© F. Pavese et al., published by EDP Sciences, 2017

1 Introductory notes

When the current version of the International Temperature Scale, the ITS-90 [1], was promulgated in 1990, the isotopic effect on the Scale was basically ignored, except originally for helium. The Scale definition only made generic reference to a “natural” composition of the substances used for the realisation of the fixed points.

Since the end of the past century, also thanks to the decreased uncertainty of the best realisations of the ITS-90, the effect of the natural variability of the isotopic composition of some of these substances was recognised as an appreciable contribution to the total uncertainty budget of the realisations of those fixed points, in some cases being the largest single contribution [2,3]. In Table 1 this fact is clearly shown. The goal of a total uncertainty budget of 30 μK for a measurement on a single cell was reached around 2010 at INRIM [4], PTB and NMIJ.

1.1 State of the art

Isotopic studies were undertaken, initially on e-H₂ (HD in H₂) [5,6] and H₂O (D₂ and ¹⁸O₂) [7–10], and later also on Ne [4,11–15].

They are relevant to ITS-90, since the triple points of e-H₂ and Ne are required in SPRT subrange 2 (25–273.16) K. The vapour pressure points at ≈17 and ≈20.3 K of e-H₂ are required in the range (13.8–273.16) K. The use of the triple point of water (TPW), which can presently be realised also in small metallic sealed cells [16,17], is prescribed for the whole part of the ITS-90 that is based on resistance-thermometer ratios, extending below 273.16 K down to 13.8 K and above 273.16 K up to the silver point, so affecting also all comparisons including these ranges, based on the resistance ratios W = R(T₉₀)/R(TPW).

In addition, the triple points of e-H₂ and Ne also affect the range covered by the interpolating gas thermometer (ICVGT), being two of the three fixed points of the ICVGT defined by the ITS-90 in the range 3–25 K − the third being the boiling point of ⁴He (or ³He).

At the time when the key comparisons (KC) CCT-K1 “Realisations of the ITS-90, 0.65 K to 24.5561 K, using rhodium–iron resistance thermometers” (1997–2001) [18], CCT-K2 “Key “Comparison of capsule-type standard platinum resistance thermometers from 13.8 K to 273.16 K” (1997–1999) [19] and CCT-K7 “Key comparison of water triple point cells” (2002–04) [20], were organised and completed, the above issue was not yet recognised as important, so not yet formally included in the protocols. Subsequent CCT-K1.1 (2006–14, results available in the BIPM KCDB only recently) [21] and EUROMET.T-K1 (2008–12, similarly) [22] did not take the isotopic effect into account, except for INRIM. CCT-K2.1 (2003) [23] and CCT-K2.4 (2006) [24] did not take the isotopic effect into account; CCT-K2.3 (2006) [25] did take the isotopic effects into account (official correction for e-H₂ and H₂O; VSL un-official evaluation for Ne, see the separate file of the Online Supplementary Information (OSI)); also CCT-K2.5 (2015) [26] did take the isotopic effects into account; CCT-K2.2 (2014) [27], not yet completed, will also take the isotopic effects into account. The EUROMET.T-K7.1 (2008–2009) [28] and APMP.T-K7 [29] included (optionally in the former) the isotopic issue in the comparisons for water.

For water, the issue also involves the present definition of the kelvin, modified in 2005 to include a reference isotopic composition [30]. In the ITS-90, for e-H₂ and H₂O, corrections to a reference composition were made formally available since the first version of the Technical Annex to the Mise en pratique of the kelvin in 2006; for neon it was since its 2014 version [31].

At present, several cases are known of ITS-90 national realisations having adopted, at least partially, isotopic reference compositions: for example, NIST for the all ranges between 4 and 273.16 K only for e-H₂ and of H₂O [32]; INRIM for both e-H₂ and Ne affecting the ICVGT [33].

