Redefinition of the International System of Units

Martin Hudlička Czech metrology institute [email protected]

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

• SI history • Measurement traceability • The need for change of SI units • Preparations for change – the kilogram – the mole – the ampere – the kelvin • Consequences for users • Further reading

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• various units used for thousands of years, some of systems stable over time • mostly based on nature or human body measures (which were thought to be constant)

– Babylonian system (example – units of length)

source: Wikipedia

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

– Egyptian system

measurement of length, volume, mass, time

bronze capacity weight measure standard

source: Wikipedia

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• many other official measurement systems for large societies (Olympic system of Greece, Roman system, ...), some of the systems adopted into later systems • English system – measurements used in England up to 1826, huge number of units for various areas – liquid measures (dram, teaspoon, tablespoon, pint, gallon, ...) – length (digit, finger, inch, nail, palm, hand, ...) – weight (grain, pound, nail, stone, ounce, ...) • Imperial system (post-1824) used in the British Empire and countries in the British sphere of influence

credit: D. Pisano, Flickr

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• United States customary units – based on English units, however significant differences exist

– example: liquid volume

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• major problem – multiple units, conversion between units usually not decimal credit: METAS

elbow

foot span

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• major problem – multiple units, conversion between units usually not decimal

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• the metric system developed from 1791 onwards by a committee of the French Academy of Sciences (use of decimal system and prefixes to express multiples), many countries joined, metre and kilogram prototypes owned by French government • 1875 – Metre convention, signed by 17 countries (only the metre and the kilogram), a set of 30 prototypes of the metre and 40 prototypes of the kilogram made from 90% Pt and 10% Ir alloy manufactured in 1889

source: Wikipedia

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• one kilogram = the same mass as one litre of water (atmospheric pressure, temperature 4 °C) • one metre = distance between two lines marked on the bar (originally ~1670 derived from a pendulum, from ~1790 defined as 1/10 000 000 of the distance between the North Pole and the Equator going through Paris) • metre definition not ideal (meridian not uniform across the world)

source: PTB museum

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• the General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), established in 1875, brought together many international organisations to establish the definitions and standards of a new system • ~1900 - three different systems of units of measure existed for electrical measurements – CGS (centimeter, gram, second) system for electrostatic units, known as Gaussian or ESU – CGS-based system for electromechanical units (EMU) – system based on units defined by the Metre Convention • 1921 – attempt to add other physical units to the Metre convention too (especially electrical quantities) • ~1945 - number of different systems of measurement used throughout the world (metric system variations, U.S. customary system, Imperial system) – change needed

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• 1960 - the 11th CGPM synthesised a set of 16 resolutions, the system was named the International System of Units (Le Système International d'Unités, SI) • the metre, kilogram, second, ampere, degree Kelvin, and candela • base units derived from invariant constants of nature (e.g. speed of light in vacuum), triple point of water and one artefact (kilogram) • derived units - defined in terms of base units or other derived units (e.g. 1 Pa = kg·m-1·s-2, 1 Ω = kg⋅m2⋅s−3⋅A−2 etc.) • 1971 – mole added to the six units

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• the 1960 system of units valid until 2018, the “new” system effective from May 2019

credit: METAS

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the kilogram (mass) The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. • 1 international prototype (Paris) • 6 sister copies (Paris) • 10 working copies (Saint-Cloud, France) • national prototypes (about 69 pieces in various countries) • comparison to the international prototype every ~40 years

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the metre (length) The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second. • can be realized in three ways – measurement of time which the light needs to travel the measured length – using of wavelength of radiation, frequency of which is measured – using a wavelength of a primary standard – laser stabilized to one of transitions, whose values and uncertainties are given by BIPM

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the metre (length) • Czech Republic – quantum length standard based on helium- neon laser ( = 633 nm,  = 612 nm and  = 543.5 nm) stabilized to hyperfine iodine transitions

credit: CMI CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the metre (length) • frequency of laser compared to the caesium standard by means of frequency comb generator and interferometry

- beat signal measurable in Hz, kHz or MHz range (depending on laser wavelength)

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the second (time) The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K. • Czech Republic – Institute of Photonics and Electronics , Czech Academy of Science • use of two commercial 5071A caesium clocks (relative stability ~5·10-13 to the ideal realization) credit: CAS CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the second (time) - atoms emit and absorb electromagnetic waves - transition between two energy states -> photon is emitted or absorbed with

frequency f0 = (E2–E1)/h - atoms prepared in one state, population of the other state registered

