# What are kilogram measurement standards

## What is the difference between a realization, a representation and an implementation in metrology?

The reference document for metrological terms is this *International Vocabulary of Metrology* (VIM). The definitions there are carefully worked out, but often they seem a bit obscure to non-metrologists and further comments may be required.

What *realization* and *reproduction* concerns ( *representation* can also be found in the literature on reproduction), its meaning can be found under the term *Measurement standard* :

Realization of the definition of a certain quantity with a specified quantity value and the associated measurement uncertainty as a reference.

In the accompanying notes 1 and 3 it is stated in particular:

NOTE 1 A “realization of the definition of a certain quantity” can be done by a measuring system, a material measure or a reference material.

NOTE 3 The term "realization" is used here in the most general sense. It describes three processes of "realization". The first consists in the physical realization of the unit of measurement from its definition and is the realization

sensu stricto. The second method, called "reproduction", does not consist in realizing the unit of measurement based on its definition, but rather in setting up a highly reproducible measurement standard based on a physical phenomenon, as is the case, for example, when using frequency-stabilized lasers to define a measurement standard for the measuring device, Josephson effect for the volt or the quantum Hall effect for the ohm. The third method is to set a material measure as a measurement standard. It occurs with the measurement standard 1 kg.

Hence the terms denote *realization* and *reproduction* an object or an experiment with certain properties.

To illustrate the difference between a strict realization and a reproduction, let's take the example of a certain quantity, the unit ohm (note that a unit is a quantity, albeit a specially selected one).

First we have to *define,* what that quantity is: This can be done in words, possibly using mathematical relationships affecting other quantities, and adding specifications to *Influencing variables* .

The ohm in the SI is defined as follows [CIPM, 1946: Resolution 2]:

The ohm is the electrical resistance between two points on a conductor when a constant potential difference of 1 volt applied to these points produces a current of 1 ampere in the conductor, the conductor not being the seat of an electromotive force.

So far, so good, or at least so it seems. We are actually a bit stuck because we can realize the ampere or the volt through current and voltage balances, but that *reproducibility* of the ohms realized in this way would be small, around the 10-6 level. And the process would be quite complex. We are saved in 1956 by Thompson and Lampard, who discovered a new theorem in electrostatics [1] which is the electrostatic dual of the Van der Pauw theorem [2,3]. This phrase basically says that you can make a capacitance standard (i.e., realize the farad or one of its submultipliers), the capacitance of which can be calculated accurately (which you cannot do with a parallel plate capacitor, for example). If we have a capacity standard, by the relationships Y. = jωC. and Z. = 1 / Y. We have the standards for admittance and impedance, that is, we have the Siemens and the Ohm, but in the AC regime.

Thus, the strict SI implementation of the ohm as a resistance standard is roughly the following:

- You are building a predictable capacitor (and ten years of your life have passed). Typically a 1 m long calculable capacitor has a capacitance of around 1 pF, which corresponds to a fairly high impedance at a kHz frequency (a short bibliography on the calculable capacitor can be found on this page).
- With the help of impedance bridges you can scale the capacitance to higher values (e.g. 1 nF).
- Use a quadrature impedance bridge to compare the
*Impedance value*of a standard resistor with calculable AC-DC behavior with that of the scaled capacitance. - They calculate the DC value of the resistor.
- Use a resistor bridge to reduce the resistance to 1 ohm.

Once you have done all the experiments (after many years), the realization of the ohm through the above chain of experiments can take more than a month. The main problem, however, is that the reproducibility of the ohm is realized in this way, albeit better than what is available through the realizations of volts and amps, is just at the 10-7-10-8 level.

Then comes the Quantum Hall Effect (QHE). A QHE element realizes one under low temperature and high magnetic field conditions *resistance* (or *Trans resistance* ) With *four connections and one resistor value*R.H. = R.K. / i, where R.K. is a constant that von Klitzing's constant, and i is an integer that as *Plateau index is called* (usually we use the corresponding plateau i = 2). By the late 1980s it was clear that QHE elements could provide resistance standards with much better reproducibility than the other methods described above: at the time on the order of 10-8 - 10-9 ;; on the order of 10-10 - 10-11 these days (two to three orders of magnitude better than with a predictable capacitor). It also turns out that the von Klitzing constant is related to two fundamental constants, the Planck constant and the elementary charge. R.K. = h / e2.

The situation in the late 1980s is therefore as follows:

- A QHE experiment is much easier to do than that of a computable capacitor (and much cheaper).
- The resistance realized by a QHE experiment is much more reproducible than that realized by a calculable capacitor experiment.
- The accuracy of the von Klitzing constant, however, is only at the level of the SI-Ohm realization, ie approximately

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