kILOGRAMOS

1. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 66, NO. 6, JUNE 2017 1267
Realization of the Kilogram Based on
the Planck Constant at NMIJ
Naoki Kuramoto, Lulu Zhang, Shigeki Mizushima, Kazuaki Fujita,
Yasushi Azuma, Akira Kurokawa, and Kenichi Fujii
Abstract—A change in the definition of the kilogram has
been proposed. The new definition will be based on the Planck
constant. After the change, the National Metrology Institute of
Japan (NMIJ) will realize the kilogram using the X-ray crystal
density method with a 28Si-enriched sphere. A pilot study to
confirm the international equivalence of the ability to realize the
kilogram from the new definition is ongoing, where the volume
measurement of a 28Si-enriched sphere by optical interferom-
etry and the sphere surface characterization by spectroscopic
ellipsometry and X-ray photoelectron spectroscopy required for
the realization were performed by NMIJ independently. The
mass of the sphere was determined with a relative standard
uncertainty of 2.4 × 10−8 based on the new definition. This
paper provides details of the measurements, the data analysis,
and the uncertainty evaluation.
Index Terms—Ellipsometry, kilogram, optical interferometry,
Planck constant, silicon crystal, X-ray photoelectron spec-
troscopy (XPS).
I. INTRODUCTION
THE International Committee for Weights and
Measures (CIPM) has proposed a change in the definition
of the unit of mass, the kilogram [1]. The new definition
will be based on a fixed value of the Planck constant and is
anticipated to be accepted in 2018 [2]. After the change in the
definition, national metrology institutes (NMIs) will realize
the kilogram based on the Planck constant. The National
Metrology Institute of Japan (NMIJ) will realize the new
kilogram definition using the X-ray crystal density (XRCD)
method [3]. This method enables the realization at the level
of 1 kg with a relative standard uncertainty of 10−8 using a
28Si-enriched sphere, and the measurements required for the
realization will be carried out by NMIJ independently.
To confirm the international equivalence of the ability to
realize the new definition by NMIs, a pilot study to compare
the realization based on the value of the Planck constant
provided by the International Council for Science, Committee
on Data for Science and Technology (CODATA) adjustment of
Manuscript received September 23, 2016; accepted September 26, 2016.
Date of publication December 2, 2016; date of current version May 10, 2017.
This work was supported by the Japan Society for the Promotion of Science
through the Grant-in-Aid for Scientific Research (B) under Grant KAKENHI
16H03901. The Associate Editor coordinating the review process was
Dr. Alessandro Ferrero. (Corresponding author: Naoki Kuramoto.)
The authors are with the National Metrology Institute of Japan/National
Institute of Advanced Industrial Science and Technology, AIST, Tsukuba
305-8563, Japan (e-mail: n.kuramoto@aist.go.jp; lulu.zhang@aist.go.jp;
s.mizushima@aist.go.jp; fujita.kazuaiki@aist.go.jp; azuma.y@aist.go.jp;
a-kurokawa@aist.go.jp; fujii.kenichi@aist.go.jp).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIM.2016.2624878
2014 [4] organized by the Consultative Committee for Mass
and Related Quantities is now ongoing. The calibration of
primary mass standards using the methods to realize the def-
inition of the kilogram is referred to as “primary realization”
in this paper. The pilot study compares the realizations at the
level of 1 kg obtained with the primary realization experiments
that are capable of determining mass with a relative standard
uncertainty of less than or equal to 2 × 10−7. As a participant
of this pilot study, the NMIJ performed the measurements
for the primary realization. In our previous report, only the
preliminary results of the realization were reported [5]. Details
of the primary realization are therefore described in this paper.
