Measurement 45 (2012) 1–13
Contents lists available at SciVerse ScienceDirect
Measurement
journal homepage: www.elsevier.com/locate/measurement
Review
Precisely measuring the Planck constant by electromechanical balances
Shisong Li a,b,⇑, Bing Han b, Zhengkun Li b, Jiang Lan a,b
a
b
Department of Electrical Engineering, Tsinghua University, Beijing 100084, PR China
National Institute of Metrology, Beijing 100013, PR China
a r t i c l e
i n f o
Article history:
Received 4 May 2011
Received in revised form 31 August 2011
Accepted 10 October 2011
Available online 18 October 2011
Keywords:
The Planck constant
Watt balance
Joule balance
Ampere balance
Voltage balance
Kilogram
a b s t r a c t
To eliminate the last artefact unit, kilogram, in the seven basic SI units, the possible new
definition of kilogram by fixing the Planck constant is being considered. National Metrology Institutes, the BIPM and academic institutions have built several electromechanical
balances such as watt balance to measure the Planck constant by an equivalence of
mechanical and electrical energies. This paper reviewed the principle, apparatus and recent
progress of different electromechanical balances. The tendency for measuring the Planck
constant and the future of kilogram have also been predicted.
Ó 2011 Elsevier Ltd. All rights reserved.
Contents
1.
2.
3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.
Possible new definitions of the kilogram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.
Basics of the mass determination using the Planck constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Principle and developments of different electromechanical balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.
Force balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2.
Watt balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3.
Energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Electromechanical experiments in progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.
NPL/NRC watt balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2.
NIST watt balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.
METAS watt balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4.
LNE watt balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.5.
BIPM watt balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.6.
NIM joule balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.7.
MSL watt balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.8.
VNIIM/MIKES superconducting magnetic levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Results and conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.1.
Measurement results of the Planck constant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2.
Discussion and possible improvements in the future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
⇑ Corresponding author at: Department of Electrical Engineering, Tsinghua University, Beijing 100084, PR China.
E-mail address: [email protected] (S. Li).
0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.measurement.2011.10.020
2
S. Li et al. / Measurement 45 (2012) 1–13
1. Introduction
1.1. Possible new definitions of the kilogram
The kilogram, unit of mass, is defined as the international prototype of kilogram (IPK) kept at the Bureau International des Poids et Mesures (BIPM), which is the last
basic unit defined by artefact in the International System
of Units (SIs). The present definition of kilogram refers to
the mass of the artefact whose major disadvantage is the
drift over time. The variation of the IPK compared with
its official copies has already been observed (as shown in
Fig. 1) [1], with five parts in 109 per year. And the absolute
drift may be even larger. As we know that definitions of the
ampere, the mole and the candela are related to the kilogram, the variation of the IPK will directly influence these
units. Thus possible new definitions, making the kilogram
more stable and accurate, are being considered. One good
method to eliminate the last artefact and its variation over
time is to relate the kilogram to basic physical constants.
Based on this idea, two approaches, precisely measuring
the Planck constant h using electromechanical balances
and determining the Avogadro constant NA by counting
atoms, are being pursued [2–6]. However, it is required
to achieve the relative standard uncertainty within
2 108 for measuring both the Planck constant and the
Avogadro constant with an agreement at least 5 108.
The content in this paper is following the electromechanical strategy in determining the Planck constant h.
Progresses have been made recently, known as the NPL,
NIST and METAS watt balance experiments [7–11]. However, a disagreement of 107 order still exists between
these results. Further improvements for reducing the
uncertainty of the Planck constant are urgently needed.
According to the 2010 CODATA evaluation [12], the Planck
constant has a precision with relative standard uncertainty
of 4.4 108. More than 90% of the uncertainty for some
other basic constants such as the rest mass of the electron
me, Avogadro constant NA, elementary charge e, Bohr magneton lB and nuclear magneton lN, is contributed by the
uncertainty of the Planck constant (shown in Fig. 2). Therefore improving the accuracy of the Planck constant is also
very important in establishing a whole and precise system
of basic physical constants.
1.2. Basics of the mass determination using the Planck
constant
Before 1990, in National Metrology Institutes (NMIs),
electrical units were maintained by artifacts which is called
‘as-maintained electrical units’. The volt and the ohm were
maintained by the average emf of groups of standard cells
and the average resistance of groups of standard resistors
respectively. To replace these laboratory units by SI definitions, the electromechanical balance was designed to realize the SI ampere (by the ampere balance) [13–15] or the
SI volt (by the voltage balance) [16–22] through an assumed equivalence of mechanical and electrical energies.
