New breakthrough for the kilogram

In this article about new scientific developments to redefine the kilogram and remove its link to a physical object, Ronnie Cohen writes about recent reports about a new scientific breakthrough in getting the most accurate estimate of Avogadro’s constant to date, which can help to redefine the kilogram. These reports have been published in the last few weeks and you can find a list of sources at the bottom of this article.

Of all the base units in the International System of Units, the kilogram is the only one that is still tied to a property of a physical object. That property is mass, commonly but incorrectly known as weight, and the object is a cylinder made of an alloy of 90 per cent platinum and 10 per cent iridium, roughly the size of a golf ball and held in a vault at the International Bureau of Weights and Measures in Sèvres, outside Paris.

Originally, the kilogram was originally defined in 1795 as a perfect decimetre of water. The idea of the original definition was that anyone with a metre ruler and some water could create their own kilogram. However, there were several problems with this definition.

The hotter water is, the less dense it is hence the less it weighs. In the second television programme of the series*, “Precision: The Measure of All Things“, about mass and moles, Marcus du Sautoy presents viewers with two perfect decimetres of water at different temperatures. The colder one had a mass of 998 grams whereas the hotter one was 957 grams. Other factors that affected the mass of water include impurities in the water, the distance above sea level and atmospheric pressure.

Two scientists, Louis Lefèvre Gineau and Giovanni Fabbroni, discovered how to measure a kilogram using a cubic decimetre of distilled water. Based on this discovery, a master metal kilogram could finally be made. It was made in 1799 out of pure platinum and clones were made and sent to towns and villages across France. However, pure platinum was soft and prone to damage despite its resistance to air and water, rendering the master kilogram and its clones inaccurate. It took almost 70 years to produce a more stable master kilogram. The new master kilogram and clones were made of platinum and iridium. The second batch become contaminated by iron, making the whole batch useless. With the growth of international trade and industry, a common measurement system, including a common system of mass, was needed and the metric system was designed to fulfil this role.

After the signing of the 1875 agreement by 17 countries to adopt the metric system, a new master kilogram was commissioned. It was made of 90% platinum and 10% iridium. All use of kilograms throughout the world today are ultimately based on this object, the International Prototype Kilogram, known as “Le Grand Kilo” or “Le Grand K” (The Big K in English). This object has been in use since 1889.

Forty identical copies of Big K were distributed to other countries to calibrate kilograms worldwide. They were only brought together three times for comparison. Each time, Big K and its copies were delicately wiped with alcohol and ether, steam-cleaned, and their mass determined. In 1992, scientists discovered that Big K had about 50 micrograms less mass than its copies. Either the copies had gained mass or Big K had lost. Scientists could only see the relative gain or loss of mass of Big K when compared to its copies. It is also possible that they had all gained or lost at different rates.

Given that Big K is the ultimate reference for all kilograms used worldwide, the consequences of an unstable kilogram are very serious. It is not just mass that is at stake. Many other phenomena rely on the kilogram, such as the joule, watt and volt. An unstable kilogram is unacceptable in fields like medicine or engineering, where very high levels of precision are required and tiny differences can cause problems.

In 2011, all 55 delegates at the General Conference of Weights and Measures agreed unanimously to redefine the kilogram according to a physical constant. They hope to achieve this by 2018. There are several possible methods that scientists are investigating. One of these methods involves the creation of a perfect sphere of pure silicon with a precise diameter. This method is based on Avogadro’s number.

Avogadro’s number represents the number of discreet particles – molecules or atoms – in a “mole” of substance. To calculate Avogadro’s number, researchers use silicon, a substance that grows perfect crystals, where each atom takes up exactly the same amount of space. They count the number of atoms in a silicon sphere of one kilogram.

The result was published in the Journal of Physical and Chemical Reference Data. It is the most accurate value of Avogadro’s number ever recorded, with a margin of error of only 0.000000018 (i.e. fewer than 20 atoms per billion#). This compares to the margin of error of 30 atoms per billion that was achieved in 2011. There is some degree of uncertainty in both numbers so more accurate to correlate them and then take their average into one more neutral value. In this case, Avogadro’s number works out as 6.02214082(11) x 10²³. The number in parentheses represents the uncertainty of the last digit in the result. This enormous number is greater than the number of grains of sand in the world.