- f0 ~ 9.2 GHz for caesium - definition introduced in the 1960s, proved to be stable over time

credit: PTB CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the ampere (electric current) The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per metre of length.

credit: PTB

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the ampere (electric current) • direct realization – current balance (Ampère, ~1900)

• Lorentz force acts between moving (blue) and non-moving (red) coil, compensated by gravitational force • relative uncertainty ~5 ppm, dependent on accuracy of kg NIST, 1912 • non-uniform current distribution in wires and magnetic field distribution in space CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the ampere (electric current) • indirect realization – Ohm’s law I = U/R, Josephson effect and quantum Hall effect enable very stable realization of units [volt] and [Ω] • not part of SI, thus not recognized as a realization -> see later in the “quantum SI”

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the kelvin (thermodynamic temperature) The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: 0.00015576 mole of 2H per mole of 1H, 0.0003799 mole of 17O per mole of 16O, and 0.0020052 mole of 18O per mole of 16O.

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the kelvin (thermodynamic temperature) • direct realization of one kelvin (t [°C] = T - 273.15) – triple point of water • Czech Republic – temperature scale -196 °C to +1048.6 °C (triple points and melting

points of various elements H20, N, Hg, Cu, ...)

credit: CMI

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the mole (amount of substance) The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is 'mol'. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. • subject to criticism since 1971, it is rather a parametric unit

• closely related to Avogadro constant NA

https://www.bipm.org/utils/en/pdf/SIApp2_mol_en.pdf

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the candela (luminous intensity) The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

credit: PTB - historically – luminous intensity I compared with a defined light source (candle, later special lamps) using a detector (human eye) - one direction and sufficiently narrow beam of light assumed

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• definition of SI units (before 2019):

the candela (luminous intensity) • today’s direct realization: radiation from a confined cavity in thermal equilibrium (Planck’s law) using absolute cryogenic radiometer for various  (visible/UV/IR radiation)

credit: CMI

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• Metre convention in the world

60 member states 42 associate states 4 international organizations

metric system was officially adopted almost everywhere in the world (although alternative units still may be used as a force of habit)

few exceptions: USA, Myanmar, Liberia

(note: USA was one of the first Metre convention signatories back in 1875, but source: Wikipedia still they do not use it !!!)

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

https://www.zmescience.com/other/map-of-countries-officially-not-using-the-metric-system/ CTU FEE K13117 Departmental seminar, 12th February 2019, Prague SI history

• confusion between units systems may cost money

1999 – NASA lost a $125 million Mars https://en.wikipedia.org/wiki Climate Orbiter (one piece of /Mars_Climate_Orbiter software used US customary units, while other used SI units) -> discrepancy between desired and actual orbit insertion altitude

https://en.wikipedia.org/wiki 1983 - Air Canada Boeing 767 ran /Gimli_Glider out of fuel more than 12 000 metres above the ground; the fuel was calculated in pounds instead of kilograms; landed securely (“glider”) CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Measurement traceability

• measurement traceability = an unbroken chain of comparisons relating an instrument's measurements to a known standard

http://www.muelaner.com/wp-content/uploads/2013/07/Traceability-NMIs.png

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Measurement traceability

• measurement traceability according to SI - impractical

credit: NIST, https://www.nist.gov/image-20360 CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Measurement traceability

• example: traceability of S-parameters – calculable impedance standards (beadles air lines, flush shorts, offset shorts) used to determine system error coefficients of a VNA – dimensional properties and material properties measurement

credit: METAS

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Measurement traceability

• example: traceability of S-parameters

- different possibilities to define the reference plane (see M. Zeier et al 2018 Metrologia 55 S23) - advanced modeling of the standards based on measured dimensions, incl. metal conductivity, surface roughness etc.

3.5 mm air line

measured outer conductor inner credit: METAS, CMI diameter of a 3.5 mm air line

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Measurement traceability

• key and complementary comparisons

countries belong to one or more regional metrology organizations (RMO) – Euramet, Afrimets, Coomet, Gulfmet, SIM, APMP

credit: BIPM

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• main motivation for change of SI – the prototypes of the kilogram change their weight (~tens of μg relative to the 1889 values due to contamination (+) and cleaning (-)) – the ampere is defined by means of an idealized and unrealistic measurement setup – the kelvin, triple point of water influen- ced by impurities and by the isotopic composition of the water; as temperature is not an additive quantity, additional definitions are necessary in order to expand the temperature scale beyond the triple point of water source: Wikipedia CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• current SI: values of the fundamental constants specified; our measurement capabilities are reflected in these values • new SI: the seven base units are defined by determining seven “defining constants” that contain these units

