# Thermodynamic Temperature of High-Temperature Fixed Points Traceable to Blackbody Radiation and Synchrotron Radiation

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## Abstract

Absolute spectral radiometry is currently the only established primary thermometric method for the temperature range above 1300 K. Up to now, the ongoing improvements of high-temperature fixed points and their formal implementation into an improved temperature scale with the *mise en pratique* for the definition of the kelvin, rely solely on single-wavelength absolute radiometry traceable to the cryogenic radiometer. Two alternative primary thermometric methods, yielding comparable or possibly even smaller uncertainties, have been proposed in the literature. They use ratios of irradiances to determine the thermodynamic temperature traceable to blackbody radiation and synchrotron radiation. At PTB, a project has been established in cooperation with VNIIOFI to use, for the first time, all three methods simultaneously for the determination of the phase transition temperatures of high-temperature fixed points. For this, a dedicated four-wavelengths ratio filter radiometer was developed. With all three thermometric methods performed independently and in parallel, we aim to compare the potential and practical limitations of all three methods, disclose possibly undetected systematic effects of each method and thereby confirm or improve the previous measurements traceable to the cryogenic radiometer. This will give further and independent confidence in the thermodynamic temperature determination of the high-temperature fixed point’s phase transitions.

## Keywords

Absolute radiometry Blackbody radiation Cryogenic substitution radiometer Filter radiometer High-temperature fixed points Irradiance mode Primary radiation standards Ratio radiometry Synchrotron radiation Thermodynamic temperature## 1 Introduction

Absolute spectral radiometry is at present the only reliable primary thermometric method for the temperature range above 1300 K [1]. The currently ongoing improvements to the high-temperature range of the ITS-90, i.e., the development of novel high-temperature fixed points (HTFP) and their formal implementation into an improved temperature scale with the *mise en pratique* for the definition of the kelvin, rely solely on thermodynamic temperature measurements based on single-wavelength absolute radiometry traceable to the cryogenic radiometer (CR) [2]. The wording “single-wavelength” for a narrow band filter radiometer is used to distinguish from “double-wavelength method”. The filter radiometers are calibrated at a sufficient number of wavelength points over their whole bandpass.

Two alternative primary thermometric methods, yielding comparable or even smaller uncertainties in thermodynamic temperature measurement, have been proposed in the literature [3, 4] but have so far not been applied to the measurement of the phase transition temperatures of HTFPs. These methods use ratios of irradiances to determine the thermodynamic temperature of HTFPs traceable to blackbody radiation (BB) and synchrotron radiation (SR).

Alternative I is the “double-wavelength method” [3]. With this method, the spectral irradiances of two BBs of different temperatures are measured with two filter radiometers (FR) of different central wavelengths. The FRs are calibrated only for their relative spectral responsivity. Based on these four measurements, the thermodynamic temperatures of the two BBs are calculated according to Planck’s law. An error function of ratios must be minimized.

Alternative II is the “blackbody-versus-synchrotron method” [4]. With this method, the spectral irradiance at the electron storage ring of PTB, the Metrology Light Source (MLS) [5], will be measured and calculated according to Schwinger’s theory. Two FRs of different central wavelengths which are calibrated only for their relative spectral responsivity are used. With the same two FRs, a BB with a large-area HTFP is measured and the thermodynamic temperature is calculated according to Planck’s law. The thermodynamic temperature is determined by fitting the ratios of measured and calculated irradiance ratios from SR and BB.

We are going to use all three methods—absolute radiometry (traceable to CR) and both alternative methods (traceable to BB and SR)—simultaneously for the temperature measurement of HTFPs. For this, a four-wavelengths ratio filter radiometer (FRFR) was developed, as a dedicated instrument for absolute thermodynamic temperature measurement. With the FRFR, four filter radiometers with their center wavelengths in the VIS and NIR spectral range are combined into a single instrument with one common aperture. With these three independent methods performed in parallel on HTFPs, we aim to compare the potential and practical limitations of all three methods, disclose possibly undetected systematic effects of each method and thereby confirm or improve the previous measurements traceable to the CR. This will give further and independent confidence in the thermodynamic temperature determination of the HTFP phase transitions.

## 2 Radiometric Methods for Thermodynamic Temperature Measurement

In the following, we give a short summary of the three radiometric methods we intend to apply with the FRFR for the thermodynamic temperature measurement of HTFPs phase transition temperatures.

### 2.1 Single-Wavelength Absolute Radiometry

*d*between them.

*G*is defined as:

*h*is Planck’s constant, \(k_{B}\) is Boltzmann’s constant,

*n*is the index of refraction of the medium, \(c_{0}\) is the speed of light in vacuum, and

*T*is the temperature inside the BB. The thermodynamic temperature

*T*is determined by iterative numerical integration of Eq. 1.

Single-wavelength absolute radiometry has been successfully and extensively used over the last two decades to measure the temperature of the phase transitions of HTFPs. Recent results on Re-C cells are for example given in [2].

