Progress of joule balance and redifination of Kilogram

Li Zheng-Kun; Zhang Zhong-Hua; Lu Yun-Feng; Bai Yang; Xu Jin-Xin; Hu Peng-Cheng; Liu Yong-Meng; You Qiang; Wang Da-Wei; He Qing; Tan Jiu-Bin

doi:10.7498/aps.67.20180581

Abstract

Kilogram, the unit of mass, is the last one of seven base units in International System of Units (SI) which is still defined and kept by a material artifact. 1 kg is defined as the mass of the International Prototype of the Kilogram (IPK) kept at the Bureau International des Poids et Mesures (BIPM) in Paris. One of the major disadvantages of this definition is the fact that the amount of material constituting the IPK changes with time. Because a more stable mass reference does not exist, the variation of IPK is completely unknown so far. The International Committee for Weights and Measures (CIPM) recommended redefining the kilogram by fixing the numerical value of the Planck constant h and called on every national metrology institute to study the measurement of the h. To avoid possible system errors from one method, more experiments especially based on different principles are expected and encouraged for the final determination of the Planck constant. The CCM required that at least three consistent results should be obtained before the redefinition. Since 1970 s, the Kibble balance (also known as the Kibble balance) experiment has been used by a number of national metrology institutes such as NPL, NIST, METAS, LNE and BIPM. The IAC including the PTB, NMIJ and NMIA used the XRCD method to measure the Avogadro constant. To make contribution to the redefinition of kilogram, the National Institute of Metrology of China (NIM) proposed a joule balance method in 2006, which is also an electrical way but different from the watt balance method in that the dynamic phase is replaced with a static phase to avoid the trouble in the dynamic measurement. The progress of these approaches and the current situation of the redefinition of the kilogram are presented in this paper. In 2013, a model apparatus was built to verify the principle of the joule balance. Then NIM started to build its new joule balance aiming to obtain an uncertainty of 10-8 level since 2013. In Dec. 2016, the new apparatus was built and could be used to measure the Planck constant h in vacuum. In May 2017, the measurement result was submitted to the Metrologia and accepted by the CODATA TGFC as the input data. However, the measurement result has an uncertainty bigger than 10-8 and was not used for the final determination of the h value. At present, the joule balance group of NIM, together with the Harbin Institute of Technology, Tsinghua University and China Jiliang University is still making great efforts to improve the joule balance apparatus. The uncertainty of 10-8 level is expected to be achieved in the next two years.

Keywords:

Authors and contacts

1.
National Institute of Metrology, The Key Laboratory of AQSIQ of China, Beijing 100029, China;
2.
Harbin Institute of Technology, Harbin 150001, China;
3.
Tsinghua University, Beijing 100084, China

Corresponding author: Li Zheng-Kun, lzk@nim.ac.cn;zzh@nim.ac.cn ; Zhang Zhong-Hua, lzk@nim.ac.cn;zzh@nim.ac.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 91536224).

