Standard Platinum Resistance 

Thermometer Calibrations from the 

Ar TP to the Ag FP

G. F. Strouse

NIST Special Publication 250-81
ii

NIST Special Publication 250-81

Standard Platinum Resistance 

Thermometer Calibrations from the 

Ar TP to the Ag FP

G. F. Strouse

Chemical Science and Technology Laboratory

Process Measurements Division

Thermometry Group

January 2008

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

 National Institute of Standards and Technology

James M. Turner, Deputy Director
Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 250-81

Natl. Inst. Stand. Technol. Spec. Publ. 250-81, 79 pages (2008)

CODEN: NSPUE2
Errata



A single-digit misprint was found in Coefficient A5 in Table 3, printed as -0.61893395 instead of 

-0.61899395. This publication has been corrected from the original published version of January 

2008.)HEUXDU\FRUUHFWLRQ
iv

1 Introduction ............................................................................................................................. 1

2 ITS-90 Overview (Ar TP to Ag FP) ....................................................................................... 1

2.1 ITS-90 equations ............................................................................................................. 2

2.2 ITS-90 thermometer specifications ................................................................................. 4

3 Description of Services ........................................................................................................... 4

3.1 Types of thermometers calibrated ................................................................................... 4

3.2 Calibration temperature ranges ....................................................................................... 5

3.3 Selecting a calibration temperature range ....................................................................... 7

3.4 Requesting an SPRT calibration ..................................................................................... 7

3.5 Guide for shipping SPRTs .............................................................................................. 7

3.6 Turn-around time ............................................................................................................ 8

3.7 ISSC database ................................................................................................................. 8

3.8 Rejected SPRTs .............................................................................................................. 8

3.9 Special Tests / Requests .................................................................................................. 9

4 Calibration System Overview ................................................................................................. 9

4.1 Calibration process.......................................................................................................... 9

4.2 Fixed point cells ............................................................................................................ 14

4.2.1 Fixed-point cell specifications .............................................................................. 14

4.2.2 ITS-90 fixed-point cell corrections ....................................................................... 18

4.3 Fixed-point cell maintenance systems .......................................................................... 20

4.3.1 Liquid baths .......................................................................................................... 20

4.3.2 Furnaces ................................................................................................................ 20

4.3.3 Maintenance system thermal characteristics ......................................................... 21

4.4 SPRT measurement system........................................................................................... 24

4.5 Measurement software .................................................................................................. 25

5 ITS-90 SPRT Calibration Methods ....................................................................................... 25

5.1 SPRT stabilization methods .......................................................................................... 25

5.2 Calibration by fixed points............................................................................................ 27

5.2.1 Ag FP .................................................................................................................... 27

5.2.2 Al FP ..................................................................................................................... 28

5.2.3 Zn FP ..................................................................................................................... 29

5.2.4 Sn FP ..................................................................................................................... 30

5.2.5 In FP ...................................................................................................................... 31

5.2.6 Ga TP .................................................................................................................... 32

5.2.7 TPW (H2O TP) ...................................................................................................... 33

5.2.8 Hg TP .................................................................................................................... 35

5.2.9 Ar TP ..................................................................................................................... 36

5.3 Calibration report .......................................................................................................... 37

5.4 On receipt of a NIST calibrated SPRT ......................................................................... 37

5.5 Determining the SPRT re-calibration interval .............................................................. 37

6 Internal Measurement Assurance .......................................................................................... 38

6.1 Fixed-point cell element ............................................................................................... 39

6.1.1 Sample purity parameter ....................................................................................... 39

6.1.2 Phase transition repeatability parameter ............................................................... 41
v

6.1.3 Constant cell pressure parameter .......................................................................... 41

6.1.4 Cell corrections parameter .................................................................................... 41

6.1.5 Design/Assembly parameter ................................................................................. 41

6.2 Furnace/Maintenance system element .......................................................................... 41

6.2.1 Vertical gradient parameter................................................................................... 41

6.2.2 Set-point control parameter................................................................................... 41

6.2.3 Fixed-point cell interaction parameter .................................................................. 42

6.3 SPRT element ............................................................................................................... 42

6.3.1 Heat-flux parameter .............................................................................................. 42

6.3.2 Immersion depth parameter .................................................................................. 43

6.3.3 Self-heating parameter .......................................................................................... 43

6.3.4 Stability parameter ................................................................................................ 43

6.3.5 Wetness parameter ................................................................................................ 44

6.3.6 Contamination parameter ...................................................................................... 44

6.3.7 Light-Piping parameter ......................................................................................... 44

6.4 Measurement system element ....................................................................................... 45

6.4.1 Repeatability parameter ........................................................................................ 45

6.4.2 Non-Linearity parameter ....................................................................................... 45

6.4.3 Ratio-error parameter ............................................................................................ 45

6.4.4 Ohm parameter...................................................................................................... 45

6.4.5 AC quadrature parameter ...................................................................................... 46

6.4.6 Current parameter ................................................................................................. 46

6.4.7 Number of readings parameter.............................................................................. 46

6.4.8 Validating resistance ratio bridges ........................................................................ 46

6.5 Realization technique .................................................................................................... 48

6.5.1 Duration of a realization curve parameter ............................................................ 48

6.5.2 SPRT immersion profile parameter ...................................................................... 48

6.6 SPRT calibration measurement assurance element ...................................................... 48

6.6.1 Check SPRT parameter ......................................................................................... 49

6.6.2 Fixed-point cell certification parameter ................................................................ 49

6.6.3 SPRT calibration results parameter ...................................................................... 50

6.6.4 External comparison parameter ............................................................................ 50

7 ITS-90 Uncertainties ............................................................................................................. 50

7.1 Fixed-point cell realization uncertainties ...................................................................... 51

7.2 Propagated fixed-point uncertainty for each ITS-90 temperature subrange ................. 53

7.3 ITS-90 non-uniqueness uncertainty contribution to SPRT calibration uncertainties ... 58

7.4 SPRT calibration uncertainty for each ITS-90 temperature subrange .......................... 58

7.5 Extrapolation uncertainty for selected ITS-90 temperature subranges ......................... 59

7.6 Temperature measurement uncertainty of a calibrated SPRT ...................................... 60

8 Quality System ...................................................................................................................... 60

9 References ............................................................................................................................. 61

10 Appendix ............................................................................................................................... 66
1

1 Introduction 

The National Institute of Standards and Technology (NIST) is in charge of realizing, 

maintaining, and disseminating the International Scale of 1990 (ITS-90) [1-5]. The Standard 

Platinum Resistance Thermometer (SPRT) Calibration Laboratory of the NIST Thermometry 

Group realizes the ITS-90 from the argon triple point (Ar TP, –189.3442 °C) to the silver 

freezing point (Ag FP, 961.78 °C) for the calibration of SPRTs. This special publication 

describes the calibration services, methods, measurement assurance, and uncertainties for the 

NIST ITS-90 calibration of SPRTs. The calibration of SPRTs below the Ar TP is performed in 

the NIST Low Temperature Calibration Facility (LTCF) and the calibration services are 

described in [6].

2 ITS-90 Overview (Ar TP to Ag FP)

The ITS-90 defines temperature through a set of specified thermometric fixed points, 

interpolation instruments, and interpolation equations [3]. Over the range from the Ar TP to the 

Ag FP, the interpolation instrument is a platinum resistance thermometer constructed with a 

strain-free platinum resistance element and meeting certain performance criteria. 

 

The ITS-90 is realized in the SPRT Laboratory entirely by fixed points over the range from the 

Ar TP to the Ag FP. Table 1 lists the ITS-90 fixed-point cells used to calibrate SPRTs. 

Calibration results obtained at a subset of the fixed points are used to determine the coefficients 

of deviation functions. Together with the SPRT reference functions, the deviation functions 

fully specify the resistance ratio versus temperature relationship of the SPRT over the full range 

of calibration. SPRTs meeting the requirements of the ITS-90 become ITS-90 defining 

interpolating instruments over the range of calibration. 

Table 1. ITS-90 fixed points used in the NIST SPRT Laboratory 

ITS-90 Fixed Point T, K t, °C

Ar TP 83.8058 –189.3442

Hg TP 234.3156 –38.8344

TPW (H2O TP) 273.16 0.01

Ga TP* 302.9166 29.7666

In FP 429.7485 156.5985

Sn FP 505.078 231.928

Zn FP 692.677 419.527

Al FP 933.473 660.323

Ag FP 1234.93 961.78

TP = triple point, FP = freezing point 

*For a smaller realization uncertainty, NIST realizes the Ga TP instead of the Ga MP [7,8]. 
2

2.1 ITS-90 equations 

For the temperature range of the SPRT Laboratory, the ITS-90 uses the two reference functions 

and eight deviation functions to cover eight temperature subranges. Table 2 shows the eight 

temperature subranges, required fixed points and the pertinent deviation functions for SPRTs 

calibrated in the NIST SPRT Laboratory. 

Table 2. ITS-90 temperature subranges, required fixed points and deviation functions for SPRTs 

calibrated in the NIST SPRT Laboratory. 

Temperature 

Subrange, °C

Required Fixed 

Points Deviation Function

–189.3442 to 0.01 Ar TP, Hg TP, 

TPW

4

     4 1–1– lnWWbWaW

–38.8344 to 

29.7646

Hg TP, TPW,

Ga TP

   2

5  5 WbWaW 1–1–

0 to 29.7646 TPW, Ga TP

 11  WaW 1–

0 to 156.5985 TPW, Ga TP, 

In FP

 10   WaW 1–

0 to 231.928 TPW, In FP, Sn 

FP

   2

9  9 WbWaW 1–1–

0 to 419.527 TPW, Sn FP, Zn 

FP

   2

8  8 WbWaW 1–1–

0 to 660.323 TPW, Sn FP, Zn 

FP, Al FP

     3

7

2

7  7  WcWbWaW 1–1–1–

0 to 961.78

TPW, Sn FP, Zn 

FP, Al FP, 

Ag FP

         

3 2

6

2

6  6   –1–1–1– WWdWcWbWaW 660.323 C

Note. NIST added subscripts to the ITS-90 coefficients as a means to easily identify the 

calibration range of the SPRT [3]. 

The resistance ratio W is defined as W = R(T90) / R(273.16 K), where R(T90) is the measured 

SPRT resistance or resistance ratio at the specified temperature and R(273.16 K) is the measured 

SPRT resistance or resistance ratio at the triple point of water [TPW, (273.16 K)]. For the 

deviation functions, 

ΔW = W – Wr

where Wr is defined by the reference functions. 

The reference function for the temperature subrange from the Ar TP to the TPW (189.3442 °C 

to 0.01 °C) is defined as: 

      



12

1

)ln( 0rln 90 273.16 5.15.1K

i

i

i TAAW
3

where the ITS-90 defined reference function coefficients A0 and Ai are given in Table 3. The 

approximate inverse function is specified as: 

  .0– 65 .0 35 K273.16x

15

1

61

90 0 















 

i

i

WBBT ri

where the error in the use of the inverse functions is ±0.1 mK. The ITS-90 defined inverse 

function coefficients B0 and Bi are given in Table 3. 

The reference function for the temperature subrange range from 0 °C to the Ag FP (0 °C to 

961.78 °C) is defined as: 

    



9

1

0r 90 –754. 48115

i

i

i TCCW

where the ITS-90 defined reference function coefficients C0 and Ci are given in Table 3. The 

approximate inverse function is specified as: 

  r

.2– 64 .1  27364 .15K

9

1

90 0   



i

i

i WDDT

where the error in the use of the inverse functions is ±0.13 mK. The ITS-90 defined inverse 

function coefficients D0 and Di are given in Table 3. 

Further and detailed information on the mathematics of the ITS-90 is found in reference 3. 

Table 3. Coefficients for the ITS-90 reference functions and approximate inverse functions. 

Reference Function

Coefficients for

T90  273.16 K

Approximate Inverse 

Function Coefficients for

T90  273.16 K

Reference Function

Coefficients for

T90  273.15 K

Approximate Inverse 

Function Coefficients for

T90  273.15 K

A0 –2.135 347 29 B0 0.183 324 722 C0 2.781 572 54 D0 439.932 854

A1 3.183 247 20 B1 0.240 975 303 C1 1.646 509 16 D1 472.418 020

A2 –1.801 435 97 B2 0.209 108 771 C2 –0.137 143 90 D2 37.684 494

A3 0.717 272 04 B3 0.190 439 972 C3 –0.006 497 67 D3 7.472 018

A4 0.503 440 27 B4 0.142 648 498 C4 –0.002 344 44 D4 2.920 828

A5 –0.618 993 95 B5 0.077 993 465 C5 0.005 118 68 D5 0.005 184

A6 –0.053 323 22 B6 0.012 475 611 C6 0.001 879 82 D6 –0.963 864

A7 0.280 213 62 B7 –0.032 267 127 C7 –0.002 044 72 D7 –0.188 732

A8 0.107 152 24 B8 –0.075 291 522 C8 –0.000 461 22 D8 0.191 203

A9 –0.293 028 65 B9 –0.056 470 670 C9 0.000 457 24 D9 0.049 025

A10 0.044 598 72 B10 0.076 201 285

A11 0.118 686 32 B11 0.123 893 204

A12 –0.052 481 34 B12 –0.029 201 193

B13 –0.091 173 542

B14 0.001 317 696

B15 0.026 025 526
4

2.2 ITS-90 thermometer specifications 

The ITS-90 gives specifications on the purity of the platinum (Pt) used for the sensor element for 

an ITS-90 defining PRT. Note that the ITS-90 does not use the word “standard” to identify 

ITS-90 defining PRTs, but NIST uses the words “standard”, “industrial”, and “miniature” to 

differentiate between a thermometer that meets ITS-90 specifications (e.g. SPRT) and one that 

does not {e.g., industrial PRT (IPRT) or miniature PRT (MPRT)[9]}. 

For temperatures below 661 °C, the ITS-90 requires that: 

W(Ga MP)  1.118 07, or W(Hg TP)  0.844 235. 

For temperatures from 661 °C to 962 °C, the ITS-90 requires that: 

W(Ag FP)  4.2844. 

Additionally, the ITS-90 states that the Pt sensor coil be strain free. 

The NIST SPRT Calibration Laboratory adds other requirements for the SPRT, such that the Pt 

sensor coil is of four-wire, non-inductively wound construction and that R(TPW) is stable prior 

to and during calibration. The R(TPW) stability requirements (Section 6.7.3) are measurement 

assurance criteria chosen to ensure that calibrated SPRT meets the stated NIST ITS-90 

realization uncertainties. 

3 Description of Services 

3.1 Types of thermometers calibrated 

There are three main types of SPRTs calibrated in the NIST SPRT Laboratory: long-stem 

(LSPRT), capsule (CSPRT), and high-temperature (HTSPRT). The specific SPRT type 

designation is used in this document when that specific type needs to identified, otherwise the 

general identifier of SPRT is used. Limitations on the allowed calibration range differ as a 

function of thermometer design. 

In order to fit the NIST fixed-point cells, the diameter of the SPRT sheath must be less than 

8 mm or LSPRTs and less than 10 mm for CSPRTs. In general, most LSPRTs and CSPRTs are 

nominally 25.5 Ω at the TPW. HTSPRTs are nominally 2.5 Ω or 0.25 Ω. However, in practice 

the SPRT range of resistance at the TPW is as large as ±10 %.

Table 4 gives the ITS-90 temperature range of use for an SPRT (all three types) for each 

combination of nominal resistance at the TPW, sheath material, and sensor support material. The 

sensor coil design (e.g. single-layer bifilar) does not impact the usable temperature range of an 

SPRT. Table 4 covers most commercially-available SPRTs, but is not considered all inclusive as 

there other non-commercial specialized or prototype SPRTs that can be calibrated at NIST on 

request. 
5

Table 4. ITS-90 temperature range suitable for NIST calibration of an SPRT, for each 

combination of nominal resistance at the TPW, sheath material, and sensor support material. 

Nominal

R(TPW), Ω

Sheath 

Material

Sensor 

Support 

Material

Lowest ITS-90 

Fixed-Point

Highest ITS-90 

Fixed-Point

Temperature 

Range of Use, 

°C

25.5

Borosilicate Mica Ar TP Zn FP

–200 to 500

Fused silica

Mica Ar TP Zn FP

Fused silica Ar TP Al FP –200 to 661 Ceramic

Stainless 

Steel Ceramic Ar TP Zn FP –200 to 500

Inconel® Ceramic Ar TP Al FP –200 to 661

2.5 Fused silica Fused silica TPW Ag FP

0 to 962

0.25 Fused silica Fused silica TPW Ag FP

3.2 Calibration temperature ranges 

Table 5 lists the various combinations of ITS-90 temperature subranges for the calibration of 

SPRTs, as offered by the NIST SPRT Calibration Laboratory. These calibration ranges are 

identified by NIST Service ID numbers. Additionally, Table 5 includes the maximum 

temperature range that the calibration is valid; this includes allowable extrapolation of specific 

subranges (range of use). 
6

Table 5. NIST calibration schedule for SPRT calibrations from the Ar TP to the Ag FP.

Service ID No. SPRT Type ITS-90 

coefficients

ITS-90

Fixed Points

Range of Use,

°C

33065S

Capsule SPRT

a4, b4 Ar TP, Hg TP, TPW –200 to 1

33070C a4, b4

a11

Ar TP, Hg TP,

TPW, Ga TP –200 to 30

33080C a4, b4

a10

Ar TP, Hg TP,

TPW, In FP –200 to 157

33090C a4, b4

a9, b9

Ar TP, Hg TP, TPW,

In FP, Sn FP –200 to 232

33100C a11 TPW, Ga TP 0 to 30

33110C a10 TPW, In FP 0 to 157

33120C a9, b9 TPW, In FP, Sn FP 0 to 232

33130C a5, b5 Hg TP, TPW, Ga TP –39 to 30

33150C

Long-Stem

SPRT

a4, b4 Ar TP, Hg TP, TPW –200 to 1

33160C a4, b4

a11

Ar TP, Hg TP,

TPW, Ga TP –200 to 30

33170C a4, b4

a10

Ar TP, Hg TP,

TPW, In FP –200 to 157

33180C a4, b4

a9, b9

Ar TP, Hg TP, TPW,

In FP, Sn FP –200 to 232

33190C a4, b4

a8, b8

Ar TP, Hg TP, TPW,

Sn FP, Zn FP –200 to 500

33200C a4, b4

a7, b7, c7

Ar TP, Hg TP, TPW, Sn 

FP, Zn FP, Al FP –200 to 661

33210C a5, b5 Hg TP, TPW, Ga TP –39 to 30

33220C a5, b5

a10

Hg TP, TPW,

Ga TP, In FP –39 to 157

33230C a5, b5

a9, b9

Hg TP, TPW, Ga TP,

In FP, Sn FP –39 to 232

33240C a5, b5

a8, b8

Hg TP, TPW, Ga TP, 

Sn FP, Zn FP –39 to 500

33250C a5, b5

a7, b7, c7

Hg TP, TPW, Ga TP,

Sn FP, Zn FP, Al FP –39 to 661

33260C a11 TPW, Ga TP 0 to 30

33270C a10 TPW, In FP 0 to 157

33280C a9, b9 TPW, In FP, Sn FP 0 to 232

33290C a8, b8 TPW, Sn FP, Zn FP 0 to 500

33300C

Long-Stem or 

High-Temperature 

SPRT

a7, b7, c7

TPW, Sn FP,

Zn FP, Al FP 0 to 661

33310C High Temperature 

SPRT a6, b6, c6, d

TPW, Sn FP, Zn FP, 

Al FP, Ag FP 0 to 962
7

The cost of a calibration changes yearly, occurring normally in February. The current calibration 

costs may be found within the NIST Technology Services webpages 

http://ts.nist.gov/MeasurementServices/Calibrations/resistance__thermometry.cfm 

or within the NIST Thermometry Group webpages 

http://www.cstl.nist.gov/div836/836.05/thermometry/calibrations/fees.htm#sprt.

3.3 Selecting a calibration temperature range 

The ITS-90 was designed with the flexibility to allow for the user to choose the minimum 

temperature range of calibration. Two ITS-90 temperature subranges, one below 0.01 °C and one 

above 0 °C, may be combined for calibrating and using an SPRT over the required temperature 

range of use. For those overlapping temperature subranges, the user of the SPRT should choose 

the smallest temperature range of need. All ITS-90 temperature subranges that overlap are 

considered to be equally valide for the determination of temperature, but with different 

uncertainties (See section 7). The non-uniqueness uncertainty from different overlapping 

temperature subranges is not significant and is discussed in section 7.3 and references 10-12. 

The most commonly selected calibration range for SPRTs is from the Ar TP to either the Zn FP 

or the Al FP. For those users interested in measuring temperature near room temperature, the 

range from 0 °C to the Ga TP is normally selected. 

