High-temperature fixed-point furnace uncertainties

Dave Lowe, Frédéric Bourson, Massimo Florio, F. Girard, G. Machin, J.
Mantilla, M J Martin, H. Nasibli, O. Pehlivan, Mohamed Sadli

► To cite this version:

Dave Lowe, Frédéric Bourson, Massimo Florio, F. Girard, G. Machin, et al. High-temperature fixed-point furnace uncertainties. AIP Conference Proceedings, 2024, 3230, pp.070006. 10.1063/5.0234816. hal-05340637

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# High-Temperature Fixed-Point Furnace Uncertainties

D. Lowe<fnref n="1" />, a), F. Bourson<fnref n="2" />, M. Florio<fnref n="3" />, F. Girard<fnref n="3" />, G. Machin<fnref n="1" />, J. Mantilla<fnref n="4" />, M. J. Martin<fnref n="4" />, H. Nasibli<fnref n="5" />, O. Pehlivan<fnref n="5" />, and M. Sadli<fnref n="2" />

**Abstract.** High-temperature fixed-points with specified temperature values for phase transition temperatures and their uncertainties can be used to establish a temperature scale above the silver point as part of the SI. Current assigned temperatures had uncertainties increased to make the data consistent; seemingly with under-reported uncertainties which may have been due to variation in furnace thermal environment not being taken fully into account. As part of another round of temperature assignments to extend the available temperature options, the effect of changing furnace temperature gradients on the realization of different high-temperature fixed-point cells was investigated. The resulting uncertainty components are reported, and these should be included in any uncertainty budget. In this work, we present data for four phase transitions: iron-carbon (Fe-C), palladium-carbon (Pd-C), ruthenium-carbon (Ru-C) and tungsten carbide-carbon (WC-C).

## INTRODUCTION

In 2019, the definitions of four base units of the SI were updated to be fixed and defined by exact values of fundamental constants: the kilogram, ampere, kelvin and mole [1]. For the kelvin this meant that the Boltzmann constant was set to exactly 1.380 649 × 10⁻²³ J K⁻<fnref n="1" />. To help realise the kelvin in practice, the SI brochure publishes, alongside the definition, the “mise en pratique for the definition of the kelvin” (MeP-K) [2]. This recommends methods, in particular thermodynamic methods, that combine simplicity with low uncertainties. The EMPIR “Realising the Redefined Kelvin” (Real-K) project [3] aims to set the framework for expansion of the MeP-K with improvements at high (>1300 K) and low (<25 K) temperatures, and maintain the relevance of ITS-90, which for many users continues to be the traceability route of choice. The high temperature aspect is addressed by investigating additional high-temperature fixed-points (HTFP) [4] with a view to adding these to the relative primary radiometric thermometry category [5].

Three of the existing HTFP were included after a world-wide collaboration in which the best primary radiometry was applied to assign thermodynamic temperature (T) to phase transitions for rhenium-carbon, platinum-carbon and cobalt-carbon systems [6,7] (a fourth, palladium-carbon, was included at larger uncertainty from a previous evaluation). These state-of-the-art measurements can now be accessed via artefacts, simplifying realisation of thermodynamic temperature. The assignment of T in [6] required different laboratories making measurements of circulated HTFP blackbodies determining a temperature and uncertainty for each. All the data were then combined into a single temperature value and uncertainty. It was found that the results were inconsistent with the uncertainties from individual laboratories: some or all of which were under-reported. This was dealt with by adding an additional fixed uncertainty component to each reported uncertainty such that the statistical test used (unity Birge ratio) was satisfied. It was proposed, though not substantiated, that this extra uncertainty was needed because of sensitivity to the position of a fixed-point cell within a furnace, i.e., the uniformity of the thermal environment could cause differences in the melting curves.

<footnote n="1">¹National Physical Laboratory, Teddington UK</footnote>

<footnote n="2">²Laboratoire commun de métrologie LNE-Cnam Paris France</footnote>

<footnote n="3">³Istituto Nazionale di Ricerca Metrologica, Turin Italy</footnote>

