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A new type of miniature negative temperature coefficient (NTC) thermistors has been developed and manufactured with Mn-Ni-Cu-Fe oxides. The prepared NTC thermistors were calibrated in the temperature range from 77 K to 300 K with 1 μA exciting currents. The automatic calibration apparatus as well as thermometric characteristics, stability, calibration equations and interchangeability of the manufactured thermistors were investigated. A mean fit equation was obtained: 1/
*T* = 8.60 × 10
^{−4} + 6.54 × 10
^{−4} ln(
*R/R*
_{ref}) + 2.46 × 10
^{−5} ln(
*R/R*
_{ref})
^{2} + 9.48 × 10
^{−7} ln(
*R/R*
_{ref})
^{3}
− 2.16 × 10
^{−8} ln(
*R/R*
_{ref})
^{4}. All the prepared NTC thermistors agreed with this fit with an error of 1.5 K. If the greater accuracy is required, a calibration is necessary, and the calibration accuracy is estimated to be ±10 mK.

Many cryogenic applications require a large number of temperatures to be monitored in various areas of cryogenic engineering and low-temperature physics. The two most commonly used parameters in cryogenic thermometers are voltage and resistance. The widely applied cryogenic temperature sensors include thermocouples, diodes, resistors and capacitors and so on. Resistors can be classified as positive temperature coefficient (PTC) or negative temperature coefficient (NTC) [

The advantages of NTC thermistors for temperature measurement are the high sensitivity to yield a high resolution and the high resistivity permits small mass units with fast response. This makes them compatible for using requiring a high output signal over a relatively narrow temperature range [

In this paper, the Mn-Ni-Cu-Fe oxides NTC thermistors of low resistivity were prepared by using the solid-state coordination reaction route, with the in-situ lead wire attachment method (ISAM) and sealed by glass, as described in our previous work [

The NTC ceramics were synthesized through solid-state route. Analytical grade nickel acetate Ni(CH_{3}COO)_{2}·4H_{2}O, copper acetate Cu(CH_{3}COO)_{2}·H_{2}O, manganese acetate Mn(CH_{3}COO)_{2}·4H_{2}O, iron oxalate FeC_{2}O_{4}·2H_{2}O and oxalic acid H_{2}CO_{4}·2H_{2}O were used as raw materials. The contents of metal ions in raw materials are determined by chemical analysis. The raw materials were accurately weighed according to their molar ratio, transferred to polypropylene jars and milled for 24 h using zirconia balls as milling medium to get a uniform mixture. The milled was dried at 75˚C, and calcined at 800˚C for 4 h in air. The calcined powder was then ground for 48 h by ball milling to get a narrow particle-size distribution.

Disk-shaped thermistors were designed by using in-situ lead wire attachment method (ISAM). Celluloid board with a height of 2.0 mm was drilled a row of holes with a diameter of about 3.5 mm , and a distance of about 2.5 mm between holes, then was grooved at both sides of the centres of holes, and the distance of between two grooves with the depth of 1.0 mm and the width of 0.05 mm is 2 mm. Two platinum lead wires ( 0.05 mm diameter) were placed into two grooves. The powders granulated with a 4% polyvinyl alcohol (PVA) organic binder were placed in the holes to form green bodies with cold-pressed using a steel die by single-end compaction and pressed at 200 MPa by isopressing process. Celluloid board with green bodies were heated in air to 400˚C at a rate of 100˚C/h, kept at that temperature for 2 h for adequate binder burnout, and subsequently heated to 1150˚C at a rate 200˚C/h and kept at that temperature for 4 h for sintering. The sintered samples were cut, and subsequently soldered copper leads and sealed by glass. So, NTC thermistors were manufactured.

XRD pattern of the sintered experimental sample in

Scare any description of the calibration device has presented in the literature, and a simple statement of the calibration device is given here. The automatic calibration apparatus, which was manufactured by Institute of Refrigeration and Cryogenics, Zhejiang University, in 2008, is now in the ownership of Beijing Institute of Aerospace Testing Technology. The automatic calibration equipment consists of three main parts, including cryostat, temperature control system and

data acquisition system. Schematic illustration of the automatic calibration facility is shown in

Six thermistors were mounted in the constant-temperature block of the cryostat and driven with a 1 µA current. The SCPRT reference thermometer placed in the constant-temperature block was measured by the Fluke. Model 1590 Supper thermometerⅡ. The thermistors calibration was carried out by recording those voltages of calibrated thermistors and reference temperature in the temperature from 77 K to120 K with 5 K intervals and with 20 K intervals from 120 K to 300 K. The calibration tables were obtained by interpolating the calibration data, and averaged to obtain a mean curve.

