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The CODATA 2017 Values of \bm{h}, \bm{e}, \bm{k}, and \bm{NAN_{\rm A}} for the Revision of the SI

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Abstract and Figures

Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.
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L13 © 2018 BIPM & IOP Publishing Ltd Printed in the UK
Bureau International des Poids et Mesures
1. Introduction
The international system of units (SI) has been slowly
evolving from an artifact based system to one based on
values of fundamental constants and invariant properties of
atoms. The quantitative limitations of the last remaining base
unit of the SI dened by an artifact, the kilogram, have been
known since at least the third verication of national kilogram
proto types (Quinn 1991, Girard 1994). As a consequence
the possible role of the fundamental constants in replacing
the kilogram has been discussed in earnest for nearly three
decades. International consensus on the foundation of a new
system of units based on exactly dened values of the Planck
constant h, elementary charge e, Boltzmann constant k, and
Avogadro constant
NA
was reached during the 24th meeting
of the General Conference on Weights and Measures (CGPM
2011). Progress in the accuracy and consistency of the research
results has enabled the 106th International Committee for
Weights and Measures (CIPM) to recommend proceeding
with the adoption of the revised SI (CIPM 2017).
The Committee on Data for Science and Technology
(CODATA), through its Task Group on Fundamental
Constants (TGFC), periodically provides the scientic and
technological communities with a self-consistent set of inter-
nationally recommended values of the basic constants and
conversion factors of physics and chemistry. Because of this
role, the CGPM invited the CODATA TGFC to carry out a
special least-squares adjustment (LSA) of the values of the
fundamental physical constants to provide values for dening
constants to form the foundation for the revised SI (CGPM
2011). The results of that adjustment are given here, namely,
the numerical values of h, e, k, and NA, each with a sufcient
number of digits to maintain consistency between the present
and revised SI as proposed by the Consultative Committee for
Units (CCU) and agreed to by the CIPM (CIPM 2016). These
numbers are recommended to the 26th CGPM to establish the
revised SI when it convenes in November 2018.
Metrologia
The CODATA 2017 values of
h
,
e
,
k
, and
NA
for the revision of the SI
DBNewell1, FCabiati, JFischer, KFujii, SGKarshenboim,
HSMargolis , Ede Mirandés, PJMohr, FNez, KPachucki, TJQuinn,
BNTaylor, MWang, BMWood and ZZhang
Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants
E-mail: dnewell@nist.gov
Received 2 August 2017, revised 19 October 2017
Accepted for publication 20 October 2017
Published 29 January 2018
Abstract
Sufcient progress towards redening the International System of Units (SI) in terms of exact
values of fundamental constants has been achieved. Exact values of the Planck constant h,
elementary charge e, Boltzmann constant k, and Avogadro constant NA from the CODATA
2017 Special Adjustment of the Fundamental Constants are presented here. These values
are recommended to the 26th General Conference on Weights and Measures to form the
foundation of the revised SI.
Keywords: international system of units, fundamental constants, SI redenition
(Some guresmay appear in colour only in the online journal)
D B Newell etal
The CODATA 2017 values of
h
,
e
,
k
, and
NA
for the revision of the SI
Printed in the UK
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MTRGAU
© 2018 BIPM & IOP Publishing Ltd
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Metrologia
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Short Communication
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Metrologia
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Metrologia 55 (20 18 ) L1 3 – L16
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2. The CODATA 2017 special adjustment
The input data for the CODATA 2017 Special Adjustment
includes the input data used in the nal CODATA 2014 regular
adjustment on which the 2014 recommended values are based.
Of these data, which are given in tablesXV-XIX of Mohr etal
(2016a), the following were omitted: the four cyclotron fre-
quency ratios, items B8, B9, B11, and B12 that have been super-
seded by the 2016 atomic mass evaluation (Huang etal 2017,
Wang et al 2017), and all measurements of the Newtonian
constant of gravitation G. Key data that were published or
accepted for publication before the 1 July 2017 closing date
of the CODATA 2017 Special Adjustment and have a signi-
cant impact on the determination of h, e, k, and NA are listed in
table1. The full list of data considered for the CODATA 2017
Special Adjustment is given in tables2–5 in Mohr etal (2018).
