EURAMET Key Comparison No. EURAMET.T-K1: Realisations of the ITS-90 from 2.6 K … ·...

EURAMET Key Comparison No. EURAMET.T-K1:

Realisations of the ITS-90 from 2.6 K to 24.5561 K,

using rhodium-iron resistance thermometers

Draft B

Christof Gaiser and Bernd Fellmuth

Physikalisch-Technische Bundesanstalt (PTB)

Abbestrasse 2-12, D-10587, Berlin, Germany

Peter Steur

Istituto Nazionale di Ricerca Metrologica (INRiM)

Strada delle Cacce 73, 10135 Torino, Italy

Anna Szmyrka-Grzebyk, Henryk Manuszkiewicz, and Leszek Lipinski

Institute of Low Temperature and Structure Research, Polish Academy of Sciences (INTiBS)

P.O. Box 1410, 50-950 Wroclaw 2, Poland

Andrea Peruzzi

Dutch Metrology Institute (VSL)

P.O. Box 654, 2600 AR Delft, the Netherlands

Richard Rusby and David Head

National Physical Laboratory (NPL)

Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom

January 2016

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1. Background

In the temperature range from 0.65 K to 24.5561 K the ITS-90 is defined by specified vapour-

pressure equations for 3He (0.65 K to 3.2 K) and

4He (1.25 K to 5.0 K) and interpolation

equations for a constant-volume gas thermometer (ICVGT) using 3He or

4He. The definitions

are given in Sections 3.1 and 3.2 of the ITS-90 text [1], and methods for realising the scale in

this range are outlined in Chapters 4 and 5 of the Guide to the Realization of the ITS-90

(formerly Supplementary Information for the ITS-90) [2].

Direct realisations of the ITS-90 by these methods require relatively sophisticated apparatus

and time-consuming experiments, and consequently they are rarely carried out. The situation

is acceptable in practice only because rhodium-iron resistance thermometers are available

which, once calibrated, are able to maintain their calibrations reliably for long periods of

time. They are the practical thermometers on which realisations of the ITS-90 are most

accurately maintained, disseminated and compared. The Key Comparison EURAMET.T-K1

is therefore a comparison of calibrated rhodium-iron resistance thermometers (RIRTs).

EURAMET.T-K1 has been coordinated by PTB and is related to the Key Comparison

CCT-K1, which in turn was coordinated by NPL [3]. Its protocol is nearly identical to that of

CCT-K1, see Appendix 1, and has been approved by Working Group 7 “Key Comparisons”

of the CCT in May 2008. Later on EURAMET.T-K1 was registered as EURAMET Project

No. 1147 and as an RMO Key Comparison in the database KCDB of the BIPM

(http://kcdb.bipm.org/), see Appendices 2 to 4.

With the scope to get direct linking with the CCT-K1 comparison, the calibrations of two

RIRTs of INRiM (serial numbers 232324 and B190) and INTiBS (serial numbers 93 and

B178) were compared in 2008 at PTB with the calibrations of the RIRTs of NPL (serial

numbers 221481 and 221485), PTB (serial numbers 229074 and 229075), and VSL (serial

number 226246) that participated in CCT-K1. The RIRTs with serial numbers 229074,

221481 and 221485 were compared again in a second run in 2012 for checking purposes.

2. Participation.

The participating laboratories are those of the listed authors. Most of the RIRTs were

manufactured by H Tinsley and Co Ltd, being Type 5187W (100 at 273 K) [4]. The RIRT

with serial number 93 was manufactured at VNIIFTRI [5]. Inputs to the comparisons

CCT-K1 and EURAMET.T-K1 are summarised in Table 1 and as follows:

NPL

In CCT-K1 the Type 5187W thermometers Nos. 221481and 221485 were used. They were

originally calibrated in 1974 to 1976 in terms of the NPL-75 gas thermometry from 2.6 K to

27.1 K [6], and the Tx1 CMN magnetic thermometry from 0.5 K to 3.1 K [7]. The NPL vapour

pressure realisations were undertaken in 1974 to 1978 and are taken to be equivalent to these

scales over the range 1.0 K to 5.0 K. The two RIRTs took also part in a EUROMET

comparison in 1992 [8].

RIRT No. 221481 is the principal NPL reference thermometer. It has been measured at the

triple points of hydrogen and neon [8], and these measurements were used to define a

quadratic function, which has been added to the NPL-75 calibration to ensure consistency

with the ITS-90 at the specified fixed points. The adjustment amounts to - 0.6 mK at

13.8033 K and - 0.2 mK at 24.5561 K. The same adjustment was applied to RIRT No.

221485. The quadratic function is

3

(T90 – TNPL-75)/mK = 0.54635 - 0.15065 (T90/K) + 0.004897 (T90/K)2.

PTB

Two Type 5187W thermometers, Nos. 229074 and 229075, were submitted. They had

originally been calibrated over the full range at NPL in 1977, and No. 229075 also took part

in the EUROMET comparison [8]. Below 4.8 K the PTB approximation to the ITS-90 is

based on the PTB copies of the NPL scales Tx1 and NPL-75, since direct vapour-pressure

realisations at PTB were not available for CCT-K1. Thermometer 229075 was calibrated by

Luther, Grohmann and Fellmuth using a dielectric-constant gas thermometer (DCGT) above

4.2 K [9]. This calibration has been adjusted to be consistent with realisations of the triple

points of hydrogen and neon, as specified in the ITS-90, and the DCGT interpolation is used

as the PTB approximation to the ITS-90 in the range from 4.8 K to 25 K. Calibration data

were supplied as individual points and as full-range polynomial equations. There were two

equations for Thermometer 229075, using the interpolating DCGT [10] and the NPL scales,

and one for Thermometer 229074, using the NPL scales. Interpolating DCGT (ITS-90

approximation) temperatures for 229074 were calculated by applying the same differences

from the NPL-75 scale as for 229075. The polynomials express temperature as a function of

resistance at specified measuring currents.

VSL

One Type 5187W RIRT, No. 226246, was submitted. This had originally been calibrated at

NPL in 1977 and it was used in the gas thermometry of Steur [11]. Traceability to the ITS-90

between 0.65 K and 4.2 K derives from vapour-pressure measurements made with 3He and

4He, both at VSL and formerly at the Kamerlingh Onnes Laboratorium [12 - 15]. The

calibration data were supplied as VSL polynomial coefficients, in ranges above and below

2.6 K, using the thermometer resistance at the measuring current of 0.3 mA.

INRIM

Two Type 5187W RIRTs, Nos. 232324 and B190, were submitted. They had originally been

calibrated at NPL in 1993 in terms of the NPL-75 gas-thermometry scale. The calibration data

were supplied as polynomial coefficients using the thermometer resistance at the measuring

current of 0.3 mA. Both RIRTs have been measured at the triple points of hydrogen and neon,

and these measurements were used to define a quadratic function, which has been added to

the NPL-75 calibration to ensure consistency with the ITS-90 at the specified fixed points.

The adjustment amounts to - 0.6 mK at 13.8033 K and - 0.1 mK at 24.5561 K for RIRT

No. B190, as well as – 0.5 mK and + 0.3 mK, respectively, for RIRT No. 232324. The

adjustment is different for the two RIRTs primarily because for RIRT No. 232324, the data

has been corrected considering the isotopic composition of the gases contained in the triple-

point cells used. Furthermore, the NPL calibration of RIRT No. 232324 was compared with

the results obtained with the ICVGT of IMGC, which works with a cryogenic pressure

transducer. The differences were published in [16, 17] and fitted with a cubic polynomial.

This polynomial was added as a second correction to the original NPL calibration. Finally,

the resulting data for zero measuring current were described by a polynomial of degree 10.

INTiBS

One Type 5187W RIRT, No. B178, and one VNIIFTRI Type, No. 93, were submitted. RIRT

No. B178 had been calibrated at NPL in 1995 in terms of the ITS-90. The calibration data

were supplied as polynomial coefficients using the thermometer resistance at the measuring

current of 0.3 mA. Both RIRTs were calibrated at the triple points of H2 and Ne, and RIRT

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No. B178 additionally at the lambda point of 4He. RIRT No. 93 carried only the fixed-point

calibration.

3. Apparatus

The cryostat used for Key Comparison EURAMET.T-K1 is the DCGT cryostat of PTB [18],

see Figure 1. It is a tank cryostat with a liquid nitrogen and liquid helium tank. The system

exhibits a shell structure starting with the outer vacuum chamber (OVC) containing shields,

covered with super insulation, providing the necessary thermal isolation from the outside. In

this chamber the liquid helium and liquid nitrogen tank is situated. All tubes through the

cryostat are placed in vacuum, thermally linked to the two tanks to minimize the heat flow on

the inner vacuum chamber (IVC). This chamber, which can be evacuated separately, is

isolated by an indium sealing from the OVC. On two different planes helium evaporation

cooling stages are installed. On these stages two isothermal gold plated shields are attached to

minimize the radiation heat flow on the experimental cell which is situated inside the lowest

shield. The coolers will be supplied with helium via thin tubes connected to the helium tank,

whereby the flow to each cooler can be regulated by cryogenic needle valves. In addition the

pressure inside the cooler can be regulated by controlling the flow through two pumping lines

via a valve situated on the top of the cryostat. These regulating systems allow for directing the

cryostat to the desired temperature region and provide a rough temperature control. The final

temperature stability of the cooling stages is made via two heaters which are regulated by

commercial temperature controllers. These controllers provide a temperature stability of a

few mK in the treated temperature range from 2.4 K to 25 K. In order to minimize the cool

down time to temperatures below the liquid nitrogen temperature, the cryostat is equipped

with an additionally cooling tube on the upper cooling stage. To start the cool down, liquid

nitrogen is send through this tube in combination with helium as exchange gas inside the

IVC. This procedure allows a cool down below 80 K in two days, followed by one further day

to reach the temperature range treated in this work. This setup has the advantage that once the

cryostat has reached the wanted temperature, even at the lowest temperatures no exchange

gas is needed, and the experimental cell is isolated from the cryogenic liquids. In addition the

whole tubing goes through the vacuum leading to the fact that the liquid level of the tanks has

no influence on the temperature distribution along the tubes. This is a clear advantage

compared to a bath cryostat, where the tubes normally go through the cryogenic liquid,

leading to varying temperature gradients. Also, to reduce the thermal gradients along the

nitrogen and helium tank, they are made of aluminium obeying a larger thermal conductivity

in comparison with the commonly used stainless steel.

The experimental cell has been made of oxygen-free high conductivity copper (OFHC). It

includes not only the capacitors for the DCGT measurement but in addition a CVGT volume

as well as vapour-pressure and triple-point cells. One optimization parameter is the weight of

the experimental cell directly connected to the heat capacity. For copper the heat capacity is

strongly temperature dependent being at 30 K a factor of 40 smaller than at room temperature

but even a factor 100 larger than at 4 K. This extremely non linear behaviour leads to strongly

temperature dependent cooling powers necessary to guarantee an acceptable cool down time.

Another optimization parameter is the thermal flow along the chamber walls, determined by

the thermal conductivity and the wall thickness. A sufficiently high flow guarantees that

gradients along the chambers are small and do not cause measurable errors in the temperature

measurement.

In order to reach temperature stabilization of the experimental cell on the level of a few tenth

of a mK, special efforts have to be made. This was performed with commercially available

5

high-precision temperature controllers and Cernox resistance thermometers exhibiting a very

large sensitivity. Even though the absolute resistance values of these thermometers is of

secondary importance because the temperature of the cell is measured via RIRTs, the sensors

mounted on the cell in combination with the temperature controller should reach a

temperature stability on the level of 50 K. To reach optimal conditions for the temperature

control, the experimental cell is thermally isolated from the lowest cooling stage to minimize

thermal flow to the cell. Therefore, the necessary cooling power has to be injected via a well

defined heat link. This heat link had to be designed under consideration of the temperature

dependent cooling power as well as the temperature dependent change in the heat capacity of

copper. A copper wire was installed. This wire ends on the top of the heater mounted on the

cell. This installation guarantees sufficiently cooling power to allow for a symmetric

temperature control on a reasonable time scale. The combination of sufficient cooling power

and heating power on the cell, a very sensitive sensor and an accurate, self-tuning PID

controller lead to the necessary stability of 50 K.

For the temperature measurement of the experimental cell, a high accuracy transformer bridge

was used. For eliminating the lead resistances, the resistance measurement was performed in

a four terminal configuration. The low-current ac bridge is automated concerning the

balancing procedure as well as the data acquisition. The calibration of the bridge is traceable

to the national standard of PTB with a relative uncertainty of 5 parts in 108 of full scale. The

wiring inside and outside the cryostat to the RIRTs were performed in the twisted pair

technique to minimize influences due to electro-magnetic stray field. In addition all wires

were contacted thermally to the nitrogen and helium tank and each of the different stages

inside the inner vacuum chamber to avoid thermal flow to the RIRT. As reference resistors

two commercially available high-precision standard resistors of nominal values of 10 and

25 were used. These resistors are calibrated at PTB and are therefore traceable to the

national standards of PTB. The RIRTs were placed into holes of the experimental cell having

appropriate inner diameters. The thermal contact between the thermometer sheath and the cell

was improved using grease.

4. Measurements

Run No. 2 in 2008 (0802)

As noted in Table 1, the first comparison run (second low-temperature run performed with the

apparatus in 2008, i.e. run No. 0802) included all 9 RIRTs. The whole run lasted from August

2008 to February 2009. Measurements were made at 28 temperatures in the range from 2.6 K

to 25.9 K At several temperatures measurements were made on more than one occasion to

check the repeatability.

After the cryostat had been cooled to liquid helium temperatures, the helium exchange gas

was pumped away, and the temperature was stabilised. Various trials of the control,

measurement and data-processing were carried out, leading to the first set of comparison

measurements and self-heating checks, using currents of 0.3 mA and 0.3 2 mA. (The widely

used term “self-heating” means the change of the thermometer resistance caused by the

measuring power.)

Automated measurements for all RIRTs at both currents were then made at a number of

temperatures in the range mentioned above. The temperature was stabilised during daytime,

and at the end of the working day the computer program for switching the bridge together

with a multiplexer and for data registration was started. For each RIRT and current, bridge-

6

ratio values were recorded over 30 minutes, and the average over the last 10 minutes was

taken as the result.