<footnote n="4">⁴Centro Español de Metrología, Madrid Spain</footnote>

<footnote n="5">⁵TUBITAK-UME, Gebze, Türkiye</footnote>

<footnote>a) Corresponding author: dave.lowe@npl.co.uk</footnote>
Much of the radiometry uncertainty budgets in [6] was based on known and understood calibration uncertainties, but some uncertainties related to the relatively new HTFP and were not as well founded. One component in particular, the furnace effect, was identified but not understood. An uncertainty value for this was arrived at for the *T* assignments by considering available data, then scaling and applying as seemed appropriate. Even then, a list of the components to consider [8] included an “unknown uncertainty” component. The furnace effect has been suggested as due to reflectivity of the fixed-point cavity being higher than allowed for at glancing incidence angles [9], giving the radiometer a larger than expected reflected contribution from the hot furnace. This explanation for the furnace effect has been qualitatively confirmed by modelling [10]. The temperature profile of the furnace therefore has the potential to influence measurements in at least three ways – reflection of the furnace in front of the HTFP blackbody, an apparent change in wall emissivity along the cavity [11] and, in extremis, by causing the solid-liquid interface to move front-to-back or back-to-front rather than radially about the cavity. To better account in the uncertainty budget for how the furnace temperature profile might affect the Real-K *T* assignment, measurements with deliberately induced gradients were carried out for all the HTFP types included in this work, namely: the iron-carbon (Fe-C), palladium-carbon (Pd-C), ruthenium-carbon (Ru-C) and tungsten carbide-carbon WC-C) phase transitions. In addition, two approaches were used to investigate the uncertainties: fixed cell position with variable furnace temperature profile and variable cell position with fixed temperature profile. From these measurements an estimate of the magnitude of the furnace effect uncertainty can be estimated.

## Furnace type

Two types of furnaces were considered. In the first, type-1, furnace independently heated zones allow a temperature gradient to be imposed on the fixed-point cell. The second, type-2, furnace has a fixed heated zone and variability is introduced by changing the position of the cell.

## Testing Laboratories

The laboratories and furnaces used for cell evaluation were

* CEM type-1 (Fe-C) and type-2 (Fe-C and Pd-C)

* CNAM type-2 (WC-C)

* INRIM type-1 (Fe-C and Pd-C)

* NPL type-2 (Ru-C) and type-2 (WC-C)

* TUBITAK type-1 (Fe-C and Pd-C)

Each melting curve (temperature plotted with time) was evaluated using the process from [7] to give: the point-of-inflection temperature (POI), the liquidus (thermodynamic) temperature and its associated uncertainty, and the melting range. The POI temperature (*T*<sub>poi</sub>) lacks any physical significance (it simply identifies a mathematical point on a curve), while the liquidus temperature (*T*<sub>liq</sub>) is the true phase transition temperature at thermodynamic equilibrium.

## RESULTS

With four fixed-point types, two furnace types and at least three fixed-point cell positions there is more data than can be provided in this paper. Instead, we will present selected results and show how the final values were arrived at. The full set of melting and freezing curves can be found in [12]. The intent here is to show what a good HTFP melting curve looks like, what a bad HTFP melting curve looks like and what the impact of each is on uncertainties.

### Illustration of good HTFP melting curve results

The key selection criteria for a good HTFP melting curve are a small melting range, small difference between POI and liquidus temperatures and a high POI. (Note that although melting range and liquidus are both determined from the minimum gradient tangent, as thermal conditions improve the point-of-inflection moves to occur later in the melting of the HTFP [and hence later in the melt curve]). Small melting range and high poi have both been used as indicators of good melting performance of HTFPs [13]. The example in Fig. 1 is a ruthenium-carbon fixed-point cell in a type-2 furnace with the selection criteria summarised in Fig. 2. Here, the melting range is smallest at a
position about 0 mm (geometric centre) or with the cell moved forward 5 mm, with the point of inflection high at these positions and the difference between POI and liquidus temperatures are small. Note it is expected the furnace temperature will drop away from the centre so that moving the cell forward will make the back of the cell hotter.

Looking at Figures 1 and 2

* There are clear changes in the gradient of some of the melting curves – most apparent at 20 mm and 10 mm, but also at 5 mm, even though that had the lowest melting range. The changes at 10 mm and 20 mm are due to the metal ingot not melting uniformly: with the cell forward (hotter at the back) the ingot has melted at the backwall whilst solid ingot material still remains at the front of the HTFP blackbody.

* The best result is neither the longest nor shortest melt, so melt duration is not a good indicator of quality

* The back 10 mm position (hotter at the front) looks good to the eye, but actually has a larger melting range.

<figure><img src="image_2.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>(b)</figcaption></figure>

**FIGURE 1.** NPL ruthenium-carbon in their type 2 furnace at offsets of 20 mm, 10 mm and 5 mm forward, centred and 10 mm back, (a) melting curves and (b) melting curve derivatives.

<figure><img src="image_4.png" /></figure>

**FIGURE 2.** Summary of temperatures from Fig. 1 of the cell at different positions in the furnace.

## Melting behaviour in type-1 versus type-2 furnace

Here we examine the question; is the same melt behaviour shown by a HTFP of the same material in both types of furnace? We look first at an Fe-C blackbody in a type-1 three-zone furnace where end zones have offsets to give positive (hot at the front) and negative gradients (Fig. 3 and Fig. 4).