II. X-RAY CRYSTAL DENSITY METHOD
The XRCD method is one of the primary approaches to
realize the kilogram at a nominal mass of 1 kg after the change
in the definition [6]. This method counts the number N of Si
atoms in a Si sphere by measuring its volume VS and lattice
constant a. The number N is given as
N =
8VS
a3
(1)
where 8 is the number of atoms per unit cell of crystalline
silicon. The mass of the sphere mS is therefore
expressed as
mS = Nm(Si) (2)
where m(Si) is the mass of a single Si atom. The relation
between the Planck constant h and the Rydberg constant R∞
is given as
R∞ =
m(e)cα2
2h
(3)
where c is the speed of light in vacuum, α is the fine structure
constant, and m(e) is the mass of a single electron. The mass
of a single Si atom m(Si) is related to m(e) by
Ar (Si)
Ar (e)
=
m (Si)
m (e)
(4)
where Ar(e) and Ar(Si) are the relative atomic masses of
electron and Si, respectively. Silicon consists of three stable
isotopes, 28Si, 29Si, and 30Si. The value of Ar(Si) can therefore
be determined by measuring the isotopic amount-of-substance
fraction of each isotope. The relation between m(Si) and h is
thus given as [6]
h
m (Si)
=
1
2
Ar (e)
Ar (Si)
α2c
R∞
. (5)
0018-9456 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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2. 1268 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 66, NO. 6, JUNE 2017
Combining (1), (2), and (5), the sphere mass ms is expressed
in terms of h using
ms =
2hR∞
cα2
Ar (Si)
Ar (e)
8 Vs
a3
. (6)
Equation (6) is established on the assumption that atoms
only occupy the lattice sites and that on all the lattice sites,
Si atoms are placed in the Si sphere. In addition, the sphere
is covered by surface layers (SL) with a main constituent of
SiO2 [3]. Equation (6) should be therefore modified to
mcore =
2hR∞
cα2
Ar (Si)
Ar (e)
8Vcore
a3
− mdeficit (7)
where mcore and Vcore are the mass and volume of the “Si core”
part, which excludes the SL, respectively, and mdeficit is the
influence of point defects (i.e., impurities and self-point defects
in the crystal) on the core mass [3]. The mass of the sphere
msphere including the mass of the SL mSL is given as
msphere = mcore + mSL. (8)
The relative standard uncertainty of R∞/(α2 Ar(e)) in (7) is
estimated to be 4.5 × 10−10 [4], and the numerical value
of h will be exactly defined at the definition change. The
value of c is defined exactly. In our previous work, Vcore, a,
and Ar(Si) of two 1 kg 28Si-enriched spheres were measured
with relative uncertainties of 1.6 × 10−8, 5 × 10−9, and
1.8 × 10−9, respectively [3]. Presently, the new kilogram
definition can be therefore realized with a relative uncertainty
at the level of 10−8 using the 28Si-enriched spheres.
III. 28Si-ENRICHED CRYSTAL SPHERE
For the primary realization of the kilogram in the pilot study,
a 28Si-enriched crystal sphere AVO28-S5c was used at NMIJ.
This sphere was manufactured by the International Avogadro
Coordination (IAC) project, and details on the sphere are given
in [3]. The values of a, Ar(Si), and mdeficit of the sphere in (7)
were already measured by the IAC project [3]. There are no
known mechanisms that change the values of a, Ar(Si), and
mdeficit of Si crystals with respect to time when the Si crystals
are kept close to room temperature. The mass of the sphere
msphere is therefore determined from the value of the Planck
constant by measuring Vcore and mSL in (7) and (8). In the
pilot study, the value of the Planck constant h provided by the
CODATA adjustment of 2014 [4] was used for the realization.
This value for h was assumed to be exact, and its uncertainty
determined by CODATA was not included in the uncertainty
of the realization.
Fig. 1 shows the surface model of the sphere derived by the
IAC project based on the surface characterization using various
analysis techniques [3]. In addition to the oxide layer (OL),
a chemisorbed water layer (CWL), a physisorbed water
layer (PWL), and a carbonaceous layer (CL) are involved.
The CWL describes a chemically absorbed water layer that
is still present under ultrahigh vacuum conditions. The CL
is a carbonaceous contamination layer formed by different
adsorbed gases and contaminants, stemming from the environ-
ment during the measurement, handling, storage, and cleaning
of the sphere. The PWL describes a physically absorbed water
Fig. 1. SL model for characterization of the 28Si sphere [3].
layer, which has to be included if measurements are performed
under ambient conditions. These layers are hereinafter referred
to as SL. For the surface characterization in the pilot study
at NMIJ, the thickness and mass of the SL were evaluated
using an X-ray photoelectron spectroscopy (XPS) system and
a spectroscopic ellipsometer. For the core characterization,
an optical interferometer was used to measure the sphere
volume. A phase shift is introduced on the reflection of the
light beam on the sphere surface. The volume measured by
the interferometer is thus the “apparent volume,” which is
different from the core volume. The apparent volume should
be corrected for the phase shift to obtain the core volume based
on information about the surface characterization. The details
of each measurement apparatus are presented in the following
sections.