In run No. 0802, RIRT No. 221481 was the so-called monitor thermometer. For the monitor

thermometer, the bridge-ratio values were recorded several times during the measurement

campaign at one temperature, namely at the beginning, in between and at the end. This

enabled to correct for the remaining small temperature drifts over the half-day campaign.

Run No. 2 in 2012 (1202)

The second comparison run (second low-temperature run started with the apparatus in 2012,

i.e. run No. 1202) included four of the RIRTs listed in Table 1, namely Nos. 229074, 221481,

221485, and 226246. The whole run lasted from September 2012 to January 2013. In this run,

RIRT No. 229074 was the monitor thermometer. The measurements at 29 temperatures in the

relevant range were performed in the same way as in run No. 0802.

Run No. 1202 was performed only for checking the overall repeatability of the comparison

experiments. For this reason, the location of the RIRTs and the connections to the measuring

leads were different compared with run No. 0802. The comparison results of

EURAMET.T-K1 presented below are exclusively based on the data obtained in run

No. 0802.

5. Data processing

Data processing started with correction of the averaged bridge-ratio values concerning

temperature drifts by considering the data obtained for the monitor thermometer. In view of

the very low drifts during the measurement campaigns (the temperature equivalents of the

corrections were at most of order 50 K), a linear interpolation between the different readings

of the monitor thermometer was possible in each case.

The second evaluation step was the determination of the zero-current ratio values (and in turn

of the corresponding resistance values) from the ratios measured with currents of 0.3 mA and

0.3 2 mA, respectively. For checking purposes, the self-heating data were reanalysed by

fitting the function ln((R/)/(P/W)) = ln(a) + b ln(T90/K) to the results for f(T90/K) =

ln((R/)/(P/W)) over the whole temperature range (R is the resistance change due to the

measuring power P). The fitting coefficients for the 9 RIRTs are given in Table 2.

The matrix of zero-current resistance values for each RIRT at temperatures Ti, i = 1, 2, ..., 28,

measured in run No. 0802 was then assembled. These are the primary data of the comparison

The matrix is given in Table 3 together with the corresponding Key Comparison Reference

Values (KCRVs), 𝑇KCRV,𝑖EURAMET, of EURAMET.T-K1 for the temperature on ITS-90. To have a

direct link to CCT-K1, it is desirable to use KCRVs, which are close to those determined in

CCT-K1, 𝑇KCRV,𝑖CCT . The 𝑇KCRV,𝑖

EURAMET values have been, therefore, deduced as follows. For the

five RIRTs included in both comparisons, see Table 1, zero-current resistance values have

been taken from Tables 3 and 5 of the report on CCT-K1 [3]. (Doing this, it had to be

considered that in the evaluation of the CCT-K1 data, near-duplicate temperatures were

averaged, leaving 43 distinct KCRVs.) The resistance and temperature values used here are

listed in Table 4. They were fitted applying an algorithm with orthogonal functions. The

fitting results showed that an order of 12 is sufficient. The coefficients of the polynomials of

order 12 are given in Table 5. Using these five polynomials, temperature values were

calculated from the resistance values contained Table 3, see Table 6. For each temperature

7

above 7 K, the KCRV 𝑇KCRV,𝑖EURAMET is finally the mean of the five calculated values. Below 7 K,

the temperature value for RIRT 221481 was not included in the mean because of systematic

deviations, see Section 7.

Table 6 contains furthermore temperature values for the RIRTs supplied by INRIM and

INTiBS resulting from their input calibration data and the resistance values listed in Table 3.

Where the original calibrations were specified for a non-zero current, the calculation of the

needed resistance values was performed using the self-heating functions, the coefficients of

which are given in Table 2. The deviations from the KCRVs are listed in Table 7.

6. Uncertainties

Uncertainties in the submitted calibrations

NPL in CCT-K1

Uncertainties are calculated at five temperatures above 4.2 K and five below 4.2 K, see [3].

The first is based on the normalisation of the NPL-75 scale to the ITS-90, and includes the

uncertainties in realizing the three fixed points required, with an additional uncertainty for

thermometer stability. The second is an uncertainty analysis of the original vapour pressure

calibrations down to 1 K. Below 1 K the uncertainty is of Tx1 as a representation of the ITS-

90. Again, a component is included for the thermometer stability.

PTB in CCT-K1

Uncertainty budgets for the two PTB thermometers were supplied see [3]. At 4.8 K and

24.6 K the budgets for Thermometer 229075 are based on the direct interpolating DCGT

calibration. That for Thermometer 229074 is derived from the comparison with 229075 as the

reference. The uncertainties are taken to vary linearly between 4.8 K and 24.6 K. Below 4.8 K

the uncertainties are based on the original Tx1 calibrations as maintained at PTB. All budgets

include a component for thermometer stability.

VSL in CCT-K1

The uncertainty is calculated at 2.2 K, see [3]. Variations from this, due to variations in the

thermometer sensitivity, are calculated in a sub-table.

INRIM

The standard uncertainty of the ICVGT calibration of RIRT No. 232324 in the temperature

range from 4.2 K to 24.5561 K has been estimated to be 0.68 mK, see Appendix 5. The

standard uncertainty of the NPL calibrations for both RIRTs is specified to be 0.5 mK.

INTiBS

The standard uncertainty of the NPL calibration for RIRT No. B178 is specified to be

0.5 mK. The fixed-point calibrations have estimated uncertainties of about 10 (lambda

point of 4He), 15 (triple point of hydrogen), and 20 (triple point of neon),

respectively, Appendix 6.

PTB, NPL, VSL calibrations from CCT-K1

For the five RIRTs included both in CCT-K1 and EURAMET.T-K1, the results of CCT-K1

are taken as input data for EURAMET.T-K1, see Section 5. The uncertainty of this data is

mainly determined by the CCT-K1 comparison uncertainties given in the corresponding table

of [3]. Since all five RIRTs were compared in one run, the component “Stability of

thermometer linking Runs 1 and 2”is, therefore, not relevant here. For the temperatures being

8

of interest, the budget is repeated in Table 8. A small additional component considers the

uncertainty of the approximation of the data given in Table 4 by the polynomials, the

coefficients of which are listed in Table 5.

Uncertainties in the EURAMET.T-K1 comparison experiments

The EURAMET.T-K1 comparison standard uncertainties uEURAMET have been estimated as

those of CCT-K1. The estimates are listed in Table 9. The component “Repeatability of

comparison measurements” has been estimated via the standard deviation of the results

obtained in the two comparison runs Nos. 0802 and 1202.

7. Results.

The primary comparison results are presented in Tables 3 and 6. The deviations from the

KCRVs are listed in Table 7 together with their uncertainty. Figures 2 to 6 illustrate the

results. Figures 2 and 3 show the deviations of the readings of RIRTs Nos. 221481 and

221485, respectively, from the KCRVs obtained in the two comparisons runs. (In run

No. 1202, the KCRVs were deduced from the readings of RIRT No. 229074 applying a

cubic-spline interpolation.) The standard deviations of all results obtained in both runs

amount to 0.16 mK (RIRT No. 221481 above 10 K) and 0.10 mK (RIRT No. 221485 in the

whole range), and the differences of the mean deviations to 0.19 mK and 0.13 mK,

respectively. Thus, the results obtained in the two runs corroborate a repeatability of the

measurements of order 0.1 mK.

Figure 4 demonstrates impressively the high stability of the five RIRTs included both in

CCT-K1 and EURAMET.T-K1, and, therefore, the direct link between the two Key

Comparisons. The standard deviation from the KCRVs amounts to 0.18 mK above 7 K, and

excluding RIRT No. 221481 to 0.25 mK in the whole range. Most of the deviations are even

well within the envelope given by the expanded uncertainty (k = 2) of CCT-K1.

Below 7 K, the deviation of the reading of RIRT No. 221481 from the KCRVs increases

systematically with decreasing temperature without changes of other important parameters,

such as the overheating due to the measuring power. As shown in Figure 5, the same effect

was observed for RIRT No. B190. Thus, it is unlikely that the deviation is caused by a simple

instability. One possible explanation could be clustering of iron atoms via diffusion over the

long periods after the fabrication of the RIRTs. Within the clusters, the magnetic moments of

the iron atoms may be pinned, i.e. permanently localised in contrast to the spin fluctuations

being typical for rhodium-iron alloys. Localised magnetic moments are the cause of the

Kondo effect, which results also in an increase of the resistivity with decreasing temperature.

However the stability of RIRTs is generally excellent, as demonstrated by most of the results

obtained. The anomalies seen here with these two RIRTs (one of which was first measured in

1973) are therefore not explained, and need further investigation.

Figure 5 shows the deviation of the readings of eight RIRTs from the KCRVs, and Figure 6

gives the same information only for the three RIRTs not included in CCT-K1.

The deviations of the fixed-point values of RIRTs Nos. B178 and 93 from the KCRVs are

listed in Table 10. The KCRVs were deduced from the readings of RIRT No. 229074

applying a cubic-spline interpolation. The deviations are partly larger than the expanded

uncertainty (k = 2), i.e. partly significant.

9

8. Conclusion and documentation of equivalences.

The level of agreement between participants is seen, in Table 7 and Figure 5, to be mostly

within ± 0.5 mK above 7 K, although there are exceptions. Below 7 K the RIRTs No. 221481

and No. B190 show both increasing systematic deviations with decreasing temperature (see

Section 7). For each temperature in the comparison, the Key Comparison Reference Value,

TKCRV, is the mean of the individual temperature values, Ti, of four (without No. 221481 for

TKCRV < 7 K) or five RIRTs (above 7 K) of the RIRTs, which were included in Key

Comparison CCT-K1, see Section 5. The TKCRV is used as the baseline for the comparison,

but has no special significance with regard to “best estimates” of ITS-90 temperature values

T90, and it is used without uncertainty.

In Figure 4, the results obtained for the RIRTs already included in CCT-K1 are shown,

together with the expanded CCT-K1 comparison uncertainties k = 2 [3]. It is remarkable that

the standard deviation is on the level of 0.2 mK manifesting that these RIRTs remained

extremely stable over a decade.

In Figure 5 it can be seen that RIRT No. B178 shows larger deviations on the level of 0.7 mK

above 13 K, but this is not of statistical significance. The already mentioned deviations below

7 K are of statistical significance. Since these deviations are suspected to be caused by

systematic long-term resistance drifts and not by calibration errors, see Section 7, they are not

considered as “significant unresolved deviations” within the meaning of the MRA Clause T.7

(http://www.bipm.org/en/cipm-mra/cipm-mra-text/). The values for RIRTs No. 221481 and

No. B190 below 7 K are, therefore, not included in Appendix 7, which gives an overview of

the results relevant for Appendix C of the KCDB. The results listed in Table 10 are also not

included in this appendix because they are only supplementary data for checking purposes.

Using the data in Table 6 the degrees of equivalence between all RIRTs have been evaluated

at all temperatures in the comparison. For this purpose, first the difference Di = (Ti – TKCRV)

has been calculated for each RIRT i. The Di values are listed in Table 7 together with the

standard uncertainty estimates, ui, for the Ti values, i.e. the original calibration data. The

uncertainty of Di, u(Di), includes ui and the EURAMET.T-K1 comparison standard

uncertainty, uEURAMET, assessed in Table 9. Then the degree of equivalence between each pair

of RIRTs i and j is given by Dij = (Di – Dj) with an expanded uncertainty (k = 2) of Uij =

2(𝑢𝑖2 + 𝑢𝑗

2 + 𝑢EURAMET2 )

0.5. The obtained degrees of equivalence are presented in Appendix 7

on one page per temperature. Each page shows the input data and a graph of the differences

with uncertainty bars at k = 2. Below this is a matrix which gives the differences Dij and

expanded uncertainties Uij for each pair of RIRTs i and j. Appendix 7 documents that no

“significant unresolved deviations” need to be noted in Appendix C of the KCDB.

Acknowledgement

The pilot authors (CG and BF) wish to acknowledge the assistance they received in the

comparison experiments and the evaluation of the results from their colleagues Norbert Haft

and Bettina Thiele-Krivoi.

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Appendices

Appendix 1: Protocol for Key Comparison EUROMET.T-K1 (PTB, INRiM, INTiBS, NMi

VSL, NPL): Realisations of the ITS-90, 2.4 K to 24.5561 K, using rhodium-iron resistance

thermometers

(File EURAMET.T-K1_Appendix_1.pdf)

Appendix 2: Status Report on RMO Comparison EURAMET.T-K1


Appendix 3: EURAMET Technical Committee Projects: Ref.: 1147, Title: Key Comparison

EUROMET.T-K1: Realisations of the ITS-90, 2.4 K to 24.5561 K, using rhodium-iron

resistance thermometers


Appendix 4: BIPM KCDB: Key and supplementary comparisons – Information:

EURAMET.T-K1


Appendix 5: Final results for INRIM Interpolating Constant Volume Gas Thermometer (with

proper calibration at home-realized fixed points)


Appendix 6: INTiBS reports Nos. 1 to 3


Appendix 7: EUROMET.T-K1 tables and graphs of results, with bilateral degrees of

equivalence


11

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9. Luther H., Grohmann K. and Fellmuth B.: Metrologia, 1996, 33, 341-352

10. Grohmann K., Luther H. and Fellmuth B.: Document CCT/96-24, BIPM 1996

11. Steur P. P. M. (1983): PhD Thesis Determination of Temperatures between 4 K and 100

K with a Gas Thermometer, Leiden University, the Netherlands

12. El Samahy A. E. (1976): PhD Thesis Thermometry between 0.5 K and 30 K, Leiden

University, the Netherlands

13. De Groot M. J., Gibb K., Heimeriks H., Durieux M. (1997): IMEKO Seminar on Low

Temperature Thermometry and Dynamic Temperature Measurement, edited by

A. Szmyrka-Grzebyk; Wroclaw, pp L104-109

14. De Groot M. J., Mooibroek J., Bloembergen P., Durieux M., Reesink A. L., Mao Yuzhu

(1993): TEMPMEKO ’93, Prague, pp 90-96

15. De Groot M. J. (1998): in Toward an International Temperature Scale from 0.65 K to

1 mK, Leiden University, edited by R. L. Rusby and P. Mohandas, NPL, pp 79-84.