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• the idea not new – already in 1870, James Clerk Maxwell was concentrating more on atomic quantities to provide a definition of the units

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• 1900 – Max Planck made use constants when he formulated his law of radiation

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• the quantities chosen as defining constants are quantities that can be measured with great precision in the old SI (relative uncertainties ideally around 10–8) • the gravitational constant is not one of these quantities, as it is known only with a relative uncertainty of 10–4 • definition of the second via the cesium frequency was kept (present-day caesium clocks rel. uncertainty ~10–16, optical atomic clocks even have stabilities of 10–18, yet none has proven to be clearly superior) source: NPL

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• the SI revision does not pretend to be for daily use • milestone in the history of civilization – from the Middle Ages until 18th and 19th centuries the units were used regionally • the numerical values of seven unit-related constants – the “defining constants” – are to be specified exactly • the seven base units (s, m, kg, A, K, cd, mol) will no longer be directly but indirectly defined • numerical values of constants may still change if such changes are necessary due to improved experimental results • even a Martian could understand what a kilogram is

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• the new “quantum” SI

https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague The need for change of SI units

• the new “quantum” SI

https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change

• how to realize “new” SI units?

• for the second and the metre (and derived units the ohm and the volt) – extremely precise measurement procedures exist (caesium atomic clock, light propagation and the quantum Hall

effect/Josephson effect), traceable directly to ΔνCs, c, h and e • for the kilogram, the mole, the ampere and the kelvin, it was necessary to develop measurement procedures of comparable precision • CODATA – provides set of internationally recommended values of physical constants; target relative uncertainty from different experiments must be consistent • 20 May 2019 – the implementation day of the “new” SI units (world day of metrology) CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change

• CODATA internationally recommended values of fundamental physical constants https://physics.nist.gov/cuu/Constants/index.html

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

• SI history • Measurement traceability • The need for change of SI units • Preparations for change – the mole – the kilogram – the ampere – the kelvin • Consequences for users • Further reading

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the mole

• attempts to determine Avogadro constant using silicon (3 isotopes) since 2003 • in highly enriched silicon, isotopes 29Si and 30Si are just impurities which can be determined by mass spectroscopy; approx. 5 kg single silicon crystal used for experiments -8 • 2011 – rel. uncertainty ~210 credit: PTB achieved under extreme experimental challenges • number of atoms in a 1 kg silicon sphere counted • the Avogadro’s constant and Planck’s constant determined in one experiment • at least 3 independent experiments required by 2018

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the mole

• Avogadro’s constant NA and Planck’s constant h related via −10 molar Planck’s constant NAh = 3.9903127110(18)10 Js/mol (rel. measurement uncertainty of 4.5  10-10)

Mu = molar mass constant  = fine-structure constant

R = Rydberg constant e Ar = relative atomic mass of electron

• Rydberg constant, speed of light and fine-structure constant determined with much higher accuracy than Planck’s constant

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the mole

• number of atoms in a silicon sphere 1). number of atoms determined from sphere volume and volume of the unit cell 2). sphere weighed once, determining the mass of a silicon atom

Problems:

• disturbing SiO2 “coat” • crystal temperature to be known within 0.001 K (lattice expansion) • atomic masses of 28Si, 29Si and 30Si must be linked to 12C, the reference value for atomic masses credit: PTB (Penning trap)

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the mole

• international Avogadro project (2004 – 2011)

- impurities: X-ray interferometry - oxidized surface: X-ray fluorescence analysis and many other techniques - sphere volume: optical interferometry using spherical waves (e.g. PTB Germany) or plane waves (e.g. NMIJ Japan) - sphere mass: both air and vacuum weighing using special artefacts derived from the 1 kg prototype - each sphere price ~1 M€

credit: PTB

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

• two different methods for realization of the kilogram

– silicon sphere (first experiments at PTB, Germany) – see the “new”mole realization

– watt balance (first experiments at NPL, United Kingdom, and NIST, USA), experimental method of linking electric quantities to the kilogram, the meter and the second

– both reached relative uncertainty of ~210-8 credit: PTB, NIST

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

• watt balance – Brian Kibble (1970s) had an idea of an improved current balance – 1st test: force which acts on a current-carrying conductor in a magnetic field is compared to the weight force of a mass standard – 2nd test: the same arrangement, the electric conductor is moved in the magnetic field and thus a voltage between its ends is generated – if the equations of these two tests are combined (magnetic induction eliminated), a relationship between current, voltage, mass, gravitational acceleration and speed is created – quantities which can be measured with much higher accuracy than the magnetic induction – first experiments NPL (UK), NIST (USA), later METAS (Switzerland) and other institutes joined the race; the same principle realized using different setups – extreme experimental effort to achieve consistent rel. unc. ~210-8 – great legacy of B. Kibble (1938-2016) – Kibble balance