IV. VOLUME MEASUREMENT AND
SURFACE CHARACTERIZATION
A. Measurement Sequence
From October to December 2015, the volume was measured
by the optical interferometer. The surface was characterized by
the XPS system in January 2016 and by the ellipsometer in
February 2016.
B. Cleaning of the 28Si Sphere
Before the volume measurement by the interferometer, the
28Si sphere was cleaned using the same procedure as that used
in the international comparisons of the mass and diameter
measurements of a 1 kg Si sphere in the IAC project [7], [8].
First, the sphere was washed with a dilute aqueous solution
of a detergent (Deconex OP164, Borer Chemie AG), during
which the sphere was rotated between two hands wearing
nitrile gloves. Next, the sphere was placed under a stream
of water purified by Milli-Q Integral system (Merck KGaA).
Finally, ethanol (Infinity Pure grade, Wako Pure Chemical
Industries, Ltd.) was poured over the sphere. After cleaning,

3. KURAMOTO et al.: REALIZATION OF THE KILOGRAM BASED ON THE PLANCK CONSTANT AT NMIJ 1269
Fig. 2. Schematic of the optical interferometer used to measure the
volume of the 28Si sphere. The 28Si sphere and the etalon are installed in
a vacuum chamber equipped with an active radiation shield to control the
sphere temperature. The uncertainty of the sphere temperature measurement
is estimated to be 0.62 mK [9].
the sphere was stored in a clean booth equipped with an air-
purified system overnight. The gloves were also dried in the
booth and were used to install the sphere in each apparatus.
Azuma et al. [3] have reported that the mass of the sphere
was slightly decreased by cleaning. To keep the sphere mass
as constant as possible during the realization, the sphere
was cleaned only in October 2015, before the volume
measurement.
C. Optical Interferometer
Fig. 2 shows a schematic of the optical interferometer
used to determine the volume of the 28Si sphere by optical
frequency tuning [9]. A Si sphere is placed in a fused-quartz
Fabry-Perot etalon. The sphere and etalon are installed in a
vacuum chamber equipped with an active radiation shield to
control the sphere temperature. The pressure in the chamber
is reduced to 10−2 Pa. A laser beam from an external cavity
diode laser is split into two beams (Beam 1 and Beam 2).
They are reflected by mirrors toward opposite sides of the
etalon. The light beams reflected from the inner surface of the
etalon plate and the adjacent surface of the sphere interfere to
produce concentric circular fringes. These are projected onto
Charge Coupled Device (CCD) cameras. Measurements of the
fractional fringe order of interference for the gaps between the
sphere and the etalon, d1 and d2, are carried out by phase-
shifting interferometry [9], [10]. The sphere diameter D is
calculated as D = L − (d1 + d2), where L is the etalon
spacing. To determine L, the sphere is removed from the light
path by a lifting device installed underneath the sphere, and
Beam 1 is interrupted by a shutter. Beam 2 passes through a
hole in the lifting device, and the beams reflected from the two
etalon plates produce fringes on a CCD camera. The fringes
are also analyzed by phase-shifting interferometry. The volume
is determined based on the diameter measurement from many
directions. The require phase shifts are produced by changing
Fig. 3. Picture of the surface characterization system using spectroscopic
ellipsometry. This system has a vacuum chamber, and the surface characteri-
zation can be performed both in air and in vacuum. This can give information
about the change in the surface characteristics when the sphere is in air and
in vacuum [15], [16].
the optical frequency of the diode laser. The optical frequency
is controlled based on the optical frequency comb, which is
used as the national length standard of Japan. The details of
the volume measurements are given in [9] and [11].
D. X-Ray Photoelectron Spectroscopy System
The main component of the XPS system is ULVAC-Phi
1600C equipped with a monochromatic Al Kα X-ray source.
The pressure in the chamber is reduced to 1.5 × 10−6 Pa.
A manipulator with a five-axis freedom manipulator is
installed in the chamber to realize the rotation of the sphere
around the horizontal and vertical axes for the mapping of
the entire surface. The sphere is placed on two rollers of the
manipulator during the measurement. The rollers are made
of polyimide for protecting the sphere surface from damage
during the rotation. The details of the XPS system are given
in [12]–[14].