Of note are data that are not included for the same reasons they
were omitted from the 2014 adjustment. In particular, the mea-
surements in muonic hydrogen and deuterium that have led to
the proton radius ‘puzzle’ were not included. These data would
have no effect on the 2017 values of h, e, k, and NA, but will be
reconsidered for the next CODATA periodic adjustment.
The CODATA 2017 Special Adjustment follows the same
procedures as the previous periodic CODATA adjustments
of the fundamental constants (Mohr and Taylor 2000, 2005,
Mohr etal 2008a, 2008b, Mohr etal 2012a, 2012b, Mohr etal
2016a, 2016b). Details of the Special Adjustment analysis
are given in Mohr etal (2018). In general, the measure the
CODATA TGFC uses for consistency of an input datum is the
normalized (or reduced) residual of that datum given by the
LSA, that is, the difference between an input datum and its
adjusted value divided by the input datum uncertainty. If a
residual for an input datum is larger than two, the TGFC iden-
ties the fundamental constant primarily inuenced by that
datum as well as other input data that inuence the same con-
stant. The uncertainties of this subset of input data are multi-
plied by a factor that is large enough that the relevant residuals
are two or less. To achieve consistency, multiplicative expan-
sion factors were applied to the uncertainties of two subsets
of input data corresponding to two adjusted constants for the
2017 Special Adjustment.
The rst subset consists of the eight input data for the
Planck and Avogadro constants listed in table1, relevant to
the adjusted value of the Planck constant. The uncertainties
of these input data are multiplied by a factor of 1.7. With this
expansion of the uncertainties of the eight data, ve have rela-
tive standard uncertainties ur at or below
, with two
at or below
, where the latter includes results from
both the Kibble balance and the x-ray crystal density (XRCD)
methods.
The second subset of expanded data consists of the input
data that determine the relative atomic mass of the proton:
the 2016 atomic mass evaluation value of
1H
and the cyclo-
tron frequency ratio of hydrogenic carbon to the proton, items
B2 and B12, respectively, of table 4 in Mohr et al (2018).
Coincidentally, an expansion factor of 1.7 was also appropriate
Table 1. Key data for the determination of h, e, k, and NA in the CODATA 2017 Special Adjustment. See Mohr etal (2017) for a complete
list of input data.
   Source IdenticationaQuantityb     Value Rel. stand. uncert ur
Schlamminger etal (2015) NIST-15 h
6.626 069 36
(
38
)
×10−34
J s
5.7 ×10−8
Wood etal (2017) NRC-17 h
6.626 070 133
(
60
)
×10−34
J s
9.1 ×10−9
Haddad etal (2017) NIST-17 h
6.626 069 934
(
88
)
×10−34
J s
1.3 ×10−8
Thomas etal (2017) LNE-17 h
6.626 070 40
(
38
)
×10−34
J s
5.7 ×10−8
Azuma etal (2015) IAC-11 NA
6.022 140 95
(
18
)
×1023
mol−1
3.0 ×10−8
Azuma etal (2015) IAC-15 NA
6.022 140 70
(
12
)
×1023
mol−1
2.0 ×10−8
Bartl etal (2017) IAC-17 NA
6.022 140 526
(
70
)
×1023
mol−1
1.2 ×10−8
Kuramoto etal (2017) NMIJ-17 NA
6.022 140 78(15)×1023
mol−1
2.4 ×10−8
Moldover etal (1988) NIST-88 R
8.314 470(15)
J mol−1 K−1
1.8 ×10−6
Pitre etal (2009) LNE-09 R
8.314 467(23)
J mol−1 K−1
2.7 ×10−6
Sutton etal (2010) NPL-10 R
8.314 468(26)
J mol−1 K−1
3.2 ×10−6
Pitre etal (2011) LNE-11 R
8.314 455(12)
J mol−1 K−1
1.4 ×10−6
Pitre etal (2015) LNE-15 R
8.314 4615(84)
J mol−1 K−1
1.0 ×10−6
Gavioso etal (2015) INRIM-15 R
8.314 4743(88)
J mol−1 K−1
1.1 ×10−6
Pitre etal (2017) LNE-17 R
8.314 4614(50)
J mol−1 K−1
6.0 ×10−7
Podesta etal (2017) NPL-17 R
8.314 4603(58)
J mol−1 K−1
7.0 ×10−7
Feng etal (2017) NIM-17 R
8.314 459
(
17)
J mol−1 K−1
2.0 ×10−6
Gaiser etal (2017) PTB-17
A
(
4He
)/
R
6.221 140
