Tests of the Stability of Chinese RhFe Resistance Thermometers at Low Temperatures
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Abstract
Rhodium–iron resistance thermometers are recommended as precise thermometers at temperatures below 25 K. The thermometers were developed at the National Physical Laboratory and produced by H. Tinsley and Co Ltd almost 50 years ago. Later, they were made by other companies and institutes as well, but despite this, the availability of the thermometers decreased and a new source of supply was needed. Several years ago, the Technical Institute of Physics and Chemistry (TIPC), Chinese Academy of Sciences, developed its own technology for making wire of Rh0.5 at% Fe alloy which was used in the production of new thermometers. These devices have been tested previously at INRIM (Italy) and later at INTiBS (Poland). INTiBS has carried out an investigation focused on the thermometers’ stability after thermal cycling treatment. This paper presents the results of stability tests of about 30 thermometers produced by TIPC in two batches. The resistance of each thermometer was measured at temperatures of about 4.6 K and 7.2 K before and after 10, 30 and 50 thermal cycles from room temperature. The methods of measurement and the design of the cryostat used for the research are also presented.
Keywords
Cryogenic thermometers Resistance thermometers Rhodium–iron thermometers Thermometer stability1 Introduction
Results of RIRTs stability for the first batch of thermometers
\(T \approx 4,36\,\hbox {K}\)  \(T \approx 7,19\,\hbox {K}\)  

\(\Delta {T},\hbox {mK}\)  \(u(\Delta T), \hbox {mK}\)  Selfheating, \({\Omega /\hbox {mA}}^{2}\)  \(\Delta T,\hbox {mK}\)  \(u(\Delta T), \hbox {mK}\)  Selfheating, \({\Omega /\hbox {mA}}^{2}\)  
No. 8007  
After 10 cycles  \(\)0.093  0.055  0.00031  0.042  0.067  0.00018 
After 30 cycles  \(\)0.053  0.052  0.024  0.068  
After 50 cycles  \(\)0.071  0.052  \(\)0.071  0.067  
No. 20102  
After 10 cycles  \(\)0.022  0.053  0.00033  0.013  0.065  0.00019 
After 30 cycles  0.023  0.053  \(\)0.036  0.065  
After 50 cycles  \(\)0.048  0.051  \(\)0.038  0.065  
No. 20107  
After 10 cycles  \(\)0.016  0.069  0.00037  \(\)3.7E\(\)05  9.1E\(\)05  0.00022 
After 30 cycles  0.004  0.067  5.6E\(\)05  8.9E\(\)05  
After 50 cycles  \(\)0.030  0.070  4.1E\(\)05  9.0E\(\)05  
No. 20108  
After 10 cycles  0.453  0.089  0.00099  \(\)0.412  0.048  0.00039 
After 30 cycles  2.373  0.081  3.442  0.048  
After 50 cycles  2.317  0.073  1.802  0.050  
No. 20109  
After 10 cycles  \(\)0.077  0.054  0.00027  \(\)0.153  0.068  0.00015 
After 30 cycles  \(\)0.052  0.056  \(\)0.152  0.074  
After 50 cycles  \(\)0.144  0.054  \(\)0.165  0.068  
No. 200912  
After 10 cycles  \(\)0.119  0.054  0.00036  \(\)0.012  0.068  0.00022 
After 30 cycles  \(\)0.030  0.051  \(\)0.019  0.067  
After 50 cycles  \(\)0.131  0.051  0.009  0.069  
No. 200913  
After 10 cycles  \(\)0.814  0.052  0.00029  \(\)1.086  0.067  0.00017 
After 30 cycles  \(\)0.875  0.052  \(\)1.024  0.067  
After 50 cycles  \(\)0.891  0.052  \(\)1.116  0.067  
No. 200918  
After 10 cycles  \(\)0.052  0.055  0.00032  0.014  0.068  0.00017 
After 30 cycles  \(\)0.078  0.052  \(\)0.071  0.068  
After 50 cycles  \(\)0.084  0.052  \(\)0.064  0.068  
No. 200920  
After 10 cycles  0.037  0.053  0.00030  0.078  0.068  0.00018 
After 30 cycles  0.087  0.053  0.050  0.068  
After 50 cycles  \(\)0.047  0.052  \(\)0.012  0.097  
No. 201017  
After 10 cycles  \(\)0.055  0.052  0.00032  \(\)0.138  0.071  0.00017 
After 30 cycles  \(\)0.066  0.059  0.049  0.084  
After 50 cycles  \(\)0.433  0.054  \(\)0.143  0.071  
No. 201020  
After 10 cycles  \(\)0.088  0.074  0.00032  \(\)0.066  0.099  0.00019 
After 30 cycles  0.049  0.084  \(\)0.008  0.096  
After 50 cycles  \(\)0.024  0.073  \(\)0.012  0.097 
Results of RIRTs stability for the second batch of thermometers
\(T \approx 4,6 \hbox {K}\)  \(T \approx 7,2 \hbox { K}\)  

