The kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI, from the French ), which is the modern standard governing the metric system. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water. The avoirdupois (or international) pound, used in both the Imperial system and U.S. customary units is defined as exactly ,
making one kilogram approximately equal to 2.2046 avoirdupois pounds.
In everyday usage, the mass of an object given in kilograms is often referred to as its weight, which is the measure of the gravitational force—or heaviness—of an object. Weight given in kilograms is technically the nonSI unit of measure known as the kilogram-force. The equivalent unit of force in the avoirdupois system of measurement is the pound-force. In strict scientific contexts, forces are typically measured with the SI unit newton.
The kilogram is the only SI base unit with an SI prefix as part of its name. It is also the only SI unit that is still defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Many units in the SI system are defined relative to the kilogram so its stability is important. After the International Prototype Kilogram had been found to vary in mass over time, the International Committee for Weights and Measures (known also by its French-language initials CIPM) recommended in 2005 that the kilogram be redefined in terms of a fundamental constant of nature. No final decision is expected before 2015.
Nature of mass
, which arises purely from mass, not weight.]]
The kilogram is a unit of mass, the measurement of which corresponds to the general, everyday notion of how “heavy” something is. However, mass is actually an inertial property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside force. According to Sir Isaac Newton's -year-old laws of motion and an important formula that sprang from his work, an object with a mass, m, of one kilogram will accelerate, a, at one meter per second per second (about one-tenth the acceleration due to earth’s gravity) when acted upon by a force, F, of one newton.
While the weight of matter is entirely dependent upon the strength of gravity, the mass of matter is invariant. 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 10kilogram object at the same rate as a 1kilogram object.
On earth, a common swing set can demonstrate the relationship of force, mass, and acceleration without being appreciably influenced by weight (downward force). If one were to stand behind a large adult sitting stationary in a swing and give him a strong push, the adult would accelerate relatively slowly and swing only a limited distance forwards before beginning to swing backwards. Exerting that same effort while pushing on a small child would produce much greater acceleration.
History
Early definitions
On 7 April 1795, the gram was decreed in France to be equal to “the absolute weight of a volume of water equal to the cube of the hundredth part of the meter, at the temperature of melting ice.” The concept of using a specified volume of water to define a unit measure of mass was first advanced by the English philosopher John Wilkins in 1668.
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 more massive than the gram—the kilogram.
At the same time, work was commissioned to precisely determine the mass of a cubic decimeter (one liter) of water.
They concluded that one cubic decimeter 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 decimeter of water at 4°C. The prototype was presented to the Archives of the Republic in June and on 10December 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 ninety years.
International prototype kilogram
The
Metre Convention was signed on 20 May 1875 and established the
SI system, which since 1889 defines the
magnitude of the kilogram to be equal to the mass of the
international prototype kilogram, 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 (more than 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 House of Breteuil in
Sèvres 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 50 years.
The IPK is one of three cylinders made in 1879. In 1883, it was found to be indistinguishable from the mass of the Kilogram of the Archives made eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPM in 1889. Thus, a cubic decimeter 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 years ago managed to make the mass of the Kilogram of the Archives equal that of a cubic decimeter of water at 4 °C to within the mass of a single excess grain of rice.
Stability of the international prototype kilogram
: K32 and K8(41). All mass changes are relative to the IPK. The initial 1889 starting-value offsets relative to the IPK have been nulled. The above are all
relative measurements; no historical mass-measurement data is available to determine which of the prototypes has been most stable relative to an invariant of nature. There is the distinct possibility that
all the prototypes gained mass over 100 years and that K21, K35, K40, and the IPK simply
gained less than the others.]]
By definition, the error in the measured value of the IPK’s mass is exactly zero; 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 process called “periodic verification.” For instance, the U.S. owns four 10%iridium (Pt10Ir) 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 U.S. Both of these, as well as those from other nations, are periodically returned to the BIPM for verification.