References

[1]	Taylor B N, Mohr P J 2001 IEEE Trans. Instrum. Meas. 50 563
[2]	The International System of Units 8th edition 2006 (www.bipm.org/en/si/)
[3]	Zhang Z H 2002 China Metrology 8 5 (in Chinese) [张钟华 2002 中国计量 8 5]
[4]	Josephson B D 1962 Phys. Lett. 1 251
[5]	von Klitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[6]	Zhang Z, He Q 2001 Modern Measurement and Test 3 3 (in Chinese) [张钟华, 贺青 2001 现代计量测试 3 3]
[7]	Davis R 2003 Metrologia 40 299
[8]	Girard G 1994 Metrologia 31 317
[9]	Li S, Zhang Z, Zhao W, Li Z, Huang S 2015 Chin. Phys. B 24 1
[10]	Draft 9th SI Brochure, https://www.bipm.org/cc/CCU/Allowed/23/Draft-SI-Brochure-2018.pdf
[11]	Andreas B, Azuma Y, Bartl G, Becker P, Bettin H, Borys M, Busch I, Gray M, Fuchs P, Fujii K 2011 Phys. Rev. Lett. 106 030801
[12]	Azuma Y, Barat P, Bartl G, Bettin H, Borys M, Busch I, Cibik L, D'Agostino G, Fujii K, Fujimoto H 2015 Metrologia 52 60
[13]	Bartl G, Becker P, Beckhoff B 2017 Metrologia 54 693
[14]	Kuramoto N, Mizushima S, Zhang L, Fujita K, Azuma Y, Kurokawa A, Okubo S, Inaba H, Fujii K 2017 Metrologia 54 716
[15]	Kibble B P 1976 Atomic Masses & Fundamental Constants (Vol.16) (New York: Plenum Press) pp545-551
[16]	Kibble B P, Robinson I A, Belliss J H 1990 Metrologia 27 173
[17]	Robinson I A 2012 Metrologia 49 113
[18]	Stock M 2013 Metrologia 50 R1
[19]	Zhang Z, He Q, Li Z 2006 Proceedings of the Conference on Precision Electromagnetic Measurement Torino, Italy, July 9-14, 2006 pp126-127
[20]	Robinson I A, Kibble B P 2007 Metrologia 44 427
[21]	Kibble B P, Robinson I A 2014 Metrologia 51 S132
[22]	Olsen P T, Elmquist R E, Phillips W D, Williams E R, Jones G R, Bower V E 1989 IEEE Trans. Instrum. Meas. 38 238
[23]	Olsen P T, Tew W L, Williams E R 1991 IEEE Trans. Instrum. Meas. 40 115
[24]	Steiner R L, Gillespie A D, Fujii K 1997 IEEE Trans. Instrum. Meas. 46 601
[25]	Steiner R L, Williams E R, Liu R 2007 IEEE Trans. Instrum. Meas. 56 592
[26]	Schlamminger S, Haddad D, Seifert F, Chao L S, Newell D B, Liu R, Steiner R L, Pratt J R 2014 Metrologia 51 S15
[27]	Schlamminger S, Steiner R L, Haddad D, Newell D B, Seifert F, Chao L S, Liu R, Williams E R, Pratt J R 2015 Metrologia 52 L5
[28]	Schlamminger S 2013 IEEE Trans. Instrum. Meas. 62 1524
[29]	Haddad D, Seifert F, Chao L S, Possolo A, Newell D B, Pratt J R, Williams C J, Schlamminger S 2017 Metrologia 54 633
[30]	Beer W, Jeanneret B, Jeckelmann B, Richard P, Courteville A, Salvadé Y, Dandliker R 1999 IEEE Trans. Instrum. Meas. 48 192
[31]	Eichenberger A, Baumann H, Jeanneret B, Jeckelmann B, Richard P, Beer W 2011 Metrologia 48 133
[32]	Baumann H, Eichenberger A, Cosandier F, Jeckelmann B, Clavel R, Reber D, Tommasini D 2013 Metrologia 50 235
[33]	Genevès G, Gournay P, Gosset A 2005 IEEE Trans. Instrum. Meas. 54 850