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

credit: BIPM

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

both sides of the equation unit watt

credit: BIPM

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

• electrical quantum effects: U ~ h/e, R ~ h/e2

푓 2푒 ℎ n , n = integer quantum numbers 푅 = 1 2 = 2 f = frequency of the Josephson device 푈 푛1ℎ 푛2푒

setting n1 = n2 = 1 4푚푔푓 fg = microwave frequency of the voltage ℎ = meas. in the gravitational mode 푓 푓 𝑔 푚 fm = dtto in the moving coil mode

the watt balance enables the measurement of Planck’s constant h

M. Gläser, M. Borys, Rep. Prog. Phys. 72 (2009) 126101 CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

• different setups of the watt balance – NIST (USA)

- superconducting magnet generates the magnetic field - Michelson interferometer provides the velocity

https://www.nist.gov/publications/details-1998-watt-balance-experiment-determining-planck- constant CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kilogram

• different setups of the watt balance – BIPM (France)

- moving coil mode and gravitational mode combined into single mode - mass of other weights – chain of comparison measurements - comparison with the international 1 kg prototype provided as well

A. Picard, et al., The BIPM Watt Balance, IEEE Trans. Instrum. Meas. 56 (2007) 538-542.

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

• the ampere realized by two procedures compatible with each other

– Ohm’s law U = R I, current I determined by measuring R using the quantum Hall effect and the U using the Josephson effect (better suited for generation of “high” currents pA – μA)

– electronic circuit that measures the electric current by counting the electrons that pass the circuit in a certain time interval, traced to

elementary charge e and the caesium frequency ΔνCs (better suited for “low” currents fA – pA)

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

• the ampere realized using Ohm’s law

quantum Hall effect T = 0.35 K (helium)

RH = 25812.807 Ω (and its integer divisors) B ~18 T (n=1) B ~10 T (n=2) etc.

credit: PTB

credit: CMI

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

• the ampere realized using Ohm’s law

T = 3.6 K (helium) Josephson effect – weakly coupled superconductors, tunnel junction external magnetic field (alternating current) is applied to the structure, which creates precise voltage (U -> f conversion)

credit: CMI

credit: PTB

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

• the reproducibility of the quantized voltage and resistance values was better than the accuracy with which the unit of the

ampere could be realized -> KJ-90 = 483597.9 GHz/V and RK-90 = 25812.807 Ω established in 1988 • since 1990s – ampere realized using QHE and JE was not treated as realization of the unit, but only as a reproduction (leaving SI) • new SI – an elegant way out:

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

• second realization of the ampere: new definition based on flux of electric charge -> electronic circuit needed to transport single electrons in a controlled way, I = n·e·f • single-electron transport developed since 1980s

- adding electron to a conductor -> energy must be applied - the smaller the “charge island”, the more energy needed - low temperatures (0.1 K for 1 μm structure) -> Coulomb blockade, the added energy cannot be applied by means of thermal excitation

credit: PTB

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

electrons “trapped” (localized) by means of potential barriers using nanotechnology semiconductors; potential barriers can be generated perpendicularly to the current flow

1). tunnel junctions (thin insulator layers in a conductor)

2). quantum dots, controllable potential barriers in semiconductors

credit: PTB

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the ampere

• single-electron pumps used to transport single electrons in a controlled manner

credit: PTB

currents typically < 100 pA

- all three voltages zero -> no electrons can flow - stream of voltages sent across gate electrodes -> electrons travelling from island to island - due to statistics – some tunneling occurs missed for f > 100 MHz -> more advanced SETs with controllable potential barriers exist (see Further reading) CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kelvin

• Maxwell-Boltzmann velocity distribution

nitrogen molecules particle speeds probability distribution in idealized gases

quantity which is characteristic of the distribution is the mean microscopic thermal energy kT

fixing k, the kelvin will be linked to the unit of energy, joule

microscopic thermal energy kT not directly accessible -> macroscopic quantities correlated with the thermal energy must be measured

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kelvin

• several “primary” thermometer principles (do not require calibration), two of them explained here

