichmust be accounted for when polishing the sphere to
itsnished dimension. Oxidation is not an issue with plat-inumand
iridium, both of which are noble metals that areroughly as cathodic
as oxygen and therefore don't oxidizeunless coaxed to do so in the
laboratory. The presenceof the thin oxide layer on a silicon-sphere
mass proto-type places additional restrictions on the procedures
thatmight be suitable to clean it to avoid changing the
layersthickness or oxide stoichiometry.All silicon-based approaches
would x the Avogadro con-stant but vary in the details of the
denition of the kilo-gram. One approach would use silicon with all
three ofits natural isotopes present. About 7.78% of silicon
com-prises the two heavier isotopes:29Si and30Si. As de-scribed
inCarbon12 above, this method woulddenethe magnitude of the
kilogram in terms of a certain num-ber of12C atoms by xing the
Avogadro constant; thesilicon sphere would be the practical
realization. This ap-proach could accurately delineate the
magnitude of thekilogram because the masses of the three silicon
nuclidesrelative to12C are known with great precision
(relativeuncertainties of 1 ppb or better). An alternative
methodfor creating a silicon sphere-based kilogram proposes touse
isotopic separation techniques to enrich the siliconuntil it is
nearly pure28Si, which has a relative atomicmass of
27.9769265325(19).[71] With this approach, theAvogadro constant
would not only be xed, but so toowould the atomic mass of28Si. As
such, the deni-tion of the kilogram would be decoupled from12C
andthe kilogram would instead be dened as1000. 6.022141791023atoms
of28Si (35.74374043 xedmoles of28Si atoms). Physicists could elect
to dene thekilogramin terms of28Si even when kilogramprototypesare
made of natural silicon (all three isotopes present).Even with a
kilogram denition based on theoreticallypure28Si, a silicon-sphere
prototype made of only nearlypure28Si would necessarily deviate
slightly from the de-ned number of moles of silicon to compensate
for vari-ous chemical and isotopic impurities as well as the eectof
surface oxides.[72]5.2.3 Ion
accumulationAnotherAvogadro-basedapproach, ionaccumulation,since
abandoned, would have dened and delineated thekilogram by precisely
creating new metal prototypes ondemand. It would have done so by
accumulating gold orbismuth ions (atoms stripped of an electron)
and countedthem by measuring the electric current required to
neu-tralize the ions. Gold (197Au) and bismuth (209Bi) werechosen
because they can be safely handled and have thetwo highest atomic
masses among the mononuclidic ele-ments that is eectively
non-radioactive (bismuth) or isperfectly stable (gold). See also
Table of nuclides.[Note
22]Withagold-baseddenitionofthekilogramforin-stance,
therelativeatomicmass of goldcouldhavebeenxedas
precisely196.9665687, fromthecur-rent value of 196.9665687(6). As
with a deni-tion based upon carbon12, the Avogadro constantwould
also have been xed. The kilogram would thenhave been dened as the
mass equal to that of pre-cisely1000. 6.022141791023atoms of
gold(precisely 3,057,443,620,887,933,963,384,315 atoms ofgold or
about 5.07700371 xed moles).In 2003, German experiments with gold
ata currentof only 10 A demonstrated a relative uncertainty
of1.5%.[73] Follow-on experiments using bismuth ions anda current
of 30 mA were expected to accumulate a massof 30 g in six days and
to have a relative uncertaintyof better than 1 ppm.[74] Ultimately,
ionaccumulationapproaches proved to be unsuitable. Measurements
re-quired months and the data proved too erratic for the tech-nique
to be considered a viable future replacement to theIPK.[75]Among
the many technical challenges of the ion-deposition apparatus was
obtaining a suciently high ioncurrent (mass deposition rate) while
simultaneously de-celerating the ions so they could all deposit
onto a tar-get electrode embedded in a balance pan. Experimentswith
gold showed the ions had to be decelerated to verylow energies to
avoid sputtering eectsa phenomenonwhereby ions that had already
been counted ricochet othe target electrode or even dislodged atoms
that had al-11ready been deposited. The deposited mass fraction in
the2003 German experiments only approached very close to100% at ion
energies of less than around 1 eV (