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 U.S.’s primary standard, originally had an official mass of micrograms (μg) in 1889; that is to say, K20 was 39µg less than the IPK. A verification performed in 1948 showed a mass of The latest verification performed in 1999 shows a mass precisely identical to its original 1889 value. Quite unlike transient variations such as this, the U.S.’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 in 1889, but as of 1989 was officially calibrated at and ten years later was Over a period of 110 years, K4 lost 41µg 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 lightly 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 days before verification. Cleaning the prototypes removes between 5 and 60µg of contamination depending largely on the time elapsed since the last cleaning. Further, a second cleaning can remove up to 10µg 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 1.11µg per month for the first 3 months after cleaning and then decreased to an average of about 1µg 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 50µg 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. This relative nature of the changes amongst the world’s kilogram prototypes is often misreported in the popular press, and even some notable scientific magazines, which often state that the IPK simply “lost 50µg” and omit the very important caveat of “in comparison to its official copies.” 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 1000µg over a period of 100 or even 50 years.”
What is known specifically about the IPK is that it exhibits a short-term instability of about 30µg 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 artifacts have been cleaned or possible changes in gravity or environment.
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 has intensified the search for a new definition of the kilogram. See Proposed future definitions, below.
Importance of the kilogram
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
meter per second squared. If the mass of the IPK were to change slightly, so too must the newton by a proportional degree. 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, and ultimately, the kilogram. 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 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 -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, in spite of the best stewardship, the average mass of the worldwide ensemble of prototypes and the mass of the IPK have likely diverged another µg since the third periodic verification years ago. Further, the world’s national metrology laboratories must wait for the fourth periodic verification to confirm whether the historical trendspersisted.
Fortunately, definitions of the SI units are quite different from their practical realizations. For instance, the meter is defined as the distance light travels in a vacuum during a time interval of of a second. However, the meter’s practical realization typically takes the form of a helium–neon laser, and the meter’s length is delineated—not defined—as 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 meter because the second—and thus the meter’s length—is abstracted via the laser comprising the meter’s practical realization. Scientists performing meter 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 (equivalent to 42µg).
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. While this is a worthwhile objective and much work towards that end is ongoing, no alternative has yet achieved the uncertainty of a couple parts in 108 (~20µg) required to improve upon the IPK. However, , the U.S.’s National Institute of Standards and Technology (NIST) had an implementation of the watt balance that was approaching this goal, with a demonstrated uncertainty of 36µg. See Wattbalance, below.
The avoirdupois pound, used in both the imperial system and U.S. customary units, is defined as exactly ,
making one kilogram approximately equal to 2.2046 avoirdupois pounds. Although both the avoirdupois (or international) pound and the kilogram are units of mass and have related unit of force the pound-force, the kilogram-force is seldom used.
Proposed future definitions
: In the following sections, wherever numeric equalities are shown in ‘concise form’—such as —the two digits between the parentheses denote the uncertainty at 1σ standard deviation (68% confidence level) in the two least significant digits of the significand.
The kilogram is the only SI unit that is still defined by an artifact. Note that the meter was also once defined as an artifact (a single platinum-iridium bar with two marks on it). However, it was eventually redefined in terms of invariant, fundamental constants of nature (the wavelength of light emitted by krypton, and later the speed of light) so that the standard can be reproduced in different laboratories by following a written specification. Today, physicists are investigating various approaches to doing the same with the kilogram.
In October 2010, the International Committee for Weights and Measures (known by its French-language initials 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. 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 watt balance (discussed below) may be able to do this.
In getting to the threshold of replacing the last artifact that underpins much of the International System of Units (SI), a variety of other fundamentally different technologies were considered and explored over many years. Some of the approaches are fundamentally very different from each other. 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, fundamental 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 fundamental 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.
The watt balance
watt balance is a project of the U.S. Government to develop 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 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 in that it employs an extra calibration step that nulls the effect of geometry. The
electric potential in the watt 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 resistance standard.
The watt balance requires exquisitely precise measurement of the local gravitational acceleration g in the laboratory, using a gravimeter. (See “FG‑5 absolute gravimeter” in External images, below). For instance, the NIST compensates for earth’s gravity gradient of 309µGal per meter when the elevation of the center of the gravimeter differs from that of the nearby test mass in the watt balance; a change in the weight of a one-kilogram test mass that equates to about 316µg/m.
In April 2007, the NIST’s implementation of the watt balance demonstrated a combined relative standard uncertainty (CRSU) of 36µg and a short-term resolution of µg. The UK’s National Physical Laboratory’s watt balance demonstrated a CRSU of 70.3µg in 2007. That watt 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.