1.2 Aim of this paper

The study in this paper intends to provide evidence of the consequences of taking the isotopic effect into account. This is best done by using the outcomes of inter-comparisons, because one can also understand to which extent such a correction have affected, and will possibly affect, the differences between laboratories, when they were obtained in studies not having taken that effect into account. In particular, the scrutiny of key comparisons already available from the BIPM KCDB is important, because that MRA exercise provides to metrology the most valuable results, also in respect to the CMC declarations. However, this paper does not intend to tackle any formal consequence that may arise from, or be related to, the isotopic corrections.

In general, a study on the effect that the correction for the isotopic composition may have on the realisation of the ITS-90 in each laboratory is worthwhile if three conditions are met:

• the isotopic composition of the samples used in a comparison are known;

• the equation to compute the temperature correction is included in the current Annex to the MeP of the kelvin;

• the correction can be applied to the results of a substantial number of participants to the comparison.

In addition, no significant effect due to possible remaining chemical impurities should exists, or it has to be taken in account (see for neon the OSI).

Hydrogen.The present information concerning the isotopic correction for hydrogen in CCT-K1 and K1.1 comparisons is quite limited, so the third condition is not met. In addition, the effect of the correction on the latter is almost irrelevant with respect to the comparison uncertainty. Similarly, for the CCT-K2.x the third condition is not met.

Water. The effect of water isotopic composition will not be analysed in this paper, being minimal in the temperature range below 25 K.

Neon. For neon it is possible to assign the isotopic composition to the gas samples used in a few open-cell realisations or contained, in most cases, in permanently-sealed cryogenic metal cells [13]. In these cases, it is possible to apply the equations in the ITS-90 Technical Annex [31] and compute the results at the reference composition. For neon all the above conditions are met for the CCT-K2, K2.1, K2.3–K2.5 (for the chemical impurity corrections see later Table 3 and the OSI).

In addition, some data are also traceable to the first International Inter-comparison of sealed cells performed in 1978–84 [34] or also ensures traceability for several results of the 1997–2005 Star Inter-comparison [12].

Therefore, in this paper the computation of the corrections and the discussion of some consequences is limited to neon, as an example of the complexity of the information needed to perform sound corrections, which may also affect the same type of corrections for other substances. See [35] for the way the information drawn from [31] should be used to take isotopic composition into account in the calibration of SPRTs on the ITS-90, and [15] for details about the needed isotopic-composition assays and their outcomes.

In the OSI, the effects of the chemical impurities in neon are briefly presented, presently not subject to correction according to [31] but only considered as an uncertainty component, to compare the importance of their effect with the isotopic effect.

2 Isotopic effects on ITS-90 for the neon triple point temperature (24.5561 K)

During a worldwide study lasted about 10 years, 26 different bottles of high-purity neon of commercial origin obtained from distillation of air, plus three certified reference mixtures, were studied, including isotopic composition and chemical impurities assays; thermal studies were performed on 34 samples drawn from them [13]. These studies and the subsequent ones on pure ²⁰Ne and ²²Ne samples [13] led to the equation, now included in [31], relating T_90,ref (ITS-90 defined value) to the value T₉₀ for the isotopic composition of the sample used, and allow to compute, from the measured resistance-ratio value, the corresponding value at T_90,ref [35].

In Table 2 the data are reported for the outcomes of several comparisons concerning neon, and in Table 3 the results for the CCT-K2.x of having taken into account the isotopic effect, based on the assay values selected after the critical evaluation of the assays, and their associated uncertainties [13,15].¹ In Table 5 the results of the isotopic corrections for the Star Inter-comparison are reported [12]. For important specific conditions concerning the way the data of each laboratory were obtained, see the OSI associated with this paper.

2.1 Taking the effect of the isotopic composition into account

We recall here that, according to the MRA, the key comparison reference value (KCRV) of the comparison CCT-K2 is common to all the subsequent integrations of its results with the results of the subsequent supplementary comparisons. It is not affected by uncertainty, as indicated in [19].