\(\Delta T,\hbox {mK}\)  \(u(\Delta T), \hbox {mK}\)  Selfheating, \(\Omega /\hbox {mA}^{2}\)  \(\Delta T,\hbox {mK}\)  \(u(\Delta T),\hbox {mK}\)  Selfheating, \(\Omega /\hbox {mA}^{2}\)  
No. LT001  
After 10 cycles  0.122  0.046  0.00013  0.058  0.040  0.00007 
After 30 cycles  0.055  0.052  0.021  0.053  
After 50 cycles  0.044  0.051  0.023  0.040  
No. LT002  
After 10 cycles  0.071  0.192  0.00013  0.081  0.052  0.00008 
After 30 cycles  \(\)0.061  0.041  0.037  0.040  
After 50 cycles  \(\)0.067  0.043  0.017  0.041  
No. LT005  
After 10 cycles  \(\)0.256  0.044  0.00011  0.188  0.211  0.00007 
After 30 cycles  \(\)0.108  0.043  \(\)0.039  0.051  
After 50 cycles  \(\)0.127  0.046  \(\)0.037  0.051  
No. LT009  
After 10 cycles  0.090  0.092  0.00013  0.051  0.157  0.00007 
After 30 cycles  \(\)0.148  0.089  \(\)0.025  0.118  
After 50 cycles  \(\)0.203  0.068  \(\)0.110  0.121  
No. LT011  
After 10 cycles  \(\)0.018  0.039  0.00016  \(\)0.003  0.176  0.00010 
After 30 cycles  \(\)0.129  0.040  \(\)0.053  0.039  
After 50 cycles  \(\)0.149  0.040  \(\)0.069  0.039  
No. LT013  
After 10 cycles  0.093  0.065  0.00016  0.044  0.115  0.00010 
After 30 cycles  0.008  0.075  \(\)0.015  0.131  
After 50 cycles  \(\)0.021  0.083  \(\)0.092  0.140  
No. LT015  
After 10 cycles  0.241  0.047  0.00013  0.151  0.114  0.00007 
After 30 cycles  \(\)0.086  0.056  \(\)0.004  0.039  
After 50 cycles  \(\)0.108  0.050  \(\)0.009  0.045  
No. LT016  
After 10 cycles  0.142  0.042  0.00016  0.045  0.040  0.00009 
After 30 cycles  0.082  0.071  0.015  0.049  
After 50 cycles  0.032  0.041  0.005  0.059  
No. LT017  
After 10 cycles  0.195  0.065  0.00013  0.110  0.099  0.00007 
After 30 cycles  \(\)0.126  0.038  \(\)0.128  0.054  
After 50 cycles  \(\)0.138  0.038  \(\)0.105  0.067  
No. LT019  
After 10 cycles  0.114  0.049  0.00011  0.063  0.048  0.00006 
After 30 cycles  0.029  0.049  0.026  0.044  
After 50 cycles  0.044  0.053  0.033  0.050  
No. 20101  
After 10 cycles  0.120  0.043  0.00025  0.115  0.102  0.00016 
After 30 cycles  0.029  0.060  \(\)0.024  0.050  
After 50 cycles  0.013  0.045  \(\)0.009  0.050  
No. 200909  
After 10 cycles  0.125  0.059  0.00011  \(\)0.007  0.098  0.00006 
After 30 cycles  0.052  0.067  0.022  0.052  
After 50 cycles  0.016  0.061  \(\)0.033  0.080  
No. 201301  
After 10 cycles  0.117  0.045  0.00015  0.048  0.095  0.00008 
After 10 cycles  0.092  0.265  \(\)0.019  0.096  
After 10 cycles  0.012  0.055  \(\)0.005  0.102 
This study is focused on measurements of the thermometer’s resistance after 50 thermal cycles between room temperature and liquid helium temperatures. The resistance of each thermometer was measured at about 4.6 K and 7.2 K before the thermal treatment and after 10, 30 and 50 thermal cycles.
2 Thermal Treatment