E. Spectroscopic Ellipsometer
Fig. 3 shows a picture of the spectroscopic ellipsometer
(Semilab GES5E) equipped with an automatic sphere rotation
system. Its spectral bandwidth ranges from 250 to 990 nm.
The ellipsometer and automatic sphere rotation system are
integrated into a vacuum chamber to characterize the SL both
in air and in vacuum, where the pressure is reduced to 1
× 10−3 Pa. The ellipsometric measurement can be carried
out over the entire sphere surface using the automatic sphere
rotation system. The details of the ellipsometer are provided
in [15] and [16].
V. REALIZATION OF THE KILOGRAM
A. Volume Measurement by Optical Interferometer
A sphere rotation mechanism installed under the sphere was
used to measure the diameter from different directions [17].
The measurement directions were based on 145 directions
that are distributed near uniformly on the sphere surface [11].
The 145 directions consisted of 11 sets of 12 directions and
1 set of 13 directions, and the etalon spacing was measured
before and after each set and was used to determine the

4. 1270 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 66, NO. 6, JUNE 2017
Fig. 4. Mollweide map projection of the distribution of the diameter based
on 145 directions for the 28Si sphere.
Fig. 5. 3-D plots of the distribution of the diameter. The peak-to-valley value
of the diameter was 69 nm.
diameters in each set. The temperature of the sphere was
measured by small platinum resistance thermometers (PRTs)
inserted into copper blocks contacted to the sphere. The copper
blocks were coated with polyether ether ketone to prevent
damage of the silicon sphere. The PRTs were calibrated using
temperature fixed points in ITS-90. The measured diameters
were converted to those at 20.000 °C using the thermal
expansion coefficient of the enriched 28Si crystal [18]. Fig. 4
shows the Mollweide map projection of the distribution of
the diameter based on the 145 directions. The 3-D plot of the
diameter is shown in Fig. 5, where the deviation from the mean
diameter is enhanced. The peak-to-valley value of the diameter
was 69 nm.
The measurement from the 145 directions was performed
16 times. The total number of measurement directions was
therefore 2320. Between each set of 145 directions, the sphere
was rotated to distribute the starting point of each set of
the measurement to the vertices of a regular dodecahedron.
Because the ten directions defined by the vertices of a regular
dodecahedron are distributed equally, this procedure therefore
distributed all of the measurement points as uniformly as
possible. The experimental standard deviation of the mean
diameter was estimated to be 0.1 nm.
The measured diameter and volume are the apparent diame-
ter and volume, which are not corrected for the phase shift due
to the SL. Table I shows the uncertainty budget in the deter-
mination of the apparent volume Vapp. The apparent volume
was determined to be 430.891 2927 × 10−6 m3 with a relative
uncertainty of 2.0 × 10−8. The largest uncertainty source is
the phase correction due to the diffraction effect [9], [10].
TABLE I
UNCERTAINTY BUDGET IN THE DETERMINATION OF THE APPARENT
VOLUME, Vapp, OF THE 28Si SPHERE AT 20.000 °C AND 0 Pa
Fig. 6. Distribution of the measurement points by XPS and ellipsometry ()
and those by ellipsometry (♦) only. The measurement points by XPS were also
characterized by ellipsometry. The identification of the measurement positions
was achieved by the three marks present on the sphere.
B. Surface Characterization Using XPS
The XPS spectra were measured at 52 points distributed
near-uniformly on the sphere surface. The 52 measurement
points were defined by dividing the sphere surface into small
cells with equal areas, and the measurement points were dis-
tributed individually in each cell. Fig. 6 shows the distribution
of the measurement points, in which the measurement points
by XPS are shown by solid diamonds.
1) Oxide Layer: The thickness of the OL was determined
by analyzing the XPS Si 2p core-level spectra, in which
peaks corresponding to the SiO2 layer and the interfacial OL
(Si2O3, SiO, and Si2O) were observed. For rigorous evaluation
of the OL thickness, accurate values of the attenuation lengths

5. KURAMOTO et al.: REALIZATION OF THE KILOGRAM BASED ON THE PLANCK CONSTANT AT NMIJ 1271
for the Si 2p electrons in SiO2, Si2O3, SiO, and Si2O were
determined by an SI-traceable X-ray reflectometry (XRR)
system at NMIJ [19] using Si flat samples with different
thicknesses of thermal SiO2. The details of the determination
of the attenuation lengths and the thickness of each layer are
summarized in [12]–[14]. The OL thickness was determined as
the sum of each OL. The average OL thickness at the 52 points
was estimated to be 1.26(9) nm [13], [14].