However, the accuracy of these early versions of electromechanical balances was limited by the electrical measurements. In 1990, new international electrical reference
standards were introduced on base of defining conventional values KJ-90 and RK-90 for the Josephson constant
and the von Klitzing constant [23]. Based on these two conventional values, electrical measurements have improved
by almost two orders of magnitude. However, the corresponding SI values of KJ and RK, which are with relative
standard uncertainties of 2.2 108 and 3.2 1010
respectively [12], have relative deviations at the level of
108 from the 1990 conventional values (without uncertainty). The electromechanical balance can measure this
SI-conventional deviation by a direct comparison of
mechanical units (force, energy or power), which can always be measured in SI, with the corresponding force, energy or power measured in laboratory electrical units
(which are not SI). The ratio of the results gives the proportionality constant c between the laboratory electrical units
and the SI units as
c¼
F
P
E
h
¼
¼
¼ K 2 RK90
F 90 P 90 E90 4 J90
ð1Þ
Fig. 1. Changes with respect to time in the calibrations of the official copies (-h-) and national prototypes (-s-) as compared to the IPK. The horizontal axis
represents the mass of the IPK and each of the curves starts on the horizontal axis at the date of its first calibration traceable to the IPK in 1889[1].
S. Li et al. / Measurement 45 (2012) 1–13
3
Fig. 2. Relationships between the Planck constant and other basic physical constants, where: R1 is the Rydberg constant, with relative standard uncertainty
ur = 5 1012; c0 is the speed of light (fixed); a is the fine-structure constant, ur = 3.2 1010; Ar(e) is the relative atomic mass of an electron,
ur = 4.0 1010; Mu is molar mass constant defined as 0.001 kg/mol (fixed); l0 is the magnetic constant (fixed); Ar(p) is the electron relative atomic mass,
ur = 8.9 1011 [12].
where F90, P90 and E90 are the electrical determined force,
power, and energy based on 1990 conventional values
while F, P, and E are in SI units of mass, length and time.
The above equation establishes a relationship between
the Planck constant h (SI value) and the weighing mass.
In the beginning, the electromechanical balance experiments would be carried out to determine h by the present
definition of the kilogram. When the uncertainty of h has
been reduced to several parts in 108, the Planck constant
can be defined as a constant without uncertainty, which
would be used to redefine the kilogram.
In this paper, we reviewed the principle, experimental
apparatus, latest progress, and recent published results of
the various electromechanical balances, and these different
designs of electromechanical balances in determining the
Planck constant were paid more attention. Based on the
comparison and analysis of these existing projects with
their historical and current measured results, future developments of the electromechanical balance method were
predicted.
tages of the early versions with the latest technologies.
These balances are slightly different in principle, and most
of the strategies are commonly used by the different versions. Here we summarize the principles and current developing situations of these balances by the three realizations
of c: the force mode (N/N), power mode (w/w), and energy
mode (J/J), corresponding to the force balance, watt
balance, and energy balance respectively.
2.1. Force balance
As we know that a general force F along the direction z
can be expressed as the partial derivative of the system energy W as F = @W/@z. By distinguishing an inductive or
capacitive electromagnetic force, two approaches: the ampere balance and the voltage balance are performed in the
force mode. For a two-coil system, the magnetic force is a
function of the mutual inductance M with the relative position of the two coils. Denoting the currents through the
two coils as I1 and I2 respectively, the electromagnetic
force is balanced by the weight of the test mass, which
can be expressed as
2. Principle and developments of different
electromechanical balances
mg ¼
The first version of electromechanical balance, the electrodynamometer (known as the ampere balance), can be
traced to the 19th century. After more than one hundred
years of development, several new versions of electromechanical balances have been built which blend most advan-
where g is the acceleration due to the local gravity. The
above equation is the principle of the ampere balance
and Fig. 3 shows the picture of an earliest ampere balance
developed by NPL. The advantage of the ampere balance is
the very simple measuring process, which can be realized
@M
I1 I2
@z
ð2Þ
4
S. Li et al. / Measurement 45 (2012) 1–13
h¼
Fig. 3. Picture of an earliest ampere balance developed by NPL (adopted
from [13]).
in only one balancing point. However, the accuracy of the
ampere balance is limited by a main weakness in precisely
measuring the geometric factor, @M/@z, which achieves a
relative standard uncertainty about several parts in 106
[13–15]. Although the ampere balance is not used for the
measurement of the Planck constant now, it is the initial
version of the watt balance and joule balance.