If the CGPM adopts the new proposal and the new definition of the kilogram becomes part of the SI, the Planck constant (h), which is a measure that relates the energy of photons to their frequency, would be precisely fixed; for example, to }} (from the 2006 CODATA value of ). Once agreed upon internationally, the kilogram would no longer be defined as the mass of the IPK. With the definition of the kilogram in terms of electric power and a frequency (the Planck constant’s J·s), electric power would be directly identical to mechanical power by definition rather than being a derivative. All the remaining units in the International System of Units (the SI) that today have dependencies upon the kilogram and the joule would also fall in place, their magnitudes ultimately defined, in part, in terms of photon oscillations rather than a -year-old metal artifact stored in a vault.
—the dark and light bands above—blooms at an ever faster rate as a free-falling corner reflector drops inside an absolute gravimeter. The pattern’s frequency sweep is timed by an atomic clock.]]
Gravity and the nature of the watt 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—nearly one percent—depending upon where on earth’s surface the measurement is made (see Earth’s gravity ). There are also subtle seasonal variations in g 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. Although g would not be a term in the definition of the kilogram, it would be crucial in the delineation 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 Pt10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the watt balance than stainless steel masses), the measured value was typically within 8 ppb of .
The virtue of electronic realizations like the watt 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 watt 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 just three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the meter. By fixing the Planck constant, the definition of the kilogram would depend only on the definitions of the second and the meter. 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 meter depends on the second and on an additional defined physical constant: the speed of light c. If the Kilogram is redefined in this manner, mass artifacts—physical objects calibrated in a watt balance, including the IPK—would no longer be part of the definition, but would instead become transfer standards.
Scales like the watt balance also permit more flexibility in choosing materials with especially desirable properties for mass standards. For instance, Pt10Ir could continue to be used so that the specific gravity of newly produced mass standards would be the same as existing national primary and check standards (≈21.55g/ml). This would reduce the relative uncertainty when making mass comparisons in air. Alternatively, entirely different materials and constructions could be explored with the objective of producing mass standards with greater stability. For instance, osmium-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 to isolate these new alloys.
The challenge with watt balances is not only in reducing their uncertainty, but also in making them truly practical realizations of the kilogram. Nearly every aspect of watt 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 watt balance used four resistance standards in 2007, each of which was rotated through the watt 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 watt balance after calibration altered their values 10ppb (equivalent to 10µg) or more. Present-day technology is insufficient to permit stable operation of watt balances between even biannual calibrations. If the kilogram is defined in terms of the Planck constant, it is likely there will only be a few—at most—watt balances initially operating in the world.
Alternative approaches to redefining the kilogram that were fundamentally different from the watt balance were explored to varying degrees with some abandoned, as follows:
Atom-counting approaches
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
carbon12 atoms. Carbon12 (
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 carbon12.” Thus, the current definition of the mole requires that (83⅓) moles 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 entities per mole (
CODATA, 2010). This new definition of the kilogram proposed to fix the Avogadro constant at precisely (from the CODATA 2006 value) with the kilogram being defined as “the mass equal to that of · }}atoms of
12C.”
The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the Planck constant—a measure relating the energy of photons to their frequency. That relative standard uncertainty has been 50parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposal would be that the uncertainty in the mass of a 12C atom—and the magnitude of the kilogram—could be no better than the current 50ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram would be subject to future refinement as improved measurements of the value of the Planck constant become available; electronic 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 83⅓ 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 84,446,8863 (≈) atoms. An imaginary realization of a 12-gram mass prototype would be a cube of 12C atoms measuring precisely 84,446,886 atoms across on a side. With this proposal, the kilogram would be defined as “the mass equal to 84,446,8863× 83⅓ atoms of 12C.” The value 84,446,886 was chosen because it has a special property; its cube (the proposed new value for the Avogadro constant) is evenly divisible by twelve. Thus with this definition of the kilogram, there would be an integer number of atoms in one gram of 12C: 50,184,508,190,229,061,679,538 atoms.