[34]	Thomas M, Espel P, Ziane D 2015 Metrologia 52 433
[35]	Thomas M, Ziane D, Pinot P 2017 Metrologia 54 468
[36]	Picard A, Fang H, Kiss A, de Mirandés E, Stock M, Urano C 2009 IEEE Trans. Instrum. Meas. 58 924
[37]	Fang H 2016 Digest of Conf. on Precision Electromagnetic Measurements (Ottawa, Canada)
[38]	Steele A G, Meija J, Sanchez C A, Yang L, Wood B M, Sturgeon R E, Mester Z, Inglis A D 2012 Metrologia 49 L8
[39]	Sanchez C A, Wood B M, Green R G, Liard J O, Inglis D 2014 Metrologia 51 S5
[40]	Wood B M, Sanchez C A, Green R G, Liard J O 2017 Metrologia 54 399
[41]	Sutton C M 2009 Metrologia 46 467
[42]	Kim D, Woo B C, Lee K C, Choi K B, Kim J A, Kim J W, Kim J H 2014 Metrologia 51 S96
[43]	Ahmedov H 2016 Proceedings of the Conference on Precision Electromagnetic Measurement Ottawa, Canada, Jul 10-15, 2016
[44]	Ahmedov H, BabayigitAskin N, Korutlu B, Orhan R 2018 Metrologia 55 326
[45]	Zhang Z, He Q, Li Z, Han B, Lu Y, Lan J, Li C, Li S, Xu J, Wang N, Wang G, Gong H 2014 Metrologia 51 s25
[46]	Xu J, Zhang Z, Li Z 2016 Metrologia 53 86
[47]	Zhang Z, Lu Y, Hu P, Liu Y, Xu J, Bai Y, Zeng T, Wang G, You Q, Li C, Li S, Wang K, He Q, Tan J 2017 IEEE Trans. Instrum. Meas. 66 1329
[48]	Li Z, Zhang Z, Lu Y, Hu P, Liu Y, Xu J, Bai Y, Zeng T, Wang G, You Q, Wang D, Li S, He Q, Tan J 2017 Metrologia 54 763
[49]	Jones N 2012 Nature 481 14
[50]	Mohr P J, Newell D B, Taylor B N, Tiesinga E 2018 Metrologia 55 125
[51]	Newell D B, Cabiati F, Fischer J, Fujii K, Karshenboim S G, Margolis H S, de Mirandés E, Mohr P J, Nez F, Pachucki K, Quinn T J, Taylor B N, Wang M, Wood B M, Zhang Z 2018 Metrologia 55 L13
[52]	CCU Recomendation U1 (2017) On the possible redefinition of the kilogram, ampere, kelvin and mole in 2018, https://www.bipm.org/cc/CCU/Allowed/23/CCU_Final_Recommendation_U1_2017.pdf [2018-7-24]
[53]	Decision CIPM/106-10, https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-Decisions-EN.pdf [2018-7-24]
[54]	Li Z, Zhang Z, He Q, Fu Y, Zhao J, Han B, Li S, Lan J, Li C 2011 IEEE Trans. Instrum. Meas. 60 2292
[55]	Lan J, Zhang Z, Li Z, He Q, Fu Y, Li S, Han B, Zhao J, Lu Y 2012 IEEE Trans. Instrum. Meas. 61 2524
[56]	Li Z, Zhang Z, He Q, Han B, Lu Y, Xu J, Li S, Li C, Wang G, Zeng T, Bai Y 2015 IEEE Trans. Instrum. Meas. 64 1676
[57]	Zhang Z, Li Z, Han B 2015 IEEE Trans. Instrum. Meas. 64 1539
[58]	Wang G, Xu J, You Q 2017 Meas. Sci. Technol. 28 015004
[59]	Yang H, Lu Y, Hu P, Li Z, Zeng T, He Q 2014 Meas. Sci. Technol. 25 233
[60]	Bai Y, Hu P, Lu Y, Li Z, Zang Z, Tan J 2016 IEEE Trans. Instrum. Meas. 66 1
[61]	Zeng T, Lu Y, Liu Y, Yang H, Bai Y, Hu P, Li Z, Zhang Z, Tan J 2016 IEEE Trans. Instrum. Meas. 65 458
[62]	You Q, Xu J, Li Z, Li S 2017 IEEE Trans. Instrum. Meas. 66 1289