(
12
)
×10−8
m3 K J−1
1.9 ×10−6
Qu etal (2017) NIM/NIST-17 k/h
2.083 6630
(
56
)
×1010
Hz K−1
2.7 ×10−6
a IAC: International Avogadro Coordination; INRIM: Istituto Nazionale di Ricerca Metrologica, Torino, Italy; LNE: Laboratoire national de métrologie et
d’essais, Trappes and La Plaine-Saint-Denis, France; NIM: National Institute of Metrology, Beijing, PRC; NIST: National Institute of Standards and Tech-
nology, Gaithersburg, MD, and Boulder, CO, USA; NMIJ: National Metrology Institute of Japan, Tsukuba, Japan; NPL: National Physical Laboratory, Ted-
dington, UK; NRC: National Research Council Canada, Ottawa, Canada; PTB: Physikalisch-Technische Bundesanstalt, Braunschweig and Berlin, Germany.
b h: Planck constant; NA: Avogadro constant;R: molar gas constant;
A
(
4He
)/
R
: molar polarizability of
4He
gas to the molar gas constant quotient;k/h: Boltz-
mann constant to Planck constant quotient.
Metrologia 55 (2018) L13
Short Communication
L15
in this case, although its application has no effect on the 2017
values of h, e, k, and NA.
3. Results
Figure 1 shows values of h inferred from the key input data
in table1 and the nal CODATA 2017 value. The values of
k inferred from the key input data in table 1 and the nal
CODATA 2017 value are shown in gure2. The nal values
and uncertainties of h, e, k, and NA from the 2017 CODATA
Special Adjustment are given in table2.
A requirement by the CGPM (2011) is that the revised SI
be consistent with the present SI. In the SI prior to rede-
nition, the following quantities have exactly dened values:
the international prototype of the kilogram
m(K)=1 kg
, the
vacuum magnetic permeability
µ0=4π×10−7Hm
−1
, the
triple point of water
TTPW =273.16 K
, and the molar mass
of carbon-12,
M
(
12C
)=
0.012 kg mol−1
. In the revised SI,
these quantities are determined experimentally with associ-
ated uncertainties. As stated in the agreed upon CCU recom-
mendation (CIPM 2016), the number of digits for the exact
numerical values of h, e, and NA to dene the revised SI are
determined by requiring that the numerical values of
m(K)
,
µ0
, and
M
(
12C)
remain consistent with their previous exact
values within their relative standard uncertainties given by
the CODATA 2017 Special Adjustment. The number of digits
for k is chosen such that
TTPW
is equal to 273.16 K within
a relative standard uncertainty at the level which TTPW can
be realized (CCT 2017). The recommended exact numerical
values of h, e, k, and NA to establish the revised SI are given
in table3.
4. Summary
Sufcient progress has been achieved towards meeting the rec-
ommendations for redening the SI in terms of exact values
of fundamental constants. The recommended exact numerical
values of h, e, k, and NA to establish the revised SI based on
fundamental constants are given. A detailed description of the
unique 2017 CODATA special adjustment is given by Mohr
etal (2017). The next regular CODATA periodic adjustment
of the fundamental constants, CODATA 2018, will also be
unique as it will be the rst one based on the exact funda-
mental constants of the revised SI.
Figure 1. Values of the Planck constant h inferred from the input
data in table1 and the CODATA 2017 value in chronological
order from top to bottom. The inner green band is ±20 parts in 109
and the outer grey band is ±50 parts in 109. KB: Kibble balance;
XRCD: x-ray-crystal-density.
Figure 2. Values of the Boltzmann constant k inferred from the key
input data in table1 and the CODATA 2017 value in chronological
order from top to bottom. The inner green band is ±5 parts in 107
and the outer grey band is ±15 parts in 107. AGT: acoustic gas
thermometry; DCGT: dielectric constant gas thermometry; JNT:
Johnson noise thermometry.
