# kilogram

Physical unit
Unit name kilogram
Unit symbol ${\ displaystyle \ mathrm {kg}}$
Physical quantity (s) Dimensions
Formula symbol ${\ displaystyle m}$
dimension ${\ displaystyle {\ mathsf {M}}}$
system International system of units
In SI units Base unit
In CGS units ${\ displaystyle \ mathrm {1 \, kg = 10 ^ {3} \, g}}$
Named after ancient Greek χίλιοι chilioi , German 'thousand'
and γράμμα gramma , German 'letter'

The kilogram (in common parlance also the kilo) is the unit of measurement used in the international system of units (SI) for mass . The unit symbol for the kilogram is kg. The definition of the kilogram is based on a numerically determined value of Planck's constant and the definitions of meters and seconds .

Originally, one kilogram was supposed to correspond to the mass of one liter of water. Since such a definition is not suitable for precise measurements, prototypes were produced and selected as a definition in the sense of a measuring standard , which was valid up to the current definition of a kilogram using natural constants. Each newer definition was chosen so that it was within the measurement accuracy of the previously applicable definition.

The unit name of the kilogram differs from the system of the International System of Units in that it begins with an SI prefix , the “kilo”; That is why decimal parts and multiples of the kilogram must not be formed from the kilogram with prefixes or prefixes , instead they are derived from the gram .

## definition

“The kilogram, unit symbol kg, is the SI unit of mass. It is defined by using the numerical value 6 for Planck's constant h .626 070 15e-34 , expressed in the unit Js, which is the same, with the meter and the second being defined bycand ΔνCs. " ${\ textstyle \ {\ frac {\ mathrm {kg} \, \ mathrm {m} ^ {2}} {\ mathrm {s}}}}$

The definitions of the SI units from 2019 do not stipulate in which form or with which experimental methods the unit is to be implemented. The responsible advisory body of the BIPM - Consultative Committee for Mass and Related Quantities (CCM) - defines in a mise en pratique which methods are recognized for realizing the kilogram. Currently these are the watt balance and the XRCD method, see below .

## history

### origin

In the course of the creation of a unified and universal system of units by the French National Assembly from 1790 onwards, a committee of scholars ( Borda , Condorcet , Laplace , Lagrange and Monge ) proposed the masses of one cubic meter, one cubic decimeter and one cubic centimeter of water as units of mass . Deviating from the proposal of the National Assembly, which assumed the length of a pendulum-seconds pendulum, one meter should be one ten millionth of the length of the earth's meridian from the north pole to the equator. In particular, the distance from Dunkirk to Barcelona should be measured along an Earth's great circle.

### French national system of units

Since the meridian measurement necessary for the determination , which was to be carried out by Méchain and Delambre , was delayed by various battles and wars, the National Assembly decided on August 1, 1793 on the basis of older data initially provisional units under the names Bar (ton), Grave ( Kilograms) and gravet (grams). They could be used with the Déci- and Centi- prefixes . On 18th Germinal 3 (April 7, 1795), Bar and Grave were deleted and the Gravet was renamed to grams, making the myriagram ten kilograms the largest unit of mass. At the same time, the water temperature for the definition of the gram was set for the first time: to freezing point . On 4th Messidor VII (June 22, 1799), the platinum-made measuring standards of meters and kilograms, which were based on the completed measurement, were handed over to the legislature. For metrological reasons (stability of the density), contrary to the valid legal definition, a cubic centimeter of water at the temperature of the greatest density was used as the water temperature when determining the gram (4.0 ° C). Although the decree of 18th Germinal 3 had expressly provided the meter as the only measuring standard, both measuring standards became legal units with the law of 19th Frimaire VIII (10 December 1799). They were later referred to as Mètre des Archives and Kilogramme des Archives , depending on where they were kept. The three time levels of the units are given the additions provisoire , républicain and définitif to distinguish them. In the case of the masses, only the gram and its multiples need to be differentiated into républicain and définitif .

