NMISA - nla.org.za€¦ · Gold FP 1064,180 °C Silver FP 961,780 °C Aluminium FP 660,323 °C Zinc FP 419,527 °C Tin FP 231,928 °C Indium FP 156,5985 °C Gallium MP 29,7646 °C

NMISAFixed Point Cell Purity

Using OME, SIE and Liquidus Point

Analysis01 August 2017

Test & Measurement 2017

Overview

• NMISA temperature laboratory primary standards

• Example fixed point realisation and uncertainty budget

• Four methods to determine uncertainty due to chemical impurity of fixed point cell material

• Results

• Conclusion


ITS-90 Fixed Point Cells

Test & Measurement 2017 SPRT

Copper FP 1084,620 °C

Gold FP 1064,180 °C

Silver FP 961,780 °C

Aluminium FP 660,323 °C

Zinc FP 419,527 °C

Tin FP 231,928 °C

Indium FP 156,5985 °C

Gallium MP 29,7646 °C

Water TP 0,01 °C

Mercury TP -38,8344 °C

Argon TP -189,3442 °C

NMISA - Fixed Point Laboratory


Tin Realisation - 231,928 °C

0.467

0.469

0.471

0.473

0.475

0.477

0.479

0.481

0.483

0.485

0 1000 2000 3000 4000 5000

Re

sist

ance

Rat

io, Ω

/Ω

Time, s

Sn77 plateau

0.469403

0.469404

0.469405

0.469406

0.469407

0.469408

0.469409

0 1000 2000 3000 4000

Re

sist

ance

Rat

io, Ω

/Ω

Time, s

Sn77 plateau

Length: 13 hoursΔtslope: -0,17 mKuimpurities : 0,35 mK

*Estimate based on Representative Comparisons


Tin Realisation - 231,928 °CType A Uncertainty Artefact 1

Phase transition realization repeatability 0,058

Total A 0,058

Type B Uncertainty K3.4 - 136

Chemical Impurity 0,350

Hydrostatic_head 0,013

Reference resistor stability 0,033

Bridge repeatability 0,015

Bridge nonlinearity 0,121

Propagated TPW 0,222

SPRT self-heating 0,003

Heat flux 0,084

Gas pressure 0,010

Slope of plateu 0,048

Total B 0,444

Total B / SQRT(3) -

Combined standard uncertainty / mK 0,448

Expanded Uncertainty (k=2, using effective df) / mK

0,922

Type A Uncertainty Artefact 1

Phase transition realization repeatability 0,058

Total A 0,058

Type B Uncertainty K3.4 - 136

Chemical Impurity 0,110

Hydrostatic_head 0,013

Reference resistor stability 0,033

Bridge repeatability 0,015

Bridge nonlinearity 0,121

Propagated TPW 0,222

SPRT self-heating 0,003

Heat flux 0,084

Gas pressure 0,010

Slope of plateu 0,048

Total B 0,295

Total B / SQRT(3) -

Combined standard uncertainty / mK 0,301

Expanded Uncertainty (k=2, using effective df) / mK

0,641


4 Methods to deal with impurity uncertainty


Method Uimp ΔTimp Recommended by CCT WG1

Sum of Individual

Estimates (SIE) x x Yes

Overall Maximum

Estimate (OME) x Yes

Estimate based on

representative comparisons

(ERC)

x No

Thermal Analysis of

liquidus point x No

This is fully consistent with the GUM that calls for all measurements to be corrected for known bias or systematic effects” [1]

Sum of Individual Estimates (SIE)

• Only method that accounts for ΔT caused by the trace impurities

• Considers liquidus line slopes (mi) and their distribution coefficient (k0i)

of each impurity

ΔTSIE = Tpure – Tobs = -Σc11i.m1

i (1)

m1i = (ko

i-1)/A (2)

u2(ΔTSIE) = Σ [u(c11i).m1

i]2 + [c11i.u(m1

i)]2 (3)

Where, c11i = impurity concentration in mol fraction for each impurity

when the sample is completely melted and

A = the first cryoscopic constant.


Sum of Individual Estimates (SIE)

Challenges to using this method:

• Limitations of chemical analysis

• Knowledge of low-concentration liquidus line slopes are still being investigated

• Chemically analysed sample may not be representative of the ingot in the cell due to contamination during manufacture and use.

• Not recommended for <99,999% pure elements• Phase diagrams are only reliable for very pure samples

“The summation is over all impurities present in the liquid… Thus, the SIE method is in explicit accordance with the notion that the temperature of the fixed point should be corrected for the influence of impurities… This is fully consistent with the GUM that calls for all measurements to be corrected for known bias or systematic effects” [1]


SIE Example Impurity Certificate

*Detection limits of undetected impurities not listed


SIE Example Impurity Certificate...

