The Electronic Kilogram • Introduction to the NIST-4 Watt Balance FEA Results

Home , Prototype

The Planck constant, h, and the redefinition of

the SI Stephan Schlamminger National Institute of Standards and Technology (NIST)

MASPG Mid-Atlantic Senior Physicists Group 09-19-2012 Outline

1.The SI and the definition of the kg

2.The principle of the Watt balance

3.The past, the present, & the future of the Ekg A brief history of units

I. Based on man.

107 m II. Based on Earth.

c III. Based on fundamental constants. ħ The current SI†

K A

mol s

cd m kg

† Système international d’unités The current SI†

μo

K A

∆ν mol s 133Cs

cd m kg

c † Système international d’unités The new SI† k e

K A

NA ∆ν mol s 133Cs

cd m kg

Kcd c

† Système international d’unités h Why fix it, if it is not broken? The kilogram

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. (1889) The kilogram

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. (1889)

CIPM 1989: The reference mass of the international prototype is that immediately after cleaning and washing by a specified method. Cylindrical height:39 mm, diameter: 39 mm Alloy 90 % platinum and 10 % iridium International Prototype: IPK Official Copies: K1, 7, 8(41), 32, 43, 47 BIPM prototypes for special use: 25 for routine use: 9,31,67 National prototypes: 12,21,5,2,16,36,6,20,23,37, 18,46, 35, 38, 24, 57, 39, 40, 50, 48, 44, 55, 49,53 distributed 56, 51, 54, 58, 68, 60,70, by raffle 65,69 New prototypes 67,71,72,74,75,77-94 Other prototypes 34

USA: K4 (1890) check standard K20 (1890) national prototype K79 (1996) 1889: -39 μg K85 (2003) watt balance 1950: -19 μg K92 (2008) 1990: -21 μg

Let’s look at washing

Change of mass relative relative #9 #31to Changemassandof The cleaning procedure takes 1 µg/year for each year since the last cleaning procedure occurred. How stable is the kilogram?

The mass of 6 out of 7 has in- creased Shortcomings

• Can be damaged or destroyed. • Collects dirt from the ambient atmosphere. • Cannot be used routinely for fear of wear. • IPK changes by 50μg/100yrs relative to the ensemble of PtIr standards. • The drift of the world wide ensembles of PtIr standards is unknown at a level of 1mg/100yrs. • Can only be accessed at the BIPM. • Cannot be communicated to extraterrestrial intelligence.

The kilogram influences other units

derived unit base units J kg m2 1 V  1 1 As As3 Two advances in metrology in “recent years” 1. Josephson Effect

Josephson Junction (JJ) array

2. Integral Quantum Hall Effect

Quantum Hall Resistor Josephson Junction

• Weak link between two superconductors

  Y1A1e 1 Y2A2e 2

21 • Electrical properties +1 h 1 d V V V  2e 2 dt n = 0 Ic I I h -1 or, V  f 2e DC only with AC 16 JJ array

19 mm

20208 Junctions -14 to +14 Volts typical: f=14..75 GHz Voltage Quantum Hall Effect

2 VH B RH = h/ie  RH   I eNs T = 278 mK I = 0.255 mA  eB  Ns   i  h 

 h  RH     ie2  Two new constants

• Josephson constant • von Klitzing constant

2e K J   h h RK  2  e GHz ( 483597.870  0.011) ( 25812.8074434  0.0000084 )  V

K J 90  RK 90  GHz 25812.807 483597.9 V A schism in metrology

SI units conventional units (base and derived)

kg A A90 m s V Ω90 V90 … W Ω W90 … … Difference between SI and 90 units

-9 -9 1 V = ( 1 - 62.0 x 10 ± 22.7 x 10 ) V90

-9 -9 1 Ω = ( 1 - 17.2 x 10 ± 0.3 x 10 ) Ω90

-9 -9 1 A = ( 1 - 44.9 x 10 ± 22.7 x 10 ) A90

-9 -9 1 C = ( 1 - 44.9 x 10 ± 22.7 x 10 ) C90

-9 -9 1 W = ( 1 - 106.9 x 10 ± 45.5 x 10 ) W90

-9 -9 1 F = ( 1 + 17.2 x 10 ± 0.3 x 10 ) F90

-9 -9 1 H = ( 1 - 17.2 x 10 ± 0.3 x 10 ) H90

http://physics.nist.gov/cuu/Constants/index.html Redefinition by committee

Oct 2011 vote on Draft resolution

passed

4 year yes Ready to new SI wait redefine

no The current SI m The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second kg The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. s The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. A 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 meter apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per meter of length. K The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. mol 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.” cd 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. The “new” SI Based on seven reference constants.

