LIU Wen-jing,ZHANG Hai-yang GAO Bo ZHENG Jia-xi HAN Dong-x LUO Er- cang),Laurent Pitres. 1)TIPC-LNE Joint Laboratory on Cryogenic Metrology Science and Technology,Chinese Academy of Science(CAS),Beijing 100190,China 2)Key Laboratory of Cryogenics,Technical Institute of Physics and Chemistry (TIPC),Chinese Academy of Sciences (CAS),Beijing 100190, China 3)University of Chinese Academy of Sciences,Beijing 100490,China 4) School of Mechanical Engineering,Beijing Institute of Petrochemical Technology,Beijing 102617,China 5)Laboratoire national de metrologie et d'essais-Conservatoire national des arts et metiers (LNE-Cnam),La Plaine-Saint Denis,Paris F93210, France Corresponding author,E-mail:zhy110.@mailipc.ac.cn bgao.@mailipc.ac.cn:jxzheng.@mailipc.ac.cn ABSTRACT In this paper,the linear thermal expansion coefficient of electrolytic though pitch copper (Cu-ETP)which used as the material of the resonator in the single pressure refractive index gas thermometer is measured high-precision and in situ by multi-modes microwave resonance method in the temperature range from 4.3K to 299 K.Two experimental measurement schemes,cooling method(5 K-299 K)and temperature control method (4.3 K-26 K),are employed for different temperature ranges.These two methods adopt the same caloulation thought which obtaining the relation of length and temperature first,then using the polynomial fitting means to get the linear thermal expansion coefficient of the resonator. The shape of the resonator installed in the cryostat is quasispch the radius in the.andaxis has litte difference,for example,the radius in one direction is a then the other wo radius are 0.001a and 1.0005a.The accurate radius of the quasi-sphere in the low temperature can be measured by multi-modes microwave resonance method which is a mature method containing much non-ideal correction in order to shorten the difference between actual and ideal environment.For cooling method,in order to reduce the impact of random errors,we collect five microwave modes (TM11,TE11,TM12, TE12 and TE13)data and repeat four runs of experiment(Run9,Run10,Run12 and Run17),taking the average value as the final result.The max deviation of radius during different modes is 0.37 Hm which shows the result has good mode consistency.Then the measurement uncertainty of radius is analyzed and all is within 0.27 m and the mode consistency is the main influencing item.The linear thermal expansion coefficient can be calculated by the polynomial fitting method and the standard uncerainty is2 repeatability is the main sour of uncertainty.As for controlling method,the same analyzing procedure is implemented,the max deviation of radius during four modes (TM11,TE11,TM12 and TE13)is 0.12 um and the deviation of different runs and the average value is within 0.0056 um which is smaller than the uncertainty of radius which has good repeatability.The standard of the radius in within 0.12 um in the whole range and the non-ideal correction and frequency stability are the two main influencing factors.The standard uncertainty of linear thermal expansion is1-Kn the two main soures are microwave modes consistency and repeatability.Due to higher stability of temperature control and lower microwave measurement noise,the results determined by temperature control method are more accurate.Finally,equations for linear thermal expansion coefficient of Cu-ETP are further developed to realize high- precision correlation between experimental data and temperature. KEY WORDS Microwave resonance;quasi-spherical;Cu-ETP:linear thermal expansion coefficient;primary thermometry 2019年5月20日世界计量日，国际单位制发生了重大变革，自此，七个基本单位全部由自然 常数定义。其中，热力学温度单位开尔文(K)将根据玻尔兹曼常数重新定义1]。在基准测温领域， 国际温度咨询委员会推荐了几种基准气体测温方法2]：介电常数气体测温法3]、声学气体测温法4]LIU Wen-jing1,2,3) , ZHANG Hai-yang1,2), GAO Bo1,2), ZHENG Jia-xi1,2), HAN Dong-xu4,1) , LUO Er￾cang2,1,3) , Laurent Pitre5,1) 1) TIPC-LNE Joint Laboratory on Cryogenic Metrology Science and Technology, Chinese Academy of Science (CAS), Beijing 100190, China 2) Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry (TIPC), Chinese Academy of Sciences (CAS), Beijing 100190, China 3) University of Chinese Academy of Sciences, Beijing 100490, China 4) School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China 5) Laboratoire national de métrologie et d'essais-Conservatoire national des arts et métiers (LNE-Cnam), La Plaine-Saint Denis, Paris F93210, France  Corresponding author, E-mail: zhy110@mail.ipc.ac.cn; bgao@mail.ipc.ac.cn; jxzheng@mail.ipc.ac.cn ABSTRACT In this paper, the linear thermal expansion coefficient of electrolytic though pitch copper (Cu-ETP) which used as the material of the resonator in the single pressure refractive index gas thermometer is measured high-precision and in situ by multi-modes microwave resonance method in the temperature range from 4.3 K to 299 K. Two experimental measurement schemes, cooling method (5 K-299 K) and temperature control method (4.3 K-26 K), are employed for different temperature ranges. These two methods adopt the same calculation thought which obtaining the relation of length and temperature first, then using the polynomial fitting means to get the linear thermal expansion coefficient of the resonator. The shape of the resonator installed in the cryostat is quasi-spherical which the radius in the x, y and z axis has little difference, for example, the radius in one direction is a, then the other two radius are 0.001a and 1.0005a. The accurate radius of the quasi-sphere in the low temperature can be measured by multi-modes microwave resonance method which is a mature method containing much non-ideal correction in order to shorten the difference between actual and ideal environment. For cooling method, in order to reduce the impact of random errors, we collect five microwave modes (TM11, TE11, TM12, TE12 and TE13) data and repeat four runs of experiment (Run9, Run10, Run12 and Run17), taking the average value as the final result. The max deviation of radius during different modes is 0.37 μm which shows the result has good mode consistency. Then the measurement uncertainty of radius is analyzed and all is within 0.27 μm and the mode consistency is the main influencing item. The linear thermal expansion coefficient can be calculated by the polynomial fitting method and the standard uncertainty is 2.2×10-7 K-1, the repeatability is the main source of uncertainty. As for controlling method, the same analyzing procedure is implemented, the max deviation of radius during four modes (TM11, TE11, TM12 and TE13) is 0.12 μm and the deviation of different runs and the average value is within 0.0056 μm which is smaller than the uncertainty of radius which has good repeatability. The standard of the radius in within 0.12 μm in the whole range and the non-ideal correction and frequency stability are the two main influencing factors. The standard uncertainty of linear thermal expansion is 2.9×10-9 K-1 and the two main sources are microwave modes consistency and repeatability. Due to higher stability of temperature control and lower microwave measurement noise, the results determined by temperature control method are more accurate. Finally, equations for linear thermal expansion coefficient of Cu-ETP are further developed to realize high￾precision correlation between experimental data and temperature. KEY WORDS Microwave resonance; quasi-spherical; Cu-ETP; linear thermal expansion coefficient; primary thermometry 2019 年 5 月 20 日世界计量日，国际单位制发生了重大变革，自此，七个基本单位全部由自然 常数定义。其中，热力学温度单位开尔文（K）将根据玻尔兹曼常数重新定义[1]。在基准测温领域， 国际温度咨询委员会推荐了几种基准气体测温方法[2]：介电常数气体测温法[3]、声学气体测温法[4] 录用稿件，非最终出版稿