(a) 0.0 0.6 ◆ TMI1 (b) -Run9-1。-Run9-2 TEll Run10-Run12 -0.5 Baaii88 TM12 0.3 ◆Runl34-Runl5 TE13 -1.0 -1.5 -2.0 ◆◆ 10 15 20 T/K 10 20 25 (c) (d) 4.0 (Mode Nonideal correction Frequency stability) (Radius fitting) 0.4F 0.2 1.0 10 15 20 25 0 15 30 25 T/K 圆8控温过程中线性热膨胀系数计算结果分析：(a,Ru1g实验中各模式线性热膨胀系数计算结果与文献值的偏差； (b)不同轮实验线性热膨胀系数平均值和最终平均值的偏差粉色背景为平均值的标准不确定度误差带；（©）多轮控温 过程中线性热膨胀系数的最终平均值；（④控温过程中线性热膨胀系数的不确定度分量占比 Figure.8 Analysis of the linear thermal expansion during temperature controlling:(a)Deviation of experiment and literature linear thermal expansion of Run10 for different modes;(b)Deviation of average thermal expansion for different runs and the final average value,pink background is the error bar of the standard uncertainty of the final average value;(c)Final average value of linear thermal expansion during controlling for different runs;(d)Uncertainty analysis of the final linear thermal expansion during controlling 慶35K 15K和24.5K下线性热藏张系数不确定度分析。 Table 3 Uncertainty analysis of linear thermal expansion at 5 K,15 K and 24.5 K Source 109a）/Kl T=5K T=15K T=24.5K Frequency fitting 0.042 0.0047 0.19 Frequency stability 0.18 0.0032 0.41 Nonideal correction 0.0058 0.019 0.029 Mode consistency 1.45 0.66 2.65 Repeatability 0.40 0.20 0.50 Radius fitting 1.93E-7 7.52E-7 2.95E-7 Total uncertainty 1.5 0.69 2.7 3.3线性热张系数关联方程 在3.1和3.2章节中，我们基于多轮、多模式实验测量获得了定压气体折射率基准测温系统中 Cu-ETP线性热膨胀系数，为便于应用，我们将avg及其标准确定度(aavg)关联为温度的多项式函数，(a) 5 10 15 20 25 -2.0 -1.5 -1.0 -0.5 0.0 TM11 TE11 TM12 TE13 T / K 10 8 ×(α mod  e α NIST ) / K -1 (b) 5 10 15 20 25 -0.6 -0.3 0.0 0.3 0.6 T / K 10 8×(αRun,avg  αavg ) / K -1 Run9-1 Run9-2 Run10 Run12 Run13 Run15 (c) 5 10 15 20 25 0.0 0.2 0.4 0.6 T / K 10 6 ×αavg / K -1 (d) 5 10 15 20 25 0.0 1.0 2.0 3.0 4.0 T / K 10 9 u (αavg ) / K -1 u(Total) u(Mode consistency) u(Nonideal correction) u(Repeatability) u(Frequency stability) u(Frequency fitting) u(Radius fitting) 图 8 控温过程中线性热膨胀系数计算结果分析: (a) Run10 实验中各模式线性热膨胀系数计算结果与文献值的偏差; (b) 不同轮实验线性热膨胀系数平均值和最终平均值的偏差，粉色背景为平均值的标准不确定度误差带; (c) 多轮控温 过程中线性热膨胀系数的最终平均值; (d) 控温过程中线性热膨胀系数的不确定度分量占比 Figure.8 Analysis of the linear thermal expansion during temperature controlling: (a) Deviation of experiment and literature linear thermal expansion of Run10 for different modes; (b) Deviation of average thermal expansion for different runs and the final average value, pink background is the error bar of the standard uncertainty of the final average value; (c) Final average value of linear thermal expansion during controlling for different runs; (d) Uncertainty analysis of the final linear thermal expansion during controlling 表 3 5 K、15 K 和 24.5 K 下线性热膨胀系数不确定度分析。 Table 3 Uncertainty analysis of linear thermal expansion at 5 K, 15 K and 24.5 K Source 109 ·u() / K-1 T = 5 K T = 15 K T = 24.5 K Frequency fitting 0.042 0.0047 0.19 Frequency stability 0.18 0.0032 0.41 Nonideal correction 0.0058 0.019 0.029 Mode consistency 1.45 0.66 2.65 Repeatability 0.40 0.20 0.50 Radius fitting 1.93E-7 7.52E-7 2.95E-7 Total uncertainty 1.5 0.69 2.7 3.3 线性热膨胀系数关联方程 在 3.1 和 3.2 章节中，我们基于多轮、多模式实验测量获得了定压气体折射率基准测温系统中 Cu-ETP 线性热膨胀系数，为便于应用，我们将avg及其标准确定度 u(avg)关联为温度的多项式函数， 录用稿件，非最终出版稿