133 ground state hfs 9.192 631 770 ·109 s-1 ∆ν( Cs) c speed of light 2.99 792 458 ·108 ms-1 h Planck’s constant 6.626 069 57* ·10-34 kg m2 s-1 e elementary charge 1.602 176 565 ·10-19 As k Boltzmann constant 1.380 6448 ·10-23 kg m2 s-1K-1 Avogadro constant 6.022 141 29 ·1023 mol-1 NA luminous efficacy 6.83 ·102 lm kg-1 m-2 s3 Kcd

* The exact numerical value will be determined by CODATA at the time of the redefiniton. The above values are today’s CODATA values. Redefinitions do happen

Adjustments of national voltage standards 1 GHz 0 1990 volt representation K J 90  483597.9 -1

V -2

5 -3 USSR -3.565 ppm USSR 4.5 ppm

4 -4 8 ppm 8 3 -5

2 -6 France -6.741 ppm France 1.32 ppm 1 -7 ppm Other -8.065 ppm 0 1972 volt representation -8 countries -1 US -1.2 ppm -9 US -9.264 ppm -2 -10 -3 -4 1972 1990

B.Taylor and T.Witt, “New International Electrical Reference Standards Based on the Josephson and Quantum Hall Effects,” Metrologia, 26, 47-62 (1989) Outline

1.The SI and the definition of the kg

2.The principle of the Watt balance

3.The past, the present, & the future of the Ekg The principle of the Watt balance

force mode velocity mode

m B B g l l F v v F

V I mg V V mg  NevB  IlB lB  evB  eE  e lB  I l v The Watt equation mg v V I The Watt equation mg v V I

force mode velocity mode

Virtual power ! Connection to Planck’s constant velocity mode

programmable josephson voltage system

Nullmeter traceable frequency fV

h h mV V  c f  2.066.. V V 2e 2e GHz Connection to Planck’s constant force mode programmable jvs

traceable frequency fR

B adjustable current source R Nullmeter

R is calibrated against a Quantum Hall Resistor RK h cRV f R VR 2e h I   R  c R  c R h R K R 2 c e R e2 Combining the two modes

h c f V c f h RV R c c V I V R  V V 2e  V RV f f h R 2e h c 4 R V c R R e2 c c f f m  V RV v VR h 4cR gv

Mass can be defined in terms of Planck’s constant. Gravity

Absolute gravimeter, can measure g to 1 ppb Gravity

1685

2012 North American Watt Balance

Absolute Gravity Comparison A a

1675 n

O C

(NAWBAG-2012) v

l a

G 1665 µ

Feb6-Feb10 2012

I N 1655

1645 Worldwide Watt Balances (WWB)

METAS (Switzerland) BIPM (France)

LNE(France)

NIM (China) MSL (New Zealand) KRISS (South Korea) PTB (Germany) ? NPL (UK)/NRC (Canada) 35 A digression… … ...

• There is another way to measure h • The International Avogadro Project

PTB, Germany NMIJ, Japan NMI, Australia METAS, Switzerland NIST, US INRIM, Italy BIPM IRMM, Belgium

Si sphere (Avogadro project) Unit cell (8 atoms per cell) A single crystal of Si

m,v

a m M 0   V  mol V  a3  83/ 2 d 3 V mol  uc 0 220

Vmol M mol V N A  8  8 3/ 2 3 Vuc m8 d220 Measurements needed

isotopic abundance & mass physics and chemistry spectroscopy of bulk and surface

volume determination

Vmol M mol V N A  8  8 3/ 2 3 Vuc m8 d220

XRD

mass metrology Measurements needed

isotopic abundance & mass physics and chemistry spectroscopy of bulk and surface

volume determination

Vmol M mol V N A  8  8 3/ 2 3 Vuc m8 d220 Measurement completed in 2003 XRD Largest contribution to the uncertainty: measurement of the isotopic abundance mass metrology

