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Chapter: 1 Units and fundamental constants
    Section: 1.1 Units
        SubSection: 1.1.2 Realization of SI units



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1.1.2 Realization of SI units

The metre

In 1975 the 16th CGPM, having examined results of recent measurements of the frequencies and wavelengths of several laser lines, recommended the use of the value 299 792 458 m s−1 for the speed of light in vacuum. In 1983, further measurements having shown no cause for changing this value, the 17th CGPM confirmed it, and re-defined the metre in terms of it and of the second defined in Section 1.1.1. The new definition, also given in Section 1.1.1, supersedes the definition based on the wavelength of a spectral line of krypton.

In order to facilitate realization of the metre by laboratory workers according to the new definition, CIPM has recommended the procedures to follow. The methods fall into two classes: (1) a time of flight measurement, using the relation l=c.t ; (2) an interferometric measurement, using a wavelength derived from a frequency by the relation λ = c/f. The first method is suitable for long distances, the second for the laboratory and small-scale engineering. To avoid the need for frequency measurements by individual workers using the second method, CIPM has listed the wavelengths: (a) of five stabilized laser radiations, with operating conditions and uncertainties; (b) of the former krypton-86 standard; and (c) of the other discharge tube standards recommended in 1963.

In most cases what is required is not realization of the unit itself, but rather measurement of a particular distance, e.g. the length of a rod or the separation of two optical flats. Interferometers, usually of the Fabry–Pérot or of the Michelson type, are employed to determine the number of waves covering the distance. The krypton-86 line gives satisfactory fringes at path differences less than half a metre, but stabilized lasers, for instance those listed by CIPM, which have much narrower lines, have increased the workable distance to over 100 m.

The kilogram

Realization of the kilogram consists of making weights equal in mass to the mass of the prototype of the kilogram. The prototype is kept by BIPM, and the various nations adhering to the Metre Convention have copies which from time to time they send to Sèvres for comparison with the prototype or with the Bureau’s copies of the prototype.

Methods of adjusting weights are well known, as also are balances for comparing them. Similarly, the production of masses which are multiples of the unit, and their calibration by means of balances, are standard practice. With reliable weights—for example, of platinum–iridium or of stainless steel—and good balances, and with a great deal of care, masses of the order of 1 kg can be compared to 1 in 109.

The second

The second of time was formerly defined as 1/86 400 of the mean solar day. Its present definition in terms of the radiation corresponding to the hyperfine transition of the caesium-133 atom was adopted at the 13th General Conference of Weights and Measures in 1966, the duration of 9 192 631 770 periods of this radiation being chosen in order to secure as close agreement as possible with astronomical definitions.

The transition of the caesium atom is observed in an atomic beam equipment designed to eliminate the major causes tending to broaden or shift the line. The atoms pass through a system of magnets in which they are deflected, and through an electrical resonator supplied with an alternating field at a frequency derived by synthesis from a quartz oscillator. When the applied frequency equals that of the spectral line, transitions between the states are induced and deflection of the atoms is reversed. A resonant line is thus observed and, if the frequency deviates from that of the spectral line, an error signal is produced and applied to the quartz oscillator to pull its frequency to the correct value. The quartz oscillator acts as the working standard, as it did when time was based on astronomical measurements.

Although the unit has been defined in terms of the caesium line, similar lines of the other atoms can be measured with great accuracy, and can then be used as standards. The frequency of the hydrogen line, for example, is 1420 405 751.77 Hz.

It is not necessary for other than highly specialized organizations to own caesium beam or similar standards with which to realize the second, for many countries broadcast frequency and time signals by which any laboratory having a suitable radio receiver can calibrate its wavemeters and electronic counters (see section 2.7.1). These transmissions are, in general, accurate to 1 in 1011, and corrections to 1 in 1012 are published later.

Electric units: the ampere, volt, ohm

Standardizing laboratories must be able to maintain the units of the quantities they deal with. Two reference standards have been extensively used to maintain electric units; they are the Weston cell for the volt, and coils of wire—manganin or other high resistivity, low thermal coefficient material—for the ohm. The ampere follows from Ohm’s law, and the other units from electrical measurements at known frequencies.

The values to be assigned to the two standards must be determined in SI units. This calibration is performed by realizing at least two of the units by methods consistent with their definitions (Section 1.1.1). For the ampere dynamometers or balances have been used, electrometers for the volt, for the ohm self or mutual inductors or a capacitor. In each of these cases some component of the system, coil, gap, etc., has to be measured. A recent improvement is the realization of the SI watt by means of a moving-coil, current balance type of experiment to a very low uncertainty. This, combined with the value of the ohm, enables the ampere and volt to be determined. The equipment for such work is costly and takes many years to build, the measurements are lengthy and laborious. The standards can therefore be calibrated by those so-called ‘absolute’ methods only at intervals of a few years.