Table 2. The CODATA 2017 adjusted values of h, e, k, and NA.
Quantity       Value Rel. stand.
uncert ur
h
6.626 070 150
(
69
)
×10−34
J s
1.0 ×10−8
e
1.602 176 6341(83)×10−19
C
5.2 ×10−9
k
1.380 649 03(51)×10−23
J K−1
3.7 ×10−7
NA
6.022 140 758(62)×1023
mol−1
1.0 ×10−8
Table 3. The CODATA 2017 values of h, e, k, and NA for the
revision of the SI.
Quantity      Value
h
6.626 070 15 ×10−34 Js
e
1.602 176 634 ×10−19 C
k
1.380 649 ×10−23 JK
−1
NA
6.022 140 76 ×1023 mol−1
Metrologia 55 (2018) L13
Short Communication
L16
Acknowledgment
The CODATA Task Group on Fundamental Constants thanks
the CGPM for inviting it to play a signicant role in the
international effort to establish a revised SI for the 21st cen-
tury, arguably the most important change to the International
System of Units since its formal adoption in 1960.
ORCID iDs
H S Margolis https://orcid.org/0000-0002-8991-3855
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Metrologia 55 (2018) L13
The CODATA 2017 Values of \bm{$h$}, \bm{$e$}, \bm{$k$}, and \bm{$N_{\rm A}$} for the Revision of the
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  • Nov 2024
Volume in nature is a foundation of present-day physics. The volume dynamics, VD, is implied by evident properties: invariance of the speed of light and zero rest mass of volume The VD includes: the existence and reality of volume portions, VPs, change tensors of VPs, including electromagnetic waves, the differential equation describing change tensors, form of wave packets, formation and propagation of VPs, real quantities are identified via the Hacking criterion. The VD implies and explains present-day physics, e. g. gravity and transmission of gravitational interaction, curvature of spacetime, general relativity as a semiclassical and averaging approximation, universal formation of quanta, a generalized Schrödinger equation, the postulates of quantum physics, the Schrödinger equation as a nonrelativistic approximation, an improved and generalized version of quantum field theory, including nonlocality & causality, without infinity – as expected, as real volume inside the light horizon cannot cause a real infinity. The VD implies, explains and clarifies properties of space, e. g. VD implies density of volume in our heterogeneous universe, VD provides the time evolution of the Hubble constant (front cover), this solves the Hubble tension, real VPs represent the wave function and its generalization, VD clarifies real zero-point-oscillations, real Casimir force and real VPs and solves the cosmological constant problem, causality with nonlocality is clarified, formation of matter has been derived, the era of cosmic ‘inflation’ has been derived and clarified, the elementary charge, the electroweak couplings and many elementary particles have been derived and explained, the cosmological parameters have been derived fundamentally. Thus, the VD clarifies, generalizes and unifies present-day physics. All results are in precise accordance with observation. Thereby, no fit has been executed, and no hypothesis has been introduced. We derive all findings in a systematic, clear & smooth manner. We summarize our results by definitions, propositions & theorems. We are classes from grade 10 or higher, courses, research clubs, enthusiasts, observers, experimentalists, mathematicians, scientists, researchers . . .
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... where M = 114.0416 × 10 -3 kg mol -1 is the molar mass of R1234ze(Z) and R = 8.3144626 J mol -1 K -1 is the molar gas constant (Newell et al., 2018). At all temperatures, the relative fitting precision of our determinations of  0 (T) resulted less than 0.03%, while the corresponding accuracy is limited by the imperfect knowledge of the composition of the sample under test, as commented below. ...
Speed of sound in gaseous cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) between 307 K and 420 K
Preprint
Full-text available
  • Sep 2024
Measurements of the speed of sound in gaseous cis-1,3,3,3-tetrafluoroprop-1-ene, (R1234ze(Z)), are presented. The measurements were performed using a quasi-spherical acoustic resonator at temperatures between 307 K and 420 K and pressures up to 1.8 MPa. Ideal-gas heat capacities and acoustic virial coefficients over the same temperature range were directly calculated from the results. The relative accuracy of our determinations of the speed of sound w(p,T) of R1234ze(Z) was approximately ±\pm 0.02%. The accuracy of the determination of the ideal gas heat capacity ratio γ0{\gamma}^{0}(T) was approximately ±\pm 0.25%. These data were found to be mostly consistent with the predictions of a fundamental equation of state of R1234ze(Z).