### International cooperation that led to the Meter Convention in 1875

France had sought international standardization from the outset, and foreign delegates had been involved in the final design of the new units in 1798/99. After France and a majority of European countries were already using the new system of units in the 19th century, international science began to make concrete efforts in 1867 to establish an international organization for measuring and weighing. This led to the formation of the International Meter Commission in Paris in 1870, whose work, interrupted by the Franco-German War , led to the International Meter Convention in 1875 . The convention not only provided for the production of new copies, but also a new international prototype for the masses. For this purpose, three 1 kg cylinders KI, KII and KIII were made from the newly developed harder, but also 5% denser alloy PtIr10 1878 and adjusted to the kilogram of the archive . To determine the volume and correct the air buoyancy, hydrostatic weighings were carried out. In comparisons made independently by several observers, no difference could be found between KIII and the kilogram in the archive in 1880 within the scope of the measurement accuracy attainable at that time after correction of the buoyancy . In 1883, the Committee for Weights and Measures therefore designated KIII as the international prototype of the kilogram . By 1884 another 40 kilogram prototypes, now adjusted to 1 kilogram ± 1 milligram, were produced. They were then calibrated after hydrostatic weighing . ${\ displaystyle {\ mathfrak {K}}}$${\ displaystyle {\ mathfrak {K}}}$

In 1889, with the corresponding formal resolution of the 1st  General Conference on Weights and Measures , the change in the definition of the kilogram from the mass of the kilogram définitif to that of the international prototype of the kilogram was completed. As part of the inspections carried out in 1939, it turned out that this meant a significant difference in the long run: Compared to the international kilogram prototype, the kilogram of the archive made from forged platinum sponge lost 430 micrograms of its mass in 58 years. Of the 40 copied kilogram prototypes, 29 were initially given by raffle to states of the Convention and other interested parties, in particular scientific societies, at cost price, one was kept in addition to KI as a reference copy with the international prototype, and two were assigned to the BIPM as working copies. The reserve stock was reduced by the acceding states, and in 1925 the number of reference copies was increased to four.

### Description of the international prototype of the kilogram, kilogram standards

Replica of the original kilogram under two glass bells

From 1889 to 2019 the international prototype of the kilogram (also known as the original kilogram ) was the reference standard for the unit of measurement, the kilogram. It is kept in a safe at the International Bureau of Weights and Measures (BIPM) in Sèvres near Paris . It is a cylinder 39 millimeters high and 39 millimeters in diameter, made of an alloy of 90% platinum and 10% iridium . The material is largely chemically inert . Its high density, like the choice of geometry, minimizes the effects of surface effects. The iridium content leads to a significantly higher hardness (175 HV ) compared to the relatively soft pure platinum , which improves the machinability during production and in particular reduces the abrasion during manipulation (this refers to any type of handling).

In addition to the International Kilogram Prototype, the International Bureau of Weights and Measures (BIPM) has other reference and working standards (→ Normal ), which are copies of the International Kilogram Prototype and are connected to it (connection = calibration on a higher standard Order). The reference standards are used for control (e.g. drift), while the working standards are used to connect the national kilogram prototypes, which are also copies of the international kilogram prototype. All copies are called kilogram prototypes and are calibrated to ± 1 milligram . The connection of the reference and working standards made with mass comparators has a relative measurement uncertainty of 3 · 10 −9 , that of the national kilogram prototypes of 5 · 10 −9 . Up to 2003, 84 kilogram prototypes had been produced in the BIPM's workshops, which are used for internal purposes as well as national kilogram prototypes.