3.4 Requesting an SPRT calibration 

The customer should include the following information on the purchase order: 

 1) Calibration service ID 

 2) SPRT number and manufacturer 

 3) SPRT serial number 

 4) R(TPW) value at 1 mA as measured before shipping 

 5) Special instructions regarding the name on the Report of Calibration, if any 

 6) Technical contact 

 7) Return shipping address 

 8) Return shipping method and account number 

 9) Shipping insurance requirement 

Additionally, if the SPRT does not require stabilization (e.g. annealing), the customer should 

specify accordingly. 

3.5 Guide for shipping SPRTs 

SPRTs may either be hand carried or shipped to NIST. In the case of hand carrying, the person 

delivering the SPRT should contact the NIST technical contact several days prior to their arrival. 

This will allow the NIST technical contact to secure a gate pass. In the case of a non-US citizen, 

the person should contact the NIST technical contact at least two weeks prior to arrival. 
8

The shipped SPRT should be packed in a suitable container, such that the SPRT should be softly 

supported within a case but not be free to rattle. This necessitates the use of packing material that 

does not become compacted. The SPRT case should be softly packed inside a shipping container, 

with at least 5 cm of resilient packing material surrounding the SPRT case on all sides. The 

shipping container must be sufficiently rigid and strong that it will not appreciably deform under 

the treatment usually given by common carriers. Styrofoam is not sufficiently rigid to be used as 

an outside container. Similarly, mailing tubes are unacceptable. Thermometers will not be 

returned in containers that are obviously unsuitable, such as those closed by nailing. Suitable 

containers will be provided when a thermometer shipping container is not satisfactory for re–use. 

3.6 Turn-around time 

The turn-around time for an SPRT calibration is a function of the calibration range, the amount 

of time required to stabilize the SPRT (if required), the existing backlog, and the time of year 

(e.g. vacation, holidays). On average, the turn-around time is about six weeks from the time the 

SPRT and purchase order arrive at NIST to the time the SPRT and Report of Calibration is 

shipped. Work on an SPRT will not commence until a valid purchase order and SPRT are both 

at NIST. However, the customer may call the NIST technical contact to arrange a delivery date 

to match with an upcoming calibration batch in an attempt to minimize the turn-around time. 

3.7 ISSC database 

Within NIST, all calibrations are entered into the Information System to Support Calibrations 

(ISSC) database. The customer can use the ISSC Customer Access Pages that exist outside of the 

NIST firewall to check the calibration status or other measurement service from the Internet via a 

web browser. On the NIST Acceptance Form (NIST-64, Test Record, Acceptance) that is sent 

back to the customer on NIST acceptance of the customer’s request for calibration, to the right of 

the "Estimated Completion Date" is the web address to review the calibration status. Also given 

is the unique username/password that is needed to access the information. The customer is 

provided status information only about the calibration listed and no other. NIST does not provide 

proprietary information over the web, and access any other customer’s information is blocked. 

The calibration status or other measurement service is available on the web site for 60 days after 

the service is completed. (No other information other than status is available on this web site.) 

Additionally, the Acceptance Form indicates the estimated turnaround time and cost, as well as 

the NIST technical contact information. 

3.8 Rejected SPRTs 

SPRTs may be rejected for one of several reasons: the SPRT can not fit in the NIST equipment 

(e.g. bowed metal sheath), the SPRT is unstable, or the SPRT is missing leads. For customers, 

whose SPRTs either fail the stabilization process or the internal measurement assurance criteria, 

a small fee is charged under Service ID 33340C. 
9

3.9 Special Tests / Requests 

Arrangements for special tests or requests outside of the calibration services listed in Table 5 

should be made with the NIST technical contact. Special tests include, but are not limited to, the 

testing or calibration of prototype thermometers, specially-designed thermometers, thermometer 

systems, resistance ratio bridges, and fixed-point cells. The validation testing of resistance ratio 

bridges is described in [13]. The certification testing of fixed-point cells is described in [14].

4 Calibration System Overview 

4.1 Calibration process 

The calibration of SPRTs using ITS-90 fixed-point cells in the SPRT Calibration Laboratory is a 

five step process consisting of the following: login SPRT, stabilization, calibration, analysis of 

results, and logout SPRT. Figure 1 shows a simplified flowchart of the SPRT calibration process. 

Figure 1. Simplified flowchart showing the five main steps for an SPRT calibration. 

First, the arrival of an SPRT with a purchase order allows the SPRT to be logged into both the 

SPRT Calibration Laboratory database and the ISSC database. The purchase order and SPRT 

must both be at NIST before calibration work can be initiated. Figure 2 shows a simplified 

flowchart of the login process. 

The integrity of the SPRT is checked during the login process (e.g. inspection of the condition of 

the glass sheath and sensor coil for glass sheath SPRTs, inspection of the condition of the 

Step 1:

Login SPRT

Step 2:

Stabilize SPRT

Step 3:

Calibrate SPRT

Step 4:

Analysis of Results

Step 5:

Logout SPRT
10

external wire leads and connectors, and measurement of the insulation resistance for metal 

sheathed SPRTs). During the login process, a unique 4-digit code (NIST ID) is assigned to the 

SPRT that is used to identify the SPRT throughout the calibration process as well as for 

historical record. The NIST ID is useful when discussing the results of a calibration with NIST 

technical staff. Additionally, the SPRT is assigned a batch code to identify the SPRTs being 

calibrated within a given batch. Up to five SPRTs may be calibrated within a batch. 

Figure 2. Simplified flowchart of the Login SPRT step.

Second, the SPRT undergoes stabilization before calibration. Figure 3 shows a simplified 

flowchart of the stabilization process. The stabilization process is achieved through the annealing 

of the Pt sensor for a specific amount of time at a specific temperature. The amount of time and 

temperature are based on the range of calibration. Section 5.1 details the NIST stabilization 

process. To qualify for calibration, the SPRT resistance must repeat at the TPW to within the 

equivalent of 0.2 mK when comparing the pre- and post-anneal R(TPW) values. The SPRT must 

stabilize to the 0.2 mK criterion within five anneal cycles or the SPRT is rejected for calibration.

The “as received” RA(TPW), prior to stabilization, is compared with the last measured historical 

NIST RH(TPW) value (if it exists) and the customer supplied RC(TPW) value (if supplied by the 

customer). If the difference between either the historical NIST or customer supplied R(TPW) 

value is greater than the “as received” RA(TPW) value by more than the equivalent of 10 mK, 

then the customer is called to discuss the treatment of their SPRT [15,16]. 

Step 1:

Login SPRT

Information Entered

 Company Addresses

 Company Technical Contact

 SPRT

 NIST Service ID

 Calibration Batch Code

 Customer RC(TPW) at 1 mA

Information Assigned

 NIST ID

 NIST Test Folder Number
11

Figure 3. Simplified flowchart of the stabilization procedure for the Stabilize SPRT step.

Third, an SPRT is calibrated from the highest to lowest required fixed-point temperature. 

Figure 4 shows a simplified flowchart of the calibration measurement pattern for a batch of 

SPRTs calibrated from the Al FP to the Ar TP. The SPRT under test is always measured at the 

TPW after any other fixed point, so that the W(t90) can be calculated and used in step four. Note 

that the Ga TP and In FP are always measured when the SPRT is calibrated over a temperature 

range that includes those fixed points. These redundant points provide a measure of the SPRT 

non-uniqueness and calibration error, which is later used an internal measurement assurance 

validation step in the calibration process (see Section 6.7.3) [17,18]. 

A dedicated check SPRT is used to measure the beginning of the plateau of the appropriate fixed 

point, then the batch of SPRTs under test are measured successively, and finally the check SPRT 

is re-measured at the fixed point. The check SPRT results are used as a total system check on the 

ITS-90 realization process. The maximum allowable changes in the check SPRT values 

[W2(SPRTcheck) – W1(SPRTcheck)] / (dW/dT90) during a fixed-point realization for SPRT 

calibration are given in Table 6. The maximum allowable change during a realization and 

between realizations is chosen to meet the stated fixed-point realization uncertainties. The data 

acquisition software only accepts data for customer SPRTs when the corresponding SPRT checkstandard data passes those criteria given in Table 6. 

Step 2:

Stabilize SPRT

Compare

“as received” RA(TPW) 

with

historical and customer 

R(TPW) values

ΔR(TPW) > 10 mK

Call Customer

Anneal

SPRT

Measure

“as received”

RA(TPW)

Measure

R(TPW)

ΔR(TPW)  0.2 mK

Continue to

ΔR(TPW) < 0.2 mK Step 3: Calibration

Anneal cycle number

n > 5

Reject SPRT
12

Figure 4. Simplified flowchart showing the SPRT calibration measurement pattern used during 

the Calibrate SPRT step.

Table 6. The maximum allowable change in the check SPRT values [W2(SPRTcheck) –

W1(SPRTcheck)] / (dW/dT90) during a fixed-point realization for SPRT calibration. 

ITS-90 Fixed Point Maximum allowable 

change, mK ITS-90 Fixed Point Maximum allowable change, mK

Ag FP 0.3 In FP 0.05

Al FP 0.2 Ga TP 0.02

Zn FP 0.2 Hg TP 0.05

Sn FP 0.1 Ar TP 0.03

Step 3:

Calibrate SPRT

Measure

R(Zn), R(TPW)

Measure

R(Sn), R(TPW)

Measure

R(Ar), R(TPW)

Measure

R(Al), R(TPW)

Measure

R(Hg), R(TPW)

Measure

R(In), R(TPW)

Measure

R(Ga), R(TPW)

Batch Measurement Pattern:

Check SPRT

SPRTs under test

Check SPRT

Continue to

Step 4: Analysis of Results
13

Fourth, the calibration results from Step 3, using the required W(t90) values for the calibration 

range, are used to calculate the ITS-90 deviation function coefficients. Figure 5 shows a 

simplified flowchart of the analysis-of-results process. The internal measurement assurance 

criteria checks are applied to the calibration results as described in Section 6.7.3.

Figure 5. Simplified flowchart showing the Analysis of Results Step. 

Fifth, the SPRT logged out process is initiated by generating the Report of Calibration. Figure 6 

shows a simplified flowchart of the SPRT logout process. The authorized signatory must sign the 

Report of Calibration before the SPRT may be returned to the customer. Unless specified 

differently by the customer, the SPRT and Report of Calibration are returned together to the 

shipping address given in the purchase order. 

Figure 6. Simplified flowchart showing the Logout SPRT step. 

Step 4:

Analysis of Results

SPRT results fail measurement 

assurance criteria

Go to

Step 2: Stabilization

(two calibration cycles permitted 

before SPRT rejection)

Calculate:

W(T90) values

ITS-90 deviation function coefficients

Apply internal measurement assurance criteria checks

SPRT results pass internal

measurement assurance criteria

Continue to 

Step 5: Generate Report of Calibration

Step 5:

Logout SPRT

Print Report of 

Calibration

Check Report of Calibration for 

accuracy of information

Return SPRT and signed Report 

of Calibration to customer
14

4.2 Fixed point cells 

All NIST-fabricated fixed-point cells contain appropriate substances of the highest available 

purity (>99.9999 % pure) [5,19,20]. A minimum of three reference cells for each fixed-point is 

available for use in the SPRT Calibration Laboratory. The freezing-point cells are “open” cells 

connected to an oil-free vacuum and gas handling system. The triple-point cells are either sealed, 

or in the case of the Ga TP connected to an oil free turbo-molecular vacuum system. The 

immersion depth for a NIST fixed-point cell is defined as the distance from the SPRT sensor 

mid-point to the top of the column of sample during the realization of that fixed point. A general 

description of each fixed-point cell is given in the text below. 

4.2.1 Fixed-point cell specifications 

As seen in Figure 7, the NIST-fabricated Ar TP cell accommodates up to seven LSPRTs from 

the top and up to six CSPRTs from the bottom of the cell [21]. A special CSPRT holder [22] 

with an outer diameter of 12 mm can be used to measure an CSPRT in the 13 mm inner diameter 

center well. The apparatus contains about 19.7 moles of liquid Ar (99.9999 mol% pure) with 

about 15.7 moles condensed into the cell giving the SPRTs an immersion depth of 10.9 cm. 

Helium gas is placed in the seven top-loading thermometer wells to increase the thermal contact 

of the SPRTs with Ar TP. 

Figure 7. NIST Ar TP cell. 

As shown in Figure 8, the Hg TP cell is realized in a NIST-fabricated all-stainless-steel cell 

[11,20,23,24]. A stainless-steel, insulation-filled, outer jacket holds the cell to increase the depth 

of the cell in the maintenance bath. Additionally, during the realization of the Hg TP, the outer 

jacket is evacuated to isolate the cell from temperature fluctuations in the maintenance bath and 
15

to increase the duration of the Hg TP plateau. The cell contains 2.5 kg of Hg (99.999 999 wt% 

pure) which provides an SPRT immersion depth of 18 cm. Following assembly of a Hg TP 

contained in a stainless-steel cell, the sealed cell is inverted to test for a Hg hammer sound (similar to 

that of a water hammer); this test is never performed with a glass Hg cell. 

Figure 8. NIST Hg TP cell. 

The commercially-acquired quartz-glass TPW cell contains about 400 cm3

 of water [25]. We use 

quartz cells because quartz does not leach impurities into the water over time while borosilicate 

does [26]. The nominal immersion depth is 30 cm for the SPRTs. As shown in Figure 9, NIST 

normally uses type A cells which allow visual determination of the partial pressure of air in the 

cell [27]. During use, the cell is completely immersed in its maintenance bath and its re-entrant 

well is completely filled with water to improve the thermal contact of the SPRT with the inner 

liquid-solid interface of the TPW cell. 

Figure 9. Type A TPW cell visual determination of the partial pressure of air in a cell. 
16

As shown in Figure 10, the NIST-fabricated Ga TP cell uses virgin Teflon for the crucible and 

cap, and a glass thermometer well and outer enclosure [8,28]. The Ga TP cell is evacuated 

during the preparation of the Ga TP and for the realization of the Ga TP. The cell contains 1 kg 

of Ga (>99.999 99 wt% pure) giving an SPRT an immersion depth of 18 cm. The reentrant well 

is completely filled with mineral oil to improve the thermal contact of the (HT)SPRT with the 

inner liquid-solid interface of the Ga TP cell. 

Figure 10. NIST Ga TP cell. 

Figure 11 shows a graphite crucible, lid, and thermometer well assembly for containing the 

appropriate metal in NIST-fabricated In FP, Sn FP, and Zn FP cells [29-32]. The sample 

volume, after allowing for a 1 cm head space between the liquid metal and the underside of the 

graphite lid, is 149 cm3. The graphite assembly fits inside a precision-bore borosilicate-glass 

envelope with ceramic-fiber blanket in the annular space between the graphite crucible and the 

borosilicate-glass envelope. A matte-finished borosilicate-glass guide tube, washed-ceramic 

fiber disks and two graphite heat shunts are installed above the graphite lid. The first heat shunt 

was placed approximately 3.2 cm and the second heat shunt was placed approximately 10.8 cm 

above the top of the graphite lid. The heat shunts thermally temper the sheath of the SPRT and 

reduce the minimum thermometer immersion required for good thermal equilibrium with the 

fixed-point metal. The glass envelope, glass guide tube and heat shunts fit snugly by design. 

The top of the glass envelope is sealed with silicone rubber stopper that contains a modified 

compression fitting with a silicone rubber o-ring, for inserting and sealing the SPRT into the 

fixed-point cell, and a stainless-steel gas filling tube for evacuating and backfilling the cell with 

an inert gas (He) to 0.25 kPa above the atmospheric pressure to prevent contamination of the 

metal. In these fixed-point cells, the immersion depth of an SPRT is 18 cm. The metal samples 

are >99.9999 wt% pure sample for tin and zinc and >99.999 99 wt% pure for indium. 

Teflon valve

Glass outer 

envelope

Teflon crucible

Glass thermometer 

well

Nylon 

support ring

Structural 

integrity 

rings

Cap plug with 

hole for 

evacuation of head 

space
17

Figure 11. NIST In FP, Sn FP, and Zn FP cells. Graphite crucible cutaway (enlarged view on 

left) shows the inside of the fixed-point cell. 

Figure 12 shows a graphite crucible, lid and thermometer well assembly for containing the 

appropriate metal in the NIST-fabricated Al FP and Ag FP cells [33,34]. The sample volume, 

after allowing for a 1 cm head space between the liquid metal and the underside of the graphite 

lid, is 149 cm3. The graphite assembly is placed inside a silica-glass envelope with a silica-glass 

re-entrant well inserted into the graphite well. The matte finish of the silica-glass re-entrant well 

prevents “light piping”. Attached to the top of the silica-glass envelope is a matte-finished silicaglass pumping tube to evacuate and back fill the cell to a pressure of 101.3 kPa with purified 

argon during use. The fixed-point cell is inserted into an Inconel protecting tube that contains a 

0.5 cm thick ceramic-fiber cushion at the bottom. Above the silica-glass envelope, there is a 

1 cm gap, then 12 Inconel disks (radiation shields) separated by 1 cm long silica-glass spacers. 

Disks of ceramic-fiber insulation fill the 18 cm space remaining above the top radiation shield. 

The radiation shields are used to thermally temper the sheath of the (HT)SPRT and reduce the 

minimum thermometer immersion required for good thermal equilibrium with the fixed-point 

metal. The matte-finished fused-silica thermometer guide tube extends about 0.5 cm above the 

top of the protecting tube. The pumping tube is used for evacuating and backfilling the cell with 

an inert gas to a pressure of 101.3 kPa. In these fixed-point cells, the immersion depth of an 

(HT)SPRT is 18 cm. 

Compression Fitting 

for (HT)SPRT

Glass outer 

envelope

Rubber Stopper

Fiberfrax 

insulation

Graphite Heat 

Shunts

Port to gas handling 

system
18

Figure 12. NIST Al FP and Ag FP cells. Only one is shown as there is no visual difference 

between the three fixed-point cells. 

4.2.2 ITS-90 fixed-point cell corrections 

The assigned ITS-90 temperatures for the various fixed points do not reflect fixed-point cell 

corrections for hydrostatic head (HH) pressure, gas pressure and a correction for SPRT external 

self heating (ESH). Realization temperature corrections are always added to the ITS-90 assigned 

fixed point temperature value. Table 7 gives the pressure corrections for the ITS-90 fixed points. 

Table 7. Description of the NIST reference fixed-point cells for realizing and disseminating 

ITS-90. 

ITS-90 fixedpoint cellGas pressure effect, 

mK/101.3 kPA

Hydrostatic-Head 

pressure effect, 

mK/cm

Ag FP 6.0 0.054

Al FP 7.0 0.016

Zn FP 4.3 0.027

Sn FP 3.3 0.022

In FP 4.9 0.033

Ga MP –2.0 –0.012

TPW –7.5 –0.0073

Hg TP 5.4 0.071

Ar TP 25 0.033

Fiberfrax 

insulation

Radiation 

shields

Fused silica 

outer envelope 

and well

Graphite 

crucible w/ 

well & cap

Thermometer 

guide tube & 

pumping tube

Inconel tube
19

The correction for immersion depth is calculated by determining the depth of immersion of an 

SPRT in the fixed-point cell and multiplying that value by the ITS-90 assigned hydrostatic-head 

pressure correction for the pertinent fixed point. 

The pressure correction is determined from the difference in the pressure of the inert gas in the 

fixed-point cell (freezing and melting points) from 101.325 kPa and multiplying that value by the 

ITS-90 assigned pressure correction for the pertinent fixed point. Triple-point cells do not require 

pressure corrections, except for the NIST Ga cell, which is realized as a triple point instead of the 

ITS-90 defined melting point. 

The ESH correction is applied to fixed-point cell realization temperatures for an excitation 

current of 1 mA. The 1 mA ESH correction value used at NIST for an SPRT making close fit or 

with a bushing in the fixed-point cell re-entrant well is 0.1 mK. 

Zero-power values are used to eliminate internal and external self-heating effects by measuring 

the SPRT at two currents and extrapolating to 0 mA. The 0 mA value, R0, is calculated from 

 

  

















2

1

2

2

2 12

110

–

–

–

ii

RR

iRR

where R1 is the resistance or ratio value at the excitation current i1 and R2 is the resistance or 

ratio at the higher current i2. 

The above corrections are made to the assigned temperature values of the ITS-90 fixed points 

prior to calculation of the ITS-90 deviation function coefficients. 

A correction is made to the measured R(TPW) value for immersion depth and ESH before the 

calculation of W(T90) [see Section 2]. The TPW cell realization temperature (TTPW) is calculated 

from: 

TTPW 273.16  TK Immersion Depth  TESH

For example, a 26.5 cm immersion depth results in TImmersion Depth of 0.193 mK and for a 1 mA 

excitation current the TESH value is 0.1 mK, thus the TTPW value is 273.15991 K 

The following equation may be used to adjust the R(TPW) value to reflect R(273.16 K): 

)(

)TPW(

(273.16 )

TW TPWr

R

KR  ,

where Wr(TTPW) is the reference function value for the realization temperature of the TPW cell 

with the SPRT. Because the temperature span between TTPW and 273.16 K is very small, 

approximating W(TTPW) of an actual SPRT by Wr(TTPW) introduces negligible error. 
20

4.3 Fixed-point cell maintenance systems 

The maintenance systems used to realize the ITS-90 fixed-point temperatures from the Ar TP to 

the Ag FP are either constructed at NIST or acquired commercially and are designed specifically 

to yield optimal performance with each fixed-point cell. As shown in Table 8 a maintenance 

system is dedicated for use with each of the nine fixed-point cells that are required for the 

calibration of SPRTs in the SPRT Calibration Laboratory. At least one spare maintenance system 

for the realization of the ITS-90 fixed points from the Hg TP to the Ag FP is available for direct 

comparison of two fixed-point cells [14,34,35]. 