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Thermodynamic Insights on the Structure‐Property Relationships in Substituted Benzenes: Are the Pairwise Interactions in Tri‐Substituted Methyl‐Nitro‐Benzoic Acids Still Valid?
Article
Full-text available
  • Feb 2025
A comprehensive experimental thermochemical study of nine methyl‐substituted nitrobenzoic acids was carried out, leading to the final standard molar enthalpies of formation in the gas phase. The combustion energies were measured using high‐precision combustion calorimetry, and the enthalpies of formation of the crystal phase were derived. The sublimation enthalpies were obtained from the vapor pressure‐temperature dependencies measured using the classic Knudsen effusion mass loss and the transpiration methods. The standard molar enthalpies of vaporisation were derived from the temperature dependence of the mass‐loss rates measured using the non‐isothermal thermogravimetry. The thermal behaviour, including melting temperatures and standard molar enthalpies of fusion, was investigated by DSC. The high‐level quantum chemical G* methods were used for the mutual validation of the experimental and theoretical gas phase enthalpies of formation of methyl‐substituted nitrobenzoic acids. The consistent set of experimental properties at the reference temperature T=298 K was evaluated and recommended for thermochemical calculations. The pairwise interactions of the substituents on the benzene ring were derived from nitro‐toluenes, methyl‐benzoic acids and nitro‐benzoic acids available in the literature, and the additivity of the contributions when three substituents are placed simultaneously in the benzene ring was discussed.
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Progress with realizing the redefined Kelvin
Article
Full-text available
  • Oct 2024
The redefinition of the kelvin is introduced followed by an overview of progress made towards realizing the redefined kelvin with particular emphasis on using primary thermometry approaches to enable traceability direct to the kelvin definition. Perspectives for temperature traceability in the short-, medium-and long-term are discussed along with the possible requirements for a future temperature scale.
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Proposal for a computable optical Clock
Article
  • Nov 2024
  • J Phys Conf
With the recent update of the SI system, all but one of the units are now based on defining the values of some fundamental constants. This development began in 1983 when the speed of light was assigned an exact fixed value. The advantage of this method is that it separates the definition from the realization, allowing new realizations to be introduced as technology advances without further redefinition. In addition, it allows unit realizations that are adapted to the scale of their intended use. Because of these advantages, we expect that one day also the last remaining object in the current SI system, the caesium atom, will also disappear. The purpose of this proposal is to outline possible paths for realizations of a future SI second based on the definition of the value of the Rydberg constant. Hydrogen and hydrogen–like systems would be the obvious candidates. The emphasis here is on the development of optical clock systems that circumvent difficulties associated with the short wavelength lasers otherwise required for cooling and driving the clock transition. The proposed clock systems based on atomic hydrogen and hydrogen–like He ⁺ , should be no more complex than current optical lattice clocks.
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Variance-reduction kinetic simulation for characterization of surface and corner effects in low-speed rarefied gas flows through long micro-ducts
Article
Full-text available
  • Oct 2024
  • MICROFLUID NANOFLUID
Microfluidic-MEMS (micro-electromechanical system) devices consist of complex subsystems in which the transfer of mass, momentum and energy is critical. This is often achieved by a pressure gradient-driven, low-speed rarefied gas transport in long micro-ducts. Gaseous rarefaction, and geometrical properties of micro-ducts, such as cross-section profile and surface roughness, play a decisive role in the segregation of the flow into inertia-driven and surface-dominated domains. In this work, a parallel stochastic kinetic particle solver that solves the low-variance Boltzmann Bhatnagar-Gross-Krook (BGK) formulation is utilized to study isothermal rarefied gas transport through polar and triangular cross-sections. The effect of geometrical features such as surface proximity to the inertial core and the role of corners, are characterized. A novel parameter to indicate surface influence is introduced, which can be gainfully used in MEMS design and optimization.