The voltage balance is the other form of the force balance. For a two-plate-capacitor system, if the voltage between the two plates is U and one of the plates is
connected to the ground, considering the electrostatic
force balanced by the weight of the test mass, the voltage
balance can be written as
mg ¼
1 @C 2
U
2 @z
ð3Þ
where C is the capacitance. The voltage balance determines
h by precisely measuring the quantity KJ. A Josephson voltage UJ is compared to the high voltage U whose value is
known in terms of the SI unit, and the ratio is determined
by counterbalancing an electrostatic force arising from the
voltage U with a known gravitational force. Consequently,
a relationship between the Planck constant and the test
mass is established as
16a
2
@C
0 cK J90 @z
l
mg
ðU 2 Þ90
ð4Þ
From 1980s to 1990s, three principal approaches: the
Kelvin-type, energy-changing method, and Liquid electrometer (as shown in Fig. 4), had ever been practised by LCIE
(France), PTB (Germany) [16,17], NBS (USA), CSIRO (Australia) [18] and the Zagreb University (Yugoslavia) [19–22]. The
main weakness of the voltage balance is the need of very
high voltage (as high as 100 kV) and a few grams of the test
mass, which lead the relative standard uncertainty of one
part in 107 being a limitation in measuring the Planck constant. The determination of h at CSIRO was carried out using
the liquid-mercury electrometer, yielded the result
h = 6.6260684(36)1034 Js with relative standard uncertainty of 5.4 107 [18]. PTB also published the result of
measuring the Planck constant h = 6.6260670(42)1034
Js with relative standard uncertainty of 6.3 107 using
the capacitor voltage balance [17]. And this work is not
being continued at present.
2.2. Watt balance
The watt balance was first proposed by Kibble at National Physical Laboratory (NPL, UK) in 1976 [24]. The watt
balance experiment is performed in two modes, namely
the weighing (force or static) mode and moving (velocity
or dynamic) mode as shown in Fig. 5. In the weighing
mode, the moving coil exited by a DC current I is strained
by a Laplace force in the magnetic field. This force is compared with the weight of test mass. While in the moving
mode, the coil is moved with a velocity v in the vertical
direction, inducting a voltage U in the moving coil. By a
combination of the two modes, the watt balance can be
written as
mg v ¼
@M @z
@U
I1 I2 ¼
I ¼ UI
@z @t
@t
ð5Þ
This relationship allows a comparison of the electrical
watt (right-hand side of the equation) to the mechanical
watt (left-hand side of the equation). The voltage U can
be traced to the Josephson voltage standard and the
Fig. 4. Three different realizations of voltage balances (adopted from [19]). (a) Kelvin-type electrometer. (b) energy-changing method. (c) liquid
electrometer.
5
S. Li et al. / Measurement 45 (2012) 1–13
Fig. 5. Schematic drawing of two modes in the watt balance experiment. (a) weighing mode. The force balance equation is IBL = mg. (b) moving mode. The
inducted voltage is U = BLv. The geometrical factor BL can be eliminated by a combination of the two equations.
current I can be expressed in terms of both Josephson voltage and QHR. By precisely measuring the proportionality
value v/(UI), the Planck constant can be determined as
h¼
4mg v
R2J90 RK90 ðUIÞ90
ð6Þ
The advantage of the watt balance experiment is avoiding measuring the geometric factor (eliminated in a combination the equations of two modes). Based on this
advantage, the watt balance experiment is now prevalently
being carried out by National Institute of Standards and
Technology (NIST, US), National Physical Laboratory (NPL,
UK), the Federal Office of Metrology (METAS, Switzerland),
Bureau International des Poids et Mesures (BIPM), Laboratoire national de métrologie et d’essais (LNE, France) and
the Measurement Standards Laboratory (MSL, New Zealand). After decades of operation and improvements, the
NPL, NIST, and METAS have published several results for
the Planck constant h [7–11,25], of which the NIST measured result of h in 2007 [10] is the best one with the relative standard uncertainty of 3.6 108. All these watt
balances are aiming for the relative standard uncertainty
Ur < 2 108.
The energy balance, in physical significance, is based on
the mechanical and electromagnetic joule equivalence.