16. Steur P. P. M., Pavese F., Peroni I., Ferri D., Pugliese A. (2003): Temperature: Its

Measurement and Control in Science and Industry, Vol. 7, D. C. Ripple et al. (ed.),

Melville, NY, American Institute of Physics, pp. 125-130

17. Steur P. P. M., Giraudi D. (2013): Temperature: Its Measurement and Control in Science

and Industry, Vol. 8, C. W. Meyer (ed.), Melville, New York, American Institute of

Physics, AIP Conference Proceedings Vol. 1552, ISBN 978-0-7354-1178-4, pp. 124-129

18. Gaiser C (2008): PhD Thesis Properties of Helium and Gas Thermometry (Aachen:

Shaker Verlag) ISBN 978-3-8322-7552-5

12

Table 1: Summary of NMIs and RIRTs participating in CCT-K1 (Runs 1 & 2) and EURAMET.T-K1 (Runs 0802 & 1202)

NMI RIRT RUN BASIS OF CALIBRATION INPUT FORMAT REFERENCES

NPL

221481

221485

221483

1 & 2, 0802 & 1202

1, 0802 & 1202

2

NPL-75 with adjustment to ITS-90

Tx1 for T < 2.6 K

Equations for T = f(R)

at 0.1 - 0.3 mA

6, 7

PTB

229075 1, 0802 IDCGT, 4.8 K to 27.0 K

NPL-75/Tx1 for full range

Equation for T = f(R) at 0.06 mA,

Equation for T = f(R) at 0.1 - 0.3 mA

9, 10

229074 1, 0802 & 1202 NPL-75/Tx1 for full range

converted to IDCGT, for T > 4.8 K

Equation for T = f(R) at 0.1 - 0.3 mA,

plus differences above 4.8 K as for 229075

INRIM

232324 0802 ICVGT, 4.2 K to 24.5561 K

NPL-75/Tx1 for full range

Equation for T = f(R) at 0 mA

Equation for T = f(R) at 0.1 - 0.3 mA

16

B190 0802 NPL-75/Tx1 for full range

with adjustment to ITS-90 for T > 4.2 K

Equation for T = f(R)

at 0.1 - 0.3 mA

INTiBS B178 0802

ITS-90 for full range

Lambda point of 4He, triple points of H2, Ne

Equation for T = f(R) at 0.3 mA

Resistance values

93 0802 Triple points of H2, Ne Resistance values

VSL

226246

1, 0802 & 1202

CVGT 2.6 K < T < 24.5561 K 3He and

4He vapour pressures, T < 4.2 K



11

12 -15

13

Table 2: Self-heating data for the 9 RIRTs included in EURAMET.T-K1: Coefficients of

the fit functions ln((R/)/(P/W)) = ln(a) + b ln(T90/K)

RIRT a b

PTB 229074 634.83 -1.3981

PTB 229075 4946.21 -1.6976

NPL 221481 4505.91 -1.5118

NPL 221485 2351.52 -1.5465

VSL 226246 4290.01 -1.6697

INRIM 232324 822.37 -1.5207

INRIM B190 4969.95 -1.8273

INTiBS B178 815.89 -1.5139

INTiBS 93 929.08 -1.5044

14

Table 3: Zero-current values of resistance, R(0 mA) in Ohm measured at the KCRVs

𝑇KCRV,𝑖EURAMET


K

PTB

229074

PTB

229075

NPL

221481

NPL

221485

VSL

226246

INRIM

232324

INRIM

B190

INTiBS

B178

2.693629 6.103451 5.993230 7.380270 6.498638 5.888739 5.756197 5.593681 5.569200

2.599898 6.050212 5.939204 7.322838 6.447764 5.838466 5.708484 5.544670 5.520364

3.000775 6.274470 6.167277 7.564901 6.662022 6.050576 5.909558 5.751712 5.726164

3.095913 6.326487 6.220165 7.620970 6.711611 6.099769 5.956183 5.799722 5.773924

3.401384 6.490383 6.386785 7.797336 6.867615 6.254734 6.103063 5.951369 5.924378

3.799888 6.697018 6.596965 8.019382 7.063900 6.450160 6.288187 6.142408 6.114122

4.201187 6.897140 6.800520 8.234048 7.253589 6.639397 6.467379 6.327445 6.297887

4.487204 7.035041 6.940745 8.381757 7.384130 6.769791 6.590871 6.454969 6.424504

4.997407 7.271589 7.181449 8.634903 7.607756 6.993496 6.802578 6.673786 6.641698

5.496231 7.491797 7.405568 8.870299 7.815663 7.201789 6.999633 6.877553 6.843860

5.975219 7.693696 7.610959 9.085853 8.006023 7.392667 7.180208 7.064308 7.029157

6.570124 7.932222 7.853690 9.340303 8.230732 7.618217 7.393514 7.285050 7.248028

7.180012 8.163772 8.089313 9.587101 8.448729 7.837178 7.600575 7.499330 7.460444

8.273874 8.549567 8.482051 9.998108 8.811627 8.202071 7.945469 7.856433 7.814183

9.465787 8.932193 8.871588 10.405372 9.171290 8.563967 8.287437 8.210603 8.164843

10.770073 9.312489 9.258763 10.809947 9.528563 8.923675 8.627291 8.562662 8.513157

11.771326 9.581047 9.532234 11.095563 9.780785 9.177730 8.867263 8.811303 8.758973

12.277592 9.710009 9.663523 11.232681 9.901862 9.299711 8.982478 8.930690 8.876990

4.200739 6.896894 6.800302 8.233817 7.253394 6.639198 6.467211 6.327265 6.297648

13.772857 10.067144 10.027168 11.612316 10.237127 9.637542 9.301510 9.261353 9.203707

15.471164 10.435631 10.402405 12.003899 10.582947 9.986136 9.630692 9.602505 9.540594

16.979618 10.735447 10.707705 12.322406 10.864310 10.269785 9.898506 9.880099 9.814615

18.571024 11.028770 11.006369 12.633877 11.139424 10.547300 10.160493 10.151759 10.082613

20.274906 11.321622 11.304646 12.944680 11.413982 10.824467 10.422087 10.423073 10.350293

21.556378 11.530438 11.517300 13.166134 11.609608 11.022102 10.608572 10.616585 10.541182

22.673744 11.706236 11.696324 13.352402 11.774169 11.188448 10.765561 10.779518 10.701973

24.463897 11.978781 11.973881 13.640824 12.028945 11.446391 11.008893 11.032259 10.951381

24.944523 12.050551 12.046945 13.716632 12.095928 11.514286 11.072919 11.098795 11.017092

15

Table 4: Zero-current values of resistance, R(0 mA), in Ohm measured at the KCRVs

𝑇KCRV,𝑖CCT . The data is taken from [3].

𝑇KCRV,𝑖CCT

K

PTB

229074

PTB

229075

NPL

221481

NPL

221485

VSL

226246

0.649875 4.854624 4.725238 6.000390 5.281841 4.708061

0.676928 4.872045 4.742804 6.020424 5.299175 4.724571

0.704354 4.889731 4.760712 6.040122 5.316999 4.741162

0.761580 4.926410 4.798252 6.081926 5.353773 4.776029

0.858421 4.988646 4.861282 6.152033 5.415979 4.834792

0.991223 5.073616 4.947326 6.247523 5.500294 4.915077

1.031584 5.099268 4.973439 6.276230 5.525717 4.939371

1.224991 5.221937 5.097910 6.413072 5.646390 5.055306

1.249542 5.237326 5.113564 6.430357 5.661598 5.069921

1.503370 5.396109 5.274709 6.606030 5.816854 5.220075

1.754822 5.551003 5.432016 6.776446 5.967301 5.366461

1.996554 5.697264 5.580650 6.936578 6.108781 5.504796

2.247655 5.846354 5.732149 7.099175 6.252346 5.645790

2.600776 6.050652 5.939773 7.321163 6.448281 5.838965

2.699911 6.106873 5.996922 7.382089 6.502062 5.892146

2.896733 6.216935 6.108893 7.501290 6.607279 5.996283

2.996648 6.272164 6.164963 7.560854 6.659906 6.048428

3.099398 6.328344 6.222094 7.621555 6.713436 6.101551

3.400235 6.489735 6.386183 7.795485 6.867022 6.254133

3.429250 6.505015 6.401743 7.811970 6.881583 6.268619

3.800903 6.697479 6.597508 8.019049 7.064425 6.450662

4.224794 6.908644 6.812265 8.245739 7.264575 6.650292

4.477522 7.030429 6.936152 8.376289 7.379822 6.765401

5.000458 7.272934 7.182907 8.635959 7.609076 6.994790

5.948165 7.682493 7.599597 9.073661 7.995466 7.382128

7.201544 8.171673 8.097486 9.595483 8.456221 7.844724

8.296372 8.557084 8.489790 10.006062 8.818778 8.209219

8.399612 8.591690 8.525014 10.042910 8.851231 8.241913

9.508020 8.945104 8.884795 10.419099 9.183443 8.576192

10.803390 9.321702 9.268239 10.819765 9.537238 8.932381

12.297309 9.714913 9.668576 11.237909 9.906492 9.304360

13.798183 10.072907 10.033088 11.618424 10.242539 9.642990

15.499566 10.441471 10.408410 12.010130 10.588490 9.991687

16.999335 10.739183 10.711565 12.326402 10.867842 10.273350

18.597377 11.033403 11.011198 12.638830 11.143805 10.551760

20.298899 11.325589 11.308730 12.948909 11.417731 10.828225

21.575444 11.533482 11.520448 13.169336 11.612478 11.024963

22.676998 11.706719 11.696871 13.352945 11.774648 11.188916

23.496448 11.832652 11.825107 13.486254 11.892446 11.308094

24.101970 11.924397 11.918522 13.583308 11.978164 11.394914

24.340317 11.960225 11.955040 13.621196 12.011668 11.428828

24.446403 11.976147 11.971241 13.638043 12.026516 11.443906

24.551354 11.991869 11.987234 13.654665 12.041190 11.458765

16

Table 5: Coefficients of the polynomials of order 12, 𝑇 = ∑ 𝑎𝑖[(𝑅 − 𝑐)/𝑑]𝑖12𝑖=0 with

c = (Rmax+Rmin)/2 and d = (Rmax-Rmin)/2, from fits to the data listed in Table 4.

Parameter /

coefficient

PTB

229074

PTB

229075

NPL

221481

NPL

221485

VSL

226246

Rmin 4.8546235 4.725238 6.00039 5.281841 4.7080605

Rmax 11.991869 11.987234 13.654665 12.0411895 11.4587645

a0 7.9045074191 7.912124286439 7.807578792230 7.80887005235 7.906877281010

a1 10.2771046918 10.279145129314 10.261830799599 10.26463273205 10.280555222722

a2 4.4458658558 4.438348428264 4.500332283534 4.49820608506 4.445658325077

a3 1.7358334235 1.733445325816 1.752497539815 1.74833527154 1.727715853501

a4 0.4834707413 0.504319041871 0.506971006482 0.53146365559 0.484563412438

a5 0.0218440496 0.026317985498 0.005350915256 0.02018937170 0.048088186903

a6 -0.2063487640 -0.305079498448 -0.202571076746 -0.31570739743 -0.229189493368

a7 0.2249716780 0.203771786948 0.273974052369 0.23293246214 0.169320194844

a8 0.2333253195 0.429435944433 0.261027689304 0.48485463411 0.289155994776

a9 -0.4623820285 -0.432421689871 -0.509418871903 -0.46462706158 -0.411344696935

a10 -0.4123067477 -0.593391512611 -0.429091694377 -0.63625941026 -0.470155590261

a11 0.1533798402 0.140421401148 0.166573862172 0.14918390975 0.136381510208

a12 0.1521319925 0.214903289625 0.156383829186 0.22928559231 0.173710533507

17

Table 6: Values of temperature given in K and resulting from the input calibration data

and the resistance values listed in Table 3 at the KCRVs 𝑇KCRV,𝑖EURAMET


K

PTB

229074

PTB

229075

NPL

221481

NPL

221485

VSL

226246

INRIM

232324

INRIM

B190

INTiBS

B178

2.693629 2.693888 2.693477 2.696983 2.693587 2.693564 2.693689 2.695690 2.694067

2.599898 2.600056 2.599807 2.603542 2.599866 2.599862 2.600022 2.602314 2.600285

3.000775 3.000859 3.000765 3.003468 3.000704 3.000771 3.000781 3.002627 3.000980

3.095913 3.095991 3.095899 3.098460 3.095844 3.095920 3.095965 3.097640 3.096116

3.401384 3.401484 3.401330 3.403416 3.401326 3.401395 3.401559 3.403387 3.401551

3.799888 3.799944 3.799857 3.801480 3.799827 3.799926 3.799967 3.801579 3.800060

4.200739 4.200749 4.200722 4.202037 4.200690 4.200795 4.200551 4.202105 4.200916

4.201187 4.201251 4.201160 4.202476 4.201112 4.201225 4.200934 4.202504 4.201447

4.487204 4.487304 4.487088 4.488299 4.487178 4.487248 4.487043 4.488257 4.487546

4.997407 4.997478 4.997339 4.998279 4.997384 4.997429 4.997277 4.998150 4.997821

5.496231 5.496228 5.496207 5.496959 5.496210 5.496279 5.496270 5.496875 5.496616

5.975219 5.975307 5.975145 5.975862 5.975214 5.975210 5.975446 5.975754 5.975619

6.570124 6.570249 6.570051 6.570622 6.570109 6.570088 6.570472 6.570661 6.570444

7.180012 7.180111 7.179792 7.180250 7.180005 7.179904 7.180392 7.180355 7.180200

8.273874 8.273941 8.273700 8.274059 8.273814 8.273855 8.274068 8.273981 8.273904

9.465787 9.465861 9.465626 9.465858 9.465754 9.465837 9.465786 9.465716 9.466012

10.770073 10.770159 10.769854 10.770134 10.770073 10.770147 10.770108 10.770097 10.770608

11.771326 11.771342 11.771159 11.771374 11.771335 11.771420 11.771339 11.771447 11.771843