In order to take the effect of the isotopic composition on T_tp,Ne into account, it is useful to summarise the exact meaning of the CCT-K2 results (not including the CCT-K2.x), and the procedure for applying the isotopic correction to them

• (a)

  Each participant used a sample of neon whose effect of the isotopic composition, at that time, was taken into account in the uncertainty budget only. This contribution to uncertainty is reported in Table 4, whose mean value amounts to 305 μK out of 361 μK of the total mean laboratory budget (85%) and out of 517 μK of the total comparison mean budget (59%) − so being the dominant contribution.

• (b)

  The results of the realisation of the triple point temperatures were compared through exchange of thermometers calibrated without taking into account the isotopic effect. However, being the triple point of neon a fixed point of the ITS-90, each participant laboratory associated to the provided measured value of the resistance ratio R_tp,Ne/R_TPW the ITS-90 temperature value, 24.5661 K, exact. When the thermometers were compared in a comparison block at NRC, the measured resistance ratios did not exactly reproduce the supplied values − being that evidence the very reason of the comparison.

• (c)

  According to the CCT-K2 protocol, although one cell (NRC F15) was taken as the reference, the value 24.5561 K was not associated to it as the KCRV of the comparison. Instead, the resulting differences in the results, expressed as ΔT_meas, were computed in [19] with respect to a T_KCRV being the weighted mean of the resulting temperatures.²

• (d)

  Normally those differences would directly express the difference in the realisations of the fixed point between the participant laboratories, T_thermal, due to thermal or technical effects. However, in this case, the measured temperatures were instead T_meas = T_thermal + DT, where:

  • •

     a DT_x is the temperature difference due to the isotopic composition of a sample with respect to the reference composition defined after 2014, the ^IUPACx(Ne) one. Thus the corrections DT_x = T_meas,x – 24.5661 K.

  • •

     all the remaining items of the uncertainty budget that are usual in a comparison, are taken into account for T_thermal. Notice that the KCRV_bc used in [19] is affected by the DT_x − see item (f) below.³ Thus, T_thermal = T_meas – DT_x = T_meas – (T_x – 24.5661 K) = 24.5661 K + (T_meas – T_x). However, the final aim of this paper is instead to find δT_thermal = T_thermal – KCRV_ac.

• (e)

  Let us start from the fact that ΔT = T_meas – T(KCRV_bc) = T_meas – wmean(T_meas). This can be approximated by replacing the weighted mean with the simple mean: ΔT = T_meas – mean(T_meas) = T_meas – mean(T_thermal) – mean(DT) = T_thermal + DT – mean(T_thermal) – mean(DT).

• (f)

  Then, one can compute the net contribution for each sample:

$$T_{\text{thermal,}x}=\text{mea}{\text{n}}_{\text{ac}}(T_{\text{thermal}})\text{+}\Delta T_{\text{meas,x}}-\text{D}{T}_{\text{x}}\text{+}\text{mean}(\text{D}{T}_x)\text{.}$$(1) where the last term takes into account the offset in the original KCRV_ac, and finally, δT_thermal = [mean_ac(T_thermal) + ΔT_meas,x – (DT_x – mean(DT_x))] – mean(T_thermal): $$\delta T_{\text{thermal}}=\Delta T_{\text{meas,}x}\text{+}(\text{mean}(\text{D}{T}_x)-\text{D}{T}_x)\text{.}$$(2)The method used in this paper aims at implementing the above procedure based on temperature values. First, one needs to compute the value of KCRV_bc, not explicitly reported in [19].

2.1.1 Main comparison (CCT-K2)

The comparison did not define a “reference cell” to which assign the ITS-90 value, 24.5561 K but, as recalled above, the temperature value of the KCRV of CCT-K2 was computed as the weighted mean of the temperature values measured in the comparison block by each calibrated thermometer participating in the comparison, leading to the ΔT_original values in Table 2: the value of T_90,K2 assigned to the KCRV was not indicated in the Final Report.