What shown in

T(K) | NTC thermistors | CX-1080 | GR-200A-1500 | CGR-1-2000 | ||||
---|---|---|---|---|---|---|---|---|

R(Ω) | dR/dT (Ω/K) | R (Ω) | dR/dT (Ω/K) | R (Ω) | dR/dT (Ω/K) | R (Ω) | dR/dT (Ω/K) | |

77 | 109,000 | −12338.4 | 836 | −115.39 | 5.01 | −0.078 | 21.65 | −0.157 |

100 | 14200 | −1095.76 | − | − | 3.85 | −0.033 | − | − |

300 | 27.6 | −0.365 | 130 | −0.55 | − | − | 11.99 | −0.015 |

Stability is the closeness of agreement between the results of the measurements of the same measurand carried out under changed conditions of measurements. Preliminary investigation of stability of NTC thermistors at 77 K was performed. Together with the six calibrated thermistors were immersed in liquid nitrogen for 300 h, and short-term stability data was obtained by subjecting NTC thermistors to 50 thermal shocks from 473 K to 77 K. Finally, resistance shifts were measured at 77 K in liquid nitrogen. Deviations of the thermistors resistance corresponded to temperature error in the range from 0.9 mK to 4.7 mK. Long-term stability data was obtained by subjecting NTC thermistors to 200 thermal shocks from ambient to liquid nitrogen. The long-term stability for themistors corresponded to temperature error not more than ±8 mK at 77 K. Compared with Germanium, Cernox^{TM}, and Carbon-Glass RTDs, therefore, the stability of NTC thermistors may be much better.

As well to known, the performance of the thermistors for temperature measurement is affected by the calibration equation. Chiachung Chen [

1 / T = A 0 + A 1 ln ( R / R ref ) + A 2 ln ( R / R ref ) 2 + A 3 ln ( R / R ref ) 3 + A 4 ln ( R / R ref ) 4 ,was the best equation for thermistors by evaluating seven calibration equations. Here, R is the specific resistance ohm value, R_{ref} is 1 ohm, and T is the absolute temperature. The software, MATLAB R2006a, is used to estimate the parameters of calibration equations. The e i was defined as follow: e i = T i − T ^ i , where e i is the error of calibration equation, T i is the dependent temperature variable and T ^ i is the predicted values of calibration equation. Four statistics, e max , e min , | e | a v e and e s t d are adopted to evaluated the precision of equation. The e max is the maximum e i value and the e min is the minimum e i value. The | e | a v e was

defined as follow: | e | a v e = ∑ | e i | n , where | e i | is the absolute value of e i , n is the number of data. The uncertainty from a calibration equation can be calculated from the standard deviation of the calibration equation: e s t d = ( ( e i − e ¯ i ) 2 n − 1 ) 0.5 ,

where e ¯ i is the average of e i . The values of estimated parameters, e max , e min , | e | a v e and e s t d of calibration equation for six NTC thermistors are listed in

It is very convenient and cost effective to have temperature sensors that match a standard curve, thus not requiring individual calibration. The mean calibration table of the thermistors for the temperature range from 77 K to 300 K is of most interest to us for the future use. So mean table of resistance versus temperature of the six calibrated thermistors was established, and fitted with the Hoge-3 equation. A mean fit equation was obtained: 1/T = 8.60 × 10^{−4} + 6.54 × 10^{−4} ln(R/R_{ref}) + 2.46 × 10^{−5} ln(R/R_{ref}) ^{2} + 9.48 × 10^{−7} ln(R/R_{ref})^{3} − 2.16 × 10^{−8} ln(R/R_{ref})^{4}.