12.277592 12.277640 12.277385 12.277666 12.277590 12.277678 12.277586 12.277765 12.278195

13.772857 13.772939 13.772689 13.772907 13.772848 13.772903 13.772586 13.773232 13.773658

15.471164 15.471308 15.471092 15.471207 15.471025 15.471188 15.470740 15.471529 15.471994

16.979618 16.979774 16.979451 16.979655 16.979647 16.979565 16.979037 16.979865 16.980530

18.571024 18.571303 18.570716 18.571139 18.571036 18.570927 18.570379 18.571401 18.571775

20.274906 20.275031 20.274723 20.274945 20.274869 20.274963 20.274286 20.275200 20.275673

21.556378 21.556442 21.556166 21.556438 21.556294 21.556551 21.555771 21.556647 21.556998

22.673744 22.673865 22.673561 22.673809 22.673668 22.673817 22.673487 22.674009 22.674596

24.463897 24.463979 24.463750 24.463988 24.463763 24.464007 24.464204 24.464344 24.464742

24.944523 24.944702 24.944416 24.944445 24.944494 24.944560 24.944680 24.944656 24.945232

18

Table 7: Comparison standard uncertainties (uEURAMET, cf. Table 9), KCRVs 𝑇KCRV,𝑖EURAMET, differences from the KCRVs and their laboratory

uncertainties. For RIRTs Nos. 229074, 229075, 221481, 221485, and 226246, the laboratory uncertainties are equal because the input data is

deduced from the results of CCT-K1 (uCCT, cf. Table 8). Uncertainties and differences are given in mK.

uEURAMET 𝑇KCRV,𝑖EURAMET

K

PTB

229074 uCCT

PTB

229075

NPL

221481

NPL

221485

VSL

226246

INRIM

232324 u232324

INRIM

B190 uB190

INTiBS

B178 uB178

0.116 2.693629 0.259 0.113 -0.152 3.354 -0.042 -0.065 0.060 0.500 2.061 0.500 0.438 0.500

0.116 2.599898 0.158 0.114 -0.090 3.645 -0.032 -0.036 0.124 0.500 2.416 0.500 0.387 0.500

0.116 3.000775 0.084 0.110 -0.010 2.693 -0.071 -0.003 0.006 0.500 1.852 0.500 0.205 0.500

0.116 3.095913 0.078 0.109 -0.015 2.546 -0.070 0.006 0.051 0.500 1.727 0.500 0.202 0.500

0.116 3.401384 0.100 0.105 -0.053 2.033 -0.058 0.011 0.176 0.500 2.003 0.500 0.168 0.500

0.115 3.799888 0.056 0.101 -0.032 1.591 -0.062 0.038 0.078 0.500 1.690 0.500 0.172 0.500

0.115 4.200739 0.010 0.096 -0.017 1.298 -0.049 0.056 -0.187 0.650 1.366 0.500 0.177 0.500

0.115 4.201187 0.064 0.096 -0.027 1.289 -0.075 0.038 -0.253 0.650 1.317 0.500 0.260 0.500

0.115 4.487204 0.100 0.098 -0.117 1.094 -0.026 0.043 -0.161 0.650 1.052 0.500 0.342 0.500

0.116 4.997407 0.071 0.100 -0.069 0.872 -0.024 0.021 -0.130 0.650 0.743 0.500 0.414 0.500

0.117 5.496231 -0.003 0.103 -0.024 0.728 -0.021 0.048 0.040 0.650 0.645 0.500 0.385 0.500

0.118 5.975219 0.088 0.105 -0.074 0.643 -0.005 -0.008 0.227 0.650 0.536 0.500 0.400 0.500

0.119 6.570124 0.124 0.108 -0.074 0.498 -0.015 -0.036 0.348 0.650 0.537 0.500 0.319 0.500

0.120 7.180012 0.099 0.111 -0.220 0.238 -0.008 -0.109 0.380 0.650 0.343 0.500 0.188 0.500

0.122 8.273874 0.067 0.117 -0.174 0.185 -0.060 -0.019 0.194 0.650 0.107 0.500 0.030 0.500

0.124 9.465787 0.074 0.123 -0.162 0.071 -0.033 0.050 -0.001 0.650 -0.071 0.500 0.225 0.500

0.143 10.770073 0.086 0.129 -0.219 0.060 -0.001 0.074 0.035 0.650 0.024 0.500 0.534 0.500

0.157 11.771326 0.016 0.135 -0.167 0.048 0.009 0.094 0.013 0.650 0.122 0.500 0.517 0.500

0.164 12.277592 0.048 0.137 -0.207 0.074 -0.002 0.087 -0.006 0.650 0.173 0.500 0.603 0.500

0.186 13.772857 0.082 0.145 -0.168 0.050 -0.009 0.046 -0.272 0.650 0.375 0.500 0.801 0.500

0.186 15.471164 0.144 0.145 -0.072 0.043 -0.139 0.024 -0.424 0.650 0.365 0.500 0.830 0.500

0.186 16.979618 0.156 0.145 -0.167 0.036 0.028 -0.054 -0.582 0.650 0.247 0.500 0.912 0.500

0.186 18.571024 0.279 0.145 -0.308 0.115 0.012 -0.097 -0.645 0.650 0.377 0.500 0.751 0.500

0.186 20.274906 0.125 0.145 -0.183 0.039 -0.037 0.057 -0.620 0.650 0.294 0.500 0.767 0.500

0.186 21.556378 0.063 0.145 -0.212 0.060 -0.084 0.172 -0.607 0.650 0.269 0.500 0.620 0.500

0.186 22.673744 0.121 0.145 -0.183 0.065 -0.076 0.073 -0.257 0.650 0.265 0.500 0.852 0.500

0.186 24.463897 0.081 0.145 -0.147 0.090 -0.134 0.109 0.307 0.650 0.446 0.500 0.844 0.500

0.186 24.944523 0.179 0.145 -0.107 -0.079 -0.029 0.037 0.156 0.650 0.133 0.500 0.709 0.500

19

Table 8: Uncertainty budget for the input data of RIRTs Nos. 229074, 229075, 221481,

221485, and 226246 based on the CCT-K1 comparison uncertainties and an

additional component considering curve fitting (the values are given in mK).

Component 2.6 K 4.2 K 10 K 13.8 K to 24.55 K

Type A

Repeatability of comparison measurements 0.04 0.05 0.07 0.07

Curve fitting 0.03 0.02 0.03 0.03

Type B

Resistance bridge linearity 0.009 0.01 0.02 0.05

Corrections to zero current 0.08 0.05 0.05 0.05

Residual temperature gradients 0.06 0.06 0.08 0.10

Combined uncertainty 0.113 0.096 0.123 0.145

Expanded uncertainty (k = 2) 0.227 0.193 0.245 0.290

20

Table 9: EUROMET.T-K1 comparison uncertainties uEUROMET

Component 2.6 K 4.2 K 10 K 13.8 K to 24.55 K

Type A

Repeatability of comparison measurements 0.06 0.08 0.08 0.14

Type B

Resistance bridge linearity 0.009 0.01 0.02 0.05

Corrections to zero current 0.08 0.05 0.05 0.05

Residual temperature gradients 0.06 0.06 0.08 0.1

Combined uncertainty 0.116 0.115 0.124 0.186

Expanded uncertainty (k = 2) 0.233 0.229 0.247 0.372

21

Table 10: Resistance values of RIRTs Nos. B178 and 93 at temperature fixed points of

the ITS-90 and deviations T from the KCRVs together with their standard

uncertainties u(T).

RIRT Triple Point R / u(R) / T / mK uT) / mK

INTiBS B178

H2

9.209984 16 -0.190 0.201

9.210028 13 0.022 0.196

9.210125 15 0.488 0.199

9.210015 20 -0.041 0.209

Ne

10.963950 20 -0.467 0.237

10.963941 20 -0.533 0.237

10.963937 20 -0.562 0.237

10.963941 17 -0.533 0.224

INTiBS 93 H2 10.561831 18 1.338 0.203

Ne 12.469906 26 0.775 0.256

22

Figure 1: The drawing shows the design of the cryostat including the experimental cell.

Starting from the top, the container of the outer vacuum chamber houses the nitrogen tank

situated above the helium tank. Both tanks as well as the inner vacuum can are thermally

isolated via superinsulation. Two evaporation coolers are connected with the helium tank

via tubes containing cryogenic needle valves. Each cooler, equipped with a pumping line,

is located on one of the two thermally isolated stages. Below these stages, inside the

shields, the experimental cell is located.

gas purifier

outer vacuumcan (OVC)

nitrogen tank

helium tank

superinsulation

inner vacuum can (IVC)

cryogenic needle valve

pumping line

2nd shield

evaporation cooler

pressure sensing tube

DCGT supply tube

1st shield

experimental cell (EC)

23

Figure 2: Deviation of the reading of RIRT No. 221481 from the KCRVs obtained in the

two comparison runs Nos. 0802 and 1202.

Figure 3: Deviation of the reading of RIRT No. 221485 from the KCRVs obtained in the

two comparison runs Nos. 0802 and 1202.

-1

0

1

2

3

4

5

0 5 10 15 20 25

T

/ m

K

T / K

T481_Run1202-T_KCRV(Mean)


STD T > 10 K

0.16 mK

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 5 10 15 20 25

T

/ m

K

T / K



STD 0.10 mK

24

Figure 4: Deviations of the readings of RIRTs Nos. 229074, 229075, 221481, 221485,

and 226246 from the KCRVs obtained in the main comparison run No. 0802. The

envelope shows the expanded comparison uncertainty of CCT-K1 [3] centred about the

base line.

Figure 5: Deviations of the readings of 8 RIRTs from the KCRVs obtained in the main

comparison run No. 0802.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 5 10 15 20 25

T i,R

un

08

02-

T KC

RV

(Me

an) (

mK

)

T / K

T_075_PTB_0802-T_KCVR(Mean)

T_074_PTB_0802-T_KCVR(Mean)

T_481_NPL_0802-T_KCVR(Mean)

T_485_NPL_0802-T_KCVR(Mean)

T_246_VSL_0802-T_KCVR(Mean)

U(CCT-K1)

STD T > 7 K:0.18 mK

STD 0.25 mK( without 481 T < 7 K )

-1

-0.5

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25

T i,R

un

0802

-TKC

RV

(Me

an) (m

K)

T / K

T_075_PTB_0802-T_KCRV(Mean)

T_074_PTB_0802-T_KCRV(Mean)

T_481_NPL_0802-T_KCRV(Mean)

T_485_NPL_0802-T_KCRV(Mean)

T_246_VSL_0802-T_KCRV(Mean)

T_B178_INTIB_NPL_0802-T_KCRV(Mean)

T_B190_INRIM_NPL_0802-T_KCRV(Mean)

T_324_INRIM_0802-T_KCRV(Mean)

25

Figure 6: Deviations of the readings of RIRTs Nos. 232324, B190, and B178 from the

KCRVs obtained in the main comparison run No. 0802.

-1

-0.5

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25

Ti,R

un

0802

-TKC

RV

(Mea

n) (m

K)

T / K

T_B190_INRIM_NPL_0802-T_KCRV(Mean)

T_324_INRIM_0802-T_KCRV(Mean)

T_B178_INTIB_NPL_0802-T_KCRV(Mean)

2007-11-14

Protocol for Key Comparison EURAMET.T-K1 (PTB, INRiM, INTiBS, NMi VSL, NPL)

Realisations of the ITS-90, 2.4 K to 24.5561 K, using rhodium-iron resistance thermometers

The measurement protocol for this regional Key Comparison is essentially the same as that used for CCT-K1, with the substitution of PTB as the pilot laboratory. In the temperature range from 2.4 K to 24.5561 K, the ITS-90 is defined by specifying vapour-pressure equa-tions for 3He (0,65 K to 3,2 K) and 4He (1,25 K to 5,0 K) and interpolation equations for a constant-volume gas thermometer using 3He or 4He. The definitions are given in Sections 3.1 and 3.2 of the ITS-90 text, and practical methods for realising the scale in this range are out-lined in Chapters 4 and 5 of the “Supplementary Information for the ITS-90”, BIPM 1990.

Realisations of the ITS-90 in this range are generally preserved and disseminated through calibrations of rhodium-iron resistance thermometers (RIRTs). The Key Comparison will be effected by comparing calibrations as have been established at PTB, INRiM, INTiBS, NMi VSL, NPL or in other national measurement institutes around the world. It is a pre-requisite of participation that the RIRTs have been calibrated in terms of an original local realisation of the ITS-90 over at least part of the range.

With the scope to get direct linking with the CCT-K1 comparison, the calibrations of two RIRTs of INRiM (serial numbers 232324 and B190) and INTiBS (serial numbers 93 and B178) will be compared in 2008 at PTB with the calibrations of the RIRTs of NMi VSL (se-rial number 226246), NPL (serial numbers 221481 and 221485), and PTB (serial numbers 229074 and 229075) that participated in CCT-K1. Measurements will be performed at a set of comparison temperatures similar in distribution to the original 31 CCT-K1 comparison tem-peratures in the range from about 2.4 K to 24.5561 K. The results will be recorded at the comparison temperatures as determined by the PTB reference RIRTs. These results will re-main blind until after the measurements are completed.

Resistance values will be reported at zero current, with the self-heating correction determined from measurements made at two different excitation currents at each of the comparison tem-peratures. Measurements at PTB will be made via an ac resistance bridge operating at 25 Hz excitation frequency and calibrated traceably to the national standard. Resistance standards will be traceable to RK-90 via sets of standard resistors traceable to the Quantized Hall Resis-tance.

In addition to the CCT-K1 measurement protocol, optionally an initial series of measurements will be performed at both PTB and the other four institutes to establish stability of the RIRTs. The resistance values will be measured at the triple point of water (TPW) and/or at the triple point of equilibrium-hydrogen (e-H2 TP) prior to their delivery to PTB. Upon delivery, the same initial measurements at the TPW and e-H2 TP will then be performed at PTB prior to performing the full comparison. Upon the return of the RIRTs, the same initial measurements will be performed again at the other four institutes. The resistance values so obtained will be shared by the four institutes and PTB for comparison to establish stability of the RIRTs. All other resistance-temperature data will remain blind until their evaluation is completed.