Table 8. NIST maintenance systems used to realize the ITS-90 from the Ar TP to the Ag FP.

ITS-90

Fixed Point

Maintenance System

Furnace / Bath Type

ITS-90

Fixed Point

Maintenance System

Furnace / Bath Type

Ag FP sodium heat pipe Ga TP single zone

Al FP sodium heat pipe TPW 43 L water bath

Zn FP three zone Hg TP 40 L ethanol bath

Sn FP three zone Ar TP 100 L Dewar

In FP three zone

4.3.1 Liquid baths 

The Ar TP cell is maintained in a stainless-steel 100 L liquid N2 (LN2) Dewar with superinsulation [21]. The top of the Dewar is modified to allow the Ar TP cell to be integrated into 

the apparatus as a single unit. The adiabatically-controlled Ar TP cell can be maintained 

indefinitely as long as the Dewar contains a sufficient quantity of LN2. 

The maintenance bath used for the Hg TP cell is a commercially-available liquid-stirred bath 

containing about 40 L of ethanol. In combination with the two-stage compressor system for 

cooling and the internal heater, the bath can achieve temperatures down to –80 °C. The bath 

depth is 54.6 cm and accommodates up to two cells. Additionally, two wells are provided for 

chilling the SPRTs prior to insertion into the Hg TP cell. Using this maintenance system, the 

Hg TP can be maintained for at least one week. 

The maintenance bath used for the TPW cell is a commercially-available liquid-stirred bath that 

contains 42 L of water and 1 L of ethanol. The Peltier-cooled bath can accommodate four TPW 

cells and two wells for chilling the SPRTs prior to insertion into the TPW cell. By operating at 

0.007 °C, this bath can maintain a TPW cell mantle for at least six months. The capability to 

simultaneously maintain four TPW cells is used for the cell certification by direct comparison. 

4.3.2 Furnaces 

There are three NIST-fabricated furnaces for realizing the Ga TP. Each of the furnaces contains 

a large cylindrical block of aluminum with a central well for the Ga TP cell. A single-zone, dcpowered single-layer bifilar-wound heater on the aluminum block controls the temperature. The 

furnances provide about a 1 mm annular space (filled with mineral oil) between the Ga TP cell 

and the wall of the well in the aluminum block. One of the three furnaces, operating at 40 °C, is 
21

used for the preparation of the outer liquid-solid interface of the Ga TP cell. In this furnace, the 

triple-point plateau will last approximately 13 h. With the other two furnace, which operate at 

29.9 °C, the triple-point plateau will last at least 6 months. 

There are five NIST-fabricated furnaces available for realizing the In FP, Sn FP and Zn FP. 

These automatically-controlled three-zone furnaces uses three dc powered heater zones (top, 

middle and bottom) with the top and bottom acting as guard zones to provide a uniform 

temperature environment over the length of the fixed-point cell. All five of the furnaces and 

control systems are interchangeable, and direct comparison of fixed-point cells of the same type 

can be made with them. An auxiliary furnace is integrated into the furnace enclosure for heating 

the SPRT prior to insertion into the fixed-point cell. Freezing-point plateaus can be maintained 

for at least 16 h using these furnaces. 

There are three NIST-fabricated, sodium-filled heat-pipe furnaces for realizing the Al FP and 

Ag FP. These automatically-controlled high-temperature furnaces use two dc powered heater 

zones for the heat pipe. One of the heaters extends slightly beyond the length of the heat pipe 

and the other “plug heater” fits in the bottom of the open-bottom heat pipe. All three of the 

furnaces and control systems are interchangeable and direct comparison of fixed-point cells of 

the same type can be made with them. Freezing-point plateaus can be maintained for at least 

16 h using these furnaces. The two auxiliary furnaces, used either to heat the SPRT prior to 

insertion into the fixed-point cell or to anneal the SPRT, are placed in a single enclosure. Each 

of the auxiliary furnaces contain a closed-end Pt protection tube placed between two closed-end 

fused silica tubes for protecting the SPRTs from metal ion contamination [15].

4.3.3 Maintenance system thermal characteristics 

Understanding the thermal characteristics of the furnaces and liquid baths with the fixed-point 

cells installed is important to minimize the impact on the fixed-point cell realization temperature 

and prevent possible breakage of the cells during use [36]. The temperature stability of the 

furnace or bath and the vertical-temperature profile over the axial length of the graphite crucible 

is determined by setting the temperature of the furnace or bath approximately 2.5 °C below the 

fixed-point temperatures of Ar, Hg, Ga, In, Sn, In, Al, and Ag and approximately 3 mK below 

that of TPW. Single-phase materials do not exhibit hydrostatic-head effects in the verticaltemperature profile. 

The temperature stability of the furnace or bath is determined by placing an SPRT into the 

thermometer well of the appropriate fixed-point cell and measuring the temperature fluctuations 

overnight (15 h). As shown in Table 9, the temperature fluctuations of the maintenance baths for 

the Ar TP, Hg TP, and TPW cells do not cause the SPRT in the cells to change more than 

±2 mK. The temperature changes in the Ga TP cell furnaces results in the largest temperature 

fluctuation of ±10 mK. The temperature variations in the three-zone furnaces for the In FP, 

Sn FP, and the Zn FP cells caused instabilities that do not exceed ±7 mK. The two-zone heat 

pipe furnaces for the Al FP and Ag FP cells give instabilities that do not exceed ±9 mK. 

The vertical-temperature profile over the length of the fixed-point cell crucible is determined by 

slowly inserting the SPRT into the fixed-point cell in 2 cm steps over the length of the crucible. 

Five minutes per increment is allotted for the SPRT to equilibrate prior to measurement. As 
22

shown in Table 9, the vertical temperature differences over the length of the re-entrant well of 

the fixed-point cells in the maintenance baths, single-zone Ga TP furnace, three-zone furnace 

and the sodium heat pipe furnace do not exceed 2 mK, 7 mK, 8 mK and 9 mK, respectively. 

Figure 13 shows a mapping of the temperatures with vertical positions for the In FP, Sn FP and 

Zn FP cells used with three-zone furnaces and that for the Al FP and Ag FP cells used with the 

two-zone heat-pipe furnace. Because of the greater depth of insertion of these cell crucibles into 

the furnaces, the measurements of the vertical temperature gradients are made with the SPRT 

starting about 5 cm above the top of the graphite crucible. 

Table 9. Thermal characteristics of furnaces and maintenance baths used at NIST to realize the 

ITS-90 from 83.8058 K to 1234.93 K Furnace and bath stability over 15 h and vertical 

temperature profile of thermometer well from 0 cm to 18 cm. 

Fixed-Point Furnace/Bath Thermometer Well Fixed-Point Furnace/Bath Thermometer Well 

 Cell Stability, ±mK Profile T, mK Cell Stability, ±mK Profile T, mK 

Ar TP 1 2 Sn FP 6 5 

Hg TP 2 4 Zn FP 7 8 

TPW 2 4 Al FP 8 8

Ga TP 10 7 Ag FP 9 9 

In FP 4 4

-100

-75

-50

-25

0

25

-25 -20 -15 -10 -5 0

(thermometer position - bottom of thermometer well), cm change in mK

Ag FP cell

Al FP cell

Zn FP cell

Sn FP cell

In FP cell

Top of crucible

Figure 13. Vertical temperature profile for two-zone sodium heat pipe furnaces containing Ag FP 

and Al FP cells and for the three-zone furnaces containing the Zn FP, Sn FP and In FP cells. 

Measurements made with the furnace temperature 2.5 °C below the freezing point of the fixedpoint cell. Single-phase materials do not exhibit hydrostatic-head effects. 
23

The ability of SPRTs of various manufacturer models to exhibit proper immersion in the NIST 

fixed-point cells was investigated. For the SPRT to be considered properly immersed (no stem 

conduction effect influencing the measurements), the thermometer must track the ITS-90 

assigned value of the hydrostatic-head effect over the bottommost 3 cm of the thermometer well. 

Proper immersion of the SPRT was verified by measuring the SPRT resistance starting at 10 cm 

from the bottom of the thermometer well, then inserting the SPRT in 2 cm steps until 4 cm from 

the bottom, and then inserting the SPRT in 1 cm steps until the bottom of the thermometer well 

was reached. After changing the immersion depth of the SPRT, the SPRT was allowed to reequilibrate at each step prior to measurement. The immersion depth of the SPRT was calculated 

from the sensor midpoint to the height of the fixed-point material column during the fixed-point 

realization. Examples of immersion (heat flux) profiles for the NIST fixed-point cells are shown 

in Section 5.2. 

As shown in Table 10, the different thermometer types that were tested all exceeded the 

minimum requirement for proper immersion by tracking the ITS-90 assigned hydrostatic-head 

effect over the bottommost 3 cm of the fixed-point cells. As expected, however, there are small 

differences between thermometer types. This is caused by the variation in the thermometer 

design to maximize radial heat transfer and to minimize axial heat transfer. The difference in the 

diameters of the thermometer and the well of the fixed-point cell may also affect the immersion 

characteristics. 

Table 10. Distance in centimeters that certain SPRTs can track the hydrostatic-head effect in 

NIST fixed-point cells, to within the uncertainty in the measurements (<0.01 mK). Fixed-point 

cells were tested over the bottommost 10 cm of the thermometer wells. A minimum of 3 cm is 

required to overcome stem conduction loss. 

Fixed-Point Winding and Former Type of SPRTs Winding and Former Type of HTSPRTs 

 Cell SLB-M CH-M CH-Q BC TC SLB-Q CH-Q TC BC

Ar TP 5 5 5 4 5

Hg TP 9 6 6 5 5 

TPW 9 8 8 7 6 7 7 8 8 

Ga TP 10 10 10 8 9 8 8 8 8 

In FP 10 8 8 7 8 9 8 8 7 

Sn FP 10 9 9 7 8 8 7 9 7 

Zn FP 9 9 9 6 8 7 7 8 6 

Al FP 7 5 6 7 7 8 6

Ag FP 6 6 7 6 

SLB-M: single-layer bifilar-mica CH-Q: coiled helix-fused silica TC: twisted coil

CH-M: coiled helix-mica BC: bird cage SLB-Q: single-layer bifilar-fused silica 
24

4.4 SPRT measurement system 

A semi-automated system controlled by a LabView program governs and performs the SPRT 

measurements (See section 4.5). The commercially-available ac resistance-ratio bridge 

(ASL F900) operating at a frequency of 30 Hz, thermostatically-controlled (25 °C ±0.01 °C) 

ac/dc reference resistors and the SPRTs are all connected through scanners with all instrumnets 

controlled via the IEEE-488 bus. The wiring that connects the SPRTs and resistors to the ASL 

F900 are all shielded, stranded, twisted pairs designed for ac measurements. In general, the 

measurement system is based on the description given in references 5 and 37. Figure 14 shows 

the general layout of the laboratory with the fixed-point cell maintenance systems distributed 

around a service raceway. This service raceway allows SPRTs to be plugged into ports for 

connection to the measurement system. 

Figure 14. General layout of the NIST SPRT Calibration Laboratory. 

The ASL F900 is a 10.5 digit ac resistance ratio bridge that uses an inductive voltage divider 

technique to ratio the unknown resistance to a know resistance. The available excitation 

frequencies are 0.5 and 1.5 times the mains carrier frequency. NIST uses the bridge at 30 Hz. 

The range of measurable ratios is from 0 to 1.299 times the value of the reference resistor. For 

the F900 the nominal settings are 105 gain and a 0.2 Hz bandwidth. For the 0.25 Ω HTSPRT, we 

use excitation currents of 14.14 mA and 20 mA; for the 2.5 Ω HTSPRT, 5 mA and 7.07 mA; for 

the 25.5 Ω LSPRT, 1 mA and 1.414 mA; and for the 25.5 Ω CSPRT, 1 mA and 2 mA.

The ASL F900 uses Tinsley 5685A Wilkins-design [38] reference resistors of nominal values of 

1 Ω, 10 Ω, and 100 Ω for 0.25 Ω, 2.5 Ω, and 25.5 Ω SPRTs, respectively. The reference resistors 

are calibrated yearly by NIST Electronics and Electrical Engineering Laboratory. The oil bath 

maintains up to 10 resistors at 25 °C ±0.01 °C. A compressed-air driven motor stirs the oil bath, 

since the electric field of induction motors was found to couple into the measurement circuits 
25

and appear as electrical noise on the ASL bridge. Using a NIST-calibrated thermistor, the 

LabView program reads the oil bath temperature every three seconds. If the oil bath temperature 

exceeds the allowable maintenance temperature limits or if communication is lost, the program 

automatically stops making measurements until the issue is corrected. 

During measurements of an SPRT, a modified Lemo connector is attached to the SPRT which 

allows quick connections to the service raceway ports. The ports are wired to a distribution box, 

and then to scanners (HP 3488As). The scanner cards are the relay equivalent of a double pole 

ten position switch. This service raceway allows SPRTs to be plugged into ports for connection 

to the measurement system. 

4.5 Measurement software 

The software used to control the measurement patterns and perform all of the measurements 

needed to calibrate an SPRT is a multi-module LabView program that utilizes an Access 

database in the background. Section 4.1 describes the modules that the program uses at different 

states during the calibration. This program was designed and created at NIST. 

5 ITS-90 SPRT Calibration Methods 

5.1 SPRT stabilization methods 

Thermal stabilization (annealing) of an SPRT prior to calibration is crucial for the thermometer 

to be stable during the calibration cycle [16,17]. Thermometer stability is necessary for the SPRT 

to be able to maintain its calibration status with the stated calibration uncertainties. The 

annealing of the Pt sensor coil is designed to remove as much mechanical strain that occur 

through general used and shipping. As described in Sections 4.1 and 6.7.3, the SPRT R(TPW) 

value after an anneal with respect to the R(TPW) measured prior to an anneal must repeat to the 

equivalent of <0.2 mK. Table 11 gives the NIST annealing protocol including the annealing 

times and temperatures for specific calibration ranges. Note that capsule SPRTs are not annealed 

due to physical constraints in the design. 

When using an SPRT above 475 °C, the thermometers require special handling to minimize their 

degradation. For glass-sheathed SPRTs, the fused-silica sheath must be protected against 

devitrification. Devitrification, the process in which the fused silica crystallizes, results from the 

presences of any oils or salts that are transferred to the sheath from the user’s hands when the 

thermometer is handled prior to exposure at temperatures above 475 °C. Devitrification is 

irreversible and will cause the sheath to become brittle and porous, eventually breaking. 

Consequently, in order to prevent possible devitrification, the SPRT is cleaned with an ethanol 

soaked wipe while wearing disposable, powder free latex or nitrile gloves (not cotton gloves). 

For metal-sheathed SPRTs, the sheath is cleaned and treated the same way as that of the glasssheathed SPRTs to prevent the transfer of oils or salts to the fixed-point cell re-entrant well. 

Additionally, metal-sheathed thermometers are not heated above 675 °C and the amount of time 

above 660 °C is minimized to prevent the loss of available oxygen inside of the sheath, thus 

making the SPRT unstable. 
26

HTSPRTs used above 700 °C require protection against metal ion contamination. Inside the two 

HTSPRT annealing furnace re-entrant wells are concentric fused silica, Pt, and fused silica test 

tubes. The Pt test tube (66 cm long with a wall thickness of 0.13 mm) protects the HTSPRT from 

metal ion contamination, while the two fused silica test tubes (66 cm long with a wall thickness 

of 1 mm) protect the Pt tube from damage. The reference grade Pt (99.9 wt% pure) test tube acts 

as an impurity acceptor, thus protecting the HTSPRT from metal ion contamination. 

In some special instances, an SPRT is not annealed if so requested by the customer. In this case, 

the temperature range of use is often between 0 °C and 30 °C and the customer does not wish to 

change the oxidation state of the SPRT which would create a step function in the customer 

R(TPW) control chart. 

Table 11. Annealing protocol for NIST calibrated SPRTs 

SPRT type and 

Max. Calibration

Temperature, °C

Annealing 

Temperature, °C

Duration at 

Annealing 

Temperature, h

Instructions for annealing and handling 

the thermometer

SPRT

 420 475 8

1) While wearing disposable, powder 

free latex or nitrile gloves, clean 

with an ethanol-soaked wipe prior 

to annealing

SPRT or HTSPRT

 661 675 2.5

1) While wearing disposable, powder 

free latex or nitrile gloves, clean 

with an ethanol-soaked wipe prior 

to annealing

2) Heat (HT)SPRT from 475 °C to 675 °C 

over 0.5 h

3) Soak (HT)SPRT at 675 °C for 2.5 h

4) Cool (HT) SPRT from 675 °C to 

475 °C over 3 h

5) Remove (HT)SPRT from 475 °C 

annealing furnace

HTSPRT

 962 975 0.5

1) While wearing disposable, powder 

free latex or nitrile gloves, clean 

with an ethanol soaked wipe prior 

to annealing

2) Heat (HT)SPRT from 475 °C to 975 °C 

over 1.5 h

3) Soak (HT)SPRT at 975 °C for 0.5 h

4) Cool (HT) SPRT from 975 °C to 

475 °C over 5 h

5) Remove (HT)SPRT from 475 °C 

annealing furnace

SPRT

0 to 30

Prior to annealing,

check with customer

Capsule SPRT No annealing allowed
27

5.2 Calibration by fixed points 

We describe below each NIST realization method of each ITS-90 fixed-point cell. The setpoint 

temperatures and duration of fused-silica rods in the thermometer re-entrant well are designed to 

optimize the realization temperature reproducibility for the NIST fixed-point cells and 

maintenance systems. Additionally, for the realization results of a fixed-point cell to be 

acceptable at NIST, the heat-flux interactions between the maintenance system, fixed-point cell 

and an SPRT are tested. As described in section 6.4.1, the SPRT must be able to track the 

hydrostatic head effect over at least the bottommost 3 cm during a heat-flux test.

5.2.1 Ag FP 

The Ag FP is achieved by following these steps: 

o The Ag ingot is melted overnight to about 5 °C above the freezing point temperature. 

o The check HTSPRT is inserted into the Ag FP cell re-entrant well from the 975 °C preheat furnace. 

o The furnace is set 1 °C below the freezing-point temperature. 

o When the check HTSPRT registers the supercool and subsequent recalesence (i.e., 

 liberation of the latent heat at the creation of the liquid-solid transition causes the 

 HTSPRT temperature to rise and stabilize at the plateau temperature), the furnace is set 

to control 0.5 °C below the freezing-point temperature. 

o The check HTSPRT is removed to the 975 °C pre-heat furnace. 

o A clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted for one minute 

 into the re-entrant well of the fixed-point cell, re-entrant well of the fixed-point cell for 

 one minute, and then withdrawn. 

o The check HTSPRT is re-inserted into the Ag FP cell from the 975 °C pre-heat 

 furnace. 

o Measurements commence one hour after realizing the Ag FP to allow for the realized 

 fixed point and check HTSPRT to achieve equilibrium (e.g. freezing plateau).

The successive insertions of the fused-silica rod insure formation of a solid mantle of silver on 

the outside of the graphite re-entrant well. The recalesence occurs on the inner surface of the 

graphite crucible. The creation of two solid-liquid interfaces is known as either a “double freeze” 

or an “induced freeze”. A heat flux test is needed to validate the realization method (e.g the 

proper creation of the inner freeze). Figure 15 gives an example of a heat-flux test for the check 

SPRT. 
28

2.0

1.5

1.0

0.5

0.0

0.5

0 2 4 6 8

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

NIST Ag 92-1

hydrostatic head

Figure 15. Heat-flux (immersion) test results during realization of the Ag FP. 

5.2.2 Al FP 

The Al FP is achieved by following these steps: 

o The Al ingot is melted overnight to about 5 °C above the freezing point temperature. 

o The check SPRT is inserted into the Al FP cell re-entrant well from the 675 °C 

 pre-heat furnace. 

o The furnace is set 1 °C below the freezing-point temperature. 

o When the check SPRT registers the supercool and subsequent recalesence, the furnace is 

 set to control 0.5 °C below the freezing-point temperature. 

o The check SPRT is removed to the 675 °C pre-heat furnace. 

o A clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted for one minute 

 into the re-entrant well of the fixed-point cell, re-entrant well of the fixed-point cell for 

 one minute, and then withdrawn. 

o The check SPRT is re-inserted into the Al FP cell from the 675 °C pre-heat furnace. 

o Measurements commence one hour after realizing the Al FP to allow for the realized 

 fixed point and check SPRT to achieve equilibrium (e.g. freezing plateau). 