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kelvin

• acoustic gas thermometer – the temperature-dependent speed of sound is measured in a gas; this speed of sound is proportional to (kBT)1/2 – speed of sound of noble gases measured using a spherical resonator – problems: purity of the meas. gas, extrapolation to zero pressure, position of acoustic transducers and receivers

credit: PTB

M. Moldover, et al., Acoustic gas thermometry, Metrologia 51 (2014) R1–R19.

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kelvin

• dielectric constant gas thermometer – determining at a constant temperature the pressure-dependent density of helium with reference to its dielectric constant – polarizability of the helium calculated with rel. unc. <10-6 in the last years; as the polarizability is low, the  is measured from the relative change of capacitance of a capacitor filled with helium (p = 7 MPa) and evacuated – problems: deformation of the capacitor due to pressure

credit: PTB

C. Gaiser, et al., Dielectric-constant gas thermometry, Metrologia 52 (2015) 217–226. CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Preparations for change – the kelvin

• CODATA comparison of different experiments

AGT = acoustic gas thermometry DCGT = dielectric constant gas thermometry JNT = Johnson noise thermometry

strict relative uncertainty criteria must have been met proved by many experiments in order to accept the new value (also for other constants)

P. J. Mohr et al., Metrologia 55 (2018) 125

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Consequences for users

• main consequences – the last artefact (1 kilogram) will be replaced – electrical measurements fully covered by SI (exact relationship between SI and CGS broken for electrical quantities; avoiding CGS magnetic units) – triple point of water will become experimentally determined – mole will no longer link to mass (role of 12C ends)

• should be sufficient at least for the 21st century, unless... – much better atomic clocks will be developed – new quantum effects will be discovered – new physical theories reducing the number of independent physical constants will be discovered

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Consequences for users

• consequence for “normal” users – none, the uncertainties far below commercial measurement systems • consequence for students – rewritten textbooks • consequences for high-precision measurements

– KJ will change by ~0.1 ppm – will affect voltage references slightly, KJ = 2e/h

– RK will change by ~0.02 ppm – only affect the QHR realizations, 2 RK = h/e

휇0 – μ0 and 0 will become experimentally determined 푍0 = 휀0 -10 -7 -1 μ0 = 4[1+2.0(2.3)10 ] 10 H·m 2ℎ uncertainty u (μ ) = u () since 휇 = 훼 ( = fine structure constant) r 0 r 0 푐푒2 – voltage and resistance uncertainties <0.1 ppm will be fully traceable to SI

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Consequences for users

• likely shifts in the values of the SI electrical units with respect to those based on the 1990 values

N. Zimmermann et al., The Redefinition of the SI: Impact on Calibration Services at NIST, NCSLI Measure J. Meas. Sci., vol. 10, no. 2, 2015

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Consequences for users

• electrical units in CGS – μ0 and 0 do not exist here

Ampere’s law

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Consequences for users

• electrical units in CGS

– Faraday’s law of electromagnetic induction

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Overview

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Further reading

D. Newell et al., The CODATA 2017 Values of h, e, k, and NA for the Revision of the SI, Metrologia, vol. 55, no. 1, pp. L13-L16, 2018.

N. Fletcher, et al., Electrical Units in the New SI: Saying Goodbye to the 1990 Values, NCSLI Measure J. Meas. Sci., vol. 9, no. 3, pp. 30-35, 2014.

R. B. Goldfarb, The Permeability of Vacuum and the Revised International System of Units, IEEE Magnetics Letters, vol. 8, pp. 1-3, 2017, Art no. 11100003.

J. R. Pratt, How to Weigh Everything from Atoms to Apples Using the Revised SI, NCSLI Measure J. Meas. Sci., vol. 9, no. 1, March 2014

F. Piquemal, et al. , Metrology in electricity and magnetism: EURAMET activities today and tomorrow, Metrologia 54 (2017) R1

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Further reading

H. Scherer, H. W. Schumacher, ANNALEN DER PHYSIK 2019, 1800371. https://doi.org/10.1002/andp.201800371

B. Andreas et al., Determination of the Avogadro constant by counting the atoms in a 28Si crystal, Phys. Rev. Lett. 106 (2011) 030801.

Y. Azuma, et al., Improved measurement results for the Avogadro constant using a 28 Si-enriched crystal, Metrologia 52 (2015) 360–375.

I. Busch, et al., Surface layer determination for the Si spheres of the Avogadro project, Metrologia 48 (2011) 62–82.

A.Picard, et al., State-of-the-art mass determination of 28Si spheres for the Avogadro project, Metrologia 48 (2011) 112–119.

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CTU FEE K13117 Departmental seminar, 12th February 2019, Prague Thank you for attention

CTU FEE K13117 Departmental seminar, 12th February 2019, Prague