Avogadro project
gyroscope rotors flown on
Gravity ProbeB, which were manufactured in the late 1990s and given their final figure at the
W.W. Hansen Experimental Physics Lab at
Stanford University. Particularly, “Gyro 4” is recorded in the
Guinness database of world records (their database, not in their book) as
the world’s roundest man-made object. According to a published report (
221kB PDF, here) and the GPB public affairs coordinator at Stanford University, of the four gyroscopes onboard the probe, Gyro4 has a maximum surface undulation from a perfect sphere of 3.4±0.4nm on the 38.1mm diameter sphere, which is a .}} Scaled to the size of earth, this is equivalent to an undulation the size of North America rising slowly up out of the sea (in molecular-layer terraces 11.9cm high), reaching a maximum elevation of 1.14±0.13m in Nebraska, and then gradually sloping back down to sea level on the other side of the continent.]]
Another Avogadro constant-based approach, known as the Avogadro project, would define and delineate the kilogram as a softball-size (93.6mm 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 0.3nm on the radius—roughly a single atomic layer. The precise lattice spacing between the atoms in its crystal structure (≈192pm) would be measured using a scanning X-ray interferometer. This permits its atomic spacing to be determined with an uncertainty of only three parts per billion. With the size of the sphere, its average atomic mass, and its atomic spacing known, the required sphere diameter can be calculated with sufficient precision and low uncertainty to enable it to be finish-polished to a target mass of one kilogram.
Experiments are being performed on the Avogadro Project’s silicon spheres to determine whether their masses are most stable when stored in a vacuum, a partial vacuum, or ambient pressure. However, no technical means currently exist to prove a long-term stability any better than that of the IPK’s because the most sensitive and accurate measurements of mass are made with dual-pan balances like the BIPM’s FB2 flexure-strip balance (see 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 artifact 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 parts per billion. Another issue to be overcome is that silicon oxidizes and forms a thin layer (equivalent to silicon atoms) of silicon dioxide (quartz) and silicon monoxide. This layer slightly increases the mass of the sphere, an effect which must be accounted for when polishing the sphere to its finish dimension. 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 Carbon12 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 1ppb 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 . With this approach, the Avogadro constant would not only be fixed, but so too would the atomic mass of 28Si. As such, the definition of the kilogram would be decoupled from 12C and the kilogram would instead be defined as }}· atoms of 28Si (≈ fixed moles of 28Si atoms). Physicists could elect to define the kilogram in terms of 28Si even when kilogram prototypes are made of natural silicon (all three isotopes present). Even with a kilogram definition based on theoretically pure 28Si, a silicon-sphere prototype made of only nearly pure 28Si would necessarily deviate slightly from the defined number of moles of silicon to compensate for various chemical and isotopic impurities as well as the effect of surface oxides.
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 counted them by measuring the electrical 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 is effectively non-radioactive (bismuth) or is perfectly stable (gold). 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 , from the current value of . As with a definition based upon carbon12, the Avogadro constant would also have been fixed. The kilogram would then have been defined as “the mass equal to that of precisely }}· atoms of gold” (precisely 3,057,443,620,887,933,963,384,315 atoms of gold or about fixed moles).
In 2003, German experiments with gold at a current of only 10µA demonstrated a relative uncertainty of 1.5%. Follow-on experiments using bismuth ions and a current of 30mA were expected to accumulate a mass of 30g in six days and to have a relative uncertainty of better than 1 ppm. Ultimately, ionaccumulation approaches proved to be unsuitable. Measurements required months and the data proved too erratic for the technique to be considered a viable future replacement to the IPK.
Among the many technical challenges of the ion-deposition apparatus was obtaining a sufficiently high ion current (mass deposition rate) while simultaneously decelerating the ions so they could all deposit onto a target electrode embedded in a balance pan. Experiments with gold showed the ions had to be decelerated to very low energies to avoid sputtering 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 1eV (<1km/s for gold).
SI multiples
Because
SI prefixes may not be concatenated (serially linked) within the name or symbol for a unit of measure, SI prefixes are used with the
gram, not the kilogram, which already has a prefix as part of its name. For instance, one-millionth of a kilogram is 1mg (one milligram), not 1µkg (one microkilogram).
| p= | n= | μ= | m= | k=
| xM = megagram (
tonne)
| xmc =
microgram (mcg)
}}
When the Greek lowercase “µ” (mu) in the symbol of microgram is typographically unavailable, it is occasionally—although not properly—replaced by Latin lowercase “u”.
