Measurement 45 (2012) Contents lists available at SciVerse ScienceDirect. Measurement. journal homepage:

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1 Measurement 45 (2012) 1 13 Contents lists available at SciVerse ScienceDirect Measurement journal homepage: Review Precisely measuring the Planck constant by electromechanical balances Shisong Li a,b,, Bing Han b, Zhengkun Li b, Jiang Lan a,b a Department of Electrical Engineering, Tsinghua University, Beijing , PR China b National Institute of Metrology, Beijing , PR China article info abstract 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 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. Introduction Possible new definitions of the kilogram Basics of the mass determination using the Planck constant Principle and developments of different electromechanical balances Force balance Watt balance Energy balance Electromechanical experiments in progress NPL/NRC watt balance NIST watt balance METAS watt balance LNE watt balance BIPM watt balance NIM joule balance MSL watt balance VNIIM/MIKES superconducting magnetic levitation Results and conclusion Measurement results of the Planck constant Discussion and possible improvements in the future Acknowledgements References Corresponding author at: Department of Electrical Engineering, Tsinghua University, Beijing , PR China. address: leeshisong@sina.com (S. Li) /$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.measurement

2 2 S. Li et al. / Measurement 45 (2012) 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 10 9 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 N A by counting atoms, are being pursued [2 6]. However, it is required to achieve the relative standard uncertainty within for measuring both the Planck constant and the Avogadro constant with an agreement at least 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 10 7 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 More than 90% of the uncertainty for some other basic constants such as the rest mass of the electron m e, Avogadro constant N A, elementary charge e, Bohr magneton l B and nuclear magneton l N, 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 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 K J-90 and R K-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 K J and R K, which are with relative standard uncertainties of and respectively [12], have relative deviations at the level of 10 8 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 c ¼ F F 90 ¼ P P 90 ¼ E E 90 ¼ h 4 K2 J 90 R K 90 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].

3 S. Li et al. / Measurement 45 (2012) Fig. 2. Relationships between the Planck constant and other basic physical constants, where: R 1 is the Rydberg constant, with relative standard uncertainty u r = ; c 0 is the speed of light (fixed); a is the fine-structure constant, u r = ; A r (e) is the relative atomic mass of an electron, u r = ; M u is molar mass constant defined as kg/mol (fixed); l 0 is the magnetic constant (fixed); A r (p) is the electron relative atomic mass, u r = [12]. where F 90, P 90 and E 90 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 10 8, 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. 2. Principle and developments of different electromechanical balances 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 advantages 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 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 I 1 and I 2 respectively, the electromagnetic force is balanced by the weight of the test mass, which can be expressed as I 1I 2 ð2þ 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

4 4 S. Li et al. / Measurement 45 (2012) 1 13 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 which achieves a relative standard uncertainty about several parts in 10 6 [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 U2 ð3þ where C is the capacitance. The voltage balance determines h by precisely measuring the quantity K J. A Josephson voltage U J 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 h ¼ 16a mg l 0 ck J ðu2 Þ 90 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 10 7 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 = (36)10 34 Js with relative standard uncertainty of [18]. PTB also published the result of measuring the Planck constant h = (42)10 34 Js with relative standard uncertainty of using the capacitor voltage balance [17]. And this work is not being continued at present 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 I 1I I ¼ UI 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) 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 4mgv h ¼ R 2 J 90 R ð6þ K 90ðUIÞ 90 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 All these watt balances are aiming for the relative standard uncertainty U r < Energy balance 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 z 1 to z 2 as mgðz 1 z 2 Þ¼½Mðz 1 Þ Mðz 2 ÞŠI 1 I 2 ð7þ where M(z 1 ) and M(z 2 ) are the mutual inductances of the two coils in position z 1 and z 2 respectively. On the left hand of the equation is the gravity potential energy change when the test mass is moved vertically from z 1 to z 2 while in the right hand, it is the electromagnetic energy change. The relative position z 1 z 2 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 4mgðz 1 z 2 Þ h ¼ K 2 J 90 R K 90ð½Mðz 1 Þ Mðz 2 ÞŠI 1 I 2 Þ 90 ð8þ 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 (1r) has been achieved recently. Now, the joule balance has finished its prototype test. The result with 10 5 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 z 1 to z 2, if the levitated body has ideal diamagnetic properties, the equivalence of a mechanical energy and the electromagnetic energy then can be written as mgðz 1 z 2 Þ¼ Z z1 z 2 IðuÞdu ðu 1 I 1 u 2 I 2 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; z 1 z 2 is the travelling range for the levitated body along the vertical; u 1, u 2 and I 1, I 2 are the magnetic fluxes and electric currents in the supporting coil at z 1 and z 2 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 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 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 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 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]).