When instead the isotopic composition is taken into account, an arbitrary choice for T_KCRV is not allowed anymore, since the ITS-90 definition was later integrated by attributing the value 24.5561 K to, and only to, neon having the reference isotopic composition, the one recommended by IUPAC, ^IUPACx(Ne): ²²x = 0.0925; ²¹x = 0.0027; ²⁰x = the rest [36].

This means that, in principle, the CCT-K2 KCRV after correction is unlikely to be equal to the CCT-K2 KCRV before correction, i.e. to the one used to express the differences in Table 2.

The T₉₀(KCRV_ac) and difference (KCRV_ac – KCRV_bc) can now be evaluated with good approximation. Should the KCRV be the simple mean of the T_meas, it would be exact to say that KCRV_ac = KCRV_bc + mean(DT_x); in this case it is a good approximation because the corrections are small with respect to the temperature values. In addition, as illustrated in Section 2.1, one is not interested in the KCRV_ac(T_meas), as it would directly come from the elaboration of the Final Report of CCT-K2, but in the KCRV_ac(T_thermal), i.e. based on the measured values cleaned from the isotopic effect, T_thermal = T_meas – DT_x.

Being not all corrections necessarily exactly consistent with each other, the resulting value of the KCRV_ac can vary somewhat depending on the correction chosen as the reference (exact) one.

In order to first obtain the value of the KCRV_bc(T_meas), the method used in this paper is the following (where #1 and #2 indicate the thermometer set)⁴:

• (i)

  the value T₉₀(Ne) = 24.5561 K, exact, corresponds to ^IUPACx(Ne);

• (ii)

  a reference sample is chosen. The choice of the NRC F15 sample seems the most obvious, since NRC was the pilot in all K2.x comparisons;

• (iii)

  for NRC's last reference cell, Cu-M-1, the isotopic-effect difference to ^IUPACx(Ne) is DT_Cu-M-1 = –6(94) μK;

• (iv)

  thus, the ITS-90 value of the NRC Cu-M-1 cell is T₉₀(Cu-M-1)_ac = 24.566 09₄ K;

• (v)

  the NRC difference measured through cell F17 [T(Cu-M-1) – T(F15)]_bc = –165(200) μK, so one gets T₉₀(F15)_ac = 24.566 25₉ K;

• (vi)

  the differences ΔT_F15 indicated in [19, exCCT-K2] are ΔT_F15#1 = T(F15 – KCRV)_#1 = –0.06(44) mK and ΔT_F15#2 = T(F15 – KCRV)_#2 = –0.12(44) mK;

• (vii)

  thus T₉₀(KCRV_bc)_#1 ≈ 24.566 32 K and T₉₀(KCRV_bc)_#2 ≈ 24.566 38 K;

• (viii)

  incidentally, the isotopic-effect from the assays is [T(Cu-M-1) – T(F15)] = –342(95) μK: this is not a discrepancy since it is a different component of the cell differences.

Figure 1 depicts graphically the above procedure.

The temperatures actually measured during the CCT-K2, T_meas, are obtained by adding to T_KCRVbc the ΔT_meas values recorded under “results” in [19] for each sample.

One could then compute the T_meas,ac by simply adding to ΔT_meas the DT_x obtained from the ITS-90 Technical Annex of [31], and then compute the weighted mean from the latter set, for both sets #1 and #2: δT_meas,ac = T_meas,corr – T(KCRV_ac). The isotopic corrections are reported in Table 3 in the column “Isotopic DT”, For the isotopic composition of the samples, see [13–15]. The KCRV_ac are reported in Table 3: T_KCRVac = 24.566 47₁ K for thermometers #1, and T_KCRVac = 24.566 55₈ K for thermometers #2, different, as expected, from the KCRVs before correction: notice that these values correspond to the values in item (viii) above well within the uncertainties. That change alone entails changes of +0.15 mK and +0.18 mK, respectively, to all the ΔT_meas = T_90bc – T_KCRVbc in Table 3 – and in Sections 2.1.4–2.1.6 – but note that pair differences are unaffected.⁵

However, the above computation is of limited interest, since the T_meas are those biased by the isotopic effect through ΔT. They should be transformed into the T_thermal, according to the procedure indicated in Section 2.1, approximated by using the simple mean of the T_meas.