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Extension of quantized-current plateaus in tunable-barrier single-electron pumps through charge screening of the electrostatic field
Article
Full-text available
  • Oct 2024
The quantized current steps produced by a dynamic quantum dot (QD) operated with an external rf signal follow the relation I = nef, where n is the number of electrons captured in the QD, e is the elementary charge, and f is the rf frequency, respectively. For the application of quantized current in the future current metrology, it is crucial to achieve robust operation across a sufficiently wide gate voltage range. Here, we report a method to extend the quantized current plateau by screening the electrostatic field. We observe that the nth plateau width abruptly increases when the corresponding plateau crosses a certain voltage value applied to a gate capacitively coupled to the QD system. Our analysis, which is based on the decay-cascade model, reveals that the plateau extension behavior originates from a change of the gate-coupling constant at the particular gate voltage. We propose that the change in the gate-coupling constant occurs when the top of the potential barrier under the gate is lower than the Fermi energy. This results in an accumulation of electrons above the potential barrier and an enhanced screening effect for the gate coupling.
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Thermodynamic study on the relative stability of 2-amino-1,3,4-thiadiazole and two alkyl-substituted aminothiadiazoles
Article
  • Sep 2024
  • J THERM ANAL CALORIM
A thermochemical study of 2-amino-1,3,4-thiadiazole, 2-amino-5-methyl-1,3,4-thiadiazole and 2-amino-5-ethyl-1,3,4-thiadiazole has been performed, aiming to establish possible correlations between energetic properties and structural characteristics of these compounds, as well as to assess to their thermodynamic stability. Calorimetric techniques (rotating bomb combustion calorimetry and Calvet microcalorimetry) complemented with a mass loss effusion method and computational calculations were used to determine the standard molar enthalpies of formation, in the gaseous phase, at T = 298.15 K, of the three thiadiazole derivatives. Theoretical calculations at the G3(MP2)//B3LYP level of theory were also performed to obtain the enthalpies of hypothetical reactions in the gaseous phase, as well as to calculate the gas-phase enthalpy of formation for the three thiadiazoles. From the two sets of results, it is possible to make a comparison between the experimental and computational values of the gas-phase enthalpy of formation. The standard Gibbs energies of formation in the crystalline and gaseous phases were also calculated, in order to evaluate the relative thermodynamic stability of the compounds. Additionally, a tautomeric analysis of the structure of each compound was performed, resulting in the establishment of a relationship between energy versus structure of the respective tautomeric forms.
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The Avogadro constant measurements using enriched 28Si monocrystals
Article
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Since 2011, the International Avogadro Coordination has been measuring the Avogadro constant by counting the atoms in enriched ²⁸Si monocrystals. This communication provides guidance on how the recently published results should be used to update the values of the Avogadro constant measured so far.
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Data and analysis for the CODATA 2017 Special Fundamental Constants Adjustment
Article
Full-text available
  • Nov 2017
The special least-squares adjustment of the values of the fundamental constants, carried out by the Committee on Data for Science and Technology (CODATA) in the summer of 2017, is described in detail. It is based on all relevant data available by 1 July 2017. The purpose of this adjustment is to determine the numerical values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A for the revised SI expected to be established by the 26th General Conference on Weights and Measures when it convenes on 13-16 November 2018.
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New measurement of the Boltzmann constant k by acoustic thermometry of helium-4 gas
Article
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The SI unit of temperature will soon be redefined in terms of a fixed value of the Boltzmann constant k derived from an ensemble of measurements worldwide. We report on a new determination of k using acoustic thermometry of helium-4 gas in a 3 l volume quasi-spherical resonator. The method is based on the accurate determination of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas constant R = 8.314 4614(50) Jmol⁻¹K⁻¹. Using the current best available value of the Avogadro constant, we obtain k = 1.380 648 78(83) × 10⁻²³ JK⁻¹ with u(k)/k = 0.60 × 10⁻⁶, where the uncertainty u is one standard uncertainty corresponding to a 68% confidence level. This value is consistent with our previous determinations and with that of the 2014 CODATA adjustment of the fundamental constants (Mohr et al 2016 Rev. Mod. Phys. 88 035009), within the standard uncertainties. We combined the present values of k and u(k) with earlier values that were measured at LNE. Assuming the maximum possible correlations between the measurements, (k present/〈k〉 − 1) = 0.07 × 10⁻⁶ and the combined u r (k) is reduced to 0.56 × 10⁻⁶. Assuming minimum correlations, (k present/〈k〉 − 1) = 0.10 × 10⁻⁶ and the combined u r (k) is reduced to 0.48 × 10⁻⁶.