7 S. Li et al. / Measurement 45 (2012) due to the high temperature coefficient ( / C), the apparatus temperature should be controlled within a variation of ± 0.4mK. A value of h = (44)10 34 Js has published by NPL watt balance with a relative standard uncertainty of [7,8], which has a 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 (13)10 34 Js with relative uncertainty expanded to [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 The FG5-105 gravimeter took part in North American Comparison of Absolute Gravimeters (NA- CAG) 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 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 when a conventional electromagnet was used [41]. After a series of improvements [42 44] and replacing the electromagnet by a superconducting magnet, the Planck constant h = (58)10 34 Js with the relative standard uncertainty of was achieved in 1998 [25]. With years in finding and eliminating sources of errors, the measurement result was improved as h = (34) Js in 2005 with a relative standard uncertainty of [9]. The latest measured value of h = (24)10 34 Js leading the relative standard uncertainty record of was published in 2007 [10]. Currently, NIST is considering a new version watt balance experiment METAS watt balance The Swiss Federal Office of Metrology (OFMET, now ME- TAS, 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 1m 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 has been reported in 2008 with 18 months operation [51]. The latest measurement result h = (20)10 34 Js with relative uncertainty of from METAS watt balance [11], has been published recently. The new version of METAS watt balance is being developed now 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 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 By now, the LNE watt balance experiment has been still in progress and the first measurements are expected in end 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 with eleven series of measurements and a relative combined standard uncertainty [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].

9 S. Li et al. / Measurement 45 (2012) Fig. 9. The LNE watt balance NIM joule balance Fig. 10. The BIPM watt 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 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 10 7, 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 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 ), programmable Josephson junction array for measuring the mutual inductance, and the vacuum system 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) 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 of the total load on the pressure balance has been achieved and the further research is being continued 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 z 1 and z 2 are determined by laser interferometer. 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 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]. 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 N A is obtained by measuring the atomic volumes of two 28 Si spheres, and the value of the Planck constant is calculated by their product N A h which can be precisely measured with relative standard uncertainty of [12]. Recently, three latest results of these two approaches have been achieved: (1) the NPL watt balance reports the latest measurement result of h = (13) Js with relative standard uncertainty of ; (2) METAS has reported its first watt balance result, h = (20)10 34 Js with relative standard uncertainty of [11]; (3) the Avogadro project reported the newest result of N A = (18) mol 1 in 2011 [67] with a derived value of h = (20) Js and the relative standard uncertainty of The 2010 CODATA recommended value of h = (29) Js with relative standard uncertainty of is the latest available 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. Identification h(/10 34 Js) Relative standard uncertainty Fig. 13. Measurement results of the Planck constant. NPL (13) METAS (20) NIST (24) NIST (58) NPL (13)

12 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(/10 34 Js) Relative standard uncertainty Avogadro ( 28 Si) (20) Voltage balance (27) Gamma p (hi) (57) Faraday constant (88) following conditions are met: (1) at least three independent experiments reach the relative standard uncertainty ; (2) at least one of these experiments shall achieve the relative standard uncertainty within ; (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 10 7 ; (2) the watt balance experiment results are discrepant. The NPL result has a relative difference at the order of 10 7 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 ) and National Department Public Benefit Research Foundation (Grant No ). The authors would like to thank professors Zhonghua Zhang and Qing He at NIM for valuable discussions. 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