One energy balance namely joule balance has launched at
National Institute of Metrology (NIM, China) since 2006
[26] which is resulting from the integration of the ampere
balance along the vertical direction from z1 to z2 as
ð7Þ
where M(z1) and M(z2) are the mutual inductances of the
two coils in position z1 and z2 respectively. On the left hand
of the equation is the gravity potential energy change
when the test mass is moved vertically from z1 to z2 while
in the right hand, it is the electromagnetic energy change.
The relative position z1–z2 is measured by an interferometer (three lasers); the mutual inductance can be realized in
terms of QHR and atomic time standard; and the current is
measured by Josephson voltage and QHR. Then the Planck
constant will be determined as
h¼
4mgðz1 z2 Þ
K 2J90 RK90 ð½Mðz1 Þ Mðz2 ÞI1 I2 Þ90
mgðz1 z2 Þ ¼
Z
z1
z2
2.3. Energy balance
mgðz1 z2 Þ ¼ ½Mðz1 Þ Mðz2 ÞI1 I2
The advantage of the joule balance is that all measurements are carried out in static and stable phases, avoiding
a dynamic measuring the velocity v. However, this requires
precise measurement of the mutual inductance [27]. After
three years effort, the uncertainty for the mutual inductance measurement better than 1 107 (1r) has been
achieved recently. Now, the joule balance has finished its
prototype test. The result with 105 level uncertainty has
been reached and better result can be expected after several improvements carried out in the near future.
Another approach of the energy balance is the superconducting magnetic levitation project. This method was
purposed by Sullivan and Frederich firstly for realizing
the SI ampere [28]. It uses the diamagnetic properties of
a superconductor in the Meissner state to attain stable levitation in a nonuniform magnetic field supplied by a coil.
This ponderomotive force is balanced with the weight of
the superconductor body. With integral of two equilibrium
positions with vertical distance from z1 to z2, if the levitated body has ideal diamagnetic properties, the equivalence of a mechanical energy and the electromagnetic
energy then can be written as
ð8Þ
IðuÞdu ðu1 I1 u2 I2 Þ=2
ð9Þ
I is the current through the coil; u = Li is the magnetic
flux where L is the effective inductance of the coil-body
system measured across the coil terminals; z1–z2 is the
travelling range for the levitated body along the vertical;
u1, u2 and I1, I2 are the magnetic fluxes and electric currents in the supporting coil at z1 and z2 respectively. If all
the magnitudes of the electrical quantities are measured
using the Josephson voltage and QHR, then the Planck constant can be calculated similarly as Eq. (8).
The superconducting magnetic levitation project has
been developed at the National Research Laboratory of
Metrology (NMIJ, Japan) [29], the D.I. Mendeleyev Research
Institute of Metrology (VNIIM, Russia) [30–35], the Centre
for Metrology and Accreditation (MIKES, Finland) [36]. This
project attained a relative standard uncertainty of 1 106
due to the loss in candidate superconductors.
3. Electromechanical experiments in progress
Among all these approaches as described in Section 2,
the early versions of balances such as the ampere balance
and the voltage balance are not pursued now. New
6
S. Li et al. / Measurement 45 (2012) 1–13
Fig. 6. The NPL Mark II watt balance (adopted from [8]).
approaches of electromechanical balances have been provided and in continued efforts to reduce the uncertainty
as much as possible via advanced technologies in recent
years. They may achieve smaller measurement uncertainties and have more favourable developing prospect. All
these experimental apparatus and latest developments
would be introduced in details as follows.
3.1. NPL/NRC watt balance
The NPL watt balance experiment was initiated in 1977
[37] shortly after Kibble’s proposal in 1976 [24]. In the first
version, a permanent magnet was used to supply the
magnetic flux for the moving coil which consisted of a flat
8-shaped coil. And the first measurement result was published with a relative standard uncertainty of 2 107 in
1990 [37]. In the same year, an improved watt balance
apparatus NPL Mark II (shown in Fig. 6) was developed,
which consists of a horizontal steel triangular frame which
supports a vacuum chamber containing a large cylindrical
permanent magnet and a balance [38]. The NPL watt balance apparatus has a standard beam, with 1200 mm in
length, weighing 44 kg. The standard mass (1 kg, 500 g,
250 g) and the moving coil are suspended on the same side
of the balance beam. The new SmCo magnet (720 mm in
diameter, 360 mm high and weighing approximately
1100 kg) supplies a magnetic flux density approximately
0.42T. The temperature of the magnet is controlled indirectly through the radiation of the case surrounding the
experiment and through the air conditioning system. The
composite coil consists of two coils (approximately 336
turns spaced 182 mm apart) wounded on a 340 mmdiameter cylindrical Pyrex coil former, connected in opposition. The working resistors are measured against the QHR
by a 25-m cable and a hysteretic Josephson junction array
is used as the voltage reference. The Michelson interferometer is used for measuring the coil position and controlling
the velocity. The constant velocity (1.3 mm/s) inducts a
0.4-V emf in the moving coil. The acceleration due to gravity g is measured by the commercial gravimeter FG5.