The successive insertions of the fused-silica rod insure formation of a solid mantle of aluminum 

on the outside of the graphite re-entrant well. The recalesence occurs on the inner surface of the 

graphite crucible. The creation of two solid-liquid interfaces is known as either a “double freeze” 

or an “induced freeze”. A heat flux test is needed to validate the realization method (e.g the 

proper creation of the inner freeze). Figure 16 gives an example of a heat-flux test for the check 

SPRT. 
29

0.8

0.6

0.4

0.2

0.0

0.2

0 2 4 6 8 10

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

NIST Al 96-1

hydrostatic head

Figure 16. Heat-flux (immersion) test results during realization of the Al FP.

5.2.3 Zn FP 

The Zn FP is achieved by following these steps: 

o The Zn ingot is melted overnight to about 5 °C above the freezing point temperature. 

o The check SPRT is inserted into the Zn FP cell re-entrant well from the 425 °C 

 pre-heat furnace. 

o The furnace is set 1 °C below the freezing-point temperature. 

o When the check SPRT registers the supercool and subsequent recalesence, the furnace is 

 set to control 0.5 °C below the freezing-point temperature. 

o The check SPRT is removed to the 425 °C pre-heat furnace. 

o A clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted into the re-

 entrant well for five minutes and withdrawn. 

o A second clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted into the 

re-entrant well for five minutes and withdrawn. 

o The check SPRT is re-inserted into the Zn FP cell from the 425 °C pre-heat 

 furnace. 

o Measurements commence one hour after realizing the Zn FP to allow for the realized 

 fixed point and check SPRT to achieve equilibrium (e.g. freezing plateau). 

The re-entrant well is filled with helium to an atmospheric pressure of 101.3 kPa to improve the 

thermal contact of the SPRT with the inner solid-liquid interface of the Zn FP cell. In the case of 

a small-diameter metal-sheathed SPRT, an aluminum bushing is used to improve thermal contact 

with the inner solid-liquid interface. 

The successive insertions of the fused-silica rod insure formation of a solid mantle of zinc on the 

outside of the graphite re-entrant well. The recalesence occurs on the inner surface of the 

graphite crucible. The creation of two solid-liquid interfaces is known as either a “double freeze” 
30

or an “induced freeze”. A heat flux test is needed to validate the realization method (e.g the 

proper creation of the inner freeze). Figure 17 gives an example of a heat-flux test for two SPRTs 

of different manufacture. 

0.6

0.4

0.2

0.0

0.2

0 2 4 6 8 10

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 17. Heat-flux (immersion) test results during realization of the Zn FP.

5.2.4 Sn FP 

The Sn FP is achieved by following these steps:

o The Sn ingot is melted overnight to about 5 °C above the freezing point temperature. 

o The check SPRT is inserted into the Sn FP cell re-entrant well from the 237 °C 

 pre-heat furnace. 

o The furnace is set 0.5 °C below the freezing-point temperature. 

o When Sn FP cell is at the realization temperature (as determined with the check SPRT), 

 the Sn cell with the check SPRT is removed from the furnace until the start of 

 recalesence. 

o At the beginning of that recalesence, the Sn FP cell is placed back into the furnace. 

o The check SPRT is removed to the 237 °C pre-heat furnace. 

o A clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted into the re-

 entrant well for three minutes and withdrawn. 

o A second clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted into the 

re-entrant well for three minutes and withdrawn. 

o The check SPRT is re-inserted into the Sn FP cell from the 237 °C pre-heat furnace. 

o Measurements commence one hour after realizing the Sn FP to allow for the realized fixed 

 point and check SPRT to achieve equilibrium (e.g. freezing plateau). 

The re-entrant well is filled with helium to an atmospheric pressure of 101.3 kPa to improve the 

thermal contact of the SPRT with the inner solid-liquid interface of the Sn FP cell. In the case of 

a small-diameter metal-sheathed SPRT, an aluminum bushing is used to improve thermal contact 

with inner solid-liquid interface. 
31

The successive insertions of the fused-silica rod insure formation of a solid mantle of tin on the 

outside of the graphite re-entrant well. The recalesence occurs on the inner surface of the 

graphite crucible. The creation of two solid-liquid interfaces is known as either a “double freeze” 

or an “induced freeze”. A heat flux test is needed to validate the realization method (e.g the 

proper creation of the inner freeze). Figure 18 gives an example of a heat-flux test for two SPRTs 

of different manufacture. 

0.6

0.4

0.2

0.0

0.2

0 2 4 6 8 10

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 18. Heat-flux (immersion) test results during realization of the Sn FP.

5.2.5 In FP 

The In FP is achieved by following these steps: 

o The In ingot is melted overnight to about 5 °C above the freezing point temperature. 

o The check SPRT is inserted into the In FP cell re-entrant well from the 164 °C 

 pre-heat furnace. 

o The furnace is set 3 °C below the freezing-point temperature. 

o When the check SPRT registers the supercool and subsequent recalesence, the furnace is 

 set to control 0.5 °C below the freezing-point temperature. 

o The check SPRT is removed to the 164 °C pre-heat furnace. 

o A clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted into the re-

 entrant well for four minutes and withdrawn. 

o A second clean, ambient-temperature fused-silica rod (7 mm diameter) is inserted into the 

re-entrant well for four minutes and withdrawn. 

o The check SPRT is re-inserted into the In FP cell from the 164 °C pre-heat furnace. 

o Measurements commence one hour after realizing the In FP to allow for the realized fixed 

 point and check SPRT to achieve equilibrium (e.g. freezing plateau). 

The re-entrant well is filled with helium to an atmospheric pressure of 101.3 kPa to improve the 

thermal contact of the SPRT with the inner solid-liquid interface of the In FP cell. In the case of 
32

a small-diameter metal-sheathed SPRT, an aluminum bushing is used to improve thermal contact 

with the inner solid-liquid interface. 

The successive insertions of the fused-silica rod insure formation of a solid mantle of indium on 

the outside of the graphite re-entrant well. The recalesence occurs on the inner surface of the 

graphite crucible. The creation of two solid-liquid interfaces is known as either a “double freeze” 

or an “induced freeze”. A heat flux test is needed to validate the realization method (e.g the 

proper creation of the inner freeze). Figure 19 gives an example of a heat-flux test for two SPRTs 

of different manufacture. 

0.6

0.4

0.2

0.0

0.2

0 2 4 6 8 10

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 19. Heat-flux (immersion) test results during realization of the In FP.

5.2.6 Ga TP 

The Ga TP in a melting mode is achieved by following these steps: 

o Evacuate the Ga TP cell using an oil-free diaphragm and turbo-molecular pumping 

 system. The Ga TP cell is evacuated during the entire realization process. 

o Check that the re-entrant well is filled with oil. 

o The Ga sample is frozen overnight by placing the Ga TP cell in a glass beaker that 

 extends over the length of the cell, and then filling the beaker with crushed dry ice. In 

 approximately three hours, the gallium in the cell freezes completely. 

o The Ga TP cell is placed in the 40 °C furnace for 45 min to establish the outer liquid-solid 

 interface 

o During the creation of the outer liquid-solid interface, an immersion heater (operating at

 40 °C) is placed into the re-entrant well for 45 min to establish a complete inner liquid-

 solid interface. 

o The check SPRT is inserted into the Ga TP cell from ambient.

o Measurements commence one hour after realizing the Ga TP to allow for the realized 

 fixed point and check SPRT to achieve equilibrium (e.g. freezing plateau). 
33

The re-entrant well is filled with mineral oil to improve the thermal contact of the SPRT with the 

Ga TP inner liquid-solid interface. In the case of a small-diameter metal-sheathed SPRT, an 

aluminum bushing is used to improve thermal contact with the inner liquid-solid interface. 

The use of an immersion heater is critical to the formation of an inner liquid-sold interface 

around the re-entrant well. The creation of two liquid-solid interfaces is known as either a 

“double melt” or an “induced melt”. A heat flux test is needed to validate the realization method 

(e.g the proper creation of the inner melt). Figure 20 gives an example of a heat-flux test for two 

SPRTs of different manufacture. 

0.05

0.00

0.05

0.10

0.15

0 2 4 6 8 10

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 20. Heat-flux (immersion) test results during realization of the Ga TP.

5.2.7 TPW (H2O TP) 

To create the solid phase of water within a TPW cell, the re-entrant well is cooled by one of 

several methods, including crushed solid CO2, heat-pipe immersion cooler, LN2-cooled copper 

rod, and LN2 cooling. For convenience, cooling using crushed solid CO2 is described below. A 

detailed description of the four methods is found in reference 39. 

The TPW is achieved by following these steps (crushed solid CO2 method): 

o The cell may be at ambient temperature or colder for initiation of the solid phase of water 

(ice). 

o Rinse the re-entrant well with ethanol to remove any water. 

o For enhanced heat transfer, add approximately 1 cm3

of ethanol to the bottom of the 

re-entrant well. 

o Place the TPW cell in a beaker of cold water (this step negates lenticular magnification 

 for seeing the actual size of the solid phase of water) 

o Add several cubic centimeters of crushed solid CO2 to the re-entrant well. 

o Continue adding a small amount of crushed solid CO2 until the ice bulb is several 

 millimeters thick (about three to five minutes). 
34

o Fill the re-entrant well with crushed solid CO2 to the same level as that of the liquid water 

 in the TPW cell. 

o For approximately 17 min, continue filling the re-entrant well to maintain the level of 

 crushed solid CO2. Any solid bridge of ice across the horizontal water surface must be 

 removed by warming the top of the cell with a hand and gently shaking the cell. 

o After approximately 17 min, allow the crushed solid CO2 to completely sublimate. 

o Place a rubber or cork stopper in the re-entrant well and place the TPW cell into the 

 maintenance system. 

o After 30 min, remove the stopper and allow water from the maintenance system to the 

 fill the re-entrant well. 

o Allow a minimum of one day for the ice to age. NIST ages the ice mantles for a 

 minimum of five days. 

o Insert an ambient-temperature rod (e.g. glass, metal) into the cell re-entrant well for 

approximately one minute to create the liquid-solid interface around the re-entrant well. 

o Check that the ice mantle is free to completely rotate around the re-entrant well by 

 slightly tilting the cell and watching for slow rotation of the mantle.

o Place a plastic-foam pad in the bottom of the re-entrant well. 

o Place an Al bushing into the re-entrant well. The bushing is chosen to provide slip fit of 

the SPRT sheath diameter to enhance thermal contact with TPW liquid-solid interface. 

o Measurements may commence 30 min after creating the inner liquid-solid interface. 

The re-entrant well is filled with water to improve the thermal contact of the SPRT with the inner 

liquid-solid interface of the TPW cell. An aluminum bushing is used to improve thermal contact 

of the SPRT with the inner liquid-solid interface. 

The creation of two liquid-solid interfaces is known as either a “double melt” or an “induced 

melt”. A heat flux test is needed to validate the realization method (e.g the proper creation of the 

inner melt). Figure 21 gives an example of a heat-flux test for two SPRTs of different 

manufacture. 

0.05

0.00

0.05

0.10

0.15

0 2 4 6 8 10

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 21. Heat-flux (immersion) test results during realization of the TPW. 
35

5.2.8 Hg TP 

The Hg TP in a melting mode is achieved by following these steps: 

o Check that the re-entrant well is filled with ethanol. 

o The Hg TP cell is placed in the maintenance bath which is then set at –45 °C to freeze the 

 Hg sample overnight. 

o The maintenance bath is set to control at –38.6 °C to initiate the outer liquid-solid 

 interface. 

o When the maintenance bath reaches the set point temperature (–38.6 °C), the inner liquid-

 solid interface of the Hg sample is induced by placing an immersion heater (operating 

 at 40 °C) into the re-entrant well for 45 min. 

o After 45 min, the immersion heater is removed and the bath-chilled SPRT is placed in the 

re-entrant well. 

o Measurements commence 30 min after realizing the Hg TP. 

The re-entrant well is filled with ethanol to improve the thermal contact of the SPRT with the 

inner liquid-solid interface of the Hg TP cell and prevent moisture from condensing and freezing 

within the re-entrant well. In the case of a small-diameter metal-sheathed SPRT, a bushing is 

used to improve thermal contact with inner liquid-solid interface. 

The use of an immersion heater is critical to the formation of an inner liquid-sold interface 

around the re-entrant well. The creation of two liquid-solid interfaces is known as either a 

“double melt” or an “induced melt”. A heat flux test is needed to validate the realization method 

(e.g the proper creation of the inner melt). Figure 22 gives an example of a heat-flux for two 

SPRTs of different manufacture. 

0.6

0.4

0.2

0.0

0.2

0 2 4 6 8

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 22. Heat-flux (immersion) test results during realization of the Hg TP.
36

5.2.9 Ar TP 

The Ar TP in a melting mode is achieved over three days by following these steps: 

o Check that the argon sample reservoir valve is closed 

o Turn on He supply to re-entrant wells 

o Remove surrogate SPRTs (e.g. evacuated spacer tubes), clean and dry re-entrant wells, 

and replace surrogate SPRTs 

o Evacuate vacuum can space overnight 

o Close vacuum valve and fill vacuum space with a small amount of He exchange gas 

o Fill Dewar with LN2 in the morning.

o Top off the Dewar with LN2 in the afternoon and slowly open the vacuum system to the 

 vacuum space. 

o Open argon sample reservoir valve (argon sample should begin to transfer to into the cell 

 as evidenced by a pressure drop in the argon pressure gauge). 

o Introduce LN2 into the center re-entrant well using the double-vacuum jacked 

 transfer system. 

o Approximately three hours is required to condense and freeze the argon sample in 

 the argon cell. The monitoring capsule SPRT in the bottom of the cell is used to 

 determine the state of the argon. 

o Remove LN2 transfer system, top off Dewar with LN2, remove the other six surrogate SPRTs and 

 slowly replace the center surrogate SPRT.

o Slowly insert any bushing required for the small-diameter metal-sheathed SPRTs. 

o Slowly insert the six SPRTs into the re-entrant wells 

o Based on the value of the monitoring capsule SPRT is used to determine the amount of 

 electrical energy needed to melt approximately 20% of the sample. 

o Close the argon sample reservoir valve 

o Allow the system to thermally equilibrate for eight hours and commence measurements 

The re-entrant well is filled with helium to an atmospheric pressure of 101.3 kPa to improve the 

thermal contact of the SPRT with inner liquid-solid interface of the Ar TP cell. In the case of a 

small-diameter metal-sheathed SPRT, a bushing is used to improve thermal contact with inner 

liquid-solid interface. 

A heat flux test is needed to validate the realization method (e.g the proper creation of the inner 

melt). Figure 23 gives an example of a heat-flux test for two SPRTs of different manufacture. 
37

0.2

0.1

0.0

0.1

0.2

0 2 4 6

Distance from bottom of well, cm Deviation from temperature at full immersion, mK

Hart 5681

Rosemount 162CE

hydrostatic head

Figure 23. Heat-flux (immersion) test results during realization of the Ar TP.

5.3 Calibration report 

Appendix A contains an example of a Report of Calibration for an SPRT calibrated from the 

Al FP to the Ar TP. The report contains ITS-90 deviation function coefficients for both 1 mA 

and 0 mA excitation currents. The uncertainties in the ITS-90 fixed-point cells are given on the 

first page of the report. Additionally, the R(0.01 °C) values for 1 mA and 0 mA [calculated from 

the last measured R(TPW) values] and the stability of the SPRT during calibration (i.e. total 

change in equivalent temperature for the R(TPW) measurements made during the calibration) are 

given. Subsequent pages within the report give the propagation of uncertainty for the fixed 

points, how the uncertainty in a R(TPW) measurement will propagate, and a 1 mA table of t90

versus W values.

5.4 On receipt of a NIST calibrated SPRT 

When the SPRT is returned to a laboratory, the first measurement should be the R(TPW). This 

value should be added to the TPW control chart and used in the denominator in the calculation of 

W. The calculated R(0.01 °C) value should be compared with the value given in the NIST Report 

of Calibration. Any difference in the values can be attributed to either a difference in the ohm 

realization, mechanical strain in the Pt sensor coil from shipping, or a difference in the TPW 

realization temperatures. NIST technical staff should be called for guidance if the difference 

between the “as received” and NIST’s “as left” R(0.01 °C) values are greater than the equivalent 

of 10 mK (e.g. 0.001 Ω). 

5.5 Determining the SPRT re-calibration interval 

No rigid recommendations can be given concerning how often a customer should send their 

SPRT to NIST for recalibration. The calibration status of the SPRT depends on the amount of 
38

thermal and physical shock that the SPRT incurs over time. At this time, the NIST viewpoint on 

determining the re-calibration interval of an SPRT is twofold. 

First, using an SPRT does not allow for a set re-calibration interval due to possible changes in 

the calibration status from thermal or mechanical shock to the Pt sensor coil. Such shock can 

change the R(TPW) value and somewhat proportionally every other R(t90) value. Therefore it is 

important that the R(TPW) be determined at an interval that is determined by you and then used 

in the calculation of W. 

Second, the R(TPW) values should be used to track the changes in the (HT)SPRT Pt sensor coil 

over time as the method of determining the re-calibration interval. This is done by entering the 

“as received” R(TPW) value into the control chart and tracking the equivalent temperature 

change in the R(TPW) over time. When the R(TPW) changes by more than the allowable 

amount, the SPRT need re-calibration. Figure 24 shows an example of an control chart for an 

SPRT as measured at the R(TPW) overtime. The ±1 mK control lines are chosen as an example 

only and do not necessarily reflect the needs of all SPRT users. 

2

1

0

1

2

04/01/06 10/01/06 04/01/07 10/01/07

Date of measurement

[R X(TPW) – R 1(TPW)], mK

Figure 24. SPRT control chart at the TPW. The ±1 mK control lines indicate when the SPRT 

requires a re-calibration. Note that the ±1 mK control lines are chosen as an example only and do 

not necessarily reflect the needs of all SPRT users

6 Internal Measurement Assurance 

As part of the NIST SPRT Calibration Laboratory Quality System [40,41] for the ITS-90 

realization of fixed-point cells and the calibration of SPRTs, an extensive internal measurement 

assurance program (IMAP) was instituted in 1990 in order to quantify, minimize, and verify the 

associated uncertainties. Reference [17] provides a detailed description of the IMAP; an 

overview is given below. 
39

This IMAP encompasses six interactive elements for the realization of the ITS-90 fixed-point 

cells and the subsequent calibration of SPRTs. As shown in Table 12, the six elements are the 

Fixed-Point Cells, Furnace/Maintenance System, SPRT, Measurement System, Realization 

Technique, and Measurement Assurance. Within those six elements, there exist twenty-eight 

parameters that contribute to the uncertainty of a NIST ITS-90 realized fixed-point cell phase 

transition and a SPRT calibration (see Section 7). Each of the six elements and twenty-eight 

parameters are discussed in this section. 

Table 12. The NIST ITS-90 Internal Measurement Assurance Program. 

Section Interactive Elements Measured Parameters

6.1 Fixed-Point Cell

sample purity corrections

phase transition 

repeatability design/assembly

constant pressure

6.2 Furnace/Maintenance System vertical gradient fixed-point cell interaction

set-point control

6.3 SPRT

heat flux contamination

immersion depth wetness

self heating light piping

stability

6.4 Measurement System

repeatability ac quadrature

non-linearity current

ratio error number of readings

ohm

6.5 Realization Technique duration of realization 

curve

SPRT immersion profile

6.6 Control Artifacts

check SPRT SPRT calibration

fixed-point cell 

certification external comparisons

6.1 Fixed-point cell element 

6.1.1 Sample purity parameter 

The Sample Purity parameter is the effect of impurities on the realized temperature (Type B, 

normal distribution) and is one component used to assign an overall uncertainty to the fixedpoint cell [43,44]. 

The NIST SPRT Laboratory uses multiple methods to estimate and validate the impurity 

uncertainty component value for an ITS-90 fixed-point cell. There are three methods that use 

variations of Raoult’s Law of Dilute Solutions to estimate the effect of impurities on the 

realization of the fixed-point cell temperature: 1) total mass fraction of impurities, 2) total mole 

fraction impurities, and 3) derivation from analysis of experimental freezing curves. A supplied 
40

material assay of the sample gives the type and amount of impurities.As an overview, Table 13 

gives four methods in order of priority. A detailed description with examples of four different 

samples of indium for each method is described in reference 42. 

Table 13. Overview of the methods used by the NIST PRT Laboratory to estimate and validate 

the impurity uncertainty component of an ITS-90 fixed-point cell. 