For the thermal cycling treatment, the thermometers were mounted in a sealed stainless steel container made of a tube with a diameter of 25 mm and a length of 130 cm. The container was pumped to about 0.1 Pa pressure and then filled with gaseous helium to ensure a good thermal exchange between thermometers and liquid helium. The container was dipped slowly into liquid helium to cool the thermometers to 4.2 K over about 5 min. Then, it was removed from the helium Dewar, and the thermometers warmed to room temperature. The procedure was repeated 10 times initially and then 20 times in each of two subsequent runs. After each treatment, the thermometers were inserted into the copper block of a cryostat for measurement.
3 Cryostat Construction
For controlling the temperature of the copper block near 4.6 K, a model 370 Lake Shore Cryotronics temperature controller, with an Allen–Bradley carbon resistance thermometer, d (Fig. 1) was applied. The temperature of the block was stable within ±0.1 mK during the thermometer tests.
At a temperature close to 7.2 K, some tests were carried out with a superconducting lead (Pb) transition (the lead sample, e, is shown in Fig. 1) used for the temperature stabilization. The lead sample was inside mutual inductance coils, f. The signal from the coil was measured via a lockin amplifier and transmitted to the PID controller. Because the accuracy of the temperature stabilization using this method was the same as obtained with the Lake Shore Controller, the second simpler methods were used for most tests.
4 RIRT Resistance Measurements
The resistance \(R_{\mathrm{T}}\) was measured relative to a 10 \(\Omega \) Tinsley standard resistor placed in a thermal enclosure outside the cryostat. The ratio resistance bridge and the standard resistor were calibrated at the Central Office of Measures (the National Measurement Institute in Poland).
The resistance \(R_{\mathrm{T}}\) and the ratios \(R_{\mathrm{X}} / R_{\mathrm{T}}\) were measured at two currents, \(I_{1} = 1 \hbox { mA}\) and \(I_{2}=\surd 2 \hbox { mA}\), and extrapolated to \(I_{0} = 0\). All numerical values of the resistances were the average of 40 measurements.
5 Tests of Thermometers Stability
6 Measurements Results

standard error of regression (function R = aT + b),

uncertainty of determination of the selfheating corrections,

uncertainty of ratio bridge,

standard resistor thermal drift,

standard thermometer reproducibility.
It can be noticed that the stability of thermometer 20108 is worse than the other four, and this is probably related to the larger selfheating, see Table 1. It seems likely that this is due to a small leak in the capsule.
7 Summary
The studies carried out at INTiBS showed that the majority of the tested RIRTs produced by TIPC are very stable—within 0.2 mK—after thermal cycling treatment between the room and liquid helium temperatures. After first 10 cooling runs the \(T''T'\) value was larger, but subsequent cycles of thermal treatment stabilized the RIRTs within the range 0.2 mK compared with the indication before thermal treatment.
Notes
Acknowledgements
Authors of the paper express thanks to Dr. L. Lipinski from INTiBS for his contribution to the elaboration of the research results.
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