Within 2007, the ITS-90 interpolation equations appropriate for the RIRTs of INRiM, INTiBS, NMi VSL, and NPL will be forwarded to the pilot together with information relating to the realisation (range, description, report or publication) and the RIRTs (source, construction).

APPENDIX 1

These interpolation equations will be used together with preliminary comparison data to check the stability of the RIRTs prior to performing the full comparison. The full comparison data will then be used to generate TINRiM – TPTB, TINTiBS – TPTB, TNMiVSL – TPTB, and TNPL – TPTB over the comparison range.

The zero-current resistance values, interpolated temperatures, temperature differences, and associated uncertainty budgets corresponding to the template used for CCT-K1 will be re-ported by INRiM, INTiBS, NMi VSL, NPL, and PTB. The Draft A report will be written by PTB, including preliminary analysis on the bilateral degrees of equivalence. Once approved by the participants, the Draft B report will be submitted to CCT-WG7 for inclusion in the BIPM Key Comparison Database, with the results cast in a form suitable for linking with CCT-K1.

Contact information:

Physikalisch-Technische Bundesanstalt (PTB) Dr. Bernd Fellmuth Abbestrasse 2-12, 10587 Berlin, Germany Phone: +49 30 34817224 Fax: +49 30 34817490 E-mail: [email protected]

Istituto Nazionale di Ricerca Metrologica (INRiM) Dr. Peter Steur Strada delle Cacce 73, 10135 Torino, Italy Phone: +39 011 3919 740 Fax: +39 011 3919 747 E-mail: [email protected]

Institute of Low Temperature and Structure Research, Polish Academy of Sciences (INTiBS) Dr. Anna Szmyrka-Grzebyk P.O. Box 1410, 50-950 Wroclaw 2, Poland Phone: +48 71 34 350 21 Fax: +48 71 34 410 29 E-mail: [email protected]

Nederlands Meetinstituut van Swinden Laboratorium (NMi VSL) Dr. Andrea Peruzzi P.O. Box 654, 2600 AR Delft, The Netherlands Phone: +31 15 269 1519 Fax: +31 15 261 2971 E-mail: [email protected]

National Physical Laboratory (NPL) Dr. David Head Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom Phone: +44 20 89436111 Fax: +44 20 86140446 E-mail: [email protected]

mailto:[email protected]

DOCUMENT JCRB-9/9(1)

Completed copy to be forwarded to a) CCXX Executive Secretary, b) relevant Key Comparison WG Chairman and c) Regional coordinator as appropriate

STATUS REPORT ON RMO COMPARISON EURAMET.T-K1

1. CCT Section/Field: Thermometry 2. CCXX Ref No(to be completed by the BIPM):

3. Type of comparison: CCXX RMO

Key Supplementary Pilot study

4. Subject area: Thermometry

5. Participating institutes (and countries): PTB (Germany), INRiM (Italy), INTiBS (Poland), NMi VSL(Netherlands), NPL (United Kingdom)Bilateral

6. Pilot laboratory: PTB (Germany)

7. Measurand, unit and nominal value(s): Key Comparison EUROMET-K1.1: Realisations of the ITS-90, 2.4 K to 24.5561 K, using rhodium-iron resistance thermometers

8. Description: The measurement protocol for this regional Key Comparison is essentially the same as thatused for CCT-K1, with the substitution of PTB as the pilot laboratory. With the scope to get direct linking with the CCT-K1 comparison, the calibrations of two RIRTs of INRiM (serial numbers 232324 and B190) and INTiBS (serial numbers 93 and B178) will be compared at PTB with the calibrations of the RIRTs of NMi VSL (serial number 226246), NPL (serial numbers 221481 and 221485), and PTB (serial numbers 229074 and 229075) that participated in CCT-K1. Measurements will be performed at a set of comparison temperatures similar in distribution to the original 31 CCT-K1 comparison temperatures in the range from about 2.4 K to 24.5561 K. The results will be recorded at the comparison temperatures as determined by the PTB reference RIRTs. These results will remain blind until the measurements are completed.

9. Progress: (Please note date and tick appropriate box to indicate current status)

Date Status Pilot Supplementary Key

2008-04-22 Proposed to CCT-WG7 X X 2008-05-22 Accepted and registered X X

2008-04-22 Protocol submitted to CCT-WG7 X X

2007-11-14 Protocol agreed X X

Measurements in progress

2013-01-15 Measurements completed X X

2013-01-15 Report in progress X Draft A Draft A X

Draft B Draft B

Report submitted to CCXX

Results approved

Approved for Equivalence

Progression to Key Comparison

Abandoned

Comments: Start of the measurements delayed due to technical problems

Publication reference: EURAMET Ref. No. 1147

10. Measurement start date:2010-03-01

11. Expected measurement completion date:2012-12-31

APPENDIX 2

DOCUMENT JCRB-9/9(1)

Completed copy to be forwarded to a) CCXX Executive Secretary, b) relevant Key Comparison WG Chairman and c) Regional coordinator as appropriate

12. Contact person’s name: Dr. Christof GaiserAddress: Abbestrasse 2-12, 10587 Berlin, Germany

Telephone: + 49 30 34817349 Fax: + 49 30 34817490 e-mail [email protected] Web address: WWW.PTB.de

13. Contact Person’s signature: Dr. Christof Gaiser 14. Date: 2013-01-15

EURAMET Technical Committee ProjectsThe Technical Committees are the forum for scientific and technical cooperation in the respective fields.

The types of cooperation are:

• Cooperation in research

• Comparison in measurement standards

• Traceability• Consultation between members

Participation in EURAMET PROJECTS is open to all EURAMET members and associates in accordance with the EURAMET Eligibility Criteria for Participation in EURAMET TC Projects.

EURAMET Eligibility Criteria for Participation in EURAMET TC Projects: pdf version for download

Ref. 1147

Title Key Comparison EUROMET.T-K1.1: Realisations of the ITS-90, 2.4 K to 24.5561 K, using rhodium-iron resistance thermometers

Description The measurement protocol for this regional Key Comparison is essentially the same as that used for CCT-K1, with the substitution of PTB as the pilot laboratory. With the scope to get direct linking with the CCT-K1 comparison, the calibrations of two RIRTs of INRiM (serial numbers 232324 and B190) and INTiBS (serial numbers 93 and B178) will be compared at PTB with the calibrations of the RIRTs of NMi VSL (serial number 226246), NPL (serial numbers 221481 and 221 485), and PTB (serial numbers 229074 and 229075) that participated in CCT-K1.

Measurements will be performed at a set of comparison temperatures similar in distribution to the original 31 CCT-K1 comparison temperatures in the range from about 2.4 K to 24.5561 K. The results will be recorded at the comparison temperatures as determined by the PTB reference RIRTs. These results will remain blind until after the measurements are completed.

Collaboration Type comparison

Subjects Thermometry (T)

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APPENDIX 3

Back to listPlease note that the search engine is connecting search terms with 'AND'.

Project Forms

Project Form 'Proposal'

Project Form 'Proposal for Traceability Projects'

Project Form 'Report'© EURAMET e.V. - Last modified: 2014-08-08

Status agreed

Starting date 2010-02-28

Coordinating Institute PTB (Germany)

Participating Partners INRIM (Italy)

INTiBS (Poland)

NPL (United Kingdom)

VSL (Netherlands)

Proposer / Coordinator Dr Christof Gaiser

Phone +49 30 3481 7349

Fax +49 30 3481 7490

E-Mail [email protected]

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EURAMET.T-K1

Information

Metrology area, branch Thermometry, Standard Platinum Resistance Thermometers

Description Realizations of the ITS-90 from 2.4 K to 24.6 K

Time of measurement 2008 - 2012

Status Report in progress, Draft A

Reference(s) EURAMET.T-K1 registration and progress formEURAMET.T-K1 Technical Protocol

Measurand Temperature: 2.4 K to 24.6 K

Transfer device(s) Rh-Fe resistance thermometers

Comparison type Key comparison

Consultative Committee

CCT (Consultative Committee for Thermometry)

Conducted by EURAMET (formerly EUROMET) (European Association of National Metrology Institutes)

Other designation(s) EURAMET Project No 1147

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APPENDIX 4

Final results for INRIM Interpolating Constant Volume Gas Thermometer (with proper calibration at home-realized fixed points)

Introduction In 2003 the results obtained with the IMGC Interpolating Constant Volume Gas Thermometer, with a cryogenic pressure transducer, were published. These results, however, relied for the calibration points on the temperatures supplied by Rhodium-Iron thermometer nr 232324, carrying a NPL calibration. In order to become independent of the NPL calibration the thermometer was, still inside the ICVGT, calibrated at 4,2 K, which validated the NPL calibration to within 0.1 mK. Successively, the thermometer was mounted inside the “Multicells”-cryocooler, for calibration at the other specified fixed points, e-H2 and Ne. During 2006, it was discussed with PTB to carry out a comparison of our RhFe with the master thermometer of PTB, enabling us to extend our calibration capabilities to below the triple point of Neon, by means of the ICVGT. Together with the participation of INTiBS (PL), NPL (UK), CNAM (FR) and NMi-VSL (NL) this project became Euromet Project 1174. In 2007 this project became regional key comparison Euromet.T-K1.1 with its protocol approved by CCT-WG7, thereby linking with CCT-K1 (through PTB, NMi-VSL and NPL). Still in 2006, thermometer 232324 was hand-carried to PTB, together with a second thermometer (B190) not related to the ICVGT. However, due to the heavy involvement of PTB in the International Boltzmann Project, the comparison was postponed until 2009. At the end of that year the thermometers were hand-carried back to INRIM. First checks at the triple point of water indicated that thermometer 232324 had remained stable during transport to within 0.1 mK, after comparison with the TPW measurements at PTB shortly before transport, and to within 0.33 mK with respect to the 2006 INRIM value. In the mean time doubts had arisen about the quality of the initial calibration of thermometer 232324 at the fixed point of hydrogen and neon (not communicated to PTB), because those measurements had been carried out with a version of the data-acquisition program still in development, and many of the checks implemented later on for the Neon-Project (Euromet 770) were still lacking. It was then agreed with PTB that INRIM would repeat the measurements at the three fixed points, for increased reliability.

2010/11 Measurements: Rhodium-Iron Thermometer nr 232324, used with the IMGC-ICVGT, has been calibrated:

- at a temperature close to 4.2 K, using the 4He Vapour Pressure Equation, performed in an apparatus prepared for this purpose, since the ICVGT is not available anymore;

- at the temperature of the e-H2 triple point with three plateaux realized in cell Ec1H2 with known deuterium content (participated in the Intl. Project on the dependence of the hydrogen triple point on deuterium content), in the “MULTICELLS” cryocooler and with the latest version of the data-acquisition software, and

- at the temperature of the Neon triple points with three plateaux realized in cell Ec2Ne of known isotopic composition, in the same cryocooler and the same software..

Procedure and results:

Initial calibration: In 2005, with thermometer 232324 still mounted inside the ICVGT, the 4.2 K 4He vapour pressure point was realized by liquefying some gas inside the gas bulb, just below the pressure transducer.

APPENDIX 5

The same equipment (pressure, capacitance, resistance) was used as for the ICVGT. The difference between the vapour pressure realization and the NPL calibration, TVP – TNPL, was found to be -0.09 mK, with an uncertainty (k=2) of 0.12 mK. Then, the thermometer was transferred to the “MULTICELLS” cryocooler where it was measured at the hydrogen and neon fixed points using the heat pulse method. The resistance value obtained at the hydrogen point was corrected for the known isotopic composition of the gas. In the absence of a CCT approved correction function for the isotopic composition of neon, no such correction has been applied, even though the isotopic composition of the gas is known, allowing to perform the correction after its formalization in the Technical Annexe to the mise en pratique of the kelvin.. The resistance values, at melted fraction F=1, were found to be R(e-H2) = 9.307746 Ω and R(Ne) = 11.021173 Ω. However, both values were affected by a rather high uncertainty of about 0.3 mK. Subsequently, some bugs were found in the data-acquisition program (then still under development), rendering these values unreliable. Just before carrying the thermometer to PTB, its resistance value at the TPW was determined as (90.489124 ± 0.000027) Ω. All INRIM and PTB measurements at the TPW include both the immersion and isotopic composition correction. All uncertainties given with ‘±’ are for k=2. November 2009, just before returning the thermometer to INRIM, PTB measured the resistance value at the TPW as (90.489200 ± 0.00030) Ω, and on its return to INRIM, at the end of 2009, its resistance value at the TPW was determined to be (90.489240 ± 0.000027) Ω. The difference between the two INRIM values is equivalent to (0.33 ± 0.11 mK), showing the stability of the thermometer during travel and mounting/dismounting for measurement. In 2010, the measurements at the ICVGT fixed points were repeated, with the difference that the 4He vapour pressure measurement was not performed in the former ICVGT bulb but in a separate apparatus, immersed directly in a helium dewar discharging to the atmosphere. Pressure measurements were performed with a RUSKA 7220, declared to be independent of the measuring gas. The RUSKA 7220 was compared in air with an older, calibrated, RUSKA 6200. The two instruments agreed to within the reading uncertainty. The13.8 K results were corrected for isotopic composition. The 2010 difference between the 4.2 K vapour pressure realization and the NPL calibration, TVP – TNPL, was found to be -0.01 mK, with an uncertainty (k=2) of 0.20 mK. Evidently, the calibration of thermometer 232324 has remained remarkably stable. Using the same cryocooler and the same sealed cells, but with the present version of the data-acquisition program and procedure, R(e-H2) and R(Ne) were found to be 9.307763 Ω and 11.021165 Ω, respectively. For as much the 2006 values were considered unreliable, the differences between the 2010 values and those of 2006 turned out to be within 0.08 ± 0.30 mK and 0.06 ± 0.35 mK, respectively, where the uncertainty values reflect mainly the repeatability of the plateaux.. Construction of the calibration function: After calibration, the differences in temperature at the INRIM fixed points with the original NPL calibration were then used to generate a quadratic polynomial dTcal(T), see Fig.1. The differences found for the hydrogen and neon point are mainly due to the different isotopic composition for these fixed points at INRIM and NPL. The temperature differences between the INRIM ICVGT and the NPL calibration (published in TMCSI 7 p. 125-1301), where the fixed points were taken from the NPL calibration, were fitted with a cubic polynomial, dTICVGT(T), see Fig.2.