Method of Analysis Application

mole fraction sum of impurity 

components 

sample assay used prior to fabrication of 

fixed-point cell

freezing curve

consistency check with mole fraction 

sum of impurity components method, 

after fabrication of fixed-point cell

direct comparison

consistency check with freezing curve 

and mole fraction sum of impurity 

components methods, after fabrication of 

fixed-point cell

1/F realization curve

alternative to freezing curve method; 

consistency check with mole fraction 

sum of impurity components methods 

after fabrication of fixed-point cell

The first method uses the total mass fraction of impurities, which gives an estimate that is 

usually low by at least a factor of two. This method does not take into account the effect 

associated with the different molecular weights of the impurities. The second method gives a 

better estimate by using a binary analysis of each impurity in the matrix metal that incorporates 

the different molecular weights of each impurity. This method is used at NIST to estimate the 

effect of impurities contained within the sample on the realization temperature of the fixed-point 

cell. The third method uses an analysis of experimental freezing curves to estimate the amount of 

impurities contained within the fixed-point cell. This method is implemented on a six-month 

interval basis as a part of the IMAP to check for sample purity changes of the cells with use. 

The estimated impurity uncertainty component value is taken as the standard uncertainty and is 

not considered a rectangular distribution and is not divided by root three. The estimated impurity 

uncertainty component value is treated as a symmetric uncertainty, though the effect is most 

likely asymmetric. 

NIST manufactures all of its own fixed-point cells (except water) and purchases the fixed-point 

cell materials from precious metal refiners. Purification and analysis of the fixed-point samples 

are performed by the refiners. As a minimum, we fabricate and test three fixed-point cells using 

the same sample lot. A sample assay for the specific sample lot is required from the refiner. The 

crosschecks that we perform are an integral part of our quality assurance. It is quite easy for 

fixed-point cells to be contaminated in the fabrication process and relying only on the 

manufacturer’s or any independent laboratories assay, or even an assay with a “margin of safety” 
41

is not sufficient. Using the freezing-curve slope is inadequate by itself, but we see this method 

as very valuable in verifying that the cell construction did not add appreciable impurities. Direct 

comparisons of cells are additional critical insurance that the cells were not contaminated in the 

fabrication process. 

6.1.2 Phase transition repeatability parameter 

The phase transition repeatability parameter is the repeatability of an SPRT used to measure 

multiple realizations of a fixed-point cell. This parameter is used as one of the components of 

uncertainty (Type A, standard deviation of the measurements) for assigning an overall 

uncertainty to the fixed-point cell. As further described in section 6.5.1, the check SPRT is 

measured at the beginning and end of every phase transition realization. This phase transition 

repeatability value gives statistical process control information on the fixed-point cell realization.

6.1.3 Constant cell pressure parameter 

The Constant Cell Pressure parameter is the gas pressure maintained inside each fixed-point cell, 

which affects the realized temperature. The uncertainty of this value is one component (Type B, 

rectangular distribution) used to assign an overall uncertainty to the fixed-point cell. As 

described in Section 4.2, the NIST freezing and melting point cells are open to a gas handling 

system for setting the pressure during realization (101.3 kPa ± 0.027 kPa). The sealed triplepoint cells are checked for integrity using a dedicated check SPRT. 

6.1.4 Cell corrections parameter 

The Cell Corrections parameter is the two pressure corrections for gas pressure and hydrostatic 

head that is applied to the realized temperature of the fixed-point cell. The uncertainty of these 

corrections on the realized temperature is one component (Type B, rectangular distribution) used 

to assign an overall uncertainty to the fixed-point cell. 

6.1.5 Design/Assembly parameter 

The Design/Assembly parameter is the interaction of the fixed-point cells during realization with 

the furnace/maintenance systems. This parameter is closely coupled with the Fixed-Point Cell 

Interaction parameter found in section 6.2: Furnace/Maintenance System. 

6.2 Furnace/Maintenance system element 

6.2.1 Vertical gradient parameter 

The Vertical Gradient parameter is measured over the length of the fixed-point cell sample 

crucible. The maximum temperature non-uniformity for any of the maintenance systems for a 

fixed-point cell is 10 mK. An example is shown in Figure 13. The Vertical Gradient parameter 

is checked once per year. 

6.2.2 Set-point control parameter 

The Set-Point Control parameter influences the duration time of a phase-transition realization of 

the fixed-point cell. During a phase transition realization, the set-point temperature control 

stability of the maintenance system is ±10 mK. See Table 9 for the maintenance system stability 

results for each fixed point. This parameter is checked every six months. Figure 25 shows the 

maintenance system stability for the fixed-point cells from the Ag FP to the Ga TP.
42

Temperature Stability of the NIST Fixed-Point Cell Furnaces

measurements made over at least 15 hours

-10

-8

-6

-4

-2

0

2

4

6

8

10

0.0 0.2 0.4 0.6 0.8 1.0

fraction of measurement time

T / mK

Ag, ±9 mK

Al, ±8 mK

Zn, ±7 mK

Sn, ±6 mK

In, ±4 mK 

Ga, ±10 mK

Figure 25. Temperature stability of the NIST fixed-point cell maintenance systems from the 

Ag FP to the Ga TP. 

6.2.3 Fixed-point cell interaction parameter 

The Fixed-Point Cell Interaction parameter is the interaction of the realized fixed-point cell with 

the maintenance system. This interaction is dependent on the designs of both the fixed-point cell 

and the maintenance system. The maintenance systems are designed to optimize the NISTdesigned fixed-point cell realization. While not directly measurable, this parameter is closely 

coupled with the Design/Assembly parameter found in section 6.1: Fixed-Point Cell Element. 

Details of the designs of and the interactions between the maintenance systems and fixed-point 

cells are in reference 36. 

6.3 SPRT element 

6.3.1 Heat-flux parameter 

The Heat-Flux parameter is one of the few ways to adequately verify that the method used to 

realize the fixed-point cell is performed properly and that the SPRT is near thermal equilibrium 

with the phase transition interface. The effect of heat flux on the temperature measured by the 

SPRT is one of the components (Type B, normal distribution) used to assign an overall 

uncertainty to the fixed-point cell. 

Proper immersion of the SPRT was verified by measuring the SPRT resistance starting at 10 cm 

from the bottom of the thermometer well, then inserting the SPRT in 2 cm steps until 4 cm from 

the bottom, and then inserting the SPRT in 1 cm steps until the bottom of the thermometer well 
43

was reached. After changing the immersion depth of the SPRT, the SPRT was allowed to 

re-equilibrate at each step prior to measurement. The immersion depth of the SPRT was 

calculated from the sensor midpoint to the height of the fixed-point material column during the 

fixed-point realization. 

The Heat Flux parameter is quantified by using the SPRT to measure the immersion profile of 

the phase transition realization of a fixed-point cell. For the SPRT to be near thermal 

equilibrium, the SPRT must be able to track the ITS-90 hydrostatic head effect over the 

bottommost 3 cm. This immersion profile is used to estimate the heat flux uncertainty 

component. Figures 15-23 gives examples of heat flux test results for the pertinent check SPRT 

for each fixed-point cell. Table 10 shows the heat flux test results for various SPRT designs. 

This parameter is checked yearly for each fixed-point cell type with the corresponding check 

SPRT. The immersion profiles of untested SPRT designs are tested prior to calibration. The heat 

flux uncertainty is calculated from the difference between the 3 cm calculated value from a linear 

fit of the bottommost 5 cm measurement values and the 3 cm value calculated from the ITS-90 

assigned hydrostatic head effect. 

6.3.2 Immersion depth parameter 

The Immersion Depth parameter is the effect of the depth of immersion of the SPRT sensor on 

the measured fixed-point cell temperature. This parameter is one of the components (Type B, 

rectangular distribution) used to assign an overall uncertainty to the fixed-point cell. Two 

variables are used to estimate this uncertainty component of the immersion depth parameter: 1) 

the uncertainty in the estimated depth of immersion of the SPRT sensor below the free sample 

surface, and 2) the uncertainty in the estimated liquid-to-solid ratio of the sample. Knowledge of 

the cell dimensions, density of the sample (liquid and solid), and the sample mass allows for the 

immersion depth correction applied to the realization temperature to be calculated with small 

uncertainty. 

6.3.3 Self-heating parameter 

The Self-Heating parameter is the SPRT sensor self-heating effect on the realized fixed-point 

cell temperature. The uncertainty of this parameter is one of the components (Type B, 

rectangular distribution) used to assign an overall uncertainty to the fixed-point cell. The 

uncertainty component is calculated from making SPRT measurements with five excitation 

currents in each fixed-point cell and calculating the range in the zero current extrapolation from 

the possible current combinations. The Self-Heating parameter is checked yearly using 

representative SPRTs of different models. 

6.3.4 Stability parameter 

The Stability parameter checks whether the SPRT is considered stable enough to achieve 

compliance with Section 6.6, Control Artifacts. Two measurements of stability are used for this 

determination: 1) prior to a calibration, the SPRT resistance, R(TPW), must repeat at the TPW to 

within the equivalence of 0.2 mK between annealing (see section 4.1); and 2) the SPRT 

resistance must repeat at the TPW to within the equivalence of 0.75 mK during the calibration 

process. 
44

6.3.5 Wetness parameter 

The Wetness parameter tests for moisture within the sheath of an SPRT. The first test is to 

measure the R(TPW) of the SPRT at currents of 1 mA, 1.41 mA, and 1 mA. The two 1 mA 

values of SPRT resistance should repeat to within 2 μΩ. A lower second 1 mA value (10 μΩ) 

may indicate that water within the sheath of the SPRT is condensing on the sensor. The second 

test involves measuring the amount of time the SPRT requires to come to equilibrium at the 

TPW from ambient conditions. A “dry” SPRT will be within 0.1 mK of equilibrium within five 

minutes. The third test involves placing the sheath of the SPRT through the bottom of a 

polystyrene cup such that the rim of the cup is near the head of the SPRT. After allowing for the 

SPRT to equilibrate at the TPW, the cup is filled with crushed dry ice. If the SPRT is “wet”, the 

condensed water will move from the sensor to the dry ice location along the SPRT sheath and a 

different R(TPW) will be measured. Based on the results of the three tests, a “wet” SPRT is 

rejected. Figure 26 shows one SPRT that passes the wetness test and one that does not. 

20

15

10

5

0

5

0 10 20 30 40 50 60

Minutes in TPW cell

[R (TPW) - Avg. R (TPW)], mK

SPRT 1X

SPRT 2Y

dry ice added

to styrofoam cup

Figure 26. Results of the wetness test for two SPRTs. SPRT 1X passes the wetness test, while 

SPRT 2Y does not. 

6.3.6 Contamination parameter 

The Contamination parameter influences the stability of an SPRT during calibration. The SPRT 

shows signs of possible contamination when the R(TPW) value increases and the W(Ga TP) 

value decreases (i.e. decrease sensitivity) over time. Details on using Pt protection tubes to 

prevent metal ion contamination above 700 °C are found in Section 4.3.

6.3.7 Light-Piping parameter 

The Light-Piping parameter is the influence of the room lights on the SPRT measurement of the 

realized temperature of the fixed-point cell. This parameter directly influences the heat-flux 

parameter within Section 3: SPRT. The light-piping effect along an SPRT sheath is the 

difference obtained when measuring an SPRT in a realized fixed-point cell with the room lights 

on and the room lights off. 
45

6.4 Measurement system element 

6.4.1 Repeatability parameter 

The Repeatability parameter of the Measurement System Element is statistically determined 

from making two similar measurements. The first method is to measure a thermostatically 

controlled (±10 mK) reference resistor over at least a 10 h period to determine the repeatability 

of only the resistance ratio bridge. The second method is to measure an SPRT in either a TPW 

cell or a Ga TP cell over at least a 10 h period to determine the repeatability of the measurement 

system under nominal SPRT calibration conditions. For either method, the repeatability is 

expected to be within 4 μΩ peak-to-peak. We use the second method to assign a value to the 

bridge repeatability uncertainty component (Type A) [43,44]. Figure 27 shows the repeatability 

of the ASL F900 while measuring an SPRT in a TPW cell. The Repeatability parameter is 

checked once every six months. 

1.0

0.0

1.0

0 25 50 Hours of measurements

(R x  R avg), μW

Figure 27. ASL F900 Measurement repeatability of an SPRT in a TPW cell. 

6.4.2 Non-Linearity parameter 

The Non-Linearity parameter is measured once per year using a commercially available Hamon 

Box network designed for ac measurement systems [13]. See Section 6.4.8 for a description on 

how to determine this parameter. 

6.4.3 Ratio-error parameter 

The Ratio-Error parameter is used to assign a value to the ratio error uncertainty component 

(Type A). The results are obtained using both a commercially available Hamon Box and a 

commercially available ratio turns unit, and verified by the results from a two-way ratio 

complements check [13,45-49]. See Section 6.4.8 for a description on how to determine this 

parameter. 

6.4.4 Ohm parameter 

The Ohm parameter is comprised of two parts. The first part is the maintenance of the ohm. The 

reference resistors (1 Ω, 10 Ω, and 100 Ω) are calibrated biannually at NIST [50]. The second 

part is the thermostatic control of those reference resistors. An oil bath maintains the reference 

resistors at a temperature of 25 °C ± 0.01 °C. The temperature coefficient of resistance of the 

reference resistor times the oil bath stability gives a value of the reference-resistor stability. The 
46

reference-resistor uncertainty component is calculated from the determination of the effect of the 

two parts of the Ohm parameter. During measurements, the software checks the second part of 

the Ohm parameter for stability compliance every three seconds.

6.4.5 AC quadrature parameter 

The AC Quadrature parameter is the ac quadrature /frequency dependence of an ac resistance 

ratio bridge. The ac quadrature uncertainty (Type B, rectangular) is the difference between the 

low frequency (30 Hz) and the high frequency (90 Hz) measurements of an SPRT in a realized 

fixed-point cell [51]. No separate parameter is assigned for the difference between ac and dc 

measurements. This parameter is checked once per year. See Section 6.4.8 for a description on 

how to determine this parameter. 

6.4.6 Current parameter 

The Current parameter is the measurement of the two excitation currents (e.g. 1 mA and 

1.41 mA) supplied by the ac resistance ratio bridge used to measure the SPRTs. The excitation 

current is calculated from the determination of the R(t90) and the measured the voltage across the 

voltage leads of the SPRT. The voltage is measured using an 8.5 digit voltmeter. This check is 

used to validate the reference ratio bridge current supply. The determined excitation currents are 

used to calculate the zero power R(t90) values. 

6.4.7 Number of readings parameter 

The Number of Readings Parameter is a fixed number of readings measured at each excitation 

current. Four sets of nine readings at each current are used to calculate a mean and standard 

deviation. In order to eliminate any possible settling effects, the first three balanced readings are 

not counted in each group of nine readings. The resistance ratio bridge is forced to rebalance 

after every group of nine readings to reduce the possibility of directional balance bias. The total 

number of readings is chosen to give enough degrees of freedom to the statistics of the 

measurements (e.g. standard deviation). The standard deviation of the thirty-six readings is 

expected to be <1 μΩ for a 25.5 Ω SPRT.

6.4.8 Validating resistance ratio bridges 

Performance assessments of the resistance ratio bridges facilitate estimation of the uncertainties 

arising from the resistance measurement. Such components are included in the overall 

uncertainty budgets assigned to the realization of the ITS-90 fixed-point cells and to the 

calibration of SPRTs. 

We utilize several methods to assess the uncertainties arising from use of the resistance ratio 

bridges [13,45-49]. They include: a Hamon-type resistance network [AEONZ resistance bridge 

calibrator (RBC)], a ratio turns tester [ASL ratio test unit (RTU)], ratio complements checks, 

tests of ac quadrature/frequency dependence, and measurement repeatability. The four 

uncertainty components derived from the performance assessment include non-linearity, ratio 

error, ac quadrature/frequency dependence, and repeatability. The results of the assessment are 

not used to “calibrate” or “correct” the resistance ratio bridge, but are used as a check for 

compliance the manufacturer’s specifications and to establish uncertainty values.
47

The ratio error uncertainty component (Type A) is the result obtained using the RBC, verified by 

the results from the ASL RTU for the ac bridges and the two-way ratio complements check. 

Figure 29 gives an example of the results from the RBC, the RTU, and the complements check 

measurements for an ASL F900, respectively. 

0.10

0.05

0.00

0.05

0.10

0.0 0.5 1.0

Bridge ratio

(Measured  Expected)  ́ 10

6

Figure 29. Results from the AEONZ RBC (closed diamonds), ASL RTU (open squares), and the 

ratio complements check (open circle) measurements for an ASL F900.

The RBC uses four base resistors wired similarly to Hamon build-up resistors [45-48]. Using the 

various series and parallel combinations of the four base resistors, the RBC gives 35 different 

four-wire resistances over the range from 16.8 W to 129.9 W. These 35 resistances are used to 

assess the non-linearity of the resistance ratio bridge. Additionally, up to 35 possible reciprocal 

values are available to quantify the ratio error. However, only 10 of these reciprocal values are 

within the ac bridge resistance range of 0.0 W to 129.9 W with a 100 W reference resistor. The 

measurement of all possible resistance ratios verifies that the resistance ratio bridge properly 

activates the internal relays used to set the number of turns to achieve balance. 

The stated accuracy of the network is better than 1 part in 108 for ac resistance ratio bridges. The 

manufacturer specifies a periodic maintenance check of the insulation resistance, nominal values 

of the four base resistors, and four-wire connections. The four base resistors are not 

thermostatically controlled and the temperature coefficient of resistance of those resistors is 3 

parts in 106 per °C. To meet the stated accuracy, the temperature instability of the resistors 

should not exceed 10 mK during the measurements. We placed the RBC used by NIST in an 

insulated box and monitor the temperature with a platinum resistance thermometer. Software for 

calculating the non-linearity and the ratio error is provided with the device. 

The ASL ratio test unit (RTU) provides 14 distinct resistance ratio values ranging from 

0.000 000 000 to 1.181 181 182. An inductive voltage divider contained within the RTU 

generates these ratio values in integer multiples of elevenths. 
48

The RTU allows the user to verify four parameters that check the operational compliance of the 

ac resistance ratio bridge with the manufacturer’s specifications. The checks ensure: 1) that the 

correct number of turns were wound on the inductive voltage divider of the user’s ac resistance 

ratio bridge, 2) that the implementation of the internal relays to set the number of turns to 

achieve balance is performed properly, 3) that the non-linearity of the ac resistance ratio bridge is 

within specification, and 4) that the effect of uneven lead resistance (up to 100 W) does not 

compromise the measurement. Since the RTU supplies the 14 ratios from the internal inductive 

voltage divider, no subsequent calibration of the RTU is necessary. No external reference 

resistors are required for these measurements. 

The ratio complements check method is another means of verifying the ratio error of resistance 

ratio bridges and is independent of the calibration values of the reference resistors used. We 

perform a two-way complements check, using two resistors nominally of the same value (e.g. 

two 100 W), by measuring the normal and reciprocal resistance ratio values of the two reference 

resistors. The ratio error is determined from the equation: 

2

[( /(1 )( / )] 10 (10 )

6

6 1221  xRRRR

  

where the R quotients are the measured ratios; and R1 and R2 are nominally 100 W for an ac 

resistance ratio bridge. 

Additionally, a three-way complements check using the ratios of three different resistors (e.g. 

10 W, 25 W, and 100 W) permuted is a simple method to spot check the non-linearity of the 

resistance ratio bridge [49]. 

6.5 Realization technique 

6.5.1 Duration of a realization curve parameter 

The Duration of a Realization Curve parameter equals the amount of time available in which to 

make SPRT measurements of a fixed-point cell phase transition, as determined from 

measurements of the fixed-point cell realization curve. The furnace set-point temperature is 

adjusted so that each cell realization curve lasts a minimum of 16 h. This is so that SPRT 

measurements are made over the first half of the realization curve where the smallest amounts of 

impurities are segregated into the solid sample. This parameter is checked as part of the Check 

SPRT parameter of the Measurement Assurance Element in section 6.6.

6.5.2 SPRT immersion profile parameter 

The SPRT Immersion Profile parameter is the result of the Heat Flux parameter measurements 

discussed in Section 6.2.1. This parameter verifies that the SPRT is in near thermal equilibrium 

with the fixed-point cell phase transition.

6.6 SPRT calibration measurement assurance element 

The Measurement Assurance Element is divided into three internal and one external 

measurement assurance parameters. The three internal parameters verify that the SPRT is 
49

calibrated to within the stated calibration uncertainties. The external parameter verifies that the 

NIST realization temperatures of the fixed-point cells and assigned uncertainties are consistent 

with other National Metrology Institutions. 

6.6.1 Check SPRT parameter 

The Check SPRT parameter is the most critical measurement parameter for the daily calibration 

of SPRTs. A check SPRT is assigned to each fixed-point cell type and measured only at that 

fixed point and the TPW cell. For each realized fixed-point cell plateau, a check SPRT is 

measured before and after all measurements with calibration SPRTs. For the fixed-point cell 

realization to be acceptable for the calibration of SPRTs, the difference between the first and 

second measured values of the check SPRT must not exceed a maximum allowable change (e.g. 

t90 = W2(t90 check SPRT) – W1(t90 check SPRT). The check SPRT is used as a total system check and 

statistical process control on the whole calibration process of an SPRT [1-3]. The data 

acquisition software checks this parameter for every phase-transition realization of a fixed-point 

cell. Figure 28 shows the control chart for the Ga TP check SPRT. 