2) Carbonaceous Layer: In the XPS C 1s core-level spectra,
peaks corresponding to the C-C/H, C-O, CF2, and CF3 bonds
were observed. In our previous work, the main constituent of
the CL was estimated to be a hydrocarbon [19]. However,
the peaks assigned both to C-C/H and to C-O bonds were
clearly observed in this work. Since ethanol was used in
the final step of the sphere cleaning, the peak assigned to
C-O bonds was estimated to be from ethanol. The main
constituents were therefore estimated to be both ethanol and
a hydrocarbon. The peaks assigned to the CF2 and CF3
bonds were assumed to be from perfluoroalkoxy (PFA). The
thickness of the CL dCL in Fig. 1 was therefore determined
on the assumption that the CL was composed of an ethanol
sublayer, a hydrocarbon sublayer, and a PFA sublayer. The
origin of the sublayer involving fluorine was estimated to be
the sphere rotation mechanism in the volume measurement by
the optical interferometer. The details of the contamination are
still under investigation. However, as described in Section IV,
the volume measurement was performed prior to the other
measurements for the primary realization. The PFA layer was
therefore involved in the analysis of all the measurements.
For determination of the thickness of each layer, the density
of each sublayer was estimated to be 0.79(20) g/cm3,
0.99(20) g/cm3, and 2.15(40) g/cm3 for the ethanol, hydrocar-
bon, and PFA sublayers, respectively, where the large uncer-
tainties were attributed to the lack of adequate information
to clarify the chemical composition of the CL. The average
thicknesses of each sublayer at the 52 points were estimated
to be 0.62(10), 0.45(6), and 0.20(4) nm for the ethanol,
hydrocarbon, and PFA sublayers, respectively. From these
results, dCL was estimated to be 1.27(12) nm. In addition,
the density of the CL was estimated to be 1.08(14) g/cm3 by
considering the thickness and density of each sublayer. The
details of the procedure to determine the CL thickness are
given in [13] and [14].
C. Surface Characterization Using
Spectroscopic Ellipsometry
Before the surface analysis of the 28Si sphere, the ellip-
someter was calibrated using Si flat samples having SiO2
layers of different thicknesses. The SiO2 layer thicknesses
were calibrated by the XRR system of NMIJ [9], [19]. The
details of the calibration procedure of the ellipsometer are
given in [9], [15], [16], and [19].
The ellipsometric measurement for the 28Si sphere was
performed at 812 points on the sphere both in air and in
vacuum. The 812 points were defined by subdividing the
sphere surface into small cells of the same area so that
the measurement points were distributed near-uniformly over
the entire surface. The distribution of the measurement points
are shown in Fig. 6, in which the measurement points by
ellipsometry are shown with open diamonds.
The surface model shown in Fig. 1 was fitted to the mea-
sured data to obtain the OL thickness dOL. In the fitting, only
dOL and the incident angle of the light relative to the surface
normal of the sphere were adjusted and the thickness of the
other layers was fixed, in which the thicknesses of the CWL
and PWL determined by gravimetry [3] and the thickness
of the CL determined by XPS in this paper were used. The
dispersion data of the optical constants (refractive index and
extinction coefficient) of the CL was estimated by combining
those of ethanol [20] and those of a hydrocarbon [19]. For
the other layers and the Si substrate, the optical constants in
the database of a simulation software (SEA, Semilab Co. Ltd.)
were used. The PWL was not considered in the determination
of dOL in vacuum.
The OL thickness was evaluated to be 1.13(29) nm in
vacuum and 0.89(30) nm in air. The weighted mean of the two
thicknesses was 1.01(30) nm. The details of the procedure to
determine the OL thickness are given in [15] and [16].
The thickness dOL was also measured using the XPS system
to be 1.26(9) nm. The weighted mean of dOL determined
by the two different techniques was 1.24(9) nm. This thick-
ness was used as the OL thickness for the evaluation of
Vcore and mSL in this work.
