the planck constant, - aps physics...the planck constant, h, stephan schlamminger national institute...
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The Planck constant, h,
Stephan Schlamminger
National Institute of Standards
and Technology (NIST)
MASPG
Mid-Atlantic Senior
Physicists Group
09-19-2012
and the redefinition of
the SI
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.
II. Based on Earth.
III. Based on fundamental constants.
107 m
ħ c
mol
K
s
m cd
A
kg
The current SI†
† Système international d’unités
mol
K
s
m cd
A
kg
The current SI†
† Système international d’unités
∆ν 133Cs
μo
c
mol
K
s
m cd
A
kg
The new SI†
† Système international d’unités
∆ν 133Cs
e
c
k
NA
Kcd
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.
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
56, 51, 54, 58, 68, 60,70,
65,69
New prototypes 67,71,72,74,75,77-94
Other prototypes 34
Cylindrical
height:39 mm, diameter: 39 mm
Alloy 90 % platinum and 10 % iridium
1889: -39 μg
1950: -19 μg
1990: -21 μg
distributed
by raffle
USA: K4 (1890) check standard
K20 (1890) national prototype
K79 (1996)
K85 (2003) watt balance
K92 (2008)
Let’s look at washing
Change o
f m
ass
rela
tive t
o #
9 a
nd #
31
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
3
2
As
m kg1
As
J1V1
derived unit base units
Two advances in metrology in “recent
years”
1. Josephson Effect
Josephson Junction (JJ) array
2. Integral Quantum Hall Effect
Quantum Hall Resistor
16
• Weak link between two superconductors
• Electrical properties
Y1A1e
1 Y2A2e
2
21
V h
2e
1
2
d
dt
or, V h
2ef
DC only with AC
V
I
n = 0
+1 V
I Ic -1
Josephson Junction
JJ array
20208 Junctions
-14 to +14 Volts
typical: f=14..75 GHz
19 mm
Voltage
Quantum Hall Effect
s
HH
eN
B
I
VR
RH = h/ie2
T = 278 mK
I = 0.255 mA
ih
eBN s
2ie
hRH
Two new constants
• Josephson constant • von Klitzing constant
V
GHz 0110870483597
2
)..(
h
eK J
00000840807443481225
2
)..(
e
hRK
V
GHz 9483597
90
.
K J
80781225
90
.
RK
A schism in metrology
SI units
(base and derived)
kg A
m s V
W Ω
…
…
conventional units
A90
V90
W90
Ω90
…
Difference between SI and 90 units
http://physics.nist.gov/cuu/Constants/index.html
1 V = ( 1 - 62.0 x 10-9 ± 22.7 x 10-9 ) V90
1 Ω = ( 1 - 17.2 x 10-9 ± 0.3 x 10-9 ) Ω90
1 A = ( 1 - 44.9 x 10-9 ± 22.7 x 10-9 ) A90
1 C = ( 1 - 44.9 x 10-9 ± 22.7 x 10-9 ) C90
1 W = ( 1 - 106.9 x 10-9 ± 45.5 x 10-9 ) W90
1 F = ( 1 + 17.2 x 10-9 ± 0.3 x 10-9 ) F90
1 H = ( 1 - 17.2 x 10-9 ± 0.3 x 10-9 ) H90
Redefinition by committee
Oct 2011
vote on Draft
resolution
passed
4 year
wait Ready to
redefine
yes new SI
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
∆ν(133Cs) ground state hfs 9.192 631 770
·109 s-1
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
NA Avogadro constant 6.022 141 29 ·1023 mol-1
Kcd luminous efficacy 6.83 ·102 lm kg-1 m-2 s3
Based on seven reference constants.