Starting from equation (1) in Section 2.1(f), the values known in it are those for: all ΔT_x from [19] and all DT_x from [31]. Note that equation (1), does not contain any absolute value of T, but only mean or relative values: however, one obtains the temperature values in Table 3 as T_thermal = 24.566 100 K + δT_90,thermal. The δT_90,thermal after correction replace the ΔT_meas before correction.

The summary of the uncertainties is reported separately in Table 4 – and commented in Section 2.2.

It is interesting to compare the δT_90,thermal with the δT_meas,ac computed before. Both are approximated: the latter because, as said, they use T_meas; the former because the simple mean replaced the weighted mean and they still use the ΔT. However, the difference between the two is fixed and only +40 μK for #1 and +95 μK for #2. The reason is that δT_90,thermal – δT_meas,ac = KCRV_bc – 24.5661 K – mean(DT_x).

It is to be noticed that, after correction for the isotopic effect, the NRC experimental difference (Cu-M-1 – F15)_NRC = –165(200) μK becomes (Cu-M-1 – F15)_thermal + 147(220) μK. However, this change does not require a correction in the procedure Section 2.1.1(v) nor an iteration of the calculations, since in (v) one must use the KCRV based on which the values of the ΔT_or in Table 2 were computed, as taken from [19].

2.1.2 Comparison K2.1 (VNIIFTRI, NRC)

In this comparison, the NRC reference cell was still F15. The isotopic composition of the VNIIFTRI sample used in the CCT-K2 is unknown, so no computation is possible to take it into account. Therefore, the measured differences +0.28 mK (#1) and +0.22 mK (#2) remain unchanged.

Should one assume that the sample in question is from the same bottle that was used for the cell participating to the 1978–84 Inter-comparison [34] and the more recent Star Inter-comparison [12], an isotopic correction of −0.29 mK would apply, leading to a difference of −0.01 mK (#1) and −0.07 mK (#2), respectively.

2.1.3 Comparison K2.3 (NMI-VSL, NRC)

In this comparison, the NRC reference cell was changed to the newest Cu-M-1, whose uncorrected difference from cell F15 has been measured at NRC (though cell F17) to be [T(Cu-M-1) – T(F15)]_bc = –165(200) μK. See Table 3 for the values before and after correction of T₉₀(12Ne), T₉₀(F15) and T₉₀(Cu-M-1)_.

NMI-VSL used INRIM cell 12Ne (5N gas sample from Messer Griesheim, with assay #11, [15] assigned isotopic correction 123 μK). Thus, from Table 3 the values after correction are [T(12Ne) – T(Cu-M-1)] = –0.00055 K, [T(12Ne) – T(F15)] = –0.00040 K and [T(12Ne) – T₉₀] = –0.00055 K.⁶

2.1.4 Comparison K2.4 (INTiBS, LNE-INM, NRC)

In this comparison, the NRC reference cell was also the newest Cu-M-1–see comparison K2.3.