In our previous work, the OL thickness on AVO28-S5c
was determined to be 0.91(14) nm at Physikalisch-Technische
Bundesanstalt by an ellipsometer calibrated using a combined
XRR/X-ray fluorescence analysis measurement [3]. The NMIJ
also determined the OL thickness to be 0.76(27) nm at NMIJ
by an ellipsometer calibrated using XRR [3]. In this paper, the
OL thickness was estimated to be 1.26(9) nm, mainly by XPS
and is slightly larger than in the previous work. This slight
difference may be explained by the following two possibilities.
One possibility is that the OL on the sphere may have contin-
ued to grow gradually after repolishing of the sphere in 2013.
It should be noticed that the OL thickness on the sphere
before repolishing was estimated to be 1.52(20) nm [21]. The
other possibility is that XPS was first introduced for the OL
thickness measurement on the Si sphere in this paper. This
new method may have detected information about the OL that
was not detected in the previous measurements. Monitoring
of the long-term stability of the OL thickness by different
methods is therefore necessary for the accurate OL thickness
measurement.
VI. DETERMINATION OF THE SPHERE MASS
A. Surface Mass of the Sphere
The mass of the SL under vacuum mSL is given as
mSL = mOL + mCL + mCWL (9)
where mOL, mCL, and mCWL are the masses of the OL, CL,
and CWL, respectively. The masses were calculated from the
thickness and density of each layer. The calculated masses
are summarized in Table II with the density and thickness
of each layer. The total mass of the SL was estimated to
be 120.6(8.9) µg.

6. 1272 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 66, NO. 6, JUNE 2017
TABLE II
MASS, THICKNESS, AND DENSITY OF SLs IN VACUUM
TABLE III
OPTICAL CONSTANTS OF EACH LAYER
B. Core Volume of the Sphere
To determine the Si core volume, the total phase retardation
on reflection at the sphere surface δ was calculated based
on the procedure in [9]. To calculate δ, the thickness and
the optical constants of each layer summarized in Table III
were used. The refractive index n of each sublayer consist-
ing of the CL was estimated to be 1.36(13), 1.47(15), and
1.35 (20) for the ethanol, hydrocarbon, and PFA sublayers,
respectively. The extinction coefficient k of each sublayer
was estimated to be for 0.0(1), 0.0(1), and 0.0(2) for the
ethanol, hydrocarbon, and PFA sublayers, respectively. The
values of n and k of the CL were estimated to be 1.40(15)
and 0.0(1), respectively, by considering the thickness of each
sublayer. The phase shift on reflection (δ − π) was estimated
to be −0.054(3) rad. The effect of this phase shift on the
gap measurement d was 2.73(16) nm. This means that the
actual diameter including the SL is larger than the apparent
diameter by 5.45(32) nm. The actual diameter Dactual is
therefore obtained by Dactual = Dapp + 2d. The phase shift
correction to obtain the Si core diameter from the apparent
diameter d0 was determined by d0 = 2(d − dtotal),
where dtotal is the sum of thicknesses of all the layers. The
value of d0 was estimated to be −0.13(8) nm. The Si core
diameter Dcore is determined to be 93.710 811 34(63) mm by
Dcore = Dapp +d0. The Si core volume was thus determined
to be 430. 891 291 × 10−6 m3 with a relative standard
uncertainty of 2.0 × 10−8.
C. Core Mass of the Sphere
The core mass mcore was determined by (7) to
be 999.698 3365 g with a relative uncertainty of 2.2 × 10−8.
Table IV shows the quantities used to determine mcore. The
relative uncertainty of the sphere core volume determination
by the optical interferometer was estimated to be 2.0 × 10−8,
being the largest uncertainty source in the determination
of mcore.
Fig. 7. Comparison of the results of the mass determinations with two
different approaches. : msphere determined by the XRCD method based on
the Planck constant and ♦: msphere determined by gravimetry based on the
present definition of the kilogram.
D. Sphere Mass
The mass of the sphere in vacuum msphere was determined
by (8) to be 999.698 4571 g with a relative uncertainty
of 2.4 × 10−8. Table V shows the uncertainty budget of the
evaluation of msphere. The largest uncertainty source is the
determination of the core volume of the sphere.