Figure 4 shows having the furnace hotter at the front can produce melts that appear to be good and partly meet the selection criteria, but while the POI temperature is higher, so also is the liquidus temperature giving a larger difference between the two. Compare this to Fe-C in a type-2 furnace at CEM (Fig. 5 and Fig. 6). Here the front hotter curve at -10 mm position might be selected as best, but it is the centre position at 0 mm that best matches the selection criteria shown in Fig. 6.
<figure><img src="image_5.png" /><figcaption>**FIGURE 3.** LNE iron-carbon in TUBITAK type-1 furnace at best uniformity (0), with negative gradient making the back of the cell hotter (–10 °C) and positive gradient with the front of cell hotter (+10 °C), (a) melting curves (b) melting curve derivatives.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**FIGURE 4.** Summary of temperatures from Fig. 3 of the cell in different temperature gradients, negative being decreasing temperature from back to front and vice versa</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**FIGURE 5.** CEM iron-carbon in their type-2 furnace at 20 mm and 10 mm back, in the centre, and at 10 mm and 20 mm forward, (a) melting curves and (b) melting curve derivatives.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>FIGURE 6. Summary of temperatures from Fig. 5 of the cell in different positions.</figcaption></figure>

For completeness illustrative data is also given for HTFP blackbodies of Pd-C, and WC-C

<figure><img src="image_9.png" /><figcaption>FIGURE 7. CEM Pd-C (a) in their type-1 (different temperature gradients along the fixed-point cell) and (b) in their type-2 (fixed-point cell at different positions in a fixed temperature profile)</figcaption></figure>

The palladium cell was the same in both cases and has a large melting range. The type-2 seems to be optimal about 5 mm back from the centre (high point-of-inflection and low melting range). The type-1 results were inconclusive as shown: poor repeatability and no obvious optimum. However, the same pattern of hot at the front having a subjectively better melting curve than hot at the back was apparent in the melting curves.

<figure><img src="image_10.png" /><figcaption>FIGURE 8. Two different WC-C fixed-point cells in different type-2 furnaces (a) their cell at LNE (position relative to arbitrary marker) and (b) their cell at NPL (position relative to centre)</figcaption></figure>
The type-2 results for WC-C in Figure 8(a) shows the expected pattern: low melting range, high low limit and small difference in limits. In Figure 8 b), it seems the optimum is at -10 mm, i.e., hotter at the front, but it could possibly be better still further back.

Overall, we have data for each fixed-point type at the optimum thermal environment and at two less-good temperature profiles. Two different furnace types have been compared and both show similar behaviour with high POI and low melting range in the most uniform thermal environment. The full results are given in [12], here we combine for the two furnace types, and the POI and liquidus temperatures to give two numbers: “best” and “normal”. For “best”, we take the smallest difference between two thermal conditions as being the change in measured fixed point temperature that might happen from not quite getting optimum conditions. We judge this to be what might be achieved with the best available equipment and careful setting up. For “normal”, we use the largest difference that results from the change in thermal environment from different positioning or imposed gradients. We judge this to be the change in fixed point temperature that might result from only roughly positioning the fixed-point cell or from not individually adjusting zone set-points. In each case we take the largest value from the results in [12], and these are shown in Table 1. Although some experimental data had lower values, we think the information in Table 1 can be used without further justification to be added as a standard uncertainty to an uncertainty budget. The uncertainties given here are consistent with those reported elsewhere for deliberately imposed temperature gradients on fixed-point cells of cobalt-carbon, platinum-carbon and rhenium-carbon [14].

<table><caption>TABLE 1 Recommended uncertainties for best and normal use</caption><thead><tr><td>Phase Transition</td><td>Best / mK</td><td>Normal / mK</td></tr></thead><tbody><tr><td>Fe-C</td><td>25</td><td>30</td></tr><tr><td>Pd-C</td><td>50</td><td>120</td></tr><tr><td>Ru-C</td><td>30</td><td>150</td></tr><tr><td>WC-C</td><td>75</td><td>115</td></tr></tbody></table>

## CONCLUSION

This work represents the most comprehensive investigation of the effect of thermal environment on the melt performance and temperature attained by HTFPs. This work has allowed us to derive normal and best uncertainties for furnace thermal effects for assignment of thermodynamic temperatures to the four fixed points studied [14]. In this work, we presented data for four phase transitions: iron carbide-carbon (Fe-C), palladium-carbon (Pd-C), ruthenium-carbon (Ru-C) and tungsten carbide-carbon (WC-C).

There seems clear evidence that as a fixed-point cell's thermal environment changes from cooler to hotter at the front, the shape of the melting curve subjectively improves but this is actually illusory as the data analysis shows. In fact, here we show that it is most important to ensure the HTFP blackbody is in the most uniform part of the furnace to obtain the best results.

## ACKNOWLEDGEMENT

This paper has been written through funding received from the EU EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme, specifically from the EMPIR project 18SIB02 "Realising the redefined kelvin".

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