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0 50 100 150 200 250 300 350

(Number of realizations) x 2

[W x(Ga)-W avg(Ga)] / mK

s.d. 0.02 mK

range: 0.07 mK

170 realizations with the Ga Check SPRT

Figure 28. Control chart for the Ga TP cell. Each data point is the average 36 readings. 

6.6.2 Fixed-point cell certification parameter 

The Fixed-Point Cell Certification parameter is used to certify new and re-certify current 

reference fixed-point cells [14]. New fixed-point cells undergo certification prior to becoming 

NIST ITS-90 defining standards. This process includes analyzing three melting and three 

freezing curves (freezing curves are not applicable for a Ga TP or TPW cells), an SPRT 

immersion profile, and three direct comparisons with the current reference cell. The realization 

temperature of a new fixed-point cell must agree with the realization temperature of the 

laboratory reference fixed-point to within the expected impurity effect difference and 

measurement uncertainties (k=2). Every six months a new phase transition realization curve of 

the current reference standard is performed to compare with the previous realizations [3, 6-8,10].
50

6.6.3 SPRT calibration results parameter 

Within the SPRT Calibration Results parameter, the calibrated SPRT must meet several ITS-90 

and NIST criteria in order to be designated as an ITS-90 defining standard with the NISTassigned calibration uncertainties. Failure of the SPRT to meet any of the criteria described 

below results in the rejection of the SPRT for use as a defining standard, and the SPRT is 

returned without calibration values. 

As discussed in section 2.2, the ITS-90 defined criterion is the minimum purity requirement of 

the platinum sensor as determined from the W(Ga MP) or W(Hg TP) and the W(Ag FP) for use 

above 660.323 °C. 

The six NIST criteria verify that the SPRT is calibrated to within the NIST assigned 

uncertainties. The software automatically checks these criteria during the calibration process. 

There are three criteria for the SPRT stability at the R(TPW). Within five annealing cycles, the 

SPRT R(TPW) value before and after an annealing cycle must repeat to within the equivalent of 

0.2 mK. The SPRT must not change by more than the equivalent of 0.3 mK for the R(TPW) 

measured before and after each other fixed-point cell. The total SPRT R(TPW) change during a 

calibration must not exceed the equivalent of 0.75 mK. 

The SPRT is measured at all of the ITS-90 fixed points over a given temperature subrange or 

subranges. The redundant fixed points (not required in the calculation of ITS-90 coefficients) 

give a measure of the error/non-uniqueness associated with the calibration of the SPRT. Based 

on measurements of a set of SPRTs (n>30), the error/non-uniqueness at the Ga MP and the In FP 

should not exceed ±0.2 mK and ±0.3 mK, respectively. Since no redundant ITS-90 fixed points 

exist between the Ar TP and the TPW, the above 0 °C temperature subrange is extrapolated to 

the Hg TP temperature to check the measured W(Hg TP). Based on measurements of a set of 

SPRTs (n>1000), the extrapolation to the Hg TP temperature should be within ±1.5 mK of the 

calibration value.

6.6.4 External comparison parameter 

The External Comparison parameter consists of three types of comparisons: key, bilateral, and 

supplemental comparisons. Results of these types of external comparisons are used at NIST to 

improve both the fixed-point cell realizations and SPRT calibrations, and assess the uncertainties 

assigned to the both the NIST ITS-90 fixed-point cells and SPRT calibrations. Detailed 

information regarding these types of comparisons is given in Refs. [34,35,52-55].

7 ITS-90 Uncertainties 

There are several levels of uncertainties that are used to determine the overall uncertainty 

assigned to the calibration of an SPRT. First, expanded uncertainties (k=2) are assigned to the 

NIST ITS-90 fixed-point cells [56]. Second, uncertainties associated with the non-uniqueness of 

the scale are assigned to the ITS-90 temperature subranges. Third, the pertinent uncertainties of 

the fixed-point cells and non-uniqueness are combined and propagated through each ITS-90 

temperature subrange to acquire an overall SPRT calibration uncertainty. In most cases, the end 

user of the SPRT will use the maximum uncertainty value for a given ITS-90 temperature 

subrange as one uncertainty component (Type B) in their overall uncertainty budget for their 

measurement of temperature. 
51

The uncertainties given in this document do not contain estimates for: 1) any effects introduced 

by transportation of the SPRT between NIST and the end user’s facility, 2) drift of the SPRT 

from use by the end user, 3) the propagated measurement and realization uncertainty of the end 

user’s TPW value [e.g. R(TPW)] and 4) any additional measurement uncertainty introduced by 

the user. 

7.1 Fixed-point cell realization uncertainties 

Table 14 gives the list of uncertainty components and the expanded uncertainties for each of the 

NIST SPRT Calibration Laboratory ITS-90 fixed-point cells. This list follows the suggestions of 

the CCT WG3 [57] and contains the same values as those found in the BIPM KCDB Appendix C 

(Calibration and Measurement Capabilities). The degrees of freedom for the Type A 

uncertainties are large enough that a coverage factor of k=2 corresponds closely to a 95 % 

coverage probability, and for the Type B uncertainties the effective degrees of freedom are 

infinite. The derivation of the uncertainty values listed in Table 14 are derived by measurements 

and calculations described in Section 6 and reference 56. 
52

Table 14. NIST SPRT Calibration Laboratory ITS-90 fixed-point cell realization uncertainties. 

Values are in millikelvins.

Unc. 

Type

Ag

FP

Al

FP

Zn

FP

Sn

FP

In

FP

Ga

TP TPW HgTP

Ar

TP

Bridge 

Repeatability A 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002

Bridge NonLinearity A 0.031 0.024 0.022 0.021 0.021 0.020 0.020 0.019 0.018

AC Bridge 

Quadrature BR 0.018 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.005

Reference 

Resistor Stability BR 0.008 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.005

Phase Transition 

Realization 

Repeatability

A 0.52 0.28 0.18 0.12 0.04 0.02 0.005 0.069 0.03

Chemical 

Impurities BN 0.29 0.27 0.17 0.06 0.07 0.01 0.01 0.01 0.05

Hydrostatic-Head 

Correction BR 0.012 0.004 0.006 0.005 0.008 0.003 0.001 0.016 0.008

SPRT SelfHeating 

Correction

BR 0.013 0.01 0.01 0.01 0.01 0.01 0.012 0.012 0.01

Heat Flux BN 0.011 0.005 0.003 0.003 0.002 0.002 0.003 0.004 0.03

Gas Pressure BR 0.023 0.027 0.016 0.013 0.019 0 0 0 0

Slope of Plateau BR 0 0 0 0 0 0 0 0 0

Isotopic 

Variation BR 0 0 0 0 0 0 0.006 0 0

Propagation of 

TPW BR 0.099 0.069 0.048 0.033 0.018 0.016 0 0.014 0.003

uc (k=1) 0.605 0.397 0.254 0.141 0.089 0.037 0.028 0.077 0.070

U (k=2) 1.21 0.79 0.51 0.28 0.18 0.07 0.06 0.15 0.14

Note: BR is a Type B uncertainty with a rectangular distribution and BN is a Type B uncertainty 

with a normal distribution. 
53

7.2 Propagated fixed-point uncertainty for each ITS-90 temperature subrange 

The total calibration uncertainty at any given temperature within an ITS-90 temperature subrange 

is determined from the combined individual uncertainties arising from the propagated 

uncertainty of each of the relevant ITS-90 fixed points and the ITS-90 non-uniqueness. The 

propagated uncertainty for a given ITS-90 temperature subrange from each ITS-90 fixed point is 

calculated by using the assigned uncertainty for that fixed point and setting the other fixed-point 

uncertainties to zero [3]. The individually propagated fixed-point uncertainties are combined by 

calculating the root sum square (RSS) to determine the overall contribution of the fixed point 

uncertainties to the uncertainty assigned to the calibrated SPRT as a function of ITS-90 

temperature subrange. 

Figures 30-37 show the uncertainty propagation curves for the ITS-90 temperature subranges. 

The propagated uncertainty curve for the TPW (0.1 mK used for convenience) given in Figure 38 

is the uncertainty incurred by the user, not an additional uncertainty in the NIST calibration. 

0.5

0.0

0.5

1.0

1.5

0 250 500 750 1000

Temperature, °C Propagated uncertainty (k =2), mK

Ag: U (1.21 mK) Al: U (0.79 mK)

Zn: U (0.51 mK) Sn: U (0.28 mK)

Total Expanded

Uncertainty

Figure 30. Propagated fixed-point uncertainty for the temperature subrange 0 °C to the Ag FP 

(0 °C to 962 °C). Only the positive uncertainty of the individually propagated fixed-point and the 

total uncertainties are shown.
54

0.5

0.0

0.5

1.0

0 200 400 600

Temperature, °C Propagated uncertainty (k =2), mK

Al: U (0.79 mK) Zn: U (0.51 mK)

Sn: U (0.28 mK) Total Expanded

Uncertainty

Figure 31. Propagated fixed-point uncertainty for the temperature subrange 0 °C to the Al FP 

(0 °C to 661 °C). Only the positive uncertainty of the individually propagated fixed-point and the 

total uncertainties are shown. 

0.5

0.0

0.5

1.0

0 200 400

Temperature, °C Propagated uncertainty (k =2), mK

Zn: U (0.51 mK) Sn: U (0.28 mK) Total Expanded

Uncertainty

Figure 32. Propagated fixed-point uncertainty for the temperature subrange 0 °C to the Zn FP 

(0 °C to 420 °C). Only the positive uncertainty of the individually propagated fixed-point and the 

total uncertainties are shown. 
55

0.2

0.0

0.2

0.4

0 100 200

Temperature, °C Propagated uncertainty (k =2), mK

Sn: U (0.28 mK) In: U (0.18 mK) Total Expanded

Uncertainty

Figure 33. Propagated fixed-point uncertainty for the temperature subrange 0 °C to the Sn FP 

(0 °C to 232 °C). Only the positive uncertainty of the individually propagated fixed-point and the 

total uncertainties are shown. 

0.1

0.0

0.1

0.2

0 50 100 150

Temperature, °C Propagated uncertainty (k =2), mK

In: U ( 0.18 mK)

and Total Expanded

Uncertainty

Figure 34. Propagated fixed-point uncertainty for the temperature subrange 0 °C to the In FP 

(0 °C to 157 °C). Only the positive uncertainty of the individually propagated fixed-point and the 

total uncertainties are shown. 
56

0.02

0.00

0.02

0.04

0.06

0.08

0 15 30

Temperature, °C Propagated uncertainty (k =2), mK

Ga: U (0.07 mK)

and Total Expanded

Uncertainty

Figure 35. Propagated fixed-point uncertainty for the temperature subrange 0 °C to the Ga TP 

(0 °C to 30 °C). Only the positive uncertainty of the individually propagated fixed-point and the 

total uncertainties are shown. 

0.1

0.0

0.1

0.2

40 20 0 20

Temperature, °C Propagated uncertainty (k =2), mK

Hg: U (0.15 mK) Ga: U (0.07 mK)

Total Expanded

Uncertainty

Figure 36. Propagated fixed-point uncertainty for the temperature subrange Hg TP to the Ga TP 

(–40 °C to 30 °C). Only the positive uncertainty of the individually propagated fixed-point and 

the total uncertainties are shown. 
57

0.1

0.0

0.1

0.2

0.3

0.4

200 150 100 50 0

Temperature, °C Propagated uncertainty (k =2), mK

Ar: U (0.14 mK) Hg: (0.15 mK) Total Expanded

Uncertainty

Figure 37. Propagated fixed-point uncertainty for the temperature subrange Ar TP to 0.01 °C 

(190 °C to 0.01 °C). Only the positive uncertainty of the individually propagated fixed-point 

and the total uncertainties are shown. 

0.0

0.2

0.4

0.6

250 0 250 500 750 1000

Temperature, °C Propagated uncertainty, mK

For a 0.1 mK uncertainty

at the H2O TP

Zn

Al

Ag

Sn

In

Ga

Ar TPW

Hg

Figure 38. Propagated fixed-point uncertainty for the TPW. A 0.1 mK uncertainty is chosen for 

convenience. This is an uncertainty incurred by the end user of the SPRT and must be adjusted to 

the end user’s TPW uncertainty. 
58

7.3 ITS-90 non-uniqueness uncertainty contribution to SPRT calibration uncertainties 

The ITS-90 contains three types of non-uniqueness labeled non-uniqueness I, II, and III [10-

12,58]. Only non-uniqueness Types I and III are applicable to the uncertainty of a calibrated 

SPRT. Type I non-uniqueness is the uncertainty associated with subrange inconsistencies: for a 

single SPRT, different ITS-90 temperature subranges give different temperatures in the 

overlapping temperature range. Type III non-uniqueness is the uncertainty due to differences in 

actual SPRTs: two SPRTs calibrated in the same way will give different temperatures for a given 

ITS-90 temperature subrange. Table 15 gives the non-uniqueness uncertainties assigned to each 

ITS-90 temperature subrange. 

Table 15. Non-uniqueness uncertainties (k=2) for each ITS-90 temperature subrange to be 

applied to an SPRT calibrated with ITS-90 fixed-point cells. 

ITS-90

Temperature Subrange

Non-Uniqueness

Type I (k=2), mK

Non-Uniqueness

Type III (k=2), mK

Ar TP to 0.01 °C 0 0.28

Hg TP to Ga MP 0 0.18

0 °C to Ga MP 0 0

0 °C to In FP 0.27 0.15

0 °C to Sn FP 0.38 0.09

0 °C to Zn FP 0.19 0.22

0 °C to Al FP 0.13 0.16

0 °C to Ag FP 0.13 1.54

7.4 SPRT calibration uncertainty for each ITS-90 temperature subrange 

The total uncertainty of the NIST-calibrated SPRT is important to the end user of the SPRT since 

that uncertainty is an essential part of the total uncertainty of the end user’s determination of 

temperature. The RSS of the maximum value for the combined propagated fixed-point cell and 

non-uniqueness contribution is used to calculate the total SPRT calibration uncertainty for each 

ITS-90 temperature subrange. Table 16 gives the maximum SPRT calibration uncertainty for 

each ITS-90 temperature subrange. 
59

Table 16. Maximum SPRT calibration uncertainty for each ITS-90 temperature subrange. 

ITS-90 Temperature Subrange Maximum Uncertainty

(k=2), mK

Ar TP to 0.01 °C 0.40

Hg TP to Ga MP 0.23

0 °C to Ga MP 0.07

0 °C to In FP 0.36

0 °C to Sn FP 0.48

0 °C to Zn FP 0.59

0 °C to Al FP 0.82

0 °C to Ag FP 1.97

7.5 Extrapolation uncertainty for selected ITS-90 temperature subranges 

The NIST Thermometry Group does not advocate extrapolating any calibrated SPRT beyond the 

temperature range of calibration. However, in practice some of the ITS-90 temperature subranges 

may be extrapolated over a small range with an additional uncertainty of less than 1 mK [3].

Table 17 gives the extrapolated uncertainty on two of the most commonly extrapolated ITS-90 

temperature subranges: Ar TP to 0.01 °C and 0 °C to the Zn FP. For these two ITS-90 

temperature subranges, the NIST Report of Calibration for the SPRT gives the 1 mA calibration 

table over the extrapolated temperature range. 

Table 17. Extrapolation uncertainties for selected ITS-90 temperature subranges and calibrated 

SPRT uncertainties in that extrapolated range. 

ITS-90

Temperature 

Subrange

Extrapolated 

Temperature 

Range, °C

Extrapolation Range 

Uncertainty (k=2), mK

Maximum SPRT Calibration 

Uncertainty (k=2) Including 

Extrapolated Range, mK

Ar TP to 0.01 °C

–189.3442 °C to 

0.01 °C

–200 to 0 0.1 0.50

0 °C to Zn FP

0 °C to 419.527 °C

0 to 500 1 1.59
60

7.6 Temperature measurement uncertainty of a calibrated SPRT 

To calculate the total uncertainty (where k=2) of a temperature measurement with a calibrated 

SPRT, first determine the expanded uncertainty of the resistance ratio measurement, including 

readout uncertainties, stabilities of any reference resistors, uncertainty of the TPW realization, 

and, if necessary, an allowance for change of the SPRT resistance at the TPW since the last 

actual measurement at the TPW. The uncertainty in equivalent temperature units is obtained by 

multiplying the error in W(t90) by dt/dW(t90), as given in the W(t90) vs. t90 table contained in the 

Report of Calibration. See Figure 38 as an example, an uncertainty curve for the propagation of 

an assumed 0.1 mK TPW uncertainty to the temperature of interest. To this uncertainty, add the 

maximum SPRT calibration uncertainty for each ITS-90 temperature subrange as a Type B 

uncertainty (Refer to Table 16). 

8 Quality System 

The NIST quality system documentation consists of tiered quality manuals, ranging from the 

highest level (QM-I) to Division level (QM-IIs) to Service level (QM-IIIs) and in some cases 

project level (QM-IVs) [41]. The NIST quality manual (QM-I) NIST is found at 

http://ts.nist.gov/QualitySystem/ 

The integrity, reliability, and traceability of the NIST measurement services relies on the NIST 

Quality System for Measurement Services, which is based on the ISO/IEC 17025 (General 

requirements for the competence of testing and calibration laboratories) [40] and the relevant 

requirements of ISO/IEC Guide 34 (General requirements for the competence of reference 

material producers) [59].

The Measurement Services Advisory Group (MSAG) serves as the corporate quality manager; 

they are assisted by staff from the National Voluntary Laboratory Accreditation Program for the 

implementation of the quality system. 

The NIST quality system for measurement services satisfies the requirements of the International 

Committee for Weights and Measures (CIPM) Mutual Recognition Arrangement (MRA) [60] for 

recognition of national measurement standards; and as such, is recognized as conformant to the 

ISO/IEC 17025 and ISO Guide 34 by the Inter-American Metrology System (SIM) Quality 

System Task Force and the Joint Committee of the Regional Metrology Organizations and the 

BIPM (JCRB). The BIPM is the International Bureau of Weights and Measures. 

In order to maintain compliance with the MRA, NIST participates in a large number of 

international comparisons with other NMIs to support our calibration measurement capabilities 

and uncertainty claims. 
61

9 References 

 

1. Preston-Thomas H., The International Temperature Scale of 1990 (ITS-90), Metrologia

27, 3-10, 1990; ibid. p 107.

2. CCT Working Group 1, "Supplementary Information for the International Temperature 

Scale of 1990", BIPM, 177 pp., 1990. 

3. Mangum B.W., Furukawa G.T., “Guidelines for realizing the International Temperature 

Scale of 1990 (ITS 90)”, NIST Technical Note 1265, 1990.

4. Mangum B.W., Furukawa G.T, Meyer, C. W., Reilly, M. L., Strouse, G. F. and Tew, W. 

L., “A Realization of the ITS-90 at the National Institute of Standards and Technology”, 

in Proc. TEMPMEKO’96, p. 33-38, 1996.

5. Strouse, G.F., "NIST implementation and realization of ITS-90 over the range of 83 K to 

1235 K: reproducibility, stability and uncertainties", in Temperature, Its Measurement 

and Control in Science and Industry, Vol. 6. p. 169-174, 1992.

6. Tew, W.L., “Calibration of Cryogenic Resistance Thermometers between 0.65 K to 

165 K on the International Temperature Scale of 1990”, NIST SP250-XX, in press. 

7. Mangum, B.W. and Thornton, D.D., CCT/78-13 (1978). 

8. Strouse, G.F. and Furukawa, G.T., “Thermal Characteristics of the NIST Fixed-Point 

Cells, Furnaces, and Maintenance Baths over the Temperature Range from 83.8058 K to

1234.93 K”, in Proc. TEMPMEKO 1999, p. 153-158, 1999.

9. Meyer, C.W. and Tew, W.L., “ITS-90 Non-uniqueness from PRT Subrange 

Inconsistencies over the Range 24.56 K to 273.16 K”, Metrologia 43, 341-352, 2006.

10. Strouse, G.F., "Investigation of the ITS 90 subrange inconsistencies for 25.5-ohm 

SPRTs", in Temperature, Its Measurement and Control in Science and Industry, Vol. 6, 

p. 165-168, 1992.

11. Strouse, G.F., "NIST assessment of ITS-90 non-uniqueness for 25.5 ohm SPRTs at 

gallium, indium and cadmium fixed points", in Temperature, Its Measurement and 

Control in Science and Industry, Vol. 6, p. 175-178, 1992.

12. Furukawa, G.T and Strouse, G.F., “Investigation of the Non-Uniqueness of the ITS-90 in 

the Range 660 °C to 962 °C”, in Proc. TEMPMEKO 2001, Vol. 1, p. 553-558, 2001. 