States that have acceded to the Meter Convention were able to receive national kilogram prototypes from the BIPM. If necessary, states could have their copies brought to the BIPM in order to link them to the BIPM working standards. The Physikalisch-Technische Bundesanstalt (PTB), which in addition to the national prototype (number 52) acquired another one (number 70) in 1987, as well as the former national prototype of the GDR (55) since 1990 and the one that was damaged in World War II in 1944 original German national prototype (22), which continues to be used as a standard with increased measurement uncertainty, has done this approximately every ten years. The individual metrological state institutes operated a similar system of reference and working standards as the BIPM, but here steel or bronze standards are used, especially those with larger and smaller nominal values, in Germany as the main standard sets of one milligram to five tons. The standards of industry and research as well as those of the state calibration authorities were derived from this. The connection of the steel standards to the platinum-iridium standards is problematic, since the air buoyancy to be corrected due to different volumes had a great influence on the measurement. Despite the demanding determination of the air density, this resulted in relative measurement uncertainties in the range of 1.5 · 10 −8 .

### History of the distribution of the prototypes

Since 1928, new prototypes have been manufactured continuously to meet the increasing demand. In addition to the newly added states, many of the larger metrological state institutes increased their holdings, and the number of reference and working copies at the BIPM also increased accordingly. At the end of the 1970s, a new manufacturing process was developed in which diamond tools are used to adjust the prototypes exclusively by facing one face and then gradually turning a polygonal bevel , which eliminates the previously necessary manual grinding with decreasing grain sizes. In order to ensure a fine-grain structure suitable for diamond machining, the alloy composition, in particular the upper limits of the secondary components, was specified more precisely and the manufacturing process of the blanks was improved by casting, forging and finally extruding material for usually seven prototypes. On the occasion of the review of the national prototypes from 1988–1992, cleaning and its effects were systematically examined and a standardized procedure was established for this purpose. As a result of the review, the focus increasingly shifted to the development of an improved mass definition. ${\ displaystyle {\ mathfrak {K}}}$

### Problems with the original kilogram

Changes in the mass of various kilogram prototypes compared to the international kilogram prototype

Comparisons of the national with the international kilogram prototype of the BIPM, so-called re-examinations, take place approximately every 50 years, so far from 1939/46 to 1953 and most recently from 1988 to 1992. Here, as with the comparison with the reference standards, it was found that the original kilogram in comparison has become 50 micrograms lighter than copies in 100 years. The cause is still unknown. The possibility that material was removed from the original kilogram during cleaning was excluded. Another explanation is that hydrogen, for example, escaped from the platinum-iridium alloy .

Because of the mentioned instabilities of the artifact-based definition, a kilogram definition was sought for the session of the General Conference on Weights and Measures in November 2018 so that it can be derived from a fundamental constant of physics. In order to achieve an improvement over the previous situation, a method for determining mass with an accuracy of the order of 10 −8 had to be developed. The redefinition using Planck's constant allows the kilogram to be derived from a fundamental constant of physics at any location.

## Realizations of the definition

With the introduction of the definition in May 2019, the BIPM also proposed two methods of implementation:

a) Realization by comparing electrical and mechanical power, whereby so-called watt balances (also called kibble balances) are used,
b) the realization by X-ray crystal density measurements (XRCD method for English X-ray crystal density method ) as the International Avogadro Coordination were used (IAC) project, shortly Avogadroprojekt.

These two implementations are presented below, as well as other possible implementations that were not proposed by BIPM in May 2019.

### Watt balance

The Watt balance is an experimental setup with which a relation between Planck's constant and the mass of a test specimen is established. First, the current in a coil is measured, which is required to keep a specimen floating. Second, voltage is measured, which induces constant movement of the coil in this magnetic field. The two measurement results are multiplied, which formally results in electrical power with the unit watt. In addition, the speed of the moving coil and the gravitational acceleration at the location of the scale must be known. Until 2018, this procedure was used to determine the value of the Planck constant based on the definition of the kilogram based on the original kilogram, which was valid until then. Since the definition of the value of Planck's constant, a watt balance has been used to “realize” the unit kilogram based on the defined value of this constant. (This means that the mass of artifacts, which do not necessarily have to weigh 1 kg, can be determined with a watt balance.) ${\ displaystyle h}$

Watt balances operate u. a. the National Research Council of Canada (which took over the work from the British National Physical Laboratory ), the US National Institute of Standards and Technology , the Swiss METAS and the BIPM .