Solution: Use enriched Si. Pictures

Si sphere

5kg 28Si crystal grown by the float zoning method Connection between h and NA

m c 2 R  e  2h Connection between h and NA

m p

2 2 mec mec M p / N A R   2h 2hmp Connection between h and NA

m p

2 2 2 mec mec M p / N A M Pc R    2h 2hmp 2h(mp / me )N A Connection between h and NA 8.9·10-11 -12 5·10 fixed 3.2·10-10 2 M Pc R  2h(mp / me )N A

4.1·10-10 Outline

1.The SI and the definition of the kg

2.The principle of the Watt balance

3.The past, the present, & the future of the Ekg The birth of the Watt balance

Atomic Masses and Fundamental Constants 5ed J H Sanders and A H Wapstra (New York: Plenum), p. 545-51 (1976). NPL-1

B. P. Kibble, I.A. Robinson, J.H. Beliss, metrologia 27, 173 (1990). One shortcoming

velocity mode (wire cold) weighing mode

B B

l1 l2

V ohmic heating mg  Nl B  l2 B v 1 I change in temperature

l2  l1(1 T) change in l Copper: α=16.6 10-6 K-1 I=10 mA, R=100 Ω

The solution (idea by P.T. Olsen) cold coil warm coil

r1 B(r) = C/r r2 B(r) = C/r

V C mg C  N2π r  N2πC  N2π r  N2πC 1 I 2 r v r1 2 The NIST way

Solenoid current cw 2r

NIST-1, conventional EM 3 kW, 8A, 0.003T d superconducting EM 5A, 0.1T h

Solenoid current ccw NIST-2 region, where B(r)=C/r balance in air NIST-3 NIST-3 Apparatus

51 The weighing mode (in more detail)

1.0kg 0.5kg 0.5kg

I+ I- The weighing mode (in more detail)

I _ N2πC  mg  I N2πC

mg  (I _  I )N2πC

Two advantages:

1.) Substitution method

2.) Current is halved, 1.0kg 0.5kg 0.5kg Heating is quartered

I+ I- The velocity mode (in more detail)

AC fields

moving coil fixed coil V 10 cm 9 cm 8 cm 7 cm 6 cm 5 cm 4 cm 3 cm 2 cm Band of 70 Pt-W wires 1 cm Voltage velocity measurement NPL-2 = NRC-1

• equal arm beam balance • design with 3 knives • SmCo permanent magnet • radial field NRC-1 magnet design The present! The present!

We will figure this out! NIST-3 v2.0

• A new, (mostly independent) team will measure a last data point with NIST-3.

• Blind measurement: The mass group will measure our masses. But they will add a to us unknown offset (-500ppb…500ppb) to the values.

Relevance

Timeline

now, 09/01/12

01Oct 2011 01Oct 2013 01Oct

3 -

Solenoid cooled down

3 - Alignment Assessment Planning

first quarter of data NIST with Order of uncertainties ≈100 x10-9 hardware

New Change of electrical • current source grounding • vacuum pumps New PJVS • knife edge Upgrades to • Interferometers Comparison of absolute gravimeter

Comparison of Data analysis, systematic tests

JJ Voltage Std. independent data point

new team starts working on NIST on working newstarts team

Goal: An An Goal: Independentmeasurement uncertainty & analysis Changes

Power Filters PJVS

GND STAR

Autocollimator for laser alignment Changes continued

Stabilization of SC current

Zener Standard Cell

Current source

In situ laser calibration Laser for velo meas

I2 stabilized HeNe Results

JJA grounded

many experiments

Bad connection to current source In the meantime we are building NIST-4 NIST-3 NIST-4 “The Thoroughbred is a horse breed best known for its use in “The Clydesdale is a cold blooded horse appreciated for its horse racing. Thoroughbreds are considered "hot-blooded" strength, style, and versatility. Like all cold-blooded horses horses, known for their agility, speed and spirit.” the Clydesdale has a stolid demeanor and is not suitable for sports other than hauling or pulling.”