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Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017
Article
Full-text available
Researchers at the National Institute of Standards and Technology(NIST) have measured the value of the Planck constant to be h=6.626 069 934(89)×10−34 h =6.626\,069\,934(89)\times 10^{-34}\,J \,s (relative standard uncertainty 13×10−913\times 10^{-9}). The result is based on over 10 \,000 weighings of masses with nominal values ranging from 0.5 \,kg to 2 \,kg with the Kibble balance NIST-4. The uncertainty has been reduced by more than twofold relative to a previous determination because of three factors: (1) a much larger data set than previously available, allowing a more realistic, and smaller, Type A evaluation; (2) a more comprehensive measurement of the back action of the weighing current on the magnet by weighing masses up to 2 \,kg, decreasing the uncertainty associated with magnet non-linearity; (3) a rigorous investigation of the dependence of the geometric factor on the coil velocity reducing the uncertainty assigned to time-dependent leakage of current in the coil.
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Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: New and previous results combined
Article
Full-text available
We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys.32 1297, Lin et al 2013 Metrologia50 417, Feng et al 2015 Metrologia52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA's method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean k̂ B is 1.380 6484(28) × 10-23 J K-1 with the relative standard uncertainty of 2.0 × 10-6. The corresponding value of the universal gas constant is 8.314 459(17) J K-1 mol-1 with the relative standard uncertainty of 2.0 × 10-6.
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A determination of the Planck constant using the LNE Kibble balance in air
Article
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A determination of the Planck constant h using the LNE Kibble balance in air was carried out in the spring of 2017. Substantial improvements since 2014, chiefly related to the mass standard, mechanical alignments, voltage measurements and type A evaluation uncertainties, leads to a h value of 6.626 070 41(38) × 10–34 J · s, with a relative standard uncertainty of 5.7 × 10–8.
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Re-estimation of argon isotope ratios leading to a revised estimate of the Boltzmann constant
Article
Full-text available
In 2013, NPL, SUERC and Cranfield University published an estimate for the Boltzmann constant (de Podesta et al 2013 Metrologia 50 354–76) based on a measurement of the limiting low-pressure speed of sound in argon gas. Subsequently, an extensive investigation by Yang et al (2015 Metrologia 52 S394–409) revealed that there was likely to have been an error in the estimate of the molar mass of the argon used in the experiment. Responding to Yang et al (2015 Metrologia 52 S394–409), de Podesta et al revised their estimate of the molar mass (de Podesta et al 2015 Metrologia 52 S353–63). The shift in the estimated molar mass, and of the estimate of kB, was large: −2.7 parts in 10⁶, nearly four times the original uncertainty estimate. The work described here was undertaken to understand the cause of this shift and our conclusion is that the original samples were probably contaminated with argon from atmospheric air. In this work we have repeated the measurement reported in de Podesta et al (2013 Metrologia 50 354–76) on the same gas sample that was examined in Yang et al (2015 Metrologia 52 S394–409) and de Podesta et al (2015 Metrologia 52 S353–63). However in this work we have used a different technique for sampling the gas that has allowed us to eliminate the possibility of contamination of the argon samples. We have repeated the sampling procedure three times, and examined samples on two mass spectrometers. This procedure confirms the isotopic ratio estimates of Yang et al (2015 Metrologia 52 S394–409) but with lower uncertainty, particularly in the relative abundance ratio R38:36. Our new estimate of the molar mass of the argon used in Isotherm 5 in de Podesta et al (2013 Metrologia 50 354–76) is 39.947 727(15) g mol⁻¹ which differs by +0.50 parts in 10⁶ from the estimate 39.947 707(28) g mol⁻¹ made in de Podesta et al (2015 Metrologia 52 S353–63). This new estimate of the molar mass leads to a revised estimate of the Boltzmann constant of kB = 1.380 648 60 (97) × 10⁻²³ J K⁻¹ which differs from the 2014 CODATA value by +0.05 parts in 10⁶.