### XRCD method

Silicon ball for the Avogadro project

An alternative definition of the kilogram would have been possible on the basis of the Avogadro project . After determining the definition via Planck's constant, the appropriate considerations for realizing the new kilogram definition are proposed.

The aim of the Avogadro project was to determine the Avogadro constant from the mass and volume of a body made of a material of known particle density and molar mass . ${\ displaystyle N _ {\ mathrm {A}}}$${\ displaystyle m}$${\ displaystyle V}$ ${\ displaystyle n}$${\ displaystyle M}$

${\ displaystyle N _ {\ mathrm {A}} = {\ frac {MVn} {m}}}$

The Avogadro constant - today set to an exact value for the definition of the unit mole - was defined until May 19, 2019 as the amount of atoms in 12 g of carbon-12, i.e. a value to be determined experimentally that, among other things, depends on the unit Was dependent on kilograms. If the greatest uncertainty factor in this is the reliability of the kilogram, the reverse would be possible: a kilogram could be defined more precisely than before by defining it as the mass of a certain number of atoms of a certain isotope.

A sufficiently accurate determination of the particle density is only possible using an X-ray laser interferometer and requires a monocrystalline material. Because of the requirements for the accuracy of the material parameters, practically only chemically ultra-pure, isotopically pure silicon -28 can be used for this. With natural silicon, which is a mixture of three isotopes, the relatively poor determinability of the mean molar mass limits the overall accuracy. The exact determination of the volume requires the production of a highly precise ball from the material. In addition, vacancy density, impurity concentrations, thickness and composition of the silicon dioxide layer on the surface and others must be taken into account. ${\ displaystyle n}$

In the case of natural silicon, the Avogadro constant could initially be confirmed with the previous accuracy. Coordinated by the Physikalisch-Technische Bundesanstalt in Braunschweig, a cooperation between eight metrological institutes produced high-purity and highly enriched silicon 28 for an experiment that was 10 times more accurate. In cooperation with the Russian Ministry of Atomic Energy, silicon was enriched to a 28 Si content of 99.994% in Russian isotope separation plants and then chemically cleaned again. At this point in time, the costs for the production of the 6 kg raw material were already 1.2 million euros. The isotope-pure 28 Si single crystal was grown at the Leibniz Institute for Crystal Growth in Berlin . After various analyzes and the cultivation of single crystals, in which the chemical purity was increased again by repeatedly using the zone melting process , the National Measurement Institute NMI-A in Australia produced two 1 kg spheres with a maximum shape deviation of 30 nm at approx 93.7 mm in diameter. Complex tests were then carried out to estimate the influence of the crystal structural defects, then the lattice parameters were determined at the Italian metrology institute INRIM using an X-ray interferometer and a comparison measurement was carried out on a crystal made of natural silicon at the American NIST. The masses of the two silicon spheres were compared with the international mass standards at the BIPM, at the NMIJ (Japan) and at the PTB under vacuum.

The volume V , including the deviations from the spherical shape, was measured with interferometers of different beam geometries at NMIJ and NMI-A, as well as at PTB, where a newly developed spherical interferometer based on a Fizeau interferometer with uncertainties below a nanometer was used.

The thickness and composition of the surface layer, which essentially consists of silicon dioxide, were investigated using electron , X-ray and synchrotron radiation to determine the total density . Among other things, an unexpectedly high level of metallic contamination of the spherical surfaces with copper and nickel silicides during the polishing process was determined and its influence on the results of sphere volume and mass was estimated, which also led to a higher measurement uncertainty than expected. Most of the reduction in the relative overall measurement uncertainty was achieved through the development of a new mass spectrometric method for determining the mean molar mass M of silicon.

In 2015, i.e. before it was set to today's value, the Avogadro constant was determined in this way with a total measurement uncertainty of 2 · 10 −8 . This has achieved the accuracy required by the Advisory Committee on Mass for a redefinition of the kilogram. Planck's constant h is included in the calculations for this experiment . By fixing the value of Planck's constant, the XRCD method is also suitable for realizing the unit kilogram.

