NOVEL TRANSFER STANDARD FOR TEMPERATURE MEASUREMENTS OF THE INTERNATIONAL AVOGADRO PROJECT

Horst Bettin1, Arnold Nicolaus1, Steffen Rudtsch2, Enrico Massa3, and Andrea Merlone3

1 Physikalisch-Technische Bundesanstalt (PTB), Bundesallee, Braunschweig, Germany 2 Physikalisch-Technische Bundesanstalt (PTB), Abbe Str, Berlin, Germany

3 Istituto Nazionale di Ricerca Metrologica (INRIM), Strada delle cacce, Torino, Italy

Abstract The International Avogadro Coordination aims at determining the Avogadro constant by measuring the molar mass, lattice parameter and density of a 28Si single crystal. As the temperature dependent quantities are measured in different apparatuses, the consistency of the temperature measurements has to be proven. An electronic temperature reference and a standard platinum resistance thermometer (SPRT) are used – in a first round - to compare the temperature measurements at the INRIM and PTB.

Introduction The International Avogadro Coordination uses a silicon single crystal grown from isotopically enriched 28Si to determine the Avogadro constant NA [1] according to NA = 8 M / (ρ a3). In this method the crystal molar mass M, lattice parameter a and density ρ must be measured. The density is determined by mass and diameter measurements of a nearly perfect sphere. Since the temperature-dependent quantities lattice parameter and diameter are measured in different apparatuses and even partly different institutes (INRIM, National Measurement Institute Australia NMI-A, National Metrology Institute of Japan NMIJ, and PTB), the consistency of the separate temperature measurements is crucial for a correct determination of NA. As the total relative uncertainty of 2 x 10-8 is required and the thermal volumetric expansion coefficient of Si is about 8 x 10-6 K-1, temperature measurements must agree to within 1 mK corresponding to 8 x 10-9 NA. A thermo-meter comparison at the reference temperature of 20 °C is performed as independent check of the temperature measurements and the equipments used.

Transfer Standards At the Working Group (WG) “Density of Solids” of PTB an electronic temperature reference was set up that automatically realizes a constant and reprodu-cible temperature at 20 °C. It consists of a dry block calibrator type OCEANUS 6 Model 580 of ISOTECH and a self-made insert equipped with two temperature controllers [2], see Fig. 1. Two super-

stable thermistors (Yellow springs, type YSI 46046) of 12.5 kOhm (at 20 °C) are used to measure the temperature and regulate the heating powers for two separated metal blocks of the insert. The short-term stability of the electronic temperature reference is well below 0.1 mK. Its temperature lied in a range of 0.6 mK over two months and the long-term drift is below 0.2 mK/month [2]. Additionally, a 25 Ω SPRT and a 25 Ω standard resistor are sent around, both calibrated at PTB and with a known history for more than 10 years.

Figure 1: Dry block calibrator and insert.

Participants and Work Plan In this first round, only the temperature measure-ments of the INRIM lattice parameter apparatus and the PTB sphere interferometer are compared. Thermometry groups of the INRIM and PTB are included for temperature calibrations traceable to the international temperature scale ITS-90. The lattice parameter is measured at the INRIM [3], with the crystal temperature measured in situ by a 100 Ω capsule SPRT (CSPRT). The present standard uncertainty of the temperature measurement by means of the SPRT is 1 mK. The readout instrument – Fluke-Hart 1590 Super-Thermometer – compares the voltage on the thermometer and a standard resistor when the same current runs across them, in one direction and again in the opposite one. The

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whole measuring chain is calibrated in situ at the triple point of water and melting point of Ga. These fixed points are calibrated against the national fixed points at the Thermodynamics division of the INRIM, which performs additional and parallel thermometer and resistor calibrations as well. The INRIM and PTB realizations of the ITS-90 at the fixed-point temperatures were compared in the key comparisons CCT.K3 [4] and EUROMET.T-K3 [5]. Good agreement was observed, in particular the temperature differences at the Ga melting point were below 0.3 mK.

Figure 2: Analyzer of the x-ray interferometer with a CSPRT inside a bore drilled in its body. Whereas most of the PTB working groups that participate in the Avogadro project are located in Braunschweig, the WG “Applied Thermometry” of PTB is in Berlin, 250 km away from Braunschweig. Therefore, the WGs in Braunschweig have fixed- point cells of their own to calibrate their SPRTs. The WG “Multiple-beam Interferometry on Material Measures” determines the diameter of the Avogadro spheres [4]. The temperature measurement is based on a capsule standard platinum resistance thermo-meter Goodrich model 162D (former Rosemount) with nominal 25.5 Ω that is hermetically sealed in a metal sheath and is a fully ITS-90 interpolation standard (see Fig. 3). It is periodically recalibrated in situ with a water triple-point cell and two gallium cells. These fixed points are calibrated in the thermometry WG of PTB. For the measurements an ac resistance ratio bridge ASL F18 is used together with a thermally isolated reference resistor. The standard uncertainty of the CSPRT temperature is estimated to 0.6 mK at 20 °C. The WG “Density of Solids” developed the electronic temperature reference and organizes the comparison. The temperature measurements of the WG are performed with a 25 Ω PRT type 162CE of Rose-mount that was calibrated at the thermometry WG of PTB. An ac resistance ratio bridge ASL F900

together with a standard resistor is used to determine the resistance of the PRT. Bridge and resistor were calibrated in the electricity division of PTB. The WG also owns two gallium cells that were calibrated in the thermometry WG of PTB. They are used to check the SPRT and the whole temperature measurement equipment. A standard uncertainty of 0.6 mK is estimated for temperatures near 20 °C.

Figure 3: Spheres interferometer with CSPRT in a copper block (and a second in the bore of a Si sphere to determine the temperature inside the sphere). After calibration at the PTB (Berlin), the transfer standards will be carried to the PTB in Braunschweig and to INRIM, where the participants will assess on the spot the performances of their temperature measurement chains. At the end, the standards will again be checked at the PTB (Berlin). The results of the comparison will be presented at the conference.

References [1] P. Becker et al., “Large-scale production of highly

enriched 28Si for the precise determination of the Avogadro constant,” Meas. Sci. Technol., vol. 17, no. 7, pp. 1854-1860, July 2006.

[2] H. Bettin, “Temperature control in the µK range for density measurements,” Proc. 20th Int. Conf. on Force, Mass & Torque IMEKO TC3, Merida, Mexico, pp. 64.1-64.9, November 27-30, 2007.

[3] A. Bergamin et al., “Lattice parameter and thermal expansion of monocrystalline silicon,” J. Appl. Phys., vol. 82, no. 1, pp. 5396-5400, December 1997.

[4] B. W. Mangum et al., “Key Comparison: Summary of comparison of realizations of the ITS-90 over the range 83.8058 K to 933.473 K: CCT key comparison CCT-K3,” Metrologia, vol. 39, no. 2, pp. 179-205, 2002.

[5] E. Renaot et al., “Report to the CCT on Key Comparison EUROMET.T-K3 (EUROMET Project 552),” www.BIPM.org, pp. 129, September 2006.

[6] R. A. Nicolaus and R. D. Geckeler, “Improving the Measurement of the Diameter of Si-Spheres," IEEE Trans. Instrum. Meas., vol. 56, no. 2, pp. 517-522, April 2007.