The following ratio methods avoid uncertainties that originate from geometrical quantities.

### 2.2 Two-Wavelengths Ratio Radiometry

*ŝ*\(_{E,{\lambda }}\) measure two temperatures [8, 9]. Relative spectral irradiance responsivities

*ŝ*\(_{E,{\lambda } }\)can be determined with lower uncertainties than absolute spectral irradiance responsivities \(s_{E,{\lambda }}\). The scaling factors

*a*and

*b*between them need not to be known.

With this ratio method, we are going to use the MLS [10] of the PTB, which is operated as a primary source standard. The MLS is equipped with a dedicated white light beamline. This beamline provides calculable SR according to Schwinger’s theory [11]. The electron energy can be set to values from 105 MeV to 630 MeV. The electron beam current can be varied from 1 pA to 200 mA.

*B*, vertical emission angle \(\psi \) and effective vertical source size \(\Sigma _{y}\).

The angular distribution of the spectral irradiance is homogeneous in the horizontal direction. It has a narrow angular distribution in the vertical direction, which is wavelength dependent. Because of this, the mean value of the spectral irradiance \(E_{{\lambda },SR}\) within the angular acceptance must be considered in Eq. 9. Furthermore, SR shows a linear polarization of the radiation in the orbital plane of the electrons and an elliptical polarization above and below the orbital plane. Because of that the FRs have to be measured in two orientations which are perpendicular to each other.

## 3 The Four-Wavelengths Ratio Filter Radiometer (FRFR)

Characteristics of the four FRs used within the FRFR

Center wavelength | 440 nm | 650 nm | 900 nm | 1550 nm |
---|---|---|---|---|

Photodiode | Si | Si | Si | InGaAs |

Configuration | Trap detector | Trap detector | Single detector | Single detector |

Figure 9 is a schematic diagram of the planned measurement scheme with the FRFR at the MLS. The white light beamline of the MLS has a stray light aperture and ends with a window of fused silica. The window has been tilted to minimize interreflections between the window and the aperture and/or the interference filters of the FRFR. The distance from the source point of the storage ring to the FRFR aperture is approx. 22 m.

## 4 Preliminary Results

### 4.1 SR Measurements

We also investigated stray light and diffraction. Stray light is caused by diffuse reflections on the inner wall of the beamline. It can be reduced by contracting the four knife-edges thus reducing the size of the stray light aperture. Figure 14a shows as a result the constrained spot on the front of the FR.

Yet similarly, diffraction due to the knife-edges of the stray light aperture appears like Figs. 14b and 15 show at top and bottom as well as left and right edges of the spot. They are wavelength dependent and affect the signal more at longer wavelengths.

First results are very promising in terms of stability and reproducibility. Nevertheless, the most crucial part will be the mitigation of interreflections as well as stray light and diffraction contributions.

### 4.2 HTFP Development

We compared phase transitions of the large-aperture and small-aperture HTFPs with the setup of Fig. 17. A temperature difference of about 0.5 K was detected [13]. The difference can be caused by lower effective emissivity or/and by “temperature drop” effect due to higher radiation loses of the large cell. After further experiments, the reasons will be better understood and then the corrections will be applied. Development of the large-area cell will be continued to reduce the temperature difference with the small one as much as possible.

## 5 Summary and Outlook

Three primary thermometric methods applying all three primary radiometric standards—cryogenic radiometer, blackbody radiator and electron storage ring—are discussed for the determination of the phase transition temperatures of HTFPs. A dedicated instrument, the FRFR, has been developed to apply all three methods with one instrument at the primary standards of PTB.

Single-wavelength absolute radiometry shows very good results and is well established. However, so far all primary measurements on HTFPs have been solely performed by this method. Additionally, it has a large geometric uncertainty contribution.

Two alternatives have been proposed to overcome this by using ratios of irradiances. With these methods, the geometry cancels out. They are traceable to blackbody radiation only or to blackbody radiation and synchrotron radiation. These alternatives are possible because of newly developed large-aperture HTFPs. They allow irradiance mode measurements. Thereby, uncertainty contributions are reduced by the absence of optical systems between source and detector.

A dedicated instrument—the FRFR—has been designed and constructed. It is going to use all three methods simultaneously and will apply all three primary radiometric standards. It consists of four filter radiometers with one common aperture.

First measurements for the determination of the alignment, temperature stability and stray light reduction were carried out with single filter radiometers at the synchrotron radiation source of PTB—the Metrology Light Source. VNIIOFI developed and characterized large-aperture HTFPs of Re-C and WC-C.

We aim to compare the potential and practical limitations of all three methods in the near future.

## Notes

### Acknowledgements

This work partly funded by the EMPIR project “Implementing the new kelvin 2”. The EMPIR is jointly funded by the EMPIR participating countries within EURAMET and the European Union.

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