13. Strouse, G.F. and Hill, K.D., “Performance Assessment of Resistance Ratio Bridges used 

for the Calibration of SPRTs,” in Temperature: Its Measurement and Control in Science 

and Industry, Vol. 7, p. 327-332, 2003.
62

14. Strouse, G.F., NIST Certification of ITS-90 Fixed-Point Cells from 83.8058 K TO 

1234.93 K: Methods and Uncertainties”, in Proc. TEMPMEKO 2004, p. 879-884, 2005.

15. Moiseeva, N.P., Pokhodun, A.I., Mangum, B.W., Strouse, G.F., “Investigation of 

Stability of HTPRTs at High Temperature”, in Proc. TEMPMEKO 1999, p371-376, 

1999.

16. Minor, D.B and Strouse G.F., “Stabilization of SPRTs for ITS-90 Calibration”, NCSLI 

Conference Proceedings, 2005.

17. Strouse, G.F., “Internal Measurement Assurance for the NIST Realization of the ITS-90 

from 83.8 K to 1234.93 K”, in Temperature: Its Measurement and Control in Science 

and Industry, Vol. 7, p. 879-884, 2003.

18. Strouse, G.F. and Mangum, B.W., "NIST Measurement Assurance of SPRT Calibrations 

on the ITS-90: A Quantitative Approach", Proceedings of the Measurement Science 

Conference, Anaheim, CA, January 1993. 

19. Strouse, G.F., Furukawa, G.T., Mangum, B.W., and Pfeiffer, E.R., “NIST Standard 

Reference Materials for Use as Thermometric Fixed Points”, NCSLI Conference 

Proceedings, 1997. 

20. Furukawa, G.T., Riddle, J.L., Bigge, W.R., and Pfeiffer, E.R., “Standard Reference 

Materials: Application of Some Metal SRMs as Thermometric Fixed Points”, NIST 

SP260-77, 140 pp, 1982. 

21. Furukawa, G.T., “Argon triple point apparatus with multiple thermometer wells”, in 

Temperature: Its Measurement and Control in Science and Industry, Vol. 6, p. 265-269, 

1992.

22. Mangum, B.W., "Platinum Resistance Thermometer Calibrations”, NBS Special 

Publication SP 250-22, 364 pp., 1987.

23. Furukawa, G.T., “Realization of the mercury triple point”, in Temperature: Its 

Measurement and Control in Science and Industry, Vol. 6, p. 281-285, 1992. 

24. Strouse, G.F. and Lippiatt, J., “New NIST Mercury Triple-Point Cells”, in Proc. 

TEMPMEKO 2001, Vol. 2, p. 783-788, 2002.

25. Zhao, M. and Strouse, G.F., “VSMOW Triple Point of Water Cells: Borosilicate versus 

Fused-Quartz”, Int. J. Thermophysics, (in press). 

26. Strouse, G.F. and Zhao, M., “The Impact of Isotopic Concentration, Impurities, and Cell 

Aging on the Water Triple Point Temperature”, Int. J. Thermophysics, (in press). 
63

27. Strouse, G.F., Furukawa, G.T., and Mangum, B.W., “Preliminary Results of a 

Comparison of Water Triple-Point Cells Prepared by Different Methods,” CCT/93-24, 

1993.

28. Strouse, G.F., “NIST Realization of the Gallium Triple Point”, in Proc. TEMPMEKO 

1999, Vol. 1, p. 147-152, 1999.

29. Strouse, G.F., “Standard Reference Materials: Standard Reference Material 1745: Indium 

Freezing-Point Standard and Standard Reference Material 2232: Indium DSC MeltingPoint Standard”, NIST SP260-132, 2001.

30. Mangum, B.W., “Determination of the Indium Freezing-point and Triple-point 

Temperatures”, Metrologia 26, 211-217, 1989. 

31. Strouse, G.F., Moiseeva, N.P., “Standard Reference Materials: Tin Freezing-Point 

Standard – SRM 741a”, NIST SP260-138, 1999. 

32. Strouse, G.F. and Ince, A.T., “Standard Reference Materials: Standard Reference 

Material 1747: Tin Freezing-Point Cell and Standard Reference Material 1748: Zinc 

Freezing-Point Cell”, NIST SP260-127, 1997. 

33. Strouse, G.F., “Standard Reference Materials: Standard Reference Material 1744: 

Aluminum Freezing-Point Standard”, NIST SP260-124, 1995.

34. Strouse, G.F., Mangum, B.W., Nubbemeyer, H.G., and Jung, H.J., “A Direct Comparison 

of Three PTB Silver Fixed-Point Cells with the NIST Silver Fixed-Point Cell”, 

CCT/93-22, 1993.

35. Mangum, B.W., Pfeiffer, E.R., Strouse, G.F., Valencia-Rodriguez, J., Lin, J.H., Yeh, 

T.I., Marcarino, P., Dematteis, R., Zhao, Y. Lium Q., Ince, A.T., Cakiroglu, F., 

Nubbemeyer H.G., and Jung, H.J., “Comparison of some NIST fixed-point cells with 

similar cells of other standards laboratories”, Metrologia 33, 215-225, 1996.

36. G.F. Strouse, “Thermal Characteristics of the NIST Fixed-Point Cells, Furnaces, and 

Maintenace Baths Over the Temperature Range from 83.8058 K to 1234.93 K” , in Proc. 

Tempmeko 1999, Vol. 1, pp. 153-158, 1999.

37. Kaeser, R.S. and Strouse, G.F., “An ITS-90 Calibration Facility”, NCSLI Conference 

Proceedings, 1994. 

38. Wilkins, F.J. and Swan, M.J., “Precision a.c./d.c. resistance standards”, in Proc. IEE 117, 

841-849, 1970.

39. Furukawa, G. T., Mangum, B.W., Strouse, G.F., “Effects of different methods of 

preparation of ice mantles of triple point of water cells on the temporal behaviour of the 

triple-point temperatures”, Metrologia 34, 215-233, 1997. 
64

40. ISO/IEC 17025:2005(E), “General requirements for the competence of testing and 

calibration laboratories”, 2005.

41. http://ts.nist.gov/QualitySystem/ 

42. Strouse, G.F., “NIST methods of estimating the impurity uncertainty component for 

ITS-90 fixed-point cells from the Ar TP to the Ag FP”, CCT/03-19, 2003. 

43. Guide to the Expression of Uncertainty in Measurement, (ISO, Geneva) 1993.

44. Taylor, B.N. and Kuyatt, C.E., "Guidelines for Evaluating and Expressing the 

Uncertainty of NIST Measurement Results", NIST Technical Note 1297, 17 pp., 1993.

45. White, D.R., “A Method for Calibrating Resistance Thermometry Bridges” in Proc. of 

TEMPMEKO 1996, p. 129-134, 1997.

46. White, D.R., Jones, K., Williams, J.M., and Ramsey, I.E., IEEE Trans. Instrum. Meas. 

46, p. 1068-1074, 1997. 

47. White, D. R. and Jones, K., “A Resistance Network”, Patent Application 

PCT/NZ95/00022, 1995. 

48. Hamon, B. V., J. Sci. Instrum. 35, p. 450-453, 1954. 

49. Tew, W. L., and Strouse, G. F., “Maintenance and Validation of a Resistance Ratio Chain 

for Platinum Resistance Thermometry” in Conference Digest of the Conference on 

Precision Electromagnetic Measurement, p. 98-99, 1998.

50. Dziuba, R.F., Boynton, P.A., Elmquist, R.E., Jarrett, D.G., Moore, T.P., and Neal, J.D. 

“NIST Measurement Service for DC Standard Resistors”, NIST Technical Note 1298, pp. 

65, 1992.

51. Cutkosky, R.D., “Frequency Dependencies of Precision Resistors”, Rev. Sci. Instrum. 59, 

p. 382, 1988.

52. Steele, A.G., Fellmuth, B., Head, D.I., Hermier, Y., Kang, K.H., Steur, P.P.M, and Tew, 

W.L. “Key Comparison: CCT-K2: Key comparison of capsule-type standard platinum 

resistance thermometers from 13.8 K to 273.16 K”, Metrologia 39, 551-571, 2002.

53. Mangum, B.W., Strouse, G.F., and Guthrie,W.F. “CCT-K3: Key Comparison of 

Realizations of the ITS-90 Over the Range 83.8058 K to 933.473 K”, NIST Technical 

Note TN1450, 2002. 

54. Nubbemeyer, H.G. and Fischer, J. “Final report on key comparison CCT-K4 of local 

realizations of aluminium and silver freezing-point temperatures”, Metrologia 39, Tech.

Suppl., 03001, 2002. 
65

55. Stock M., Solve S., del Campo D., Chimenti V., Méndez-Lango E., Liedber H., Steur 

P.P.M., Marcarino P., Dematteis R., Filipe E., Lobo I., Kang K.H., Gam K.S., Kim Y.-G., 

Renaot E., Bonnier G., Valin M., White R., Dransfield T.D., Duan Y., Xiaoke Y., Strouse 

G., Ballico M., Sukkar D., Arai M., Mans A., de Groot M., Kerkhof O., Rusby R., Gray 

J., Head D., Hill K., Tegeler E., Noatsch U., Duris S., Kho H.Y., Ugur S., Pokhodun A., 

Gerasimov S.F. “Final Report on CCT-K7: Key comparison of water triple point cells” 

Metrologia 43, Tech. Suppl., 03001, 2006.

56. Strouse, G.F. and Tew, W. L., "Assessment of Uncertainties of Calibration of Resistance 

Thermometers at the National Institute of Standards and Technology", NISTIR 5319, 16 

pp., 1994.

57. White, D.R., Yamazawa, G K., Ballico, M., Chimenti, V., Duris, S., Filipe, E., Ivanova, 

A., Kartal Dogan, A., Mendez-Lango, E., Meyer, C., Pavese. F., Peruzzi, A., Renaot, E., 

Rudtsch, S., “Uncertainties in the Realisation of the SPRT Sub-ranges of the ITS-90”, 

CCT-WG3, 2006. 

58. Mangum B.W., Bloembergen P., Chattle M.V., Fellmuth B., Marcarino P., Pokhodun 

A.I., “On the International Temperature Scale of 1990 (ITS-90). Part I: Some 

definitions”, Metrologia 34, 427-429, 1997.

59. ISO Guide 34:2000(E), “General requirements for the competence of reference material 

producers”, 2000. 

60. CIPM, “Mutual recognition of national measurement standards and of calibration and 

measurement certificates issued by national metrology institutes”, 

www.bipm.org/utils/en/pdf/mra_2003.pdf, 1999 (rev. 2003). 
66

10 Appendix 

Appendix A. Report of Calibration for an SPRT calibrated from the Al FP to the Ar TP. 
67

REPORT OF CALIBRATION 

International Temperature Scale of 1990 

Standard Platinum Resistance Thermometer 

Rosemount Model 162CE 

 Serial Number 4415 

Submitted by: 

NIST Thermometry Group 

Gaithersburg, Maryland 20899 USA 

This standard platinum resistance thermometer (SPRT) was calibrated with an AC bridge operating at a frequency of 30 Hz 

with continuous measuring currents of 1 mA and 1.414 mA. In accordance with the International Temperature Scale of 1990 

(ITS-90) that was officially adopted by the Comite ́ International des Poids et Mesures (CIPM) in September 1989, the 

subranges from 83.8058 K to 273.16 K and from 273.15 K to 933.473 K, with the following fixed points and their stated 

expanded uncertainties (k = 2), were used to calibrate the thermometer. For a detailed description of the ITS-90, see NIST 

TN1265, 190 pp., (1990), entitled "Guidelines for Realizing the International Temperature Scale of 1990 (ITS-90)." For a 

description of the uncertainties, see NISTIR 5319, 16 pp., (1994), entitled "Assessment of Uncertainties of Calibration of 

Resistance Thermometers at the National Institute of Standards and Technology." 

 Fixed Point Temperature Expanded Uncertainty 

where k = 2

T90 () t90 (°C) (m) 

 Ar TP 83.8058 –189.3442 0.14

 Hg TP 234.3156 –38.8344 0.15

 H2O TP 273.16 0.01 0.05

 Sn FP 505.078 231.928 0.28

 Zn FP 692.677 419.527 0.51

 Al FP 933.473 660.323 0.79

The following values were determined for the coefficients of the pertinent deviation functions of the ITS-90, as given in the 

attached material describing the scale. The attached tables were generated using these values. 

Coefficients for Zero-Power Dissipation Calibration Coefficients for 1 mA Calibration 

a4 = 8.9020748E-4 b4 = 6.7368979E-4 a4 = –1.2579994E-4 b4 = 1.0678395E-5 

a7 = –1.6485848E-4 b7 = –9.4825566E-6 a7 = –1.6462789E-4 b7 = –8.4598339E-6 

c7 = 2.2976905E-6 c7 = 1.8898584E-6 

The resistance of this thermometer at 273.16 was calculated to be 25.72334 Wat 0 mA and 25.72336 Wat 1 mA. During 

calibration, the resistance at 273.16 changed by the equivalent of 0.4 mat 0 mA and 0.5 mat 1 mA. This thermometer 

is satisfactory as a defining instrument of the ITS-90 in accordance with the criteria that W(302.9146 ) 1.11807 or 

W(234.3156 ) 0.844235. Measurements and analysis performed by Gregory Strouse. 

For the Director, 

National Institute of Standards and Technology 

Dean C. Ripple September 14, 2007 

Leader, Thermometry Group Test No.: 275339-07

Process Measurements Division Purchase Order No.: Group Internal 
68

Tables: 

The table given in this Report of Calibration was calculated from the 1 mA coefficients for your SPRT. The first column of 

the table lists values of temperature. Unless otherwise requested, the second column lists values of W(T90) = 

R(T90)/R(273.16 K), the ratio of the resistance at the stated temperature T90 to the resistance at 273.16 K. The third column 

lists values of dT90/dW(T90), derived from the ITS-90 equations. The dT90/dW(T90) values are included to facilitate 

interpolation between table values of T90. The uncertainty introduced by using linear interpolation is less than 0.1 mK. 

Discussion of the uncertainty propagation curves:

The curves show the uncertainties propagated at various temperatures from uncertainties made in the calibration of an SPRT. 

Note that if a thermometer is calibrated with a +1 K uncertainty at a calibration point and if that thermometer is subsequently 

used to determine the temperature of the same calibration point when accurately realized, the indicated temperature is then 

1 K lower than the assigned value for that calibration point. The uncertainty propagation curves depend not only upon the 

particular calibration point at which the uncertainty occurred, but also upon which other fixed points were used in the 

calibration. The calibration point at which the assumed uncertainty was made is indicated in the legend and calibration at the 

other fixed point(s), is assumed to have been performed without uncertainty. A calibration uncertainty in a fixed point for the 

temperature subranges below 273.16 K does not introduce an uncertainty in the calibration of the thermometer above 

273.15 K; likewise, a calibration uncertainty in the temperature subranges above 273.16 K does not introduce an uncertainty 

in the calibration of the thermometer below 273.16 K. A special exception to this is the temperature subrange from 

234.3156 K to 302.9146 K (triple point of mercury to the melting point of gallium). 

Uncertainty: 

The total uncertainty of the NIST-calibrated SPRT is an essential part of the total uncertainty of the end user’s determination 

of temperature. The RSS of the maximum value for the combined propagated fixed-point cell and non-uniqueness 

contribution is used to calculate the total SPRT calibration uncertainty for each ITS-90 temperature subrange. The table 

below gives the maximum SPRT calibration uncertainty for each ITS-90 temperature subrange. 

Maximum NIST SPRT calibration uncertainty for each ITS-90 temperature subrange. 

ITS-90 Temperature Subrange Maximum Uncertainty

(k=2), mK

Ar TP to 0.01 °C 0.40

Hg TP to Ga MP 0.23

0 °C to Ga MP 0.07

0 °C to In FP 0.36

0 °C to Sn FP 0.48

0 °C to Zn FP 0.59

0 °C to Al FP 0.82

0 °C to Ag FP 1.97

To calculate the total uncertainty (where k=2) of a temperature measurement with your calibrated SPRT, first determine the 

expanded uncertainty of your measurement of the resistance ratio, including readout uncertainties, stabilities of any reference 

resistors, uncertainty of your realization of the triple point of water (TPW), and, if necessary, an allowance for change of the 

SPRT resistance at the TPW since the last actual measurement at the TPW. The uncertainty in equivalent temperature units 

is obtained by multiplying the error in W by dt/dW, as given in the W vs. t table below. (As an example, an uncertainty curve 

for the propagation of an assumed 0.1 mK TPW uncertainty to the temperature of interest is included.) To this uncertainty, 

add the maximum SPRT calibration uncertainty for each ITS-90 temperature subrange as a Type B uncertainty. (Refer to the 

above table). 
69

ITS-90 Uncertainty Propagation

83.8058 K to 273.16 K

0.1

0.0

0.1

0.2

0.3

75 125 175 225 275

Temperature, K Propagated uncertainty (k =2), mK

Ar: U (0.14 mK)

Hg: U (0.15 mK)

Total Expanded

Uncertainty

ITS-90 Uncertainty Propagation

273.15 K to 933.473 K

0.3

0.0

0.3

0.6

0.9

250 450 650 850

Temperature, K Propagated uncertainty (k =2), mK

Al: U (0.79 mK)

Zn: U (0.51 mK)

Sn: U (0.28 mK)

Total Expanded

Uncertainty
70

R (273.16 K) ITS-90 Uncertainty Propagation in W (T 90)