The microgram is often abbreviated “mcg”, particularly in pharmaceutical and nutritional supplement labeling, to avoid confusion since the “µ” prefix is not well recognized outside of technical disciplines. Note however, that the
abbreviation “mcg”, is also the
symbol for an obsolete
CGS unit of measure known as the “millicentigram”, which is equal to 10µg.
The decagram (dag) is in Central Europe ofter abbreviated “dkg” (from local languages spelling “dekagram”) and is used for usual quantities of food (mostly cheese and meat).
The unit name “megagram” is rarely used, and even then, typically only in technical fields in contexts where especially rigorous consistency with the units of measure is desired. For most purposes, the unit “
tonne” is instead used. The tonne and its symbol, t, were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPM for use with the SI. According to the BIPM, “In English speaking countries this unit is usually called ‘metric ton’.” Note also that the unit name “megatonne” or “megaton” (Mt) is often used in general-interest literature on
greenhouse gas emissions whereas the equivalent value in scientific papers on the subject is often the “teragram” (Tg).
== Glossary ==
Abstracted: Isolated and its effect changed in form, often simplified or made more accessible in the process.
Artifact: A simple human-made object used directly as a comparative standard in the measurement of a physical quantity.
Check standard:
# A standard body’s backup replica of the international prototype kilogram (IPK).
# A secondary kilogram mass standard used as a stand-in for the primary standard during routine calibrations.
Definition: A formal, specific, and exact specification.
Delineation: The physical means used to mark a boundary or express the magnitude of an entity.
Disseminate: To widely distribute the magnitude of a unit of measure, typically via replicas and transfer standards.
IPK: Abbreviation of “international prototype kilogram” (CG image), the mass artifact in France internationally recognized as having the defining mass of precisely one kilogram.
Magnitude: The extent or numeric value of a property
National prototype: A replica of the IPK possessed by a nation.
Practical realization: A readily reproducible apparatus to conveniently delineate the magnitude of a unit of measure.
Primary national standard:
# A replica of the IPK possessed by a nation
# The least used replica of the IPK when a nation possesses more than one.
Prototype:
# A human-made object that serves as the defining comparative standard in the measurement of a physical quantity.
# A human-made object that serves as the comparative standard in the measurement of a physical quantity.
# The IPK and any of its replicas
Replica: An official copy of the IPK.
Sister copy: One of six official copies of the IPK that are stored in the same safe as the IPK and are used as check standards by the BIPM.
Transfer standard: An artifact or apparatus that reproduces the magnitude of a unit of measure in a different, usually more practical, form.
See also
1795 in science
1799 in science
Inertia
International System of Units (SI)
International Bureau of Weights and Measures (BIPM)
International Committee for Weights and Measures (CIPM)
General Conference on Weights and Measures (CGPM)
Gram
Grave (orig. name of the kilogram, history of)
Gravimetry
Kilogram-force
Liter
Metric system
Metric ton
Mass
Mass versus weight
Milligrams per cent
National Institute of Standards and Technology (NIST)
Newton
SI base units
Standard gravity
Watt balance
Weight
Notes
References
External links
National Institute of Standards and Technology (NIST): NIST Improves Accuracy of ‘Watt Balance’ Method for Defining the Kilogram
The UK’s National Physical Laboratory (NPL): An overview of the problems with an artifact-based kilogram
NPL: Avogadro Project
NPL: NPL watt balance
Metrology in France: Watt balance
Australian National Measurement Institute: Redefining the kilogram through the Avogadro constant
International Bureau of Weights and Measures (BIPM): Home page
NZZ Folio: What a kilogram really weighs
NPL: What are the differences between mass, weight, force and load?
BBC: Getting the measure of a kilogram
NPR: This Kilogram Has A Weight-Loss Problem, an interview with National Institute of Standards and Technology physicist Richard Steiner
Nature: Elemental shift for kilo, article about the silicone-28 sphere
Category:SI base units
Category:Units of mass
![WKF 2010-10-27 -75 kg AZE Aghayev [10] JPN Matsuhisa [7] with Slow Motion](http://web.archive.org./web/20110907085143im_/http://i.ytimg.com/vi/pswM1I8n6Y0/0.jpg "WKF 2010-10-27 -75 kg AZE Aghayev [10] JPN Matsuhisa [7] with Slow Motion")