The NPL watt balance system has a simple structure and
can be easily realized in the two measurement modes. However, in the moving mode, the standard beam leads an arc
motion of a circle. To minimize this non-vertical motion,
the balance beam is designed as long as 1200 mm which is
inconvenient in realizing the vacuum environment. The permanent magnet can supply strong magnetic field easily, but
Fig. 7. The NIST watt balance (adopted from [45]).
S. Li et al. / Measurement 45 (2012) 1–13
due to the high temperature coefficient (3.6 104/°C), the
apparatus temperature should be controlled within a variation of ± 0.4mK. A value of h = 6.62607095(44)1034 Js has
published by NPL watt balance with a relative standard
uncertainty of 6.6 108 [7,8], which has a 3 107 difference from the NIST watt balance result published in 2007
[10]. An important system error and uncertainty source
has been found recently, and the latest result from NPL watt
balance is 6.6260712(13)1034 Js with relative uncertainty expanded to 2 107 [11].
In 2009, the NPL Mark II watt balance was transferred to
the National Research Council, Institute for National Measurement Standards (NRC-INMS, Canada) [39]. A new laboratory was constructed in Ottawa for the transferred
watt balance in 2009 and its renovation was completed
in February 2010. The FG5-105 gravimeter took part in
North American Comparison of Absolute Gravimeters (NACAG) 2010, providing a direct comparison with the absolute gravimeter in the NIST watt balance. Preliminary
comparison of the conventional Hysteretic Josephson Array
Voltage System (HJVS) and the Programmable Josephson
Array Voltage System (PJVS) associated with the watt balance experiment agrees within (0.09 ± 0.54) nV at the
nominal level of 1 V [40]. The balance reassembly included
programmable Josephson array system, the mass lifts, electronics, laser and interferometer and initial tests have been
carried out in the new laboratory. A further scientific
research is continued.
3.2. NIST watt balance
The first design of the watt balance at National Institute
of Standards and Technology (NIST, USA) started in 1980
[25]. One feature in the NIST watt balance (shown in
Fig. 7) is a wheel (diameter approximately 620 mm) being
used as the balance beam. By this design, the horizontal
motion is reduced. However, it may lead misalignment
effect due to the wheel radius imperfection and an unexpected horizontal velocity in the moving mode. Another
different design is that the radial magnetic flux density
(0.1T) is supplied by a coil system composed of two series-opposition connected main coils (each consists of ten
separate segments). But due to the size of the solenoid dewar, the total height of the NIST watt balance is about 6 m.
Different from the fixed velocity control in the other watt
balances, the inducted voltage (1.018 V, speed 2 mm/s)
is regulated in the NIST watt balance to compare against
a Josephson voltage reference. Three different 100 X transfer resistors, calibrated against the QHR, are used for the
current measurement. In the weighing mode, the weight
of a standard 1 kg mass (Pt-Ir or stainless steel) will be
balanced by the circular moving coil (diameter is about
0.7 m) with a 10 mA DC current. One laser interferometer
is located under the standard mass pan to determine the
wheel position. The other three interferometers are located
on the moving coil for the velocity control in the moving
mode. The commercial absolute gravimeter FG5 is used
for the measurement of the acceleration due to the local
gravity.
The first measurement result was published in 1989 with
a relative standard uncertainty of 1.3 106 when a
7
conventional electromagnet was used [41]. After a series
of improvements [42–44] and replacing the electromagnet
by a superconducting magnet, the Planck constant
h = 6.62606891(58)1034 Js with the relative standard
uncertainty of 8.7 108 was achieved in 1998 [25]. With
years in finding and eliminating sources of errors, the
measurement result was improved as h = 6.62606901(34)
1034 Js in 2005 with a relative standard uncertainty of
5.2 108 [9]. The latest measured value of h = 6.626
06891(24)1034 Js leading the relative standard uncertainty record of 3.6 108 was published in 2007 [10].