• Watt balance to measure h • Watt balance to realize the kg • Optimized for the best measurement of h • Optimized for reliable operation • Highly sophisticated • Ease of Use • Costly to operate and maintain • Low maintenance • Lifetime: ≈10 years • Lifetime: >30 years picture source: wikipedia.org NIST-4

• Design has started. • Baseline design: Wheel balance with permanent magnet system. • Magnet is designed and plans are at a manufacturer • Prepare the infrastructure. • Think about alternative design ideas.

NIST-4 magnet

• SmCo magnet rings provide field.

• wide gap (3cm) 15 cm long.

• symmetric design, field minimum.

• Field ≈0.54 T.

• Magnet separates.

• full iron enclosure provides shielding

8 parts:

1-3 outer yoke

Top view 5-7 inner yoke (not to scale) 4 & 8 magnets Access to the coil To access the coil, the magnet separates:

upper third

middle third

lower third

Total mass of the magnetic circuit: 850 kg Mass of one magnet ring: 44 kg Mass of the lower part of the magnet: 330 kg FEA results

• calculated by MagNet • Flux in Iron < 0.9 T

• Field in gap is 0.54 T • coil radius is 21.5 cm F  N2 rBI F N  N0.732 I A F N  500..1000 I A

N  680..1370 Field quality Vacuum Vessel is designed Magnet in vacuum vessel NIST-4 next steps

• Prepare infrastructure (crane, clean power, vacuum pumps). • Building a device to verify the magnet. • Work on an alternative mechanical design. • Design load lock for the masses.

Outline

1.The SI and the definition of the kg

2.The principle of the Watt balance

3.The past, the present, & the future of the Ekg Thank you for your attention!

Jon Pratt, group leader Stephan Darine Frank Ruimin David Schlamminger Haddad Seifert Liu Newell part-time:

Leon Ed Shawn Chao Williams Zhang The End Summary

• Current definition of the kilogram. • Shortcomings of the definition. • Quantum electrical metrology. • Principle of the Watt balance (velocity mode, weighing mode). • Account of the past, present and future of the electronic kilogram • Introduction to the NIST-4 Watt balance FEA results

• Top 2/3 of the magnet. • The lower 1/3 is a meter below.

• At the beginning we can use the top 2/3 of the magnet to tweak our system. We should be able to make a complete Watt balance experiment with that, until we have settled for an induction coil. • The field is not as uniform. • Shielding is not perfect.

Field quality of the upper 2/3 External Demagnetizing field on PM

slopes -μom recoil curve: B(H)  Br  m0mr H L1 B L2 B(H)  m mH (0,Br) load curve 1: 0 WP1 B(H)  m mH  m mnI load curve 2: 0 0 slope μ μ o r ∆B WP2 m  Br H  Bwp1  Br working point 1: wp1 m  m mo (mr  m) r

 B mnI mB  mm m nI H  r  B  r o r working point 2: wp2 m (m  m) (m  m) wp2 m  m H o r r r (Hc,0) nI mmomr nI change in B: B  mr  m

smaller m is better Additional H-field at the Magnet additional field from weighing current (1000 x larger)

Result from FEA:

top magnet: Hext is parallel to B

66 kA/m

66 kA/m bottom magnet:

Hext is anti-parallel to B

Since there are two magnets, the effect cancels. One magnet gets stronger, the other weaker by the same amount! Semi Analytic result

0.06 T (10 % )

slope: slope: 1.09 μo -1.75 μo

70 kA/m (1000x than with weighing current) Yoke Material at working point H-field in Yoke due to weighing current

H in Yoke < 0.2 A/m

0.2/800 = 250 ppm

6.82 A-t (10 mA 682 turns) H-field in PM caused by weighing current H in Magnet ≈70 A/m, see next slide.

6.82 A-t (10 mA 682 turns) Uncertainty as a function of mass The Watt balance master equation

h W mgv  90  SI h90 W UI90

with

4 34 h90  2  6.6260688543610 Js K J 90 RK 90