* 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
1
0
-1
-2
-3
-4
1972 volt representation
USSR 4.5 ppm
France 1.32 ppm
US -1.2 ppm
pp
m 2
3
4
5
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
USSR -3.565 ppm
France -6.741 ppm
Other -8.065 ppm countries
US -9.264 ppm
1990 volt representation
8 p
pm
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)
Adjustments of national voltage standards
V
GHz 948359790 .K J
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
velocity mode
The principle of the Watt balance
I
l
v F
m
g
B
force mode
IlBNevBmg
l
v
F
V
l
VeeEevB
I
mglB
v
VlB
B
The Watt equation
IVvmg
The Watt equation
IVvmg
force mode velocity mode
Virtual power !
B
v
Nullmeter
programmable josephson voltage system
traceable frequency fV
e
hfcV VV
2
GHz
V
e
h m..066.2
2
velocity mode
Connection to Planck’s constant
Connection to Planck’s constant
B
programmable jvs
traceable frequency fR
force mode
R adjustable current
source
R is calibrated against a Quantum Hall Resistor RK
2e
hcRcR RKR
2
2
e
hc
e
hfc
R
VI
R
RRVR
Nullmeter
hffc
cc
e
hc
e
hfc
e
hfc
R
VVIV VR
R
RVV
R
RRVVVR
4
2
22
Combining the two modes
hgv
ff
c
ccm VRv
R
RVV
4
Mass can be defined in terms of Planck’s constant.
Gravity
Absolute gravimeter,
can measure
g to 1 ppb
Gravity
1645
1655
1665
1675
1685
µG
al
NIS
T
NO
AA
NR
Can
Av
era
ge
2012 North American Watt Balance
Absolute Gravity Comparison
(NAWBAG-2012)
Feb6-Feb10 2012
Worldwide Watt Balances (WWB)
35
BIPM (France)
LNE(France)
NPL (UK)/NRC (Canada)
NIM (China)
MSL (New Zealand)
KRISS (South Korea)
PTB (Germany) ?
METAS (Switzerland)
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)
V
m
3
220
2/3888
dm
VM
V
VN mol
uc
molA
m,v
A single crystal of Si
a0
mol
mol
MV
Unit cell (8 atoms per cell)
3
220
2/33
0 8 daVuc
Measurements needed
3
220
2/3888
dm
VM
V
VN mol
uc
molA
mass metrology
isotopic abundance & mass
spectroscopy
volume determination
XRD
physics and chemistry
of bulk and surface
Measurements needed
3
220
2/3888
dm
VM
V
VN mol
uc
molA
mass metrology
volume determination
XRD
physics and chemistry
of bulk and surface
Measurement completed in
2003
Largest contribution to the
uncertainty:
measurement of the
isotopic abundance
Solution: Use enriched Si.
isotopic abundance & mass
spectroscopy
Pictures
Si sphere
5kg 28Si crystal grown
by the float zoning method
Connection between h and NA
h
cmR e
2
2
Connection between h and NA
p
Apee
hm
NMcm
h
cmR
2
/
2
22
pm
Connection between h and NA
Aep
P
p
Apee
Nmmh
cM
hm
NMcm
h
cmR
)/(22
/
2
222
pm
Connection between h and NA
Aep
P
Nmmh
cMR
)/(2
2
3.2·10-10
5·10-12 8.9·10-11
4.1·10-10
fixed
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
B
l1
BlI
mg2BNl
v
V1
)1(12 Tll
ohmic heating
change in temperature
change in l Copper: α=16.6 10-6 K-1
I=10 mA, R=100 Ω
velocity mode (wire cold)
B
l2
weighing mode
The solution (idea by P.T. Olsen)
B(r) = C/r
cold coil
r1 B(r) = C/r
warm coil
r2
CNr
CrN
v
Vπ2π2
1
1 CNr
CrN
I
mgπ2π2
2
2
The NIST way
Solenoid current ccw
d
h
2r
region, where B(r)=C/r
Solenoid current cw
NIST-1, conventional EM
3 kW, 8A, 0.003T
NIST-2
superconducting EM
5A, 0.1T
NIST-3 balance in air
51
NIST-3 Apparatus
The weighing mode (in more detail)
0.5kg
I-
0.5kg 1.0kg
I+
The weighing mode (in more detail)
0.5kg
I-
0.5kg 1.0kg
I+
CNImgCNI π2π2_
CNIImg π2)( _
Two advantages:
1.) Substitution method
2.) Current is halved,
Heating is quartered
The velocity mode (in more detail)
moving coil
fixed coil
V
AC fields
10 cm
9 cm
8 cm
7 cm
6 cm
5 cm
4 cm
3 cm
2 cm
1 cm Band of 70 Pt-W wires
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 01O
ct
2011
01O
ct
2013
new
team
sta
rts
work
ing o
n N
IST-3
Assessment
Planning
Order of
hardware
Solenoid cooled down
now, 09/01/12
first quarter of data
uncertainties ≈100 x10-9
Alignment
Change of electrical
grounding
New PJVS
New
• current source
• vacuum pumps
• knife edge
Upgrades to
• Interferometers
Data analysis, systematic tests
Comparison of
absolute gravimeter
Goal:
An independent
data
poin
t w
ith N
IST-3
Independent
measu
rem
ent
& u
ncert
ain
ty a
naly
sis
Comparison of
JJ Voltage Std.