Cited By

[1]	Taylor B N, Mohr P J 2001 IEEE Trans. Instrum. Meas. 50 563
[2]	The International System of Units 8th edition 2006 (www.bipm.org/en/si/)
[3]	Zhang Z H 2002 China Metrology 8 5 (in Chinese) [张钟华 2002 中国计量 8 5]
[4]	Josephson B D 1962 Phys. Lett. 1 251
[5]	von Klitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[6]	Zhang Z, He Q 2001 Modern Measurement and Test 3 3 (in Chinese) [张钟华, 贺青 2001 现代计量测试 3 3]
[7]	Davis R 2003 Metrologia 40 299
[8]	Girard G 1994 Metrologia 31 317
[9]	Li S, Zhang Z, Zhao W, Li Z, Huang S 2015 Chin. Phys. B 24 1
[10]	Draft 9th SI Brochure, https://www.bipm.org/cc/CCU/Allowed/23/Draft-SI-Brochure-2018.pdf
[11]	Andreas B, Azuma Y, Bartl G, Becker P, Bettin H, Borys M, Busch I, Gray M, Fuchs P, Fujii K 2011 Phys. Rev. Lett. 106 030801
[12]	Azuma Y, Barat P, Bartl G, Bettin H, Borys M, Busch I, Cibik L, D'Agostino G, Fujii K, Fujimoto H 2015 Metrologia 52 60
[13]	Bartl G, Becker P, Beckhoff B 2017 Metrologia 54 693
[14]	Kuramoto N, Mizushima S, Zhang L, Fujita K, Azuma Y, Kurokawa A, Okubo S, Inaba H, Fujii K 2017 Metrologia 54 716
[15]	Kibble B P 1976 Atomic Masses & Fundamental Constants (Vol.16) (New York: Plenum Press) pp545-551
[16]	Kibble B P, Robinson I A, Belliss J H 1990 Metrologia 27 173
[17]	Robinson I A 2012 Metrologia 49 113
[18]	Stock M 2013 Metrologia 50 R1
[19]	Zhang Z, He Q, Li Z 2006 Proceedings of the Conference on Precision Electromagnetic Measurement Torino, Italy, July 9-14, 2006 pp126-127
[20]	Robinson I A, Kibble B P 2007 Metrologia 44 427
[21]	Kibble B P, Robinson I A 2014 Metrologia 51 S132
[22]	Olsen P T, Elmquist R E, Phillips W D, Williams E R, Jones G R, Bower V E 1989 IEEE Trans. Instrum. Meas. 38 238
[23]	Olsen P T, Tew W L, Williams E R 1991 IEEE Trans. Instrum. Meas. 40 115
[24]	Steiner R L, Gillespie A D, Fujii K 1997 IEEE Trans. Instrum. Meas. 46 601
[25]	Steiner R L, Williams E R, Liu R 2007 IEEE Trans. Instrum. Meas. 56 592
[26]	Schlamminger S, Haddad D, Seifert F, Chao L S, Newell D B, Liu R, Steiner R L, Pratt J R 2014 Metrologia 51 S15
[27]	Schlamminger S, Steiner R L, Haddad D, Newell D B, Seifert F, Chao L S, Liu R, Williams E R, Pratt J R 2015 Metrologia 52 L5
[28]	Schlamminger S 2013 IEEE Trans. Instrum. Meas. 62 1524
[29]	Haddad D, Seifert F, Chao L S, Possolo A, Newell D B, Pratt J R, Williams C J, Schlamminger S 2017 Metrologia 54 633
[30]	Beer W, Jeanneret B, Jeckelmann B, Richard P, Courteville A, Salvadé Y, Dandliker R 1999 IEEE Trans. Instrum. Meas. 48 192
[31]	Eichenberger A, Baumann H, Jeanneret B, Jeckelmann B, Richard P, Beer W 2011 Metrologia 48 133
[32]	Baumann H, Eichenberger A, Cosandier F, Jeckelmann B, Clavel R, Reber D, Tommasini D 2013 Metrologia 50 235
[33]	Genevès G, Gournay P, Gosset A 2005 IEEE Trans. Instrum. Meas. 54 850