E. Comparison of the Mass Determinations
For the evaluation of the reliability of the primary real-
ization, the sphere mass was also determined by referring to
mass standards traceable to the International Prototype of the
Kilogram (IPK) in March 2016 using a vacuum balance after
the surface characterization by XPS [22], [23]. Fig. 7 shows
the comparison of the results of the mass determinations.
The masses determined by the two different approaches agree
within their uncertainties. This good consistency demonstrates
that the primary realization of the kilogram at NMIJ in this
paper is highly reliable.
VII. CALIBRATION OF THE TRAVELING STANDARDS
In the pilot study, the participants calibrate their own
traveling standards and send them to the Bureau International
des Poids et Mesures (BIPM), where mass comparisons among
the traveling standards from all the participants are carried
out. At NMIJ, two platinum-iridium weights and two stainless
steel weights were used as the traveling standards. The masses
of the weights were compared with that of the 28Si sphere
determined in this paper from the value of the Planck constant.
The BIPM is now carrying out the mass comparisons. The
results of the pilot study are scheduled to be published in
June 2017.
VIII. EFFECT OF CLEANING ON THE SPHERE MASS
To confirm the effect of cleaning on the sphere mass, the
sphere was cleaned in March 2016 after the mass measurement
by the vacuum balance by the same procedure described in
Section IV. After the cleaning, the surface was again character-
ized using the XPS system in April and May 2016 [13], [14].
The peaks corresponding to CF2 and CF3 were not observed.
The thicknesses of the hydrocarbon sublayer and the ethanol
sublayer decreased to 0.27(4) nm and 0.45(7) nm, respectively.

7. KURAMOTO et al.: REALIZATION OF THE KILOGRAM BASED ON THE PLANCK CONSTANT AT NMIJ 1273
TABLE IV
QUANTITIES USED TO DETERMINE THE CORE MASS mcore
TABLE V
UNCERTAINTY BUDGET OF THE SPHERE MASS msphere
On the other hand, the OL thickness measured after the
cleaning was in good agreement with that measured before the
cleaning. Based on the results of this surface characterization,
the mass of the SLs mSL after the cleaning was estimated to
be 100.1(7.5) µg. The reduction of mSL introduced by the
cleaning was therefore estimated to be 20.5(3.9) µg, with a
correlation coefficient between the two XPS measurements
of 0.9. After the XPS measurement in April and May 2016,
the mass of the sphere was measured again referring to
mass standards traceable to the IPK in June 2016 using
the vacuum balance. The mass measured in June 2016 was
smaller than that measured in March 2016. The mass reduction
was determined to be 25.6(3.7) µg [22], [23]. This good
consistency of the mass decrease obtained by the two different
approaches shows that the surface characterization for the
primary realization at NMIJ is highly reliable.
IX. CONCLUSION
For the pilot study on the primary realization of the kilogram
after the definition change, the mass of a 1-kg 28Si sphere
was determined based on the value of the Planck constant h
using the XRCD method at NMIJ independently. The h
value provided by the 2014 CODATA fundamental adjustment
was used for the realization, and this value was assumed
to be exact. The sphere volume was determined by optical
interferometry, and the surface was characterized by XPS
and spectroscopic ellipsometry. Summarizing the results of
the volume measurement and the surface characterization,
the sphere mass was determined with a relative standard
uncertainty of 2.4 × 10−8. The sphere mass was also measured
by the vacuum balance based on the present definition of the
kilogram. The sphere masses determined by the two different
approaches agree within their uncertainties, demonstrating that
the primary realization at NMIJ is highly reliable.
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Naoki Kuramoto was born in Kanagawa, Japan,
in 1971. He received the B.S., M.S., and
Ph.D. degrees in chemistry from Saga University,
Saga, Japan, in 1993, 1995, and 1998, respectively.
From 1995 to 1998, he was a Research Fellow
of the Japan Society for the Promotion of Science
(DC1, for doctoral course student). From 1998 to
1999, he was with the Tokyo University of Agricul-
ture and Technology, Tokyo, Japan, in the field of
physical acoustics. In 1999, he joined the National
Metrology Institute of Japan/the National Institute of
Advanced Industrial Science and Technology (formerly the National Research
Laboratory of Metrology), Tsukuba, Japan, where he is currently a Senior
Researcher with the Mass Standards Group. His current research interests
include laser interferometry and mass standards.