Changes
GND STAR
PJVS
Autocollimator for laser alignment
Power Filters
In situ laser calibration
I2 stabilized HeNe
Zener Standard Cell
Laser for velo meas
Changes continued
Stabilization of SC current
Current source
Results
Bad connection to current
source
JJA grounded
many experiments
In the meantime we are building NIST-4
• Watt balance to measure h
• Optimized for the best measurement of h
• Highly sophisticated
• Costly to operate and maintain
• Lifetime: ≈10 years
• Watt balance to realize the kg
• Optimized for reliable operation
• Ease of Use
• Low maintenance
• Lifetime: >30 years
“The Clydesdale is a cold blooded horse appreciated for its
strength, style, and versatility. Like all cold-blooded horses
the Clydesdale has a stolid demeanor and is not suitable
for sports other than hauling or pulling.”
“The Thoroughbred is a horse breed best known for its use in
horse racing. Thoroughbreds are considered "hot-blooded"
horses, known for their agility, speed and spirit.”
picture source: wikipedia.org
NIST-3 NIST-4
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.
1-3 outer yoke
5-7 inner yoke
4 & 8 magnets
8 parts:
• 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
Top view
(not to scale)
NIST-4 magnet
To access the coil, the magnet separates:
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
upper
third
lower
third
middle
third
Access to the coil
FEA results
• Field in gap is 0.54 T
• coil radius is 21.5 cm
• calculated by MagNet
• Flux in Iron < 0.9 T
rBINF 2
A
N732.0N
I
F
A
N1000..500
I
F
1370..680N
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!
part-time:
Jon Pratt,
group leader Darine
Haddad
Ruimin
Liu
David
Newell
Stephan
Schlamminger
Leon
Chao
Ed
Williams
Shawn
Zhang
Frank
Seifert
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 B
H
(0,Br)
HBHB rr mm0)(
(Hc,0)
recoil curve: L1
load curve 1: mHHB 0)( m
nI
L2
load curve 2: mnImHHB 00)( mm
WP2
WP1
working point 1: )(1
m
BH
ro
rwp
mmr
r
wp Bm
mB
m
1
working point 2: )()(2
m
mnI
m
BH
rro
rwp
mmm m
nImmBB
r
rorwp
m
mm2
∆B slope μoμr
slopes -μom
change in B: m
nImB
r
ro
m
mm
smaller m
is better
Additional H-field at the Magnet additional field from weighing current (1000 x larger)
top magnet: Hext is parallel to B
bottom magnet:
Hext is anti-parallel to B
66 kA/m
66 kA/m
Result from FEA:
Since there are two magnets, the effect cancels.
One magnet gets stronger, the other weaker by the same amount!
Semi Analytic result
slope:
1.09 μo
70 kA/m (1000x than
with weighing current)
slope:
-1.75 μo
0.06 T
(10 % )
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
90
90
90 UI
mgv
W
W
h
h SI
with
Js1036854068626.64 34
90
2
90
90
KJ RK
h
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