[34]	Thomas M, Espel P, Ziane D 2015 Metrologia 52 433
[35]	Thomas M, Ziane D, Pinot P 2017 Metrologia 54 468
[36]	Picard A, Fang H, Kiss A, de Mirandés E, Stock M, Urano C 2009 IEEE Trans. Instrum. Meas. 58 924
[37]	Fang H 2016 Digest of Conf. on Precision Electromagnetic Measurements (Ottawa, Canada)
[38]	Steele A G, Meija J, Sanchez C A, Yang L, Wood B M, Sturgeon R E, Mester Z, Inglis A D 2012 Metrologia 49 L8
[39]	Sanchez C A, Wood B M, Green R G, Liard J O, Inglis D 2014 Metrologia 51 S5
[40]	Wood B M, Sanchez C A, Green R G, Liard J O 2017 Metrologia 54 399
[41]	Sutton C M 2009 Metrologia 46 467
[42]	Kim D, Woo B C, Lee K C, Choi K B, Kim J A, Kim J W, Kim J H 2014 Metrologia 51 S96
[43]	Ahmedov H 2016 Proceedings of the Conference on Precision Electromagnetic Measurement Ottawa, Canada, Jul 10-15, 2016
[44]	Ahmedov H, BabayigitAskin N, Korutlu B, Orhan R 2018 Metrologia 55 326
[45]	Zhang Z, He Q, Li Z, Han B, Lu Y, Lan J, Li C, Li S, Xu J, Wang N, Wang G, Gong H 2014 Metrologia 51 s25
[46]	Xu J, Zhang Z, Li Z 2016 Metrologia 53 86
[47]	Zhang Z, Lu Y, Hu P, Liu Y, Xu J, Bai Y, Zeng T, Wang G, You Q, Li C, Li S, Wang K, He Q, Tan J 2017 IEEE Trans. Instrum. Meas. 66 1329
[48]	Li Z, Zhang Z, Lu Y, Hu P, Liu Y, Xu J, Bai Y, Zeng T, Wang G, You Q, Wang D, Li S, He Q, Tan J 2017 Metrologia 54 763
[49]	Jones N 2012 Nature 481 14
[50]	Mohr P J, Newell D B, Taylor B N, Tiesinga E 2018 Metrologia 55 125
[51]	Newell D B, Cabiati F, Fischer J, Fujii K, Karshenboim S G, Margolis H S, de Mirandés E, Mohr P J, Nez F, Pachucki K, Quinn T J, Taylor B N, Wang M, Wood B M, Zhang Z 2018 Metrologia 55 L13
[52]	CCU Recomendation U1 (2017) On the possible redefinition of the kilogram, ampere, kelvin and mole in 2018, https://www.bipm.org/cc/CCU/Allowed/23/CCU_Final_Recommendation_U1_2017.pdf [2018-7-24]
[53]	Decision CIPM/106-10, https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-Decisions-EN.pdf [2018-7-24]
[54]	Li Z, Zhang Z, He Q, Fu Y, Zhao J, Han B, Li S, Lan J, Li C 2011 IEEE Trans. Instrum. Meas. 60 2292
[55]	Lan J, Zhang Z, Li Z, He Q, Fu Y, Li S, Han B, Zhao J, Lu Y 2012 IEEE Trans. Instrum. Meas. 61 2524
[56]	Li Z, Zhang Z, He Q, Han B, Lu Y, Xu J, Li S, Li C, Wang G, Zeng T, Bai Y 2015 IEEE Trans. Instrum. Meas. 64 1676
[57]	Zhang Z, Li Z, Han B 2015 IEEE Trans. Instrum. Meas. 64 1539
[58]	Wang G, Xu J, You Q 2017 Meas. Sci. Technol. 28 015004
[59]	Yang H, Lu Y, Hu P, Li Z, Zeng T, He Q 2014 Meas. Sci. Technol. 25 233
[60]	Bai Y, Hu P, Lu Y, Li Z, Zang Z, Tan J 2016 IEEE Trans. Instrum. Meas. 66 1
[61]	Zeng T, Lu Y, Liu Y, Yang H, Bai Y, Hu P, Li Z, Zhang Z, Tan J 2016 IEEE Trans. Instrum. Meas. 65 458
[62]	You Q, Xu J, Li Z, Li S 2017 IEEE Trans. Instrum. Meas. 66 1289

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