Dr. Kuramoto is a member of the Japan Society of Applied Physics and the
Chemical Society of Japan.
Lulu Zhang was born in Beijing, China, in 1968.
She received her M.S. and Ph.D. degrees from
Osaka University, Osaka, Japan, in 1995 and 1998,
respectively.
From 1997 to 1998, she was a fellow with the
Japan Society for the Promotion of Science. From
1998 to 2004, she was a post doctoral researcher at
the National Institute of Advanced Industrial Science
and Technology (AIST), Tsukuba, Japan. She joined
the National Metrology Institute of Japan (NMIJ),
AIST, in 2004, where she is currently a senior
research scientist in the Surface and Nano Analysis Research Group. Her
research interests include surface analysis and thickness metrology of thin
films.
Shigeki Mizushima was born in Toyama, Japan,
in 1972. He received the B.S. and M.S. degrees in
physics from the University of Tokyo, Tokyo, Japan,
in 1995 and 1997, respectively.
He is currently with the National Metrology
Institute of Japan/the National Institute of Advanced
Industrial Science and Technology, Tsukuba, Japan.
His current research interests include mass and
gravity measurements.
Kazuaki Fujita was born in Hyogo, Japan, in 1990.
He received the B.S. and M.S. degrees in engineer-
ing from the Tokyo Institute of Technology, Tokyo,
Japan, in 2013 and 2015, respectively.
He joined the National Metrology Institute of
Japan (the National Research Laboratory of Metrol-
ogy)/the National Institute of Advanced Indus-
trial Science and Technology, Tsukuba, Japan, in
2015. His current research interests include surface
analysis for mass standards.
Yasushi Azuma was born in Yamagata, Japan, in
1972. He received the B.S., M.S., and Ph.D. degrees
in technology from Chiba University, Chiba, Japan,
in 1995, 1997, and 2000, respectively. His doc-
toral work focused on the electronic structure and
molecular orientation of ultra-thin films of π conju-
gated molecules studied by multiple surface analysis
technique.
He was a Research Fellow of the Japan Soci-
ety for the Promotion of Science from 1999 to
2000. He joined the National Metrology Institute
of Japan/National Institute of Advanced Industrial Science and Technology,
Tsukuba, Japan, in 2001, where he is currently a Senior Research Scientist
with the Surface and Nano-Analysis Research Group. His current research
interests include the development of thickness metrology and standard mate-
rials consisting of thin and multilayer films.
Akira Kurokawa was born in Ehime, Japan,
in 1962. He received the B.S., M.S., and
Ph.D. degrees in engineering from Osaka
University, Suita, Japan, in 1985, 1987, and 1991,
respectively. His doctoral work focused on the ion
beam induced surface segregation.
He joined the Electrotechnical Laboratory
(currently the National Institute of Advanced
Industrial Science and Technology), Tsukuba,
Japan, where he is involved in the development of
the silicon oxidation process with high-purity ozone
gas and the uniform silicon dioxide thin film fabrication. He has been the
Chief of the Surface and Nano-Analysis Section with the National Metrology
Institute of Japan, Tsukuba.
Kenichi Fujii received the B.E., M.E., and
Ph.D. degrees from Keio University, Yokohama,
Japan, in 1982, 1984, and 1997, respectively. His
doctoral work focused on the absolute measurement
of the density of silicon crystals.
In 1984, he joined the National Metrology Institute
of Japan (NMIJ, formerly the National Research
Laboratory of Metrology), Tsukuba, Japan. In 1988,
he started an absolute measurement of the den-
sity of silicon crystals for the determination of the
Avogadro constant. He developed a scanning-type
optical interferometer for measuring the diameter of the silicon sphere. From
1994 to 1996, he was with the National Institute of Standards and Technology,
Gaithersburg, MD, USA, as a Guest Researcher of the Electricity Division to
engage on the watt balance experiment. He is currently the Prime Senior
Researcher with the Research Institute for Engineering Measurement and the
Leader of the Mass Standards Group with NMIJ.
Dr. Fujii is a member of the CODATA Task Group on Fundamental
Constants and the Consultative Committee for Units of the International
Committee for Weights and Measures. He serves as the Coordinator of
the International Avogadro Coordination project, and the Chairperson of the
Working Group on Density and Viscosity of the Consultative Committee for
Mass and Related Quantities.