INTiBS used INRIM cell E3Ne (5N gas sample from Messer Griesheim, with assay #11, [15] assigned isotopic correction 123 μK). Thus, from Table 3 one gets the value of T₉₀(E3Ne) and the values after correction are [T(E3Ne) – T(Cu-M-1)] = –0.00015 K, [T(E3Ne) – T(F15)] = 0 K and [T(E3Ne) – T_KCRV] = –0.00015 K.⁷

LNE-INM used cell Ne02/1 (5N gas sample from Air Liquide, with assay #14, [15] assigned isotopic correction −32 μK). Thus, from Table 3 one gets the value of T₉₀(Ne02/1) and the values after correction are [T(Ne02/1) – T(Cu-M-1)] = –0.00042 K, [T(Ne02/1)−T(F15)] = −0.00027 K and [T(Ne02/1) – T_KCRV] = –0.00042 K.⁷

2.1.5 Comparison K2.5 (NMIJ-AIST, INRIM, NRC)

This comparison is the only one supplied with the results corrected for the isotopic composition of the samples. This requires an inverse computation in order to get the values before correction. For this comparison, the NRC reference cell was also the newest Cu-M-1–as with comparisons K2.3 and K2.4.

NMIJ-AIST used its cell Ne-5 (5N gas sample from AirWater, with assay #7, [15] assigned isotopic correction 4 μK). Thus, from Table 3 one gets the value of T₉₀(Ne-5) and the values after correction are [T(Ne-5) – T(Cu-M-1)] = –0.00032 K, [T(Ne-5) – T(F15)] = –0.00018 K and [T(Ne-5) – T_KCRV] = 0.00032 K.⁷

INRIM used cell Ec2Ne (5N gas sample from Messer Griesheim, with assay #11, [15] assigned isotopic correction 123 μK). Thus, from Table 3 one gets the value of T₉₀(Ec2Ne) and the values after correction are [T(Ec2Ne) – T(Cu-M-1)] = 0.00059 K, [T(Ec2Ne) – T(F15)] = 0.00044 K and [T(Ec2Ne) – T_KCRV] = 0.00059 K.⁷

2.2 Uncertainty of the CCT-K2 comparisons

The uncertainty issue has been treated separately in Table 4, since its complex analysis requires a full table.

Table 3 shows an important issue: every comparison exercise adds uncertainty to the previous results, in average a 30% more when comparing U_KC to U_TOTlab. In addition, as expected, the increase is larger for the late K2.1–K2.5 (≈30%) than for the original K2 (≈20%).

Another very important issue is that, by strongly decreasing the uncertainty on the isotopic composition, one strongly affects the overall laboratory uncertainty budget of the comparison of neon samples: in fact the average contribution of the isotopic effect is of 305(97) μK out of a total of 361(145) μK, so accounting for more than half.

Since the isotopic uncertainty drops in average from 305(97) to 37(33) μK, the laboratory differences decrease by about 30% in average after compensating for the isotopic effect, and the comparison uncertainty accordingly: the benefit of the corrections amounts in average to 60(15)%, i.e. it cuts the comparison uncertainty by more than half.

3 Discussion and final remarks

Figure 2 shows a graphical representation of data reported in Table 3: the mean value of the original deviations ΔT_or is −147(268) μK⁷ for set #1 and −166(309) μK for set #2, while those after correction, δT_iso = (T_90ac – KCRV_ac), are −175(306) μK for set #1 and −187(388) μK for set #2, thus basically the same: this only means that the (obviously unknown) thermal contributions to the deviations are dominant.

However, when subtracting from the original differences the contribution of the isotopic effect, in Figure 4 one gets for δT_thermal,ac −167(233) μK for set #1 and −147(240) μK for set #2, where the uncertainty is reduced by 60% in average, as already observed in Table 4. In addition, apart for two samples, the deviations after correction are within the interval (+0.3, −0.2) mK, while in Figure 2 they were in the wider interval (+0.4, −0.8) mK.

Therefore, by taking into account the isotopic effect, one can have a substantial improvement in the quality of the comparison results of the CCT-K2.x, though the uncertainty will necessarily increase progressively by adding up new comparisons, as it happened for the supplementary comparisons on the same fixed point − see Table 4 and Section 2.2.