Currently, NIST is considering a new version watt balance
experiment.
3.3. METAS watt balance
The Swiss Federal Office of Metrology (OFMET, now METAS, Switzerland) began the watt balance experiment in
1997 [46]. The main difference between the METAS watt
balance (Fig. 8) and the other existing watt balances is
the highly compact design. The total apparatus is as small
as 1 m 1 m 1.5 m, which has advantages including cutting off the vibration frequency range, an easier control of
the temperature and the convenient design of the vacuum.
This needs a rational integrated design of the mechanical
part. In the METAS watt balance, the mechanism is a mixture between a beam and a wheel balance (a parallelogram
structure with two arms and two vertical boxes assembled
together with BeCu strips), which could induce an up or
down motion of the two vertical parts rolling over the
arm ends [47–49]. A mass comparator is used for the residual force measurement and it can avoid most of the hysteretic and non-vertical problems [50]. A mechanical lifter
from the outside of the vacuum chamber is used for transferring the coil from the parallelogram structure to the
comparator frame. For the magnet system, the permanent
(SmCo) magnet produces a horizontal, parallel and homogeneous magnetic flux density (0.6T). The moving coil is
8-shape with 2000 turns. A DC current (3 mA) is required
to balance the weight of the 100-g test mass (pure gold,
platinum alloys, stainless steel or gold plated copper cylinders) in the weighing mode, and a 0.5-V emf will be
inducted in the moving coil with a 3 mm/s constant velocity in the moving mode. The velocity is measured by a
Fabry–Perot interferometer. FG5 is used for measuring
the absolute gravity acceleration.
In the current version of the METAS watt balance, the
reproducibility for the apparatus with 1.4 107 has been
reported in 2008 with 18 months operation [51]. The latest
measurement result h = 6.6260691(20)1034 Js with relative uncertainty of 2.9 107 from METAS watt balance
[11], has been published recently. The new version of
METAS watt balance is being developed now.
3.4. LNE watt balance
The Laboratoire national de métrologie et d’essais (LNE,
France) watt balance started in 2002 [52]. In the LNE project as shown in Fig. 9, the force comparator and the suspension with the coil are moved together to avoid
possible misalignment and to minimize hysteresis effects
8
S. Li et al. / Measurement 45 (2012) 1–13
Fig. 8. The METAS watt balance (adopted from [45,47]).
by a guiding translation stage. For the magnetic system, a
large-size SmCo permanent magnet is used to produce a
single radical magnetic flux density as high as 1T [53].
The circular coil is 266 mm in diameter with 600 turns.
In the weighing mode, a 5-mA DC current though the coil
produces a 2.5 N Laplace force corresponding to the weight
of a 500-g standard mass. In the moving mode, the constant velocity of 2 mm/s of the coil produces a 1-V
inducted emf in the 40 mm effective travel length (total
72 mm). The velocity and the position of the moving coil
are controlled by an interferometer placed at the bottom
of the set-up. Different from the other watt balances, a cold
atoms gravimeter is constructed in the LNE project [54],
which has an advantage of allowing the value of g to be
transferred from one laboratory to the other with a relative
uncertainty of few parts in 109. By now, the LNE watt
balance experiment has been still in progress and the first
measurements are expected in end 2011.
3.5. BIPM watt balance
The BIPM watt balance (shown in Fig. 10) was proposed
in 2002 [55]. A commercial weighing cell is used for the
force measurements, and a 100 g test mass is balanced
with the Laplace force (1 N) produced by the coil
(250 mm diameter, 1160 turns) with constant DC current
of 1 mA in the radical magnetic flux density (0.5T). The
vertical displacement of the moving coil is 20 mm with a
constant velocity of 0.2 mm/s, inducing a motional emf of
0.1 V. The vertical coil displacement and velocity are measured by means of a Michelson interferometer. One of the
main features of the BIPM watt balances is the simultaneous measurement for the force and velocity, which
would reduce the influence of systematic changes of the
magnetic field. Another different design is the superconducting moving coil and the cryogenic permanent magnet
(SmCo) in a cryostat (4 K) to solve the magnet drift problems due to the high temperature coefficient [56]. However, this may cause difficulty for the coil alignments.