### Other implementation options that were not suggested

#### Ion accumulation

Another possibility would have been to generate a weighable mass with the help of an ion beam (electrically charged atoms) and to collect the ions. By measuring the electrical current of the ion beam and the time, the mass of an atom can then be calculated in kilograms. The Physikalisch-Technische Bundesanstalt had been carrying out experiments with gold since 1991, replaced gold with bismuth (including bismuth) in 2004 , but discontinued the experiments in 2008 because it proved impossible to obtain competitive results with this method until a decision was made about the redefinition .

#### Magnetic levitation experiment

A magnet is made to float in an inhomogeneous magnetic field. Its mass can be calculated from the position of the magnet in this field. This approach was originally followed by the then Japanese National Research Laboratory of Metrology , but has since been abandoned because of the lack of achievable accuracy. Japan is also involved in the Avogadro project.

## literature

Wiktionary: Kilogram  - explanations of meanings, word origins, synonyms, translations
Commons : Kilogram  - collection of images, videos, and audio files

## Individual evidence

1. Kilos on duden.de
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3. New definitions in the International System of Units (SI). (PDF) PTB , accessed on September 28, 2019 .
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5. a b c Mise en pratique for the definition of the kilogram in the SI. (PDF; 269 kB) BIPM: Consultative Committee for Mass and Related Quantities, May 20, 2019, accessed on June 2, 2019 (English, downloadable from the BIPM website ).
6. a b Jean-Pierre Maury: Poids et mesures, République, mètre, liter, kilo, MJP. Grandes lois de la République. In: La digithèque de matériaux juridiques et politiques (MJP). Université de Perpignan, 2007, accessed on June 14, 2019 (French).
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8. ^ TJ Quinn New Techniques in the Manufacture of Platinum-Iridium Mass Standards. Platinum Metals Review 30 (1986), No. 2, pp. 74-79
9. G. Girard: The Third Periodic Verification of National Prototypes of the Kilogram (1988-1992). In: Metrologia , 31, 1994, pp. 317-336, doi: 10.1088 / 0026-1394 / 31/4/007
10. Does the Watt balance replace the original kilogram from 1889? - Article by Holger Dambeck at Spiegel Online , September 16, 2005.
11. Canada assumes weighty mantle , article in Nature from August 24, 2009 (English)
12. ^ International Avogadro Project. BIPM; accessed on December 8, 2018.
13. Yvonne Zimber: 6 kg isotope-pure silicon-28 for the international Avogadro project . Website of the Physikalisch-Technische Bundesanstalt, March 26, 2007.
14. Silicon & Germanium. Retrieved November 18, 2018 .
15. 1.83 Avogadro's constant. Webmaster Department 3, June 13, 2016, accessed November 18, 2018 .
16. Appearance of a diva . ( Memento from March 4, 2016 in the Internet Archive ) Physikalisch-Technische Bundesanstalt
17. Guido Bartl et al .: Interferometric determination of the topographies of absolute sphere radii using the sphere interferometer of PTB . In: Meas Sci Technol , 21, 2010, p. 115101, doi: 10.1088 / 0957-0233 / 21/11/115101 .
18. Olaf Rienitz et al .: Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty - Part 1: Theoretical derivation and feasibility study. Int J Mass Spectrom 289, 2010, pp. 47-53, doi: 10.1016 / j.ijms.2009.09.010 .
19. Y. Azuma et al .: Improved measurement results for the Avogadro constant using a 28 Si-enriched crystal , Metrologia 52, 2015, 360-375, doi: 10.1088 / 0026-1394 / 52/2/360 .
20. Ion accumulation. Physikalisch-Technische Bundesanstalt. This project has ended. The information about this is used for documentation purposes. Generation of 5 mA DC bismuth current 2004, optimization of the ion beam apparatus for maximum transmission , 2007, and new determination of the atomic mass constant through the accumulation of around 0.3 g bismuth , 2008.