In some cases, it is also possible to compare cell differences of INRIM production or of cells of other NMIs directly measured also at INRIM [4] with the values obtained from the K2.x ones.

In Figure 3 the following cells are shown, all sealed with gas taken from the same bottle of gas (Messer Greisheim, analysis #11 [15]): from the left, 2000: INTiBS (INRIM) cell 15Ne; 2000: VSL (INRIM) cell 12Ne [25] that was made in the same batch (21 Oct 1999) of cell 15Ne; 2001: INRIM cell E3Ne [24], that was made in the same batch (24 Aug 2000) of cell E4Ne; 2001: PTB (INRIM) E1Ne (12 Dec 1999) [12] that was sealed two months before the E2Ne to E4Ne batch; 2002: INRIM Ec1Ne and Ec2Ne (reference cell) [4]; finally, 2015: INRIM Ec29Ne that was sealed from the same bottle of gas after its return back to INRIM after the assays at IRMM, and measured in 2015. All results are compatible with each other except the last one with respect to the 2002 ones. The +94 μK increase of T_tp in 2015 is attributed in [15] to a possible change for unknown reasons of gas isotopic composition within the bottle during the years.

The results of the CCT-K2.x can also be compared in Figure 4 with the results of the largest direct comparison of samples in sealed cells made after the Int84 [34]: the Star Inter-comparison [12], whose data are compared in Table 5 using the data of Table 2.

Figure 4 (right part) makes self-evident the improvement of the Star data (right part) with respect to the K2.x data (left part). Only two samples are outlying: INM Ne02/1 and NIST 201. The latter is greyed in Table 5 because traceability back to the right filling gas is unsure. With its exclusion, the mean of the corrected differences is 56(68) μK (compared with 74(87) μK before isotopic correction), thus basically not significant at the U level being the measurement uncertainty (k = 1) of ≈47 μK. Except one, all deviations are now within ±50 μK.

4 Conclusions

The inter-comparisons were taken as the main basis of the analysis in this paper because, in order to evaluate the importance of the effect of the isotopic correction, one needs to have a number of “comparable” data.

This does not necessarily mean that the authors suggest to always “correct” previous data, e.g. due to uncorrected significant chemical-impurity effects. However, in this way, one can get the correct understanding of the often-complex procedure to be used for performing the isotopic correction. Originally, that study was undertaken mainly for the latter purpose, then we considered it worth also for comparing different types of inter-comparisons.

The technical conclusions are as follows.

• The exercise made on the KC2 has shown that the total uncertainty of the results for neon can be reduced to less than half by making the isotopic correction, because up to 80% of the original uncertainty budget was due to the contribution of the unknown isotopic compositions (Tab. 3).

• Being the original KC2 uncertainty budget made of two main components − the isotopic one and the instrumental one − the results of the corrected data show instead that the resulting inter-comparison dispersion of the degrees of equivalence (DoE) for the corrected data is basically the same, though the values are obviously different. This means that the instrumental and thermal uncertainty components (including the not-small comparison contribution) is of the same order of magnitude of the isotopic corrections. So one gets basically the same size of the DoEs, but less uncertain.

• The same exercise made on other types of inter-comparisons have shown the superiority of the direct-cell comparison, especially clear for the Star Inter-comparison (Tab. 4 and related figure) − see also the OSI.

• Concerning the effect of the chemical impurities (see the OSI), there is not yet, at present, a formal obligation from CCT to make a correction, at least for the cryogenic range: nothing on this matter is included yet in the Technical Annexe to the ITS-90 [31], though CCT documents of the Working Groups already exist. Therefore that Section is placed in the OSI, together with more information on direct-cell inter-comparisons. However, the contribution to the final values and uncertainties of the chemical impurities, though variable depending on their level, in the worst cases can be substantial and even larger than the isotopic effect.

Supplementary Material

Supplementary Material supplied by the authors. Access here

References

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