The work was led by Dr Giovanni Mana, a researcher from the National Institute for Metrology Research in Turin. He said, “Prior to redefining the kilogram, we must demonstrate that the new realization is indistinguishable from the present one, to within the accuracy of the world’s best balances. Otherwise, when changing from the present definition to the new one, all users in science, industry, and commerce must change the mass value of all the existing artifacts. The absence of technologies to redefine the kilogram is the biggest impediment to a redefinition of the whole system of measurement units, which is expected to deliver even more solid foundations and reliability to precision measurements and to set the stage for further innovations in technology and science.

This method could redefine the kilogram and would mean that the kilogram definition is no longer tied to a physical object. Like the metre and the second, which are both based on physical constants, it would mean that any laboratory with the right equipment could reproduce this measurement without reference to an original prototype.

You can read more about the research at the following links:


# This article uses the term “billion” is the sense of 1000 million. This is the normal meaning of the word as used in the media.

* This programme is available on BBC i-player until Monday 17 August.

9 thoughts on “New breakthrough for the kilogram”

  1. This article uses the word weight a lot when only the word mass should be used. The weight of a mass would not be expressed in grams, but in newtons.

    “The colder one weighed 998 grams whereas the hotter one weighed 957 grams. ”

    In the above sentence, the word weighed needs to be changed to “had a mass of”.

    “Each time, Big K and its copies were delicately wiped with alcohol and ether, steam-cleaned, and weighed. ”

    Should end with: “and had their mass determined”.

    “In 1992, scientists discovered that Big K had become about 50 micrograms lighter than its copies. Either the copies had gained weight or Big K had lost weight. Scientists could only see the relative weight gain or loss of Big K when compared to its copies. It is also possible that they have all gained or lost weight at different rates.”

    lighter—> less massive
    gained/lost weight —> gained/lost mass
    weight gain or loss —> mass gain or loss
    gained or lost weight —> gained or lost mass

    We do need to be technically correct on this. It is very important.

    Editor. The article has been amended in accordance with Daniel’s suggestion


  2. It would be nice to see this article technically correct. The silicon spheres are 93.75 mm in diameter as far as I can find out. I have little idea of the size of a golf ball but I am sure it is not 94 mm, I have also seen the sphere described as a softball size, I will pass on that one!


  3. The bad news is that the silicon was made in Russia, refined in Germany and machined in Australia.
    Will not adopting that erode all trace of British heritage?


  4. “…it would mean that any laboratory with the right equipment could reproduce this measurement.”
    Given the lengthy process of producing the raw material and the sheer difficulty of producing the prototype, I can’t see there being too many laboratories that could achieve this level of accuracy. And even if they did, surely we’re left with another physical artefact, ie a sphere of silicon, or am I missing something?


  5. Brian AC,

    The golf ball reference is to the master kilogram prototype, not the silicon sphere. Of course it is a cylinder, not a ball.

    I looked up the density of the 90/10 platinum-iridium alloy, it is about 21.53 g/cm³, so the volume of Le Grand Kilogram should be about 46.45 cm³. If a sphere, it would be 44.6 mm in diameter. (Actual shape is cylinder with equal height and diameter, about 39 mm.) A regulation golf ball has a maximum mass, and a minimum diameter, which is 42.7 mm. If your figure for the silicon sphere is correct, a little over 2X larger.


  6. @ Modernman
    You are missing the watt balance. The BIPM has published a complete plan on their website. I am a fairly technical guy and the details go over my head, so I’m not surprised the media can’t do it justice; I can’t either. Perhaps I can give a slightly better outline.

    The kilogram, mole, ampere and kelvin all have their current definitions and four natural constants are experimentally determined, Boltzman’s constant, Planck’s constant, Avogadro’s number, and the elemental charge of the electron. IF (still a big if) we had sufficient confidence in the experimental numbers, metrologists could declare them (like the speed of light) and from the values, redefine the kilogram, mole, ampere and kelvin, equal to current value, but more precisely defined, with a more reproducible recipe. The watt balance inter-relates the other three (at least the BIPM says that, I don’t fully grasp it) and it takes both.

    They have a proforma laid out, using the first five (and generally accepted) figures for each constant, followed xxxx showing the framework for redefinition, they just need better experiments to fill in the x’s.

    I have shot my wad. If anyone has a better understanding, please chime in.


  7. Apropos sophisticated metrology, I came across this BBC program on YouTube about measurement:

    As Spock would say: “Fascinating, Captain!” 🙂


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