The BIPM watt balance is now in atmospheric pressure
and room temperature on an optical table without proper
damping of ground vibrations or adequate thermal isolation. All the major components of the BIPM watt balance
apparatus are available with experimental tests, and the
first measurement of the Planck constant h has been
carried out recently, obtaining a relative standard deviation of 5 106 with eleven series of measurements and
a relative combined standard uncertainty 5 105 [57].
Currently, the BIPM group is focusing on the fabrication
of the definitive magnetic circuit, the design on the future
cryogenic watt balance, and improvements of the vibration
isolation and temperature stability [58].
S. Li et al. / Measurement 45 (2012) 1–13
9
Fig. 9. The LNE watt balance.
Fig. 10. The BIPM watt balance.
3.6. NIM joule balance
In 2006, NIM proposed a joule balance method for precisely measuring the Planck constant [26]. The advantage
of joule balance is avoiding the dynamic measurement U/
v in the watt balance experiment. However, this is based
on the precise measurement of the mutual inductance.
After three years of effort, the relative uncertainty for the
mutual inductance measurement better than 1 107
has been achieved recently. The initial experiment apparatus has been built shown in Fig. 11. In the present version,
characteristics of the balance is that, in a set scale (40 mm
in vertical), the beam can be adjusted to keep balancing at
any oblique angle from the horizontal plan by a feedback
system including a displacement sensor and a torque actuator. The residual force can be directly read according to
the feedback torque. The balance platform is isolated to
reduce vibrations and a glass-wrapped room is used to
diminish the air flow. The magnetic system is constituted
by a movable coil (140 mm in diameter, 1764 turns) and
two fixed coils (each contains 4 series coils). The moving
coil and a 200-g test mass are suspended on the same side
of beam. By adjusting a DC voltage of the feedback system,
the moving coil can be freely moved along the vertical
direction and stopped at any arbitrary positions. In the
effective displacement along the vertical direction
(17 mm), an interferometer is used for measuring its relative position. The two fixed coil are symmetrical and
series-opposition connected, supplying a radial magnetic
flux density (0.008T). A current source is developed with
a short-term (30 min) stability of several parts in 107, supplying a 250 mA DC current. However, owing to the resistance of the fixed and moving coils, the heating problem is
conspicuous. To solve this problem, the magnetic system
will soon be replaced by a superconducting magnetic system. The imminent work of the joule balance includes the
assembly work for the superconducting magnetic system,
10
S. Li et al. / Measurement 45 (2012) 1–13
Fig. 11. The NIM joule balance.
Fig. 12. The MSL watt balance.
alignments for the fixed and moving coils, research on a
high precise current source (5-10A, dispersion better than
1 107), programmable Josephson junction array for
measuring the mutual inductance, and the vacuum system.
3.7. MSL watt balance
The Measurement Standards Laboratory (MSL, New
Zealand) also purposed a very different approach of watt
balance to measure the Planck constant. The MSL watt
balance uses a twin pressure balance to supply an accurate
vertical motion of the attached coil [59,60]. As shown in
Fig. 12, each of the two pressure balances consists of a
loaded piston which can be freely rotating in a close-fitting
vertical cylinder. When the piston moves in the cylinder, a
centring force, as much as several newtons, will be produced on the piston due to the gas compression. A differential pressure sensor is used for measuring the difference of
these two pressures. The left-hand balance generates a reference pressure while the right supports the coil in a radial
magnetic field. In the weighing mode, the twin of pressure
balances is performed as a weighing device to comparing
11
S. Li et al. / Measurement 45 (2012) 1–13
the gravitational force of a test mass with the electromagnetic force of the carrying-current coil in the magnetic
field. In the moving mode, a low-frequency (0.1–1 Hz)
oscillatory movement of the coil in the magnetic field is
investigated to measure the geometrical factor BL, using a
programmable Josephson array [61,62]. This dynamic
method has advantages in better mapping of the magnetic
field, the use of phase sensitive detection to reduce noise,
and a smaller and simpler balance apparatus. Currently, a
resolution of 5 109 of the total load on the pressure balance has been achieved and the further research is being
continued.
By precisely measuring all these parameters, the Planck
constant will be calculated.
Now, this project is limited by unwanted energy losses
including the horizontal force components on the trajectory or the distortion of the object. A measurement for
these energy losses in candidate superconductors [36]
show that this impact is as high as approximately
1 106 in the comparison of mechanical and electrical
energy which is consistent with the previous results from
NMIJ (Japan). For avoiding such energy losing problems,
Kibble suggested the experiment being conducted in a
two-phase manner similar as the watt balance experiment
[63].