*Detection limits of undetected impurities not listed


SIE Example Impurity Certificate...

*Consider recommended list of common impurities for Tin in the analysis [1]

* High detection limits; inclusion of these "elements in the uncertainty calculation would lead to an unphysically high uncertainty”[1]

xx

x

xx

x

x

x

x

xx

x

xx

xxxx


Overall Maximum Estimate (OME)

• Simpler method that can be applied to fixed point cells with a quoted purity eg; 99,9999% or to those with chemical assays

• Does not consider liquidus line slopes (mi) and the distribution coefficient (k0

i) of each impurity

ΔTOME = Tpure – Tobs = c11/A (4)

Where c11, the impurity mol fraction, can be calculated as either:

c11 = (1-(x%/100)), or (5)

c11 = -Σc11i (6)

u2(ΔTOME) = (ΔTOME)/3 (7)

“Even though OME provides and overall estimate for expected temperature change it should not be used to correct…. –ΔTOME to +ΔTOME

is equally likely” [1]


0.469403

0.469404

0.469405

0.469406

0.469407

0.469408

0.469409

0 1000 2000 3000 4000 5000

Re

sist

ance

Rat

io, Ω

/Ω

Time, s

Sn77 plateau

Estimate Based on Representative Comparisons (ERC) and Thermal Analysis

Length: 13 hoursΔtslope: -0,17 mK

uimp-ERC : 0,35 mKuimp-thermal : 0,11 mKuimp-OME : 0,21 mKuimp-SIE : 0,11 mK

F=1 F=0


Tin Realisation: 231,928 °C

Method Validation (SIE):Parameter NMISA Calculation Fellmuth and Hill [2]

Expected U(Purity) (mK): 0,169

ΔT(OME) (mK) 0,297 0,304

U(ΔTOME)(mK) 0,171 0,176

sum of k>=0.1 det imp. 3,49E-07

ΔTimp1,d (mK) 0,103 0,112

U(ΔTOME) (mK):k>=0.1 detected 0,060

sum of k>=0.1 undet imp. 3,42E-07

ΔTimp1,u (mK) 0,101 0,101

U(ΔTOME) (mK):k>=0.1 undetected 0,058

sum of k<0.1 imp. 3,11E-07

ΔTimp1,d + ΔTimp1,u (mK) 0,092 0,091

U(ΔTOME) (mK):k<0.1 0,053

ΔTSIE (mK) -0,131 -0,124

U(ΔTSIE) (mK) 0,067 0,065

Fixed Point: Tin

Purity: 99,999 99%

0.000

0.002

0.004

0.006

0.008

U(ΔTOME)(mK)

Dif

fere

nce

, mK

U(ΔTOME)(mK) U(ΔTSIE) (mK) ΔTSIE (mK)

Results


Fixed points analysed:

2 x Mercury, 1 x Gallium, 4 x Tin, 2x Zinc, 2 x Aluminium, 4 x Silver, 3 x Copper

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-40 60 160 260 360 460 560 660 760 860 960 1060

Un

cert

ain

ty, m

K

Temperature, °C

NMISA Chem Imp U@K=1Manufacturer's Plot Thermal analysis (F0,5-F1)Expected U(Purity) (mK):U(ΔTOME)(mK)U(ΔTSIE) (mK)

No impurities detected!

Same fixed point cell shares two chemical certificates

Conclusion

• Uncertainty Estimation based on Representative Comparisons (ERS) is not ideal and results in unnecessarily larger uncertainty

• Uncertainty based on thermal analysis is useful, especially for cell certifications

• OME method based on just the percent purity of the sample agrees with the other methods and is especially suitable for when certificates of impurity analysis is not available

• The detailed OME and SIE methods require certificates of impurity analysis which is often unavailable, especially for older legacy cells. These are the preferred methods as they can account for the detection limits of undetected impurities.

References[1] B. Fellmuth, et al, Guide to the Realization of the ITS-90 – Fixed Points:

Influence of Impurities, 2015, Consultative Committee for Thermometry (CCT) -Working Group 1 (CCT-WG1), International Committee for Weights and Measures (CIPM), The Bureau International des Poids et Mesures (BIPM)

[2] B. Fellmuth and KD Hill, Estimation of influence of impurities on the freezing of Tin, Metrologia 43 (2006), pg’s 71-83

Documents

NMISA - nla.org.za€¦ · Gold FP 1064,180 °C Silver FP 961,780 °C Aluminium FP 660,323 °C Zinc FP 419,527 °C Tin FP 231,928 °C Indium FP 156,5985 °C Gallium MP 29,7646 °C