1 In TMCSI the differences were given as T(NPL)-T(ICVGT).

The quantity [dTICVGT(T) - dTcal(T)] was then added to the original NPL calibration function of degree 10, to yield the final INRIM ICVGT calibration. The resulting values (R,T) were fitted with a polynomial of the same degree, see Fig.3.

The polynomial has the form ( )∑

−Ω

= 100

//

i

i BARcKT with coefficient values:

A 9 B 3 C0 12.35609 C6 –1.28777C1 13.47556 C7 -1.41377 C2 5.95298 C8 –0.05572C3 1.97411 C9 0.81367 C4 0.27622 C10 0.36226 C5 –0.43130

Fig.1 The correction function due to the calibration at the fixed points, dTcal(T), after return to INRIM, with respect to the original NPL function of RhFe232324.

Calibration correction function (INRIM-NPL)

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 5 10 15 20 25 30

T / K

d T /

mK

Fig.2 The fit, dTICVGT(T), to the published data TICVGT-TNPL.

(T ICVGT-T NPL)/mK

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0 5 10 15 20 25 30

T , K

d T,

mK

Fig.3 The net change due to the INRIM ICVGT results and the INRIM calibration at the fixed points, added to the original NPL calibration function (=dTICVGT(T) - Tcal(T)) to arrive at the INRIM calibration.

T ICVGT-T NPL

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 5 10 15 20 25 30

T / K

d T /

mK

Uncertainty budget: The main part of the ICVGT budget, as published, is retained, with the exception of the item ‘thermometer calibration’ since the fixed-point calibration is now obtained with INRIM-realized fixed points. The as-published value for this item of 0.25 mK is thus substituted by the actual uncertainty pertaining to the INRIM fixed point realization.

Table 1.Uncertainty budget as published, without fixed point contribution (k=1) / mK: Contribution Density = 300 mol/m3 Density = 184 mol/m3 Transducer 0.28 0.41 Pressure balance calibration 0.11 0.11 Masses calibration 0.02 0.02 Residual Pressure 0.01 0.01 Hydrostatic head 0.08 0.14 Transducer calibration 0.28 0.46 Gas purity 0.13 0.13 Capacitance standard 0.01 0.02 Capacitance bridge 0.13 0.20 Capacitance noise 0.10 0.16 Temperature control 0.20 0.20 Resistance bridge 0.01 0.01

TOTAL 0.51 0.73

TOTAL (k=2) 1.02 1.46

Considering the densities of the working gas applied (three runs out of four at close to 200 mol/m3), an overall uncertainty for the ICVGT measurements of 1.30 mK (k=2) seems appropriate.

Uncertainty budget for the fixed point measurements:

Table 2. 2005 4He vapour pressure point near 4.2 K (k=1), in mK: Contribution Value

RUSKA pressure balance (0.32 Pa) 0.003 Non-linearity room-temperature pressure transducer (0.40 Pa) 0.004 Readings room-temperature pressure transducer (0.11 Pa) 0.001 Zero stability room-temperature pressure transducer (0.0003 Pa) 0.000 Hydrostatic head (3 Pa) 0.030 Resistance measurement 0.050

Total (k=1) 0.06 Expanded (k=2) 0.12

Because of the unreliability of the 2005/6 values at the hydrogen and neon fixed points, no uncertainty budget is given for these.

Table 4. 2010 4He vapour pressure point near 4.2 K (k=1), in mK: Contribution Value

pressure reading/calibration 0.005 Hydrostatic effect (liquid) 0.070 Hydrostatic effect (gas) 0.040 Delay due to pressure change (atmospheric pressure) 0.050 Resistance measurement 0.020 Standard resistor calibration 0.020 Selfheating 0.020


Table 5. 2010 calibration at the e-H2 fixed point (k=1), in mK: Contribution Value

Plateau reproducibility 0.011 Ortho-para conversion 0.010 Thermal exchange with the shield 0.015 Impurity 0.030 Isotopic composition 0.006 Hydrostatic effect 0.003 Resistance measurement 0.010 Standard resistor calibration 0.020


Table 6. 2010 calibration at the Ne fixed point (k=1), in mK: Contribution Value

Plateau reproducibility 0.014 Thermal exchange with the shield 0.015 Impurity 0.075 Isotopic composition (scale definition) 0.140 Hydrostatic effect 0.019 Resistance measurement 0.010 Standard resistor calibration 0.020


Table 7. Total uncertainty budget (k=2) / mK: ICVGT as published (TMSCI 7, 125-130), from Table 1 1.30 Calibration a 4.2 K, from Table 4 0.20 Calibration at 13.8 K, from Table 5 0.09 Calibration at 24.6 K, from Table 6 0.32

TOTAL (using max contribution from propagation)

1.31

Fig.4 The propagation of the uncertainty deriving from the fixed point calibration

Additional information for thermometer 232324 (NPL certificate) for T< 2.6 K: x = ((R - 4.557101) - (5.713564 - R)) / (5.713564-4.55101)

T = 4th order polynomial in x with coefficients: C0 1.52899342 C1 1.03707949 C2 0.03557204 C3 0.00808965 C4 0.00001244

For T> 2.6 K the certificate gives: x = ((R - 5.713564) - (11.355637 - R)) / (11.355637-5.713564)

T = 10th order polynomial in x with coefficients: C0 10.40161756 C1 11.06574693 C2 4.49545720 C3 1.46898635 C4 0.24849810 C5 0.08345290 C6 -0.00178366 C7 -0.52204378 C8 -0.48889039 C9 0.14515427 C10 0.19615699

Propagation of (k =2) uncertainty from the fixed point calibration

0.000.050.100.150.200.250.300.35

0 5 10 15 20 25 30

T / K

dT /

mK

APPENDIX 6

EURAMET.T-K1 table and graph of results, with bilateral degrees of equivalence

Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 2.600056 0.114 0.158 0.326 PTB 229075 2.599807 0.114 -0.090 0.326 NPL 221485 2.599866 0.114 -0.032 0.326 VSL 226246 2.599862 0.114 -0.036 0.326

INRIM 232324 2.600022 0.500 0.124 1.027 INTiBS B178 2.600285 0.500 0.387 1.027

TKCVR / K ucomp / mK 2.599898 0.116

Matrix of equivalences Differences and uncertainties: Dij = (Ti – Tj) and Uij (k = 2) in mK

Thermometer Lab, S/N j

PTB 229074 PTB 229075 NPL 221485 VSL 226246 INRIM 232324 INTiBS B178

Lab, S/N i Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij / mK / mK / mK / mK / mK / mK

PTB 229074 0.248 0.461 0.190 0.461 0.194 0.461 0.034 1.077 -0.229 1.077

PTB 229075 -0.248 0.461 -0.058 0.461 -0.054 0.461 -0.214 1.077 -0.477 1.077

NPL 221485 -0.190 0.461 0.058 0.461 0.004 0.461 -0.156 1.077 -0.419 1.077

VSL 226246 -0.194 0.461 0.054 0.461 -0.004 0.461 -0.160 1.077 -0.423 1.077

INRIM 232324 -0.034 1.077 0.214 1.077 0.156 1.077 0.160 1.077 -0.263 1.452

INTiBS B178 0.229 1.077 0.477 1.077 0.419 1.077 0.423 1.077 0.263 1.452

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK

EURAMET.T-K1 : Nominal temperature, T90 = 2.60 KDegrees of equivalence, Di, and expanded uncertainties (k = 2), Ui, in mK

APPENDIX 7



INRIM 232324 2.693689 0.500 0.060 1.027 INTiBS B178 2.694067 0.500 0.438 1.027

TKCVR / K ucomp / mK 2.693629 0.116





PTB 229074 0.411 0.459 0.301 0.459 0.324 0.459 0.199 1.077 -0.179 1.077

PTB 229075 -0.411 0.459 -0.110 0.459 -0.087 0.459 -0.212 1.077 -0.590 1.077

NPL 221485 -0.301 0.459 0.110 0.459 0.023 0.459 -0.102 1.077 -0.480 1.077

VSL 226246 -0.324 0.459 0.087 0.459 -0.023 0.459 -0.125 1.077 -0.503 1.077

INRIM 232324 -0.199 1.077 0.212 1.077 0.102 1.077 0.125 1.077 -0.378 1.452

INTiBS B178 0.179 1.077 0.590 1.077 0.480 1.077 0.503 1.077 0.378 1.452

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 3.000781 0.500 0.006 1.027 INTiBS B178 3.000980 0.500 0.205 1.027

TKCVR / K

ucomp / mK

3.000775 0.116




Lab, S/N i Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij

/ mK / mK / mK / mK / mK / mK

PTB 229074 0.094 0.452 0.155 0.452 0.087 0.452 0.078 1.075 -0.121 1.075

PTB 229075 -0.094 0.452

0.061 0.452 -0.007 0.452 -0.016 1.075 -0.215 1.075

NPL 221485 -0.155 0.452 -0.061 0.452

-0.068 0.452 -0.077 1.075 -0.276 1.075

VSL 226246 -0.087 0.452 0.007 0.452 0.068 0.452

-0.009 1.075 -0.208 1.075

INRIM 232324 -0.078 1.075 0.016 1.075 0.077 1.075 0.009 1.075 -0.199 1.452

INTiBS B178 0.121 1.075 0.215 1.075 0.276 1.075 0.208 1.075 0.199 1.452

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 3.095991 0.109 0.078 0.318 PTB 229075 3.095899 0.109 -0.015 0.318 NPL 221485 3.095844 0.109 -0.070 0.318 VSL 226246 3.095920 0.109 0.006 0.318

INRIM 232324 3.095965 0.500 0.051 1.027 INTiBS B178 3.096116 0.500 0.202 1.027

TKCVR / K

ucomp / mK

3.095913 0.116






PTB 229074 0.093 0.450 0.148 0.450 0.072 0.450 0.027 1.075 -0.124 1.075

PTB 229075 -0.093 0.450

0.055 0.450 -0.021 0.450 -0.066 1.075 -0.217 1.075

NPL 221485 -0.148 0.450 -0.055 0.450

-0.076 0.450 -0.121 1.075 -0.272 1.075

VSL 226246 -0.072 0.450 0.021 0.450 0.076 0.450

-0.045 1.075 -0.196 1.075

INRIM 232324 -0.027 1.075 0.066 1.075 0.121 1.075 0.045 1.075 -0.151 1.452

INTiBS B178 0.124 1.075 0.217 1.075 0.272 1.075 0.196 1.075 0.151 1.452

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 3.401559 0.500 0.176 1.027 INTiBS B178 3.401551 0.500 0.168 0.313

TKCVR / K ucomp / mK 3.401384 0.116





PTB 229074 0.153 0.443 0.158 0.443 0.089 0.443 -0.076 1.073 -0.068 1.073

PTB 229075 -0.153 0.443 0.005 0.443 -0.064 0.443 -0.229 1.073 -0.221 1.073

NPL 221485 -0.158 0.443 -0.005 0.443 -0.069 0.443 -0.234 1.073 -0.226 1.073

VSL 226246 -0.089 0.443 0.064 0.443 0.069 0.443 -0.165 1.073 -0.157 1.073

INRIM 232324 0.076 1.073 0.229 1.073 0.234 1.073 0.165 1.073 0.008 1.452

INTiBS B178 0.068 1.073 0.221 1.073 0.226 1.073 0.157 1.073 -0.008 1.452

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 3.799967 0.500 0.078 1.026 INTiBS B178 3.800060 0.500 0.172 1.026

TKCVR / K ucomp / mK 3.799888 0.115





PTB 229074 0.088 0.433 0.118 0.433 0.018 0.433 -0.022 1.071 -0.116 1.071

PTB 229075 -0.088 0.433 0.030 0.433 -0.070 0.433 -0.110 1.071 -0.204 1.071

NPL 221485 -0.118 0.433 -0.030 0.433 -0.100 0.433 -0.140 1.071 -0.234 1.071

VSL 226246 -0.018 0.433 0.070 0.433 0.100 0.433 -0.040 1.071 -0.134 1.071

INRIM 232324 0.022 1.071 0.110 1.071 0.140 1.071 0.040 1.071 -0.094 1.451

INTiBS B178 0.116 1.071 0.204 1.071 0.234 1.071 0.134 1.071 0.094 1.451

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 4.200551 0.650 -0.187 1.320 INTiBS B178 4.200916 0.500 0.177 1.026

TKCVR / K ucomp / mK 4.200739 0.115





PTB 229074 0.027 0.425 0.060 0.425 -0.046 0.425 0.198 1.354 -0.167 1.069

PTB 229075 -0.027 0.425 0.032 0.425 -0.073 0.425 0.170 1.354 -0.195 1.069

NPL 221485 -0.060 0.425 -0.032 0.425 -0.106 0.425 0.138 1.354 -0.227 1.069

VSL 226246 0.046 0.425 0.073 0.425 0.106 0.425 0.244 1.354 -0.121 1.069

INRIM 232324 -0.198 1.354 -0.170 1.354 -0.138 1.354 -0.244 1.354 -0.365 1.672

INTiBS B178 0.167 1.069 0.195 1.069 0.227 1.069 0.121 1.069 0.365 1.672

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 4.200934 0.650 -0.253 1.320 INTiBS B178 4.201447 0.500 0.260 1.026

TKCVR / K

ucomp / mK

4.201187 0.115






PTB 229074 0.091 0.425 0.139 0.425 0.026 0.425 0.317 1.354 -0.196 1.069

PTB 229075 -0.091 0.425

0.048 0.425 -0.065 0.425 0.226 1.354 -0.287 1.069

NPL 221485 -0.139 0.425 -0.048 0.425

-0.113 0.425 0.178 1.354 -0.335 1.069

VSL 226246 -0.026 0.425 0.065 0.425 0.113 0.425

0.291 1.354 -0.222 1.069

INRIM 232324 -0.317 1.354 -0.226 1.354 -0.178 1.354 -0.291 1.354 -0.513 1.672

INTiBS B178 0.196 1.069 0.287 1.069 0.335 1.069 0.222 1.069 0.513 1.672

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 4.487043 0.650 -0.161 1.320 INTiBS B178 4.487546 0.500 0.342 1.026