At the turn of the century it had been thought that easier and more precise maintenance of standard resistors and cells might be effected by means of electrical equipment specified to reproduce as closely as was then possible the practical, or ‘absolute’, ampere and ohm defined as decimal powers of the CGS units. The mass of silver deposited by electrolysis of silver nitrate and the dimensions of a column of mercury were specified by international agreement, and from 1909 they served as official representations of the practical ampere and ohm. Calibrations made in that way were said to be in ‘international units’—not to be confused with the ‘International System of Units, SI’, whose electrical units are those of the ideal practical system.

Experience soon showed that the construction and measurements involved in realizing those international units were as lengthy and complicated as those required for the ‘absolute’ methods, which were themselves yielding greater accuracy as new techniques and improved facilities became available. Most national laboratories therefore chose to ‘monitor’ their working standards of resistance and electromotive force by absolute measurements although they continued to label them in international units until 1948, when it was decided to revert to the definitions of the practical ampere, volt and ohm as the basis for labelling them. At that time the figures given by BIPM for the differences between the units realized by the two systems were:

1 ‘mean international ohm’ = 1.000 49 Ω

1 ‘mean international volt’  = 1.000 34 V

From these figures, and the results of international comparisons of the standards, each laboratory could relabel its standards of resistance and e.m.f.

During the first half of the century standards laboratories obtained from their absolute measurements or their equipment reproducing the international units, and from the international comparisons carried out under the auspices of BIPM, a precision of maintenance adequate for the needs of industry. Since 1950, however, demands for smaller and smaller uncertainties have been increasing so rapidly as to render a corresponding improvement of absolute methods an almost impossible task. Two phenomena connected with atomic constants (see section 1.2.3) were therefore chosen to calibrate working standards of e.m.f. and of resistance. In the first, predicted by Josephson in 1962, the potential difference between two superconductors separated by a narrow gap assumes discrete values that are multiples of hf/2e, where f is the frequency of electromagnetic waves irradiating the junction, h is the Planck constant, e the electronic charge, and 2e/h is the ‘Josephson constant’ KJ. The second, the quantum Hall effect, discovered by von Klitzing in 1980, is that for certain semiconductors at low temperatures and in high magnetic fields the Hall resistance, defined as the ratio of the Hall voltage to the source-to-drain current, is quantized in steps RK/i where RK, the ‘von Klitzing constant’, is h/e2, and i is an integer.

From the results of the best recent absolute measurements CIPM evaluated the Josephson and von Klitzing constants in SI units, and recommended that from 1 January 1990 national laboratories should maintain their standards of e.m.f. by means of the Josephson effect, using a value of the Josephson constant

   KJ = 483 597.9 (1 ± 0.4 × 10−6 ) GHz/V ,

and their standards of resistance by the quantum Hall effect, using a value of the von Klitzing constant

   RK = 25 812.807 (1 ± 0.2 × 10−6) Ω

The kelvin

The unit of thermodynamic temperature, the kelvin, is defined by assigning the value 273.16 K to the temperature of the triple point of water. The determination of other temperatures in terms of this unit requires measurements, by means of a gas thermometer for example, which can be evaluated in accordance with the thermodynamic definition of temperature. Absolute measurements of this kind are difficult, and their accuracy is usually less than the reproducibility attainable by non-absolute methods based on the fixed points of various substances, and interpolation or extrapolation by instruments such as resistance thermometers, thermocouples, and optical pyrometers. This situation has led to the adoption, by international agreement, of a practical temperature scale, IPTS-68, based on the use of these more reproducible methods, and adjusted to conform to the best available knowledge of the thermodynamic temperatures of fixed points. In January 1990 that scale was replaced by a new one to be known as ITS-90 (see section 2.3.1).

The mole

Although the mole is defined in terms of number of entities, it is usually realized by weighing rather than by counting. A mole of atoms of an element X, for example, is obtained by weighing an amount, in grams, of X, equal to its relative atomic mass (atomic weight); similarly a mole of molecules of a substance Y is obtained by weighing an amount, in grams, of Y, equal to its relative molecular mass (molecular weight).

In the case of perfect gases, 1 mole of molecules occupies the same volume, independently of the particular gas, at any given temperature and pressure. This relation provides a method for measuring equal amounts of substance of perfect gases. The method of volume comparison can be extended to non-perfect gases, because the corrections to apply are well known.

Ratios of amounts of substance liberated in electrolytic reactions can be determined by measuring the corresponding quantities of electricity.
For example, 1 mole of Ag and 1 mole of Cu(1/2) are deposited on a cathode by the same quantity, approximately 96 485 C, of electricity.

The candela

The definition of the candela in subsection 1.1.1 was promulgated by the 16th CGPM, in 1979, to replace that based on black-body radiation. The secondary standards of luminous intensity are tungsten-filament lamps powered by a specified direct current. They are calibrated by comparison with the monochromatic radiation prescribed in the definition, account being taken of their ‘relative spectral luminous efficiencies’, V(λ) (see subsection 2.5.3), recommended by CIPM. This experimentally determined function is a relation between the sensitivity of the average eye and the wavelength of the light falling on it. There are two such functions, V(λ) for photopic vision, V'(λ) for scotopic vision. By their means photometric quantities are defined in purely physical terms as quantities proportional to the sum or integral of a spectral power distribution, weighted according to a specific function of wavelength.


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