Research 1: C Sutton

1. A measurement of the Planck
constant using pressure metrology
C M Sutton
Measurement Standards Laboratory of New Zealand
Industrial Research Limited
Acknowledgement: Many people - MSL, IRL, overseas collaborators …
NZIP Conference, Wellington, 17 - 19 October 2011
v1014f

2. Contents
Introduction
The Planck constant & how it relates to the kilogram
Watt balance
How it works
A pressure balance watt balance
Concept
How it compares with other watt balances
Research activities
Summary
2

3. Introduction
Why measure the Planck constant?
Because the present artefact
kilogram is limiting
development of the SI
The International System of Units
and
A new definition of the
kilogram in terms of the
Planck constant is a way
forward
International prototype kilogram
( IPK)
3

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 108 - or worse?
Limiting other units Apparent variations in mass
ampere with time for copies of the IPK
mole
candela
In particular: The ampere
could be defined in terms of
quantum phenomena
Josephson volt
Quantum Hall effect
and realised with a relative
standard uncertainty uR ~ 10-9
4

5. 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 Link kg to NA
Watt balance - Kibble 1975 Counting atoms in sphere
USA, Canada of single crystal 28Si
France (2), International collaboration
Switzerland, - Australia, France, Germany,
China, Italy,Japan, USA, …
New Zealand … Budget several M€!
5

6. Current results for h & NA
Lowest uR = 3.0 × 10-8
BUT span of results is 31 × 10-8 cAr ( e ) M 0α 2
h=
More measurements needed! 2 R∞ N A
6.022143
Target accuracy:
Avogadro constant /(10 23 mol-1)
uR ≈ 2 × 10-8
6.022142
USA
watt balance
6.022141
Silicon
Challenging:
sphere
6.022140 ~2 s in 3 years or
UK ~2 mm in 100 km!
watt balance
6.022139
6.022138
CODATA 2006 NIST wb 2007 NPL wb 2007 IAC 2010
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7. A watt balance - how it works
Mechanical versus electrical power - two modes
Weighing Dynamic
mode mode
Factor γ = U/v from
dl ~ coil length dynamic mode
( )
uu r
r r uu r uu r r
r
( )
r r r r r
F=I ∫ dl × B = I ⋅ γ = m g U =∫ ν × B ⋅ dl = − ∫ dl × B ⋅ v = −γ ⋅ v
mg U UI f J2
Hence γ= = and m= =C h
I v gv gv
When I & U are measured
– with quantum electrical standards
» Josephson volt, quantum Hall resistance
7

8. Concept - pressure balance watt balance
Weighing mode
Two pressure balances Aim: Table-top
As force comparator size watt balance
Coil fixed on piston
Dynamic mode
Oscillatory coil motion
~ 1 Hz, noise rejection
Gas pressure balance:
• No piston-cylinder contact
- aerodynamic bearing
- strong piston centring forces
• Small piston-cylinder gap
- < 1 µm
8

9. What do other watt balances look like?
Quite different!
Traditional mass/force balance
Coil hanging from gimbals USA watt balance
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 voltage
measurement
Susceptible to noise
9

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
0.8
0.6
u (dp ) /mPa
Nearly good
0.4 enough
0.2
0.0
0 50 100 150 200 250
10 Mass /g

11. Research - Pressure balances 2
Investigating 0.75
0.5
Damped resonant behaviour
Amplitude /mm
0.25
To improve short-term repeatability 0
0 20 40 60
Damping depends on -0.25
-0.5
pressure, gas, geometry -0.75
Time /s
Due to non-adiabatic behaviour of gas
– With NIST Gaithersburg
20
& DH Instruments, USA
CEC
DHI
15
Aim to
Q = π /λ
reduce damping
10
& increase Q
5
0
0 1 2 3
11 Period t 0 /s

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 of
angular contact ball bearings
Prototype made
– Currently being tested
12

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 γ
Rejects noise at other frequencies
Ground vibration 1.E-04
Low from 1 Hz to 3 Hz 1.E-05
Acceleration /(m/s2)
Matches preferred Level of vibration
1.E-06
frequency range
0.1 Hz to 5 Hz 1.E-07
–To avoid Velocity /(m/s)
1.E-08
mechanical
resonances
1.E-09
Amplitude /m
1.E-10
0.1 1 10 100
13 Frequency /Hz

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
Apparent displacement /nm
1.5
0.5
-0.5
-1.5
-2.5
550 650 750 850 950
Time /s
14

15. Research - Induced voltage measurement
Via ac Josephson voltage standard
Have purchased cryo-cooler New cryo-cooled cryostat
Plan to purchase PJVS
Programmable Josephson
voltage standard
With NIST Boulder, USA
Investigating
Differential sampling voltmeter
To measure the difference between
the induced coil voltage and the
ac Josephson voltage
With NIST Gaithersburg, USA
15

16. Research - Magnetic field
Trial calculations on magnet design
0.9532 0.9306
With HTS110
Radial induction B (MSL) /Tesla
Radial induction B (LNE) /Tesla
0.9305
0.9530
LNE calculation
Obtained similar variations 0.9528
MSL calculation 0.9304
0.9303
Of B with z to lab in France 0.9526
0.9302
0.9524
Rig to measure RTC 0.9522
0.9301
0.9300
Reversible temperature 0.9520
0 10 20 30 40 50 60 70 80 90
0.9299
coefficient Distance z in air gap /mm
Of permanent magnets
Want ~zero RTC
With Electron Energy, USA
16

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?
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