TKCVR / K ucomp / mK 4.487204 0.115





PTB 229074 0.217 0.427 0.126 0.427 0.057 0.427 0.261 1.354 -0.242 1.070

PTB 229075 -0.217 0.427 -0.091 0.427 -0.160 0.427 0.044 1.354 -0.459 1.070

NPL 221485 -0.126 0.427 0.091 0.427 -0.069 0.427 0.135 1.354 -0.368 1.070

VSL 226246 -0.057 0.427 0.160 0.427 0.069 0.427 0.204 1.354 -0.299 1.070

INRIM 232324 -0.261 1.354 -0.044 1.354 -0.135 1.354 -0.204 1.354 -0.503 1.672

INTiBS B178 0.242 1.070 0.459 1.070 0.368 1.070 0.299 1.070 0.503 1.672

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 4.997277 0.650 -0.130 1.321 INTiBS B178 4.997821 0.500 0.414 1.027

TKCVR / K ucomp / mK 4.997407 0.116





PTB 229074 0.140 0.434 0.095 0.434 0.050 0.434 0.201 1.356 -0.343 1.071

PTB 229075 -0.140 0.434 -0.045 0.434 -0.090 0.434 0.061 1.356 -0.483 1.071

NPL 221485 -0.095 0.434 0.045 0.434 -0.045 0.434 0.106 1.356 -0.438 1.071

VSL 226246 -0.050 0.434 0.090 0.434 0.045 0.434 0.151 1.356 -0.393 1.071

INRIM 232324 -0.201 1.356 -0.061 1.356 -0.106 1.356 -0.151 1.356 -0.544 1.673

INTiBS B178 0.343 1.071 0.483 1.071 0.438 1.071 0.393 1.071 0.544 1.673

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 5.496228 0.103 -0.003 0.312 PTB 229075 5.496207 0.103 -0.024 0.312 NPL 221485 5.496210 0.103 -0.021 0.312 VSL 226246 5.496279 0.103 0.048 0.312

INRIM 232324 5.496270 0.650 0.040 1.321 INTiBS B178 5.496616 0.500 0.385 1.027

TKCVR / K ucomp / mK 5.496231 0.117





PTB 229074 0.021 0.441 0.018 0.441 -0.051 0.441 -0.043 1.357 -0.388 1.073

PTB 229075 -0.021 0.441 -0.003 0.441 -0.072 0.441 -0.064 1.357 -0.409 1.073

NPL 221485 -0.018 0.441 0.003 0.441 -0.069 0.441 -0.061 1.357 -0.406 1.073

VSL 226246 0.051 0.441 0.072 0.441 0.069 0.441 0.008 1.357 -0.337 1.073

INRIM 232324 0.043 1.357 0.064 1.357 0.061 1.357 -0.008 1.357 -0.345 1.673

INTiBS B178 0.388 1.073 0.409 1.073 0.406 1.073 0.337 1.073 0.345 1.673

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 5.975446 0.650 0.227 1.321 INTiBS B178 5.975619 0.500 0.400 1.027

TKCVR / K ucomp / mK 5.975219 0.118





PTB 229074 0.162 0.447 0.093 0.447 0.096 0.447 -0.139 1.359 -0.312 1.075

PTB 229075 -0.162 0.447 -0.069 0.447 -0.066 0.447 -0.301 1.359 -0.474 1.075

NPL 221485 -0.093 0.447 0.069 0.447 0.003 0.447 -0.232 1.359 -0.405 1.075

VSL 226246 -0.096 0.447 0.066 0.447 -0.003 0.447 -0.235 1.359 -0.408 1.075

INRIM 232324 0.139 1.359 0.301 1.359 0.232 1.359 0.235 1.359 -0.173 1.674

INTiBS B178 0.312 1.075 0.474 1.075 0.405 1.075 0.408 1.075 0.173 1.674

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK




INRIM 232324 6.570472 0.650 0.348 1.322 INTiBS B178 6.570444 0.500 0.319 1.028

TKCVR / K

ucomp / mK

6.570124 0.119






PTB 229074 0.198 0.455 0.139 0.455 0.160 0.455 -0.224 1.360 -0.195 1.077

PTB 229075 -0.198 0.455

-0.059 0.455 -0.038 0.455 -0.422 1.360 -0.393 1.077

NPL 221485 -0.139 0.455 0.059 0.455

0.021 0.455 -0.363 1.360 -0.334 1.077

VSL 226246 -0.160 0.455 0.038 0.455 -0.021 0.455

-0.384 1.360 -0.355 1.077

INRIM 232324 0.224 1.360 0.422 1.360 0.363 1.360 0.384 1.360 0.029 1.674

INTiBS B178 0.195 1.077 0.393 1.077 0.334 1.077 0.355 1.077 -0.029 1.674

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 7.180111 0.111 0.099 0.327 PTB 229075 7.179792 0.111 -0.220 0.327 NPL 221481 7.180250 0.111 0.238 0.327 NPL 221485 7.180005 0.111 -0.008 0.327 VSL 226246 7.179904 0.111 -0.109 0.327

INRIM 232324 7.180392 0.650 0.380 1.322 INRIM B190 7.180355 0.500 0.343 1.028 INTiBS B178 7.180200 0.500 0.188 1.028

TKCVR / K ucomp / mK 7.180012 0.120



PTB 229074 PTB 229075 NPL 221481 NPL 221485 VSL 226246 INRIM 232324 INRIM B190 INTiBS B178

Lab, S/N i Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij / mK / mK / mK / mK / mK / mK / mK / mK

PTB 229074 0.319 0.463 -0.139 0.463 0.107 0.463 0.208 0.463 -0.281 1.362 -0.244 1.079 -0.089 1.079

PTB 229075 -0.319 0.463 -0.458 0.463 -0.212 0.463 -0.111 0.463 -0.600 1.362 -0.563 1.079 -0.408 1.079

NPL 221481 0.139 0.463 0.458 0.463 0.246 0.463 0.347 0.463 -0.142 1.362 -0.105 1.079 0.050 1.079

NPL 221485 -0.107 0.463 0.212 0.463 -0.246 0.463 0.101 0.463 -0.388 1.362 -0.351 1.079 -0.196 1.079

VSL 226246 -0.208 0.463 0.111 0.463 -0.347 0.463 -0.101 0.463 -0.489 1.362 -0.452 1.079 -0.297 1.079

INRIM 232324 0.281 1.362 0.600 1.362 0.142 1.362 0.388 1.362 0.489 1.362 0.037 1.675 0.192 1.675

INRIM B190 0.244 1.079 0.563 1.079 0.105 1.079 0.351 1.079 0.452 1.079 -0.037 1.675 0.155 1.454

INTiBS B178 0.089 1.079 0.408 1.079 -0.050 1.079 0.196 1.079 0.297 1.079 -0.192 1.675 -0.155 1.454

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 8.273941 0.117 0.067 0.338 PTB 229075 8.273700 0.117 -0.174 0.338 NPL 221481 8.274059 0.117 0.185 0.338 NPL 221485 8.273814 0.117 -0.060 0.338 VSL 226246 8.273855 0.117 -0.019 0.338


TKCVR / K

ucomp / mK

8.273874 0.122




Lab, S/N i Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij Dij Uij

/ mK / mK / mK / mK / mK / mK / mK / mK

PTB 229074 0.241 0.478 -0.118 0.478 0.127 0.478 0.086 0.478 -0.127 1.365 -0.040 1.083 0.037 1.083

PTB 229075 -0.241 0.478

-0.359 0.478 -0.114 0.478 -0.155 0.478 -0.368 1.365 -0.281 1.083 -0.204 1.083

NPL 221481 0.118 0.478 0.359 0.478

0.245 0.478 0.204 0.478 -0.009 1.365 0.078 1.083 0.155 1.083

NPL 221485 -0.127 0.478 0.114 0.478 -0.245 0.478

-0.041 0.478 -0.254 1.365 -0.167 1.083 -0.090 1.083

VSL 226246 -0.086 0.478 0.155 0.478 -0.204 0.478 0.041 0.478 -0.213 1.365 -0.126 1.083 -0.049 1.083

INRIM 232324 0.127 1.365 0.368 1.365 0.009 1.365 0.254 1.365 0.213 1.365 0.087 1.676 0.164 1.676

INRIM B190 0.040 1.083 0.281 1.083 -0.078 1.083 0.167 1.083 0.126 1.083 -0.087 1.676 0.077 1.456

INTiBS B178 -0.037 1.083 0.204 1.083 -0.155 1.083 0.090 1.083 0.049 1.083 -0.164 1.676 -0.077 1.456

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 9.465861 0.123 0.074 0.349 PTB 229075 9.465626 0.123 -0.162 0.349 NPL 221481 9.465858 0.123 0.071 0.349 NPL 221485 9.465754 0.123 -0.033 0.349 VSL 226246 9.465837 0.123 0.050 0.349

INRIM 232324 9.465786 0.650 -0.001 1.323 INRIM B190 9.465716 0.500 -0.071 1.030 INTiBS B178 9.466012 0.500 0.225 1.030

TKCVR / K ucomp / mK 9.465787 0.124





PTB 229074 0.236 0.493 0.003 0.493 0.107 0.493 0.024 0.493 0.075 1.369 0.145 1.088 -0.151 1.088

PTB 229075 -0.236 0.493 -0.233 0.493 -0.129 0.493 -0.212 0.493 -0.161 1.369 -0.091 1.088 -0.387 1.088

NPL 221481 -0.003 0.493 0.233 0.493 0.104 0.493 0.021 0.493 0.072 1.369 0.142 1.088 -0.154 1.088

NPL 221485 -0.107 0.493 0.129 0.493 -0.104 0.493 -0.083 0.493 -0.032 1.369 0.038 1.088 -0.258 1.088

VSL 226246 -0.024 0.493 0.212 0.493 -0.021 0.493 0.083 0.493 0.051 1.369 0.121 1.088 -0.175 1.088

INRIM 232324 -0.075 1.369 0.161 1.369 -0.072 1.369 0.032 1.369 -0.051 1.369 0.070 1.677 -0.226 1.677

INRIM B190 -0.145 1.088 0.091 1.088 -0.142 1.088 -0.038 1.088 -0.121 1.088 -0.070 1.677 -0.296 1.457

INTiBS B178 0.151 1.088 0.387 1.088 0.154 1.088 0.258 1.088 0.175 1.088 0.226 1.677 0.296 1.457

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K

ucomp / mK

10.770073 0.143






PTB 229074 0.305 0.545 0.026 0.545 0.087 0.545 0.012 0.545 0.051 1.386 0.062 1.109 -0.448 1.109

PTB 229075 -0.305 0.545

-0.279 0.545 -0.218 0.545 -0.293 0.545 -0.254 1.386 -0.243 1.109 -0.753 1.109

NPL 221481 -0.026 0.545 0.279 0.545

0.061 0.545 -0.014 0.545 0.025 1.386 0.036 1.109 -0.474 1.109

NPL 221485 -0.087 0.545 0.218 0.545 -0.061 0.545

-0.075 0.545 -0.036 1.386 -0.025 1.109 -0.535 1.109

VSL 226246 -0.012 0.545 0.293 0.545 0.014 0.545 0.075 0.545 0.039 1.386 0.050 1.109 -0.460 1.109

INRIM 232324 -0.051 1.386 0.254 1.386 -0.025 1.386 0.036 1.386 -0.039 1.386 0.011 1.689 -0.499 1.689

INRIM B190 -0.062 1.109 0.243 1.109 -0.036 1.109 0.025 1.109 -0.050 1.109 -0.011 1.689 -0.510 1.471

INTiBS B178 0.448 1.109 0.753 1.109 0.474 1.109 0.535 1.109 0.460 1.109 0.499 1.689 0.510 1.471

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 11.771342 0.135 0.016 0.414 PTB 229075 11.771159 0.135 -0.167 0.414 NPL 221481 11.771374 0.135 0.048 0.414 NPL 221485 11.771335 0.135 0.009 0.414 VSL 226246 11.771420 0.135 0.094 0.414


TKCVR / K ucomp / mK 11.771326 0.157





PTB 229074 0.183 0.585 -0.032 0.585 0.007 0.585 -0.078 0.585 0.003 1.400 -0.106 1.127 -0.501 1.127

PTB 229075 -0.183 0.585 -0.215 0.585 -0.176 0.585 -0.261 0.585 -0.180 1.400 -0.289 1.127 -0.684 1.127

NPL 221481 0.032 0.585 0.215 0.585 0.039 0.585 -0.046 0.585 0.035 1.400 -0.074 1.127 -0.469 1.127

NPL 221485 -0.007 0.585 0.176 0.585 -0.039 0.585 -0.085 0.585 -0.004 1.400 -0.113 1.127 -0.508 1.127

VSL 226246 0.078 0.585 0.261 0.585 0.046 0.585 0.085 0.585 0.081 1.400 -0.028 1.127 -0.423 1.127

INRIM 232324 -0.003 1.400 0.180 1.400 -0.035 1.400 0.004 1.400 -0.081 1.400 -0.109 1.699 -0.504 1.699

INRIM B190 0.106 1.127 0.289 1.127 0.074 1.127 0.113 1.127 0.028 1.127 0.109 1.699 -0.395 1.482

INTiBS B178 0.501 1.127 0.684 1.127 0.469 1.127 0.508 1.127 0.423 1.127 0.504 1.699 0.395 1.482

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK




INRIM 232324 12.277586 0.650 -0.006 1.341 INRIM B190 12.277765 0.500 0.173 1.052 INTiBS B178 12.278195 0.500 0.603 1.052

TKCVR / K

ucomp / mK

12.277592 0.164






PTB 229074 0.255 0.605 -0.026 0.605 0.050 0.605 -0.039 0.605 0.054 1.407 -0.125 1.136 -0.555 1.136

PTB 229075 -0.255 0.605

-0.281 0.605 -0.205 0.605 -0.294 0.605 -0.201 1.407 -0.380 1.136 -0.810 1.136

NPL 221481 0.026 0.605 0.281 0.605

0.076 0.605 -0.013 0.605 0.080 1.407 -0.099 1.136 -0.529 1.136

NPL 221485 -0.050 0.605 0.205 0.605 -0.076 0.605

-0.089 0.605 0.004 1.407 -0.175 1.136 -0.605 1.136

VSL 226246 0.039 0.605 0.294 0.605 0.013 0.605 0.089 0.605 0.093 1.407 -0.086 1.136 -0.516 1.136

INRIM 232324 -0.054 1.407 0.201 1.407 -0.080 1.407 -0.004 1.407 -0.093 1.407 -0.179 1.704 -0.609 1.704

INRIM B190 0.125 1.136 0.380 1.136 0.099 1.136 0.175 1.136 0.086 1.136 0.179 1.704 -0.430 1.488

INTiBS B178 0.555 1.136 0.810 1.136 0.529 1.136 0.605 1.136 0.516 1.136 0.609 1.704 0.430 1.488

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K ucomp / mK 13.772857 0.186