3.8. VNIIM/MIKES superconducting magnetic levitation
The D.I. Mendeleyev Research Institute for Metrology
(VNIIM, Russia) [30–35] in conjunction with the Centre
for Metrology and Accreditation (MIKES, Finland) [36] are
investigating the superconducting magnetic levitation project. As described in Section 2.3, the standard magnetic flux
is set up using a programmable DC source and read by a
SQUID reading device. It is calibrated by the flux from a
rectangular voltage pulse against the Josephson junction.
The current is measured by the voltage drop across a resistance standard calibrated in terms of QHR. The equilibrium
positions z1 and z2 are determined by laser interferometer.
4. Results and conclusion
4.1. Measurement results of the Planck constant
Precisely measuring the Planck constant by electromechanical balances is worldwide pursued in metrology.
Other methods, such as gamma p, the precise measuring
Avogadro constant, Faraday constant, can also obtain the
value of h. Fig. 13 shows the historical and recent experimental results in determining the Planck constant by different methods including the CODATA recommend values
[64–67,11,12].
At present, two methods, the electromechanical balance
and the Avogadro project, are most concerned. In the Avogadro project, the Avogadro constant NA is obtained by measuring the atomic volumes of two 28Si spheres, and the
value of the Planck constant is calculated by their product
NAh which can be precisely measured with relative standard
uncertainty of 7.0 1010 [12]. Recently, three latest results
of these two approaches have been achieved: (1) the NPL
watt balance reports the latest measurement result of
h = 6.6260682(13) Js with relative standard uncertainty of
2.0 107; (2) METAS has reported its first watt balance result, h = 6.6260691(20)1034 Js with relative standard
uncertainty of 2.9 107 [11]; (3) the Avogadro project reported the newest result of NA = 6.02214078(18)
1023 mol1 in 2011 [67] with a derived value of h = 6.62
607008(20) Js and the relative standard uncertainty of
3.0 108. The 2010 CODATA recommended value of
h = 6.62606957(29) Js with relative standard uncertainty
of 4.4 108 is the latest available.
4.2. Discussion and possible improvements in the future
The Consultative Committee for Mass (CCM) recommends that kilogram should not be redefined until the
Table 1
List of the Planck constant h measured by watt balance.
Fig. 13. Measurement results of the Planck constant.
Identification
h(/1034Js)
Relative standard uncertainty
NPL-10
METAS-10
NIST-07
NIST-98
NPL-90
6.6260712(13)
6.6260691(20)
6.62606891(24)
6.62606891(58)
6.6260682(13)
2.0 107
2.9 107
3.6 108
8.7 108
2.0 107
12
S. Li et al. / Measurement 45 (2012) 1–13
Table 2
Summary of the Planck constant h measured by the other different
approaches.
Methods
h(/1034Js)
Relative standard
uncertainty
Avogadro (28Si)
Voltage balance
Gamma p (hi)
Faraday
constant
6.62607008(20)
6.6260678(27)
6.6260724(57)
6.6260657(88)
3.0 108
4.1 107
8.6 107
1.3 106
following conditions are met: (1) at least three independent
experiments reach the relative standard uncertainty
5 108; (2) at least one of these experiments shall achieve
the relative standard uncertainty within 2 108; (3) all results shall agree within 95% level of confidence. Therefore,
different methods determining the Planck constant have
to be encouraged. A summary of the measured results using
watt balance approach and the other methods are listed in
Table 1 and Table 2 respectively.
It is seen from Table 1 and Table 2 that (1) results
obtained from two different approaches, for example, the
Avogadro project and the watt balance method, still have
a difference of parts in 107; (2) the watt balance experiment
results are discrepant. The NPL result has a relative difference at the order of 107 from the NIST and METAS results.
These discordances may be caused by unknown systematic
errors which should be reduced to the satisfactory level.
Consequently, for the existing balances, further investments should be increased for producing or improving the
measurement results, and different electromechanical
balances, in any case, should be encouraged in the future.
Acknowledgements
This work is supported by National Natural Science
Foundation of China (Grant No. 51077120) and National
Department Public Benefit Research Foundation (Grant
No. 201010010). The authors would like to thank professors Zhonghua Zhang and Qing He at NIM for valuable discussions. Thanks also go to all the reviewers for the helpful
suggestions.
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