A measurement of the Planck constant using pressure metrology

C M SuttonMeasurement Standards Laboratory of New Zealand

Industrial Research Limited

v1014f

Acknowledgement: Many people - MSL, IRL, overseas co llaborators …

NZIP Conference, Wellington, 17 - 19 October 2011

2

Contents

� Introduction� The Planck constant & how it relates to the kilogra m

�Watt balance� How it works

�A pressure balance watt balance� Concept� How it compares with other watt balances� Research activities

�Summary

3

Introduction

�Why measure the Planck constant?

� Because the present artefact kilogram is limiting development of the SI� The International System of Units

� A new definition of the kilogram in terms of the Planck constant is a way forward

and

International prototype kilogram( IPK)

4

What is the problem with the kilogram?

�The present kilogram is the mass of the IPK- International Prototype kilogram� Only reliable to ~ 50 µg or 5 parts in 10 8 - or worse?� Limiting other units� ampere� mole� candela

Apparent variations in masswith time for copies of the IPK

In particular: The ampere could be defined in terms of quantum phenomena� Josephson volt� Quantum Hall effectand realised with a relativestandard uncertainty uR ~ 10-9

5

� Link kg to NA� Counting atoms in sphere

of single crystal 28Si� International collaboration

- Australia, France, Germany,Italy,Japan, USA, …

� Budget several M€!

Solution - re-define the kilogram

� .. In terms of a fundamental constant� Planck constant h or Avogadro constant NA

� Only current options likely to achieve accuracy uR < 5 ×××× 10-8

� Link kg to h� Watt balance - Kibble 1975

� USA, Canada� France (2),

Switzerland,China,New Zealand …

6

Current results for h & NA

� Lowest uR = 3.0 ×××× 10-8

� BUT span of results is 31 ×××× 10-8

� More measurements needed !

6.022138

6.022139

6.022140

6.022141

6.022142

6.022143

CODATA 2006 NIST wb 2007 NPL wb 2007 IAC 2010

Avo

gadr

o co

nsta

nt /(

1023

mol

-1) Target accuracy:

uR ≈≈≈≈ 2 ×××× 10-8

( ) 20

A2rcA e M

hR N

α

∞

=

Challenging:~2 s in 3 years or ~2 mm in 100 km!

USAwatt balance

UKwatt balance

Silicon sphere

7

A watt balance - how it works

� Mechanical versus electrical power - two modes

Dynamic mode

Weighing mode

γ= × = ⋅ =∫uurr r r r

F I dl B I m g

~ coil length dl

( ) ( )U B dl dl B v vν γ= × ⋅ = − × ⋅ = − ⋅∫ ∫uur uur rr rr r

Factor γγγγ = U/v from dynamic mode

� When I & U are measured– with quantum electrical standards

» Josephson volt, quantum Hall resistance

m g U

I vγ = = and

2JfU I

m C hg v gv

= =Hence

8

Gas pressure balance:• No piston-cylinder contact

- aerodynamic bearing- strong piston centring forces

• Small piston-cylinder gap- < 1 µµµµm

Concept - pressure balance watt balance

�Weighing mode� Two pressure balances

� As force comparator� Coil fixed on piston

�Dynamic mode� Oscillatory coil motion

� ~ 1 Hz, noise rejection

Aim: Table-top size watt balance

9

What do other watt balances look like?

�Quite different!�Traditional mass/force balance

� Coil hanging from gimbals

�Various means to move coil� Beam, wheel, flexures …

� Un-wanted forces, motions� Need to control coil position

– all six degrees of freedom

�Constant coil velocity� In dynamic mode

� dc induced voltagemeasurement

� Susceptible to noise

USA watt balance

10

Research - Pressure balances 1

�Weighing performance� MSL twin pressure balance 2

� Repeatability vs load, (AB)4 or (AB)5 loading sequence– A ~ unloaded, B ~ loaded, Calculate dp and u(dp)

» DHI pressure balances

� Near zero load u(dp) ~ 0.25 mPa or 2.5 ×××× 10-9 of line pressure

0.0

0.2

0.4

0.6

0.8

0 50 100 150 200 250

Mass /g

u(d

p) /

mP

a Nearly good enough

11

Research - Pressure balances 2

� Investigating� Damped resonant behaviour

� To improve short-term repeatability

� Damping depends on� pressure, gas, geometry� Due to non-adiabatic behaviour of gas

– With NIST Gaithersburg& DH Instruments, USA

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

0 20 40 60

Time /s

Am

plitu

de /m

m0

5

10

15

20

0 1 2 3

Period t 0 /s

Q =

ππ ππ/ λ

λ λ λ

CEC

DHI

Aim toreduce damping

& increase Q

12

Research - Pressure balances 3

�New pressure balance design� With IRL Mechanical workshop

� Stationary piston– Allows wires to coil on piston

� Rotating cylinder� Trial design for cylinder rotation

– Axis defined by matched pair ofangular contact ball bearings

� Prototype made– Currently being tested

13

Research - Ground vibration at IRL

�Noise rejection� Choose oscillation frequency - for dynamic mode

�Where background noise is low

� Fourier analysis of d & U - to give γγγγ�Rejects noise at other frequencies

� Ground vibration�Low from 1 Hz to 3 Hz

� Matches preferredfrequency range�0.1 Hz to 5 Hz

–To avoidmechanicalresonances

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

0.1 1 10 100Frequency /Hz

Leve

l of v

ibra

tion

Amplitude /m

Velocity /(m/s)

Acceleration /(m/s 2)

14

Research - Dynamic coil position measurement

�High-speed heterodyne laser interferometry� For measuring oscillatory coil motion� ~ 1 MHz sample rate

� Developing processing electronics� With Intelligent Machines & Devices Group

-2.5

-1.5

-0.5

0.5

1.5

2.5

550 650 750 850 950

Time /s

App

aren

t dis

plac

emen

t /nm

15

New cryo-cooled cryostat

Research - Induced voltage measurement

�Via ac Josephson voltage standard� Have purchased cryo-cooler� Plan to purchase PJVS

� Programmable Josephsonvoltage standard

� With NIST Boulder, USA

� Investigating� Differential sampling voltmeter

� To measure the difference betweenthe induced coil voltage and theac Josephson voltage

� With NIST Gaithersburg, USA

16

0.9520

0.9522

0.9524

0.9526

0.9528

0.9530

0.9532

0 10 20 30 40 50 60 70 80 90

Distance z in air gap /mm

Rad

ial i

nduc

tion

B (

LNE

) /T

esla

0.9299

0.9300

0.9301

0.9302

0.9303

0.9304

0.9305

0.9306

Rad

ial i

nduc

tion

B (

MS

L) /T

esla

LNE calculationMSL calculation

Research - Magnetic field

�Trial calculations on magnet design� With HTS110� Obtained similar variations

� Of B with z to lab in France

�Rig to measure RTC� Reversible temperature

coefficient� Of permanent magnets� Want ~zero RTC� With Electron Energy, USA

17

Summary

� Pressure balance watt balance� Concept established

� Significantly different from existing watt balances

� Research initiated on key factors� Influencing feasibility and performance

� Aiming for operational watt balance� In some form, mid-2013� Results in advance of Dec 2014 - CODATA

Any questions?