Sample No. | Parameters | e max (mK) | e min (mK) | | e | a v e (mK) | e s t d (mK) | |
---|---|---|---|---|---|---|

1 | A0 | 8.64 × 10^{−}^{4} | 9.6 | −5.1 | 2.53 | 3.41 |

A1 | 6.59 × 10^{−}^{4} | |||||

A2 | 2.35 × 10^{−}^{5} | |||||

A3 | 1.06 × 10^{−}^{6} | |||||

A4 | −2.26 × 10^{−}^{8} | |||||

2 | A0 | 9.18 × 10^{−}^{4} | 8.31 | −7.36 | 3.03 | 3.98 |

A1 | 6.45 × 10^{−}^{4} | |||||

A2 | 2.37 × 10^{−}^{5} | |||||

A3 | 9.28 × 10^{−}^{7} | |||||

A4 | −1.99 × 10^{−}^{8} | |||||

3 | A0 | 8.11 × 10^{−}^{4} | 7.87 | −6.25 | 2.84 | 3.60 |

A1 | 6.62 × 10^{−}^{4} | |||||

A2 | 2.30 × 10^{−}^{5} | |||||

A3 | 1.21 × 10^{−}^{6} | |||||

A4 | −2.84 × 10^{−}^{8} | |||||

4 | A0 | 8.26 × 10^{−}^{4} | 9.12 | −6.74 | 2.45 | 3.45 |

A1 | 6.57 × 10^{−}^{4} | |||||

A2 | 2.63 × 10^{−}^{5} | |||||

A3 | 7.90 × 10^{−}^{7} | |||||

A4 | −1.87 × 10^{−}^{8} | |||||

5 | A0 | 8.85 × 10^{−}^{4} | 7.77 | −4.94 | 2.49 | 3.21 |

A1 | 6.43 × 10^{−}^{4} | |||||

A2 | 2.55 × 10^{−}^{5} | |||||

A3 | 8.20 × 10^{−}^{7} | |||||

A4 | −1.77 × 10^{−}^{8} | |||||

6 | A0 | 8.56 × 10^{−}^{4} | 9.96 | −5.98 | 2.90 | 3.78 |

A1 | 6.56 × 10^{−}^{4} | |||||

A2 | 2.55 × 10^{−}^{5} | |||||

A3 | 9.74 × 10^{−}^{7} | |||||

A4 | −2.28 × 10^{−}^{8} |

the dependence of the temperature deviation ΔT of the six calibrated NTC thermistors from their mean fit curve on the temperature. The deviations from the mean curve are combined with the variation among the NTC thermistors, which is concluded that application of the mean curve will resulted in a measurement of error of ±1.5 K in the temperature range from 77 K to 300 K. Therefore, to significantly improve on accuracy, specific calibration of the prepared NTC thermistors is required, and the calibration accuracy is estimated to be ±10 mK, which is shown in

A new type of NTC thermistors had been designed, manufactured and calibrated in the temperature range from 77 K to 300 K. They showed good thermometric properties, stability and high thermal sensitivity. The accuracy and precision of the prepared thermistors with the Hoge-3 equation fit were as good as other commercial NTC Resistors. A mean fit equation was obtained: 1/T = 8.60 × 10^{−4} + 6.54 × 10^{−4} ln(R/R_{ref}) + 2.46 × 10^{−5} ln(R/R_{ref})^{2} + 9.48 × 10^{−7} ln(R/R_{ref})^{3} − 2.16 × 10^{−8} ln(R/R_{ref})^{4}. All the prepared NTC thermistors agreed with this fit with an error of 1.5 K. If the greater accuracy is required, a calibration is necessary, and the calibration accuracy is estimated to be ±10 mK. Therefore, their widespread application is important in cryogenic engineering and experimental physics.

This work was supported in part by Beijing Institute of Aerospace Testing Technology and Material Physics and Chemistry Research Center of the Xingjiang Technical Institute of Physics and Chemistry, the Chinese Academy of Science. The authors are grateful to Ying Wang, Xue Dong and Dongfang Wang for measuring the six prepared thermistors.

The authors declare no conflicts of interest regarding the publication of this paper.

Lan, Y.Q., Yang, S.Y., Chen, G.M. and Yang, S.F. (2020) Characteristics of a Type of NTC Thermistors for Cryogenic Applications. Advances in Materials Physics and Chemistry, 10, 167-177. https://doi.org/10.4236/ampc.2020.108012