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An improved electronic determination of the Boltzmann constant by Johnson noise thermometry
Article
Full-text available
Recent measurements using acoustic gas thermometry have determined the value of the Boltzmann constant, k, with a relative uncertainty less than 1 × 10⁻⁶. These results have been supported by a measurement with a relative uncertainty of 1.9 × 10⁻⁶ made with dielectric-constant gas thermometry. Together, the measurements meet the requirements of the International Committee for Weights and Measures and enable them to proceed with the redefinition of the kelvin in 2018. In further support, we provide a new determination of k using a purely electronic approach, Johnson noise thermometry, in which the thermal noise power generated by a sensing resistor immersed in a triple-point-of-water cell is compared to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. The experimental setup differs from that of the 2015 determination in several respects: a 100 Ω resistor is used as the thermal noise source, identical thin coaxial cables made of solid beryllium-copper conductors and foam dielectrics are used to connect the thermal and quantum-accurate noise sources to the correlator so as to minimize the temperature and frequency sensitivity of the impedances in the connecting leads, and no trimming capacitors or inductors are inserted into the connecting leads. The combination of reduced uncertainty due to spectral mismatches in the connecting leads and reduced statistical uncertainty due to a longer integration period of 100 d results in an improved determination of k = 1.380 649 7(37) × 10⁻²³ J K⁻¹ with a relative standard uncertainty of 2.7 × 10⁻⁶ and a relative offset of 0.89 × 10⁻⁶ from the CODATA 2014 recommended value. The most significant terms in the uncertainty budget, the statistical uncertainty and the spectral-mismatch uncertainty, are uncorrelated with the corresponding uncertainties in the 2015 measurements.
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A new 28Si single crystal: Counting the atoms for the new kilogram definition
Article
Full-text available
A new single crystal from isotopically enriched silicon was used to determine the Avogadro constant N A by the x-ray-crystal density method. The new crystal, named Si28-23Pr11, has a higher enrichment than the former 'AVO28' crystal allowing a smaller uncertainty of the molar mass determination. Again, two 1 kg spheres were manufactured from this crystal. The crystal and the spheres were measured with improved and new methods. One sphere, Si28kg01a, was measured at NMIJ and PTB with very consistent results. The other sphere, Si28kg01b, was measured only at PTB and yielded nearly the same Avogadro constant value. The mean result for both 1 kg spheres is N A = 6.022 140 526(70) × 10²³ mol⁻¹ with a relative standard uncertainty of 1.2 × 10⁻⁸. This value deviates from the Avogadro value published in 2015 for the AVO28 crystal by about 3.9(2.1) × 10⁻⁸. Possible reasons for this difference are discussed and additional measurements are proposed.
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Determination of the Avogadro constant by the XRCD method using a 28Si-enriched sphere
Article
Full-text available
To determine the Avogadro constant N A by the x-ray crystal density method, the density of a ²⁸Si-enriched crystal was determined by absolute measurements of the mass and volume of a 1 kg sphere manufactured from the crystal. The mass and volume were determined by an optical interferometer and a vacuum mass comparator, respectively. The sphere surface was characterized by x-ray photoelectron spectroscopy and spectroscopic ellipsometry to derive the mass and volume of the Si core of the sphere excluding the surface layers. From the mass and volume, the density of the Si core was determined with a relative standard uncertainty of 2.3 × 10⁻⁸. By combining the Si core density with the lattice constant and the molar mass of the sphere reported by the International Avogadro Coordination (IAC) project in 2015, a new value of 6.022 140 84(15) × 10²³ mol⁻¹ was obtained for N A with a relative standard uncertainty of 2.4 × 10⁻⁸. To make the N A value determined in this work usable for a future adjustment of the fundamental constants by the CODATA Task Group on Fundamental Constants, the correlation of the new N A value with the N A values determined in our previous works was examined. The correlation coefficients with the values of N A determined by IAC in 2011 and 2015 were estimated to be 0.07 and 0.28, respectively. The correlation of the new N A value with the N A value determined by IAC in 2017 using a different ²⁸Si-enriched crystal was also examined, and the correlation coefficient was estimated to be 0.21.
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