PTB 229074 0.250 0.667 0.032 0.667 0.091 0.667 0.036 0.667 0.354 1.432 -0.293 1.167 -0.719 1.167

PTB 229075 -0.250 0.667 -0.218 0.667 -0.159 0.667 -0.214 0.667 0.104 1.432 -0.543 1.167 -0.969 1.167

NPL 221481 -0.032 0.667 0.218 0.667 0.059 0.667 0.004 0.667 0.322 1.432 -0.325 1.167 -0.751 1.167

NPL 221485 -0.091 0.667 0.159 0.667 -0.059 0.667 -0.055 0.667 0.263 1.432 -0.384 1.167 -0.810 1.167

VSL 226246 -0.036 0.667 0.214 0.667 -0.004 0.667 0.055 0.667 0.318 1.432 -0.329 1.167 -0.755 1.167

INRIM 232324 -0.354 1.432 -0.104 1.432 -0.322 1.432 -0.263 1.432 -0.318 1.432 -0.647 1.722 -1.073 1.722

INRIM B190 0.293 1.167 0.543 1.167 0.325 1.167 0.384 1.167 0.329 1.167 0.647 1.722 -0.426 1.509

INTiBS B178 0.719 1.167 0.969 1.167 0.751 1.167 0.810 1.167 0.755 1.167 1.073 1.722 0.426 1.509

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K

ucomp / mK

15.471164 0.186






PTB 229074 0.216 0.667 0.101 0.667 0.283 0.667 0.120 0.667 0.568 1.432 -0.221 1.167 -0.686 1.167

PTB 229075 -0.216 0.667

-0.115 0.667 0.067 0.667 -0.096 0.667 0.352 1.432 -0.437 1.167 -0.902 1.167

NPL 221481 -0.101 0.667 0.115 0.667

0.182 0.667 0.019 0.667 0.467 1.432 -0.322 1.167 -0.787 1.167

NPL 221485 -0.283 0.667 -0.067 0.667 -0.182 0.667

-0.163 0.667 0.285 1.432 -0.504 1.167 -0.969 1.167

VSL 226246 -0.120 0.667 0.096 0.667 -0.019 0.667 0.163 0.667 0.448 1.432 -0.341 1.167 -0.806 1.167

INRIM 232324 -0.568 1.432 -0.352 1.432 -0.467 1.432 -0.285 1.432 -0.448 1.432 -0.789 1.722 -1.254 1.722

INRIM B190 0.221 1.167 0.437 1.167 0.322 1.167 0.504 1.167 0.341 1.167 0.789 1.722 -0.465 1.509

INTiBS B178 0.686 1.167 0.902 1.167 0.787 1.167 0.969 1.167 0.806 1.167 1.254 1.722 0.465 1.509

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 16.979774 0.145 0.156 0.472 PTB 229075 16.979451 0.145 -0.167 0.472 NPL 221481 16.979655 0.145 0.036 0.472 NPL 221485 16.979647 0.145 0.028 0.472 VSL 226246 16.979565 0.145 -0.054 0.472


TKCVR / K ucomp / mK 16.979618 0.186





PTB 229074 0.323 0.667 0.120 0.667 0.128 0.667 0.210 0.667 0.738 1.432 -0.091 1.167 -0.756 1.167

PTB 229075 -0.323 0.667 -0.203 0.667 -0.195 0.667 -0.113 0.667 0.415 1.432 -0.414 1.167 -1.079 1.167

NPL 221481 -0.120 0.667 0.203 0.667 0.008 0.667 0.090 0.667 0.618 1.432 -0.211 1.167 -0.876 1.167

NPL 221485 -0.128 0.667 0.195 0.667 -0.008 0.667 0.082 0.667 0.610 1.432 -0.219 1.167 -0.884 1.167

VSL 226246 -0.210 0.667 0.113 0.667 -0.090 0.667 -0.082 0.667 0.528 1.432 -0.301 1.167 -0.966 1.167

INRIM 232324 -0.738 1.432 -0.415 1.432 -0.618 1.432 -0.610 1.432 -0.528 1.432 -0.829 1.722 -1.494 1.722

INRIM B190 0.091 1.167 0.414 1.167 0.211 1.167 0.219 1.167 0.301 1.167 0.829 1.722 -0.665 1.509

INTiBS B178 0.756 1.167 1.079 1.167 0.876 1.167 0.884 1.167 0.966 1.167 1.494 1.722 0.665 1.509

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 18.571303 0.145 0.279 0.472 PTB 229075 18.570716 0.145 -0.308 0.472 NPL 221481 18.571139 0.145 0.115 0.472 NPL 221485 18.571036 0.145 0.012 0.472 VSL 226246 18.570927 0.145 -0.097 0.472


TKCVR / K

ucomp / mK

18.571024 0.186






PTB 229074 0.587 0.667 0.164 0.667 0.267 0.667 0.376 0.667 0.924 1.432 -0.098 1.167 -0.472 1.167

PTB 229075 -0.587 0.667

-0.423 0.667 -0.320 0.667 -0.211 0.667 0.337 1.432 -0.685 1.167 -1.059 1.167

NPL 221481 -0.164 0.667 0.423 0.667

0.103 0.667 0.212 0.667 0.760 1.432 -0.262 1.167 -0.636 1.167

NPL 221485 -0.267 0.667 0.320 0.667 -0.103 0.667

0.109 0.667 0.657 1.432 -0.365 1.167 -0.739 1.167

VSL 226246 -0.376 0.667 0.211 0.667 -0.212 0.667 -0.109 0.667 0.548 1.432 -0.474 1.167 -0.848 1.167

INRIM 232324 -0.924 1.432 -0.337 1.432 -0.760 1.432 -0.657 1.432 -0.548 1.432 -1.022 1.722 -1.396 1.722

INRIM B190 0.098 1.167 0.685 1.167 0.262 1.167 0.365 1.167 0.474 1.167 1.022 1.722 -0.374 1.509

INTiBS B178 0.472 1.167 1.059 1.167 0.636 1.167 0.739 1.167 0.848 1.167 1.396 1.722 0.374 1.509

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K

ucomp / mK

20.274906 0.186






PTB 229074 0.308 0.667 0.086 0.667 0.162 0.667 0.068 0.667 0.745 1.432 -0.169 1.167 -0.642 1.167

PTB 229075 -0.308 0.667

-0.222 0.667 -0.146 0.667 -0.240 0.667 0.437 1.432 -0.477 1.167 -0.950 1.167

NPL 221481 -0.086 0.667 0.222 0.667

0.076 0.667 -0.018 0.667 0.659 1.432 -0.255 1.167 -0.728 1.167

NPL 221485 -0.162 0.667 0.146 0.667 -0.076 0.667

-0.094 0.667 0.583 1.432 -0.331 1.167 -0.804 1.167

VSL 226246 -0.068 0.667 0.240 0.667 0.018 0.667 0.094 0.667 0.677 1.432 -0.237 1.167 -0.710 1.167

INRIM 232324 -0.745 1.432 -0.437 1.432 -0.659 1.432 -0.583 1.432 -0.677 1.432 -0.914 1.722 -1.387 1.722

INRIM B190 0.169 1.167 0.477 1.167 0.255 1.167 0.331 1.167 0.237 1.167 0.914 1.722 -0.473 1.509

INTiBS B178 0.642 1.167 0.950 1.167 0.728 1.167 0.804 1.167 0.710 1.167 1.387 1.722 0.473 1.509

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K

ucomp / mK

21.556378 0.186






PTB 229074 0.275 0.667 0.003 0.667 0.147 0.667 -0.109 0.667 0.670 1.432 -0.206 1.167 -0.557 1.167

PTB 229075 -0.275 0.667

-0.272 0.667 -0.128 0.667 -0.384 0.667 0.395 1.432 -0.481 1.167 -0.832 1.167

NPL 221481 -0.003 0.667 0.272 0.667

0.144 0.667 -0.112 0.667 0.667 1.432 -0.209 1.167 -0.560 1.167

NPL 221485 -0.147 0.667 0.128 0.667 -0.144 0.667

-0.256 0.667 0.523 1.432 -0.353 1.167 -0.704 1.167

VSL 226246 0.109 0.667 0.384 0.667 0.112 0.667 0.256 0.667 0.779 1.432 -0.097 1.167 -0.448 1.167

INRIM 232324 -0.670 1.432 -0.395 1.432 -0.667 1.432 -0.523 1.432 -0.779 1.432 -0.876 1.722 -1.227 1.722

INRIM B190 0.206 1.167 0.481 1.167 0.209 1.167 0.353 1.167 0.097 1.167 0.876 1.722 -0.351 1.509

INTiBS B178 0.557 1.167 0.832 1.167 0.560 1.167 0.704 1.167 0.448 1.167 1.227 1.722 0.351 1.509

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K

ucomp / mK

22.673744 0.186






PTB 229074 0.304 0.667 0.056 0.667 0.197 0.667 0.048 0.667 0.378 1.432 -0.144 1.167 -0.731 1.167

PTB 229075 -0.304 0.667

-0.248 0.667 -0.107 0.667 -0.256 0.667 0.074 1.432 -0.448 1.167 -1.035 1.167

NPL 221481 -0.056 0.667 0.248 0.667

0.141 0.667 -0.008 0.667 0.322 1.432 -0.200 1.167 -0.787 1.167

NPL 221485 -0.197 0.667 0.107 0.667 -0.141 0.667

-0.149 0.667 0.181 1.432 -0.341 1.167 -0.928 1.167

VSL 226246 -0.048 0.667 0.256 0.667 0.008 0.667 0.149 0.667 0.330 1.432 -0.192 1.167 -0.779 1.167

INRIM 232324 -0.378 1.432 -0.074 1.432 -0.322 1.432 -0.181 1.432 -0.330 1.432 -0.522 1.722 -1.109 1.722

INRIM B190 0.144 1.167 0.448 1.167 0.200 1.167 0.341 1.167 0.192 1.167 0.522 1.722 -0.587 1.509

INTiBS B178 0.731 1.167 1.035 1.167 0.787 1.167 0.928 1.167 0.779 1.167 1.109 1.722 0.587 1.509

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK





TKCVR / K

ucomp / mK

24.463897 0.186






PTB 229074 0.228 0.667 -0.009 0.667 0.215 0.667 -0.028 0.667 -0.226 1.432 -0.365 1.167 -0.763 1.167

PTB 229075 -0.228 0.667

-0.237 0.667 -0.013 0.667 -0.256 0.667 -0.454 1.432 -0.593 1.167 -0.991 1.167

NPL 221481 0.009 0.667 0.237 0.667

0.224 0.667 -0.019 0.667 -0.217 1.432 -0.356 1.167 -0.754 1.167

NPL 221485 -0.215 0.667 0.013 0.667 -0.224 0.667

-0.243 0.667 -0.441 1.432 -0.580 1.167 -0.978 1.167

VSL 226246 0.028 0.667 0.256 0.667 0.019 0.667 0.243 0.667 -0.198 1.432 -0.337 1.167 -0.735 1.167

INRIM 232324 0.226 1.432 0.454 1.432 0.217 1.432 0.441 1.432 0.198 1.432 -0.139 1.722 -0.537 1.722

INRIM B190 0.365 1.167 0.593 1.167 0.356 1.167 0.580 1.167 0.337 1.167 0.139 1.722 -0.398 1.509

INTiBS B178 0.763 1.167 0.991 1.167 0.754 1.167 0.978 1.167 0.735 1.167 0.537 1.722 0.398 1.509

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK



Thermometer Ti / K ui / mK Di / mK Ui / mK PTB 229074 24.944702 0.145 0.179 0.472 PTB 229075 24.944416 0.145 -0.107 0.472 NPL 221481 24.944445 0.145 -0.079 0.472 NPL 221485 24.944494 0.145 -0.029 0.472 VSL 226246 24.944560 0.145 0.037 0.472


TKCVR / K ucomp / mK 24.944523 0.186





PTB 229074 0.286 0.667 0.258 0.667 0.208 0.667 0.142 0.667 0.023 1.432 0.046 1.167 -0.530 1.167

PTB 229075 -0.286 0.667 -0.028 0.667 -0.078 0.667 -0.144 0.667 -0.263 1.432 -0.240 1.167 -0.816 1.167

NPL 221481 -0.258 0.667 0.028 0.667 -0.050 0.667 -0.116 0.667 -0.235 1.432 -0.212 1.167 -0.788 1.167

NPL 221485 -0.208 0.667 0.078 0.667 0.050 0.667 -0.066 0.667 -0.185 1.432 -0.162 1.167 -0.738 1.167

VSL 226246 -0.142 0.667 0.144 0.667 0.116 0.667 0.066 0.667 -0.119 1.432 -0.096 1.167 -0.672 1.167

INRIM 232324 -0.023 1.432 0.263 1.432 0.235 1.432 0.185 1.432 0.119 1.432 0.023 1.722 -0.553 1.722

INRIM B190 -0.046 1.167 0.240 1.167 0.212 1.167 0.162 1.167 0.096 1.167 -0.023 1.722 -0.576 1.509

INTiBS B178 0.530 1.167 0.816 1.167 0.788 1.167 0.738 1.167 0.672 1.167 0.553 1.722 0.576 1.509

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PTB

229

074

PTB

229

075

NPL

221

481

NPL

221

485

VSL

2262

46

INR

IM 2

3232

4

INR

IM B

190

INTi

BS

B17

8

Di

/ mK


Date post:	21-Feb-2020
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