13.8033 K to 1234.93 K

0.0

0.2

0.4

0.6

0 200 400 600 800 1000 1200

Temperature, K Propagated uncertainty, mK

For a 0.1 mK

uncertainty

at 273.16 K

Zn

Al

Ag

Sn

In

Ga

TPW Ar

Hg
71

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

-200 0.16987204 -150 0.38537815

-199 0.17417541 232.3761 -149 0.38962614 235.4056

-198 0.17848559 232.0087 -148 0.39387111 235.5728

-197 0.18280176 231.6866 -147 0.39811309 235.7390

-196 0.18712316 231.4065 -146 0.40235210 235.9041

-195 0.19144907 231.1652 -145 0.40658817 236.0681

-194 0.19577884 230.9597 -144 0.41082131 236.2309

-193 0.20011183 230.7873 -143 0.41505156 236.3926

-192 0.20444749 230.6454 -142 0.41927895 236.5529

-191 0.20878529 230.5318 -141 0.42350349 236.7120

-190 0.21312473 230.4442 -140 0.42772522 236.8697

-189 0.21746537 230.3807 -139 0.43194416 237.0262

-188 0.22180679 230.3393 -138 0.43616035 237.1812

-187 0.22614861 230.3184 -137 0.44037380 237.3349

-186 0.23049046 230.3162 -136 0.44458456 237.4872

-185 0.23483204 230.3313 -135 0.44879264 237.6381

-184 0.23917302 230.3624 -134 0.45299807 237.7877

-183 0.24351315 230.4080 -133 0.45720088 237.9358

-182 0.24785217 230.4670 -132 0.46140111 238.0825

-181 0.25218984 230.5382 -131 0.46559877 238.2278

-180 0.25652597 230.6207 -130 0.46979390 238.3717

-179 0.26086035 230.7134 -129 0.47398652 238.5142

-178 0.26519281 230.8154 -128 0.47817666 238.6554

-177 0.26952321 230.9260 -127 0.48236435 238.7951

-176 0.27385138 231.0443 -126 0.48654962 238.9335

-175 0.27817721 231.1695 -125 0.49073248 239.0706

-174 0.28250058 231.3011 -124 0.49491297 239.2063

-173 0.28682138 231.4384 -123 0.49909112 239.3407

-172 0.29113953 231.5808 -122 0.50326694 239.4738

-171 0.29545494 231.7278 -121 0.50744047 239.6056

-170 0.29976754 231.8788 -120 0.51161172 239.7361

-169 0.30407726 232.0335 -119 0.51578073 239.8654

-168 0.30838405 232.1913 -118 0.51994751 239.9934

-167 0.31268787 232.3519 -117 0.52411209 240.1202

-166 0.31698867 232.5150 -116 0.52827449 240.2458

-165 0.32128641 232.6801 -115 0.53243474 240.3702

-164 0.32558108 232.8469 -114 0.53659286 240.4935

-163 0.32987265 233.0152 -113 0.54074886 240.6156

-162 0.33416109 233.1847 -112 0.54490278 240.7366

-161 0.33844641 233.3552 -111 0.54905463 240.8566

-160 0.34272858 233.5263 -110 0.55320443 240.9754

-159 0.34700761 233.6979 -109 0.55735220 241.0932

-158 0.35128349 233.8699 -108 0.56149797 241.2099

-157 0.35555623 234.0419 -107 0.56564175 241.3257

-156 0.35982583 234.2139 -106 0.56978356 241.4404

-155 0.36409230 234.3858 -105 0.57392342 241.5542

-154 0.36835565 234.5572 -104 0.57806134 241.6670

-153 0.37261590 234.7283 -103 0.58219735 241.7789

-152 0.37687305 234.8987 -102 0.58633147 241.8898

-151 0.38112713 235.0685 -101 0.59046370 241.9999

-150 0.38537815 235.2375 -100 0.59459407 242.1091
72

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

-100 0.59459407 -50 0.79901192

-99 0.59872259 242.2175 -49 0.80306243 246.8829

-98 0.60284928 242.3250 -48 0.80711157 246.9658

-97 0.60697415 242.4317 -47 0.81115936 247.0485

-96 0.61109722 242.5377 -46 0.81520580 247.1308

-95 0.61521850 242.6428 -45 0.81925089 247.2129

-94 0.61933802 242.7472 -44 0.82329465 247.2946

-93 0.62345577 242.8509 -43 0.82733708 247.3762

-92 0.62757178 242.9538 -42 0.83137818 247.4574

-91 0.63168606 243.0560 -41 0.83541796 247.5384

-90 0.63579862 243.1575 -40 0.83945642 247.6191

-89 0.63990947 243.2584 -39 0.84349357 247.6996

-88 0.64401863 243.3586 -38 0.84752941 247.7798

-87 0.64812612 243.4582 -37 0.85156395 247.8598

-86 0.65223193 243.5571 -36 0.85559719 247.9396

-85 0.65633609 243.6554 -35 0.85962913 248.0191

-84 0.66043860 243.7532 -34 0.86365979 248.0984

-83 0.66453947 243.8503 -33 0.86768917 248.1774

-82 0.66863873 243.9469 -32 0.87171727 248.2563

-81 0.67273637 244.0429 -31 0.87574409 248.3349

-80 0.67683240 244.1384 -30 0.87976963 248.4133

-79 0.68092685 244.2333 -29 0.88379392 248.4916

-78 0.68501971 244.3277 -28 0.88781693 248.5696

-77 0.68911100 244.4217 -27 0.89183869 248.6475

-76 0.69320073 244.5151 -26 0.89585919 248.7251

-75 0.69728890 244.6080 -25 0.89987844 248.8026

-74 0.70137553 244.7005 -24 0.90389644 248.8800

-73 0.70546062 244.7925 -23 0.90791320 248.9571

-72 0.70954419 244.8841 -22 0.91192871 249.0342

-71 0.71362624 244.9752 -21 0.91594299 249.1111

-70 0.71770677 245.0658 -20 0.91995602 249.1878

-69 0.72178581 245.1561 -19 0.92396783 249.2644

-68 0.72586335 245.2459 -18 0.92797840 249.3409

-67 0.72993940 245.3353 -17 0.93198775 249.4173

-66 0.73401398 245.4243 -16 0.93599586 249.4936

-65 0.73808708 245.5130 -15 0.94000276 249.5699

-64 0.74215872 245.6012 -14 0.94400843 249.6460

-63 0.74622891 245.6891 -13 0.94801288 249.7221

-62 0.75029764 245.7766 -12 0.95201611 249.7981

-61 0.75436494 245.8637 -11 0.95601813 249.8741

-60 0.75843080 245.9504 -10 0.96001893 249.9501

-59 0.76249523 246.0369 -9 0.96401851 250.0260

-58 0.76655824 246.1229 -8 0.96801688 250.1020

-57 0.77061983 246.2087 -7 0.97201404 250.1780

-56 0.77468002 246.2941 -6 0.97600998 250.2540

-55 0.77873881 246.3791 -5 0.98000470 250.3300

-54 0.78279620 246.4639 -4 0.98399822 250.4061

-53 0.78685220 246.5483 -3 0.98799051 250.4823

-52 0.79090681 246.6324 -2 0.99198160 250.5586

-51 0.79496005 246.7162 -1 0.99597146 250.6350

-50 0.79901192 246.7997 0 0.99996012 250.7112
73

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

0 0.99996012 50 1.19783766

1 1.00394739 250.7978 51 1.20176442 254.6629

2 1.00793345 250.8746 52 1.20568997 254.7409

3 1.01191828 250.9514 53 1.20961433 254.8190

4 1.01590190 251.0282 54 1.21353748 254.8971

5 1.01988430 251.1050 55 1.21745943 254.9752

6 1.02386548 251.1818 56 1.22138018 255.0533

7 1.02784544 251.2586 57 1.22529973 255.1315

8 1.03182419 251.3355 58 1.22921807 255.2097

9 1.03580171 251.4123 59 1.23313522 255.2879

10 1.03977803 251.4892 60 1.23705116 255.3662

11 1.04375313 251.5661 61 1.24096591 255.4445

12 1.04772701 251.6430 62 1.24487945 255.5228

13 1.05169968 251.7200 63 1.24879180 255.6012

14 1.05567113 251.7970 64 1.25270294 255.6796

15 1.05964137 251.8740 65 1.25661289 255.7580

16 1.06361040 251.9510 66 1.26052163 255.8365

17 1.06757821 252.0280 67 1.26442918 255.9150

18 1.07154481 252.1051 68 1.26833553 255.9936

19 1.07551020 252.1822 69 1.27224068 256.0721

20 1.07947437 252.2593 70 1.27614463 256.1507

21 1.08343734 252.3364 71 1.28004738 256.2294

22 1.08739909 252.4136 72 1.28394894 256.3080

23 1.09135963 252.4907 73 1.28784929 256.3868

24 1.09531896 252.5679 74 1.29174845 256.4655

25 1.09927708 252.6452 75 1.29564642 256.5443

26 1.10323399 252.7224 76 1.29954318 256.6231

27 1.10718969 252.7997 77 1.30343875 256.7019

28 1.11114418 252.8770 78 1.30733312 256.7808

29 1.11509747 252.9543 79 1.31122630 256.8597

30 1.11904954 253.0317 80 1.31511828 256.9387

31 1.12300041 253.1091 81 1.31900906 257.0177

32 1.12695006 253.1865 82 1.32289865 257.0967

33 1.13089851 253.2640 83 1.32678704 257.1757

34 1.13484576 253.3414 84 1.33067424 257.2548

35 1.13879179 253.4189 85 1.33456024 257.3339

36 1.14273662 253.4965 86 1.33844505 257.4131

37 1.14668024 253.5740 87 1.34232866 257.4923

38 1.15062266 253.6516 88 1.34621107 257.5715

39 1.15456387 253.7292 89 1.35009230 257.6508

40 1.15850387 253.8069 90 1.35397232 257.7301

41 1.16244267 253.8845 91 1.35785116 257.8094

42 1.16638026 253.9622 92 1.36172880 257.8888

43 1.17031665 254.0400 93 1.36560525 257.9682

44 1.17425183 254.1177 94 1.36948050 258.0476

45 1.17818581 254.1955 95 1.37335456 258.1271

46 1.18211859 254.2733 96 1.37722743 258.2066

47 1.18605016 254.3512 97 1.38109910 258.2862

48 1.18998053 254.4291 98 1.38496958 258.3658

49 1.19390969 254.5070 99 1.38883887 258.4454

50 1.19783766 254.5850 100 1.39270697 258.5250
74

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

100 1.39270697 150 1.58459633

101 1.39657388 258.6047 151 1.58840390 262.6348

102 1.40043959 258.6844 152 1.59221029 262.7163

103 1.40430411 258.7642 153 1.59601549 262.7979

104 1.40816744 258.8440 154 1.59981952 262.8795

105 1.41202958 258.9238 155 1.60362236 262.9611

106 1.41589053 259.0037 156 1.60742403 263.0427

107 1.41975029 259.0836 157 1.61122451 263.1244

108 1.42360886 259.1635 158 1.61502381 263.2062

109 1.42746623 259.2435 159 1.61882194 263.2879

110 1.43132242 259.3235 160 1.62261888 263.3697

111 1.43517742 259.4036 161 1.62641464 263.4516

112 1.43903123 259.4837 162 1.63020923 263.5334

113 1.44288384 259.5638 163 1.63400263 263.6154

114 1.44673527 259.6439 164 1.63779486 263.6973

115 1.45058551 259.7241 165 1.64158591 263.7793

116 1.45443456 259.8043 166 1.64537578 263.8613

117 1.45828242 259.8846 167 1.64916447 263.9433

118 1.46212910 259.9649 168 1.65295199 264.0254

119 1.46597458 260.0452 169 1.65673832 264.1076

120 1.46981888 260.1256 170 1.66052348 264.1897

121 1.47366199 260.2060 171 1.66430746 264.2719

122 1.47750391 260.2865 172 1.66809027 264.3541

123 1.48134464 260.3669 173 1.67187189 264.4364

124 1.48518419 260.4474 174 1.67565234 264.5187

125 1.48902255 260.5280 175 1.67943162 264.6011

126 1.49285972 260.6086 176 1.68320972 264.6834

127 1.49669570 260.6892 177 1.68698664 264.7658

128 1.50053050 260.7698 178 1.69076239 264.8483

129 1.50436412 260.8505 179 1.69453696 264.9308

130 1.50819654 260.9313 180 1.69831035 265.0133

131 1.51202778 261.0120 181 1.70208257 265.0959

132 1.51585784 261.0928 182 1.70585362 265.1785

133 1.51968671 261.1737 183 1.70962349 265.2611

134 1.52351439 261.2545 184 1.71339218 265.3437

135 1.52734089 261.3354 185 1.71715971 265.4264

136 1.53116621 261.4164 186 1.72092606 265.5092

137 1.53499034 261.4974 187 1.72469123 265.5920

138 1.53881329 261.5784 188 1.72845523 265.6748

139 1.54263505 261.6594 189 1.73221806 265.7576

140 1.54645563 261.7405 190 1.73597971 265.8405

141 1.55027502 261.8216 191 1.73974019 265.9234

142 1.55409323 261.9028 192 1.74349950 266.0064

143 1.55791026 261.9840 193 1.74725764 266.0894

144 1.56172610 262.0652 194 1.75101460 266.1724

145 1.56554076 262.1465 195 1.75477039 266.2555

146 1.56935424 262.2278 196 1.75852501 266.3386

147 1.57316654 262.3091 197 1.76227846 266.4217

148 1.57697765 262.3905 198 1.76603074 266.5049

149 1.58078758 262.4719 199 1.76978184 266.5881

150 1.58459633 262.5533 200 1.77353177 266.6714
75

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

200 1.77353177 250 1.95953989

201 1.77728054 266.7546 251 1.96323037 270.9678

202 1.78102813 266.8380 252 1.96691968 271.0531

203 1.78477455 266.9213 253 1.97060784 271.1384

204 1.78851980 267.0047 254 1.97429483 271.2238

205 1.79226389 267.0882 255 1.97798066 271.3092

206 1.79600680 267.1716 256 1.98166533 271.3947

207 1.79974854 267.2551 257 1.98534884 271.4801

208 1.80348912 267.3387 258 1.98903119 271.5657

209 1.80722852 267.4223 259 1.99271238 271.6513

210 1.81096676 267.5059 260 1.99639241 271.7369

211 1.81470382 267.5896 261 2.00007128 271.8226

212 1.81843972 267.6733 262 2.00374899 271.9083

213 1.82217445 267.7570 263 2.00742555 271.9940

214 1.82590801 267.8408 264 2.01110094 272.0798

215 1.82964040 267.9246 265 2.01477517 272.1657

216 1.83337163 268.0084 266 2.01844825 272.2515

217 1.83710169 268.0923 267 2.02212016 272.3375

218 1.84083058 268.1762 268 2.02579092 272.4234

219 1.84455830 268.2602 269 2.02946051 272.5095

220 1.84828486 268.3442 270 2.03312895 272.5955

221 1.85201025 268.4283 271 2.03679623 272.6816

222 1.85573447 268.5123 272 2.04046235 272.7678

223 1.85945753 268.5964 273 2.04412732 272.8540

224 1.86317942 268.6806 274 2.04779112 272.9402

225 1.86690015 268.7648 275 2.05145377 273.0265

226 1.87061971 268.8490 276 2.05511526 273.1128

227 1.87433810 268.9333 277 2.05877560 273.1992

228 1.87805533 269.0176 278 2.06243477 273.2857

229 1.88177139 269.1020 279 2.06609279 273.3721

230 1.88548629 269.1864 280 2.06974965 273.4586

231 1.88920003 269.2708 281 2.07340535 273.5452

232 1.89291260 269.3553 282 2.07705990 273.6318

233 1.89662400 269.4398 283 2.08071328 273.7185

234 1.90033424 269.5243 284 2.08436552 273.8052

235 1.90404332 269.6089 285 2.08801659 273.8920

236 1.90775123 269.6935 286 2.09166651 273.9788

237 1.91145798 269.7782 287 2.09531527 274.0656

238 1.91516356 269.8629 288 2.09896288 274.1525

239 1.91886799 269.9477 289 2.10260932 274.2395

240 1.92257124 270.0324 290 2.10625462 274.3264

241 1.92627334 270.1173 291 2.10989875 274.4135

242 1.92997427 270.2021 292 2.11354173 274.5006

243 1.93367404 270.2871 293 2.11718355 274.5877

244 1.93737265 270.3720 294 2.12082422 274.6749

245 1.94107010 270.4570 295 2.12446373 274.7622

246 1.94476638 270.5420 296 2.12810209 274.8495

247 1.94846150 270.6271 297 2.13173929 274.9368

248 1.95215546 270.7122 298 2.13537533 275.0242

249 1.95584826 270.7974 299 2.13901022 275.1116

250 1.95953989 270.8826 300 2.14264395 275.1991
76

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

300 2.14264395 350 2.32285790

301 2.14627653 275.2867 351 2.32643273 279.7340

302 2.14990795 275.3743 352 2.33000639 279.8244

303 2.15353822 275.4619 353 2.33357891 279.9149

304 2.15716733 275.5496 354 2.33715027 280.0055

305 2.16079528 275.6374 355 2.34072047 280.0962

306 2.16442208 275.7252 356 2.34428952 280.1869

307 2.16804773 275.8130 357 2.34785741 280.2777

308 2.17167222 275.9009 358 2.35142414 280.3685

309 2.17529555 275.9889 359 2.35498972 280.4595

310 2.17891773 276.0769 360 2.35855414 280.5504

311 2.18253876 276.1649 361 2.36211740 280.6415

312 2.18615862 276.2531 362 2.36567951 280.7326

313 2.18977734 276.3412 363 2.36924046 280.8238

314 2.19339490 276.4295 364 2.37280026 280.9150

315 2.19701130 276.5177 365 2.37635890 281.0063

316 2.20062655 276.6061 366 2.37991638 281.0977

317 2.20424065 276.6945 367 2.38347270 281.1892

318 2.20785359 276.7829 368 2.38702787 281.2807

319 2.21146537 276.8714 369 2.39058188 281.3723

320 2.21507600 276.9600 370 2.39413474 281.4639

321 2.21868548 277.0486 371 2.39768643 281.5557

322 2.22229380 277.1372 372 2.40123697 281.6475

323 2.22590096 277.2260 373 2.40478635 281.7393

324 2.22950698 277.3147 374 2.40833457 281.8313

325 2.23311183 277.4036 375 2.41188164 281.9233

326 2.23671553 277.4925 376 2.41542754 282.0153

327 2.24031808 277.5814 377 2.41897229 282.1075

328 2.24391947 277.6704 378 2.42251588 282.1997

329 2.24751971 277.7595 379 2.42605831 282.2920

330 2.25111879 277.8486 380 2.42959958 282.3844

331 2.25471672 277.9378 381 2.43313970 282.4768

332 2.25831349 278.0270 382 2.43667865 282.5693

333 2.26190911 278.1163 383 2.44021645 282.6619

334 2.26550357 278.2057 384 2.44375309 282.7545

335 2.26909688 278.2951 385 2.44728856 282.8473

336 2.27268904 278.3845 386 2.45082288 282.9401

337 2.27628003 278.4741 387 2.45435604 283.0329

338 2.27986988 278.5637 388 2.45788804 283.1259

339 2.28345857 278.6533 389 2.46141887 283.2189

340 2.28704610 278.7430 390 2.46494855 283.3120

341 2.29063248 278.8328 391 2.46847707 283.4052

342 2.29421770 278.9226 392 2.47200442 283.4984

343 2.29780177 279.0125 393 2.47553062 283.5917

344 2.30138468 279.1025 394 2.47905565 283.6851

345 2.30496644 279.1925 395 2.48257953 283.7786

346 2.30854704 279.2826 396 2.48610224 283.8722

347 2.31212649 279.3727 397 2.48962379 283.9658

348 2.31570478 279.4630 398 2.49314418 284.0595

349 2.31928192 279.5532 399 2.49666341 284.1533

350 2.32285790 279.6436 400 2.50018147 284.2471
77

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

400 2.50018147 450 2.67459807

401 2.50369838 284.3411 451 2.67805656 289.1439

402 2.50721412 284.4351 452 2.68151387 289.2422

403 2.51072869 284.5292 453 2.68497000 289.3406

404 2.51424211 284.6234 454 2.68842496 289.4391

405 2.51775436 284.7176 455 2.69187874 289.5377

406 2.52126545 284.8120 456 2.69533135 289.6363

407 2.52477537 284.9064 457 2.69878278 289.7351

408 2.52828414 285.0009 458 2.70223303 289.8340

409 2.53179173 285.0954 459 2.70568210 289.9329

410 2.53529817 285.1901 460 2.70913000 290.0320

411 2.53880343 285.2848 461 2.71257671 290.1311

412 2.54230754 285.3796 462 2.71602225 290.2303

413 2.54581048 285.4745 463 2.71946661 290.3297

414 2.54931225 285.5695 464 2.72290979 290.4291

415 2.55281286 285.6646 465 2.72635180 290.5286

416 2.55631230 285.7597 466 2.72979262 290.6283

417 2.55981058 285.8550 467 2.73323226 290.7280

418 2.56330769 285.9503 468 2.73667072 290.8278

419 2.56680364 286.0457 469 2.74010800 290.9277

420 2.57029842 286.1411 470 2.74354410 291.0277

421 2.57379203 286.2367 471 2.74697902 291.1278

422 2.57728448 286.3323 472 2.75041275 291.2280

423 2.58077575 286.4281 473 2.75384531 291.3283

424 2.58426586 286.5239 474 2.75727668 291.4287

425 2.58775481 286.6198 475 2.76070686 291.5292

426 2.59124258 286.7158 476 2.76413587 291.6298

427 2.59472919 286.8118 477 2.76756369 291.7305

428 2.59821463 286.9080 478 2.77099033 291.8313

429 2.60169889 287.0042 479 2.77441578 291.9322

430 2.60518199 287.1006 480 2.77784005 292.0332

431 2.60866393 287.1970 481 2.78126313 292.1343

432 2.61214469 287.2935 482 2.78468503 292.2355

433 2.61562428 287.3901 483 2.78810574 292.3367

434 2.61910270 287.4867 484 2.79152527 292.4381

435 2.62257995 287.5835 485 2.79494361 292.5396

436 2.62605603 287.6804 486 2.79836076 292.6412

437 2.62953094 287.7773 487 2.80177673 292.7429

438 2.63300468 287.8743 488 2.80519151 292.8447

439 2.63647724 287.9714 489 2.80860510 292.9466

440 2.63994864 288.0687 490 2.81201750 293.0486

441 2.64341886 288.1660 491 2.81542872 293.1507

442 2.64688791 288.2633 492 2.81883875 293.2529

443 2.65035579 288.3608 493 2.82224758 293.3552

444 2.65382249 288.4584 494 2.82565523 293.4576

445 2.65728802 288.5560 495 2.82906169 293.5601

446 2.66075238 288.6538 496 2.83246695 293.6627

447 2.66421557 288.7516 497 2.83587103 293.7654

448 2.66767758 288.8496 498 2.83927391 293.8683

449 2.67113841 288.9476 499 2.84267561 293.9712

450 2.67459807 289.0457 500 2.84607611 294.0742
78

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

500 2.84607611 550 3.01457360

501 2.84947542 294.1773 551 3.01791283 299.4699

502 2.85287354 294.2806 552 3.02125085 299.5785

503 2.85627046 294.3839 553 3.02458766 299.6873

504 2.85966619 294.4874 554 3.02792326 299.7961

505 2.86306073 294.5909 555 3.03125765 299.9051

506 2.86645408 294.6946 556 3.03459083 300.0142

507 2.86984623 294.7983 557 3.03792279 300.1234

508 2.87323718 294.9022 558 3.04125354 300.2327

509 2.87662694 295.0061 559 3.04458308 300.3421

510 2.88001551 295.1102 560 3.04791140 300.4516

511 2.88340288 295.2144 561 3.05123851 300.5613

512 2.88678905 295.3187 562 3.05456440 300.6710

513 2.89017402 295.4231 563 3.05788908 300.7809

514 2.89355780 295.5275 564 3.06121255 300.8909

515 2.89694039 295.6322 565 3.06453479 301.0010

516 2.90032177 295.7369 566 3.06785583 301.1112

517 2.90370196 295.8417 567 3.07117564 301.2215

518 2.90708094 295.9466 568 3.07449424 301.3319

519 2.91045873 296.0516 569 3.07781163 301.4424

520 2.91383532 296.1568 570 3.08112779 301.5531

521 2.91721071 296.2620 571 3.08444274 301.6638

522 2.92058490 296.3674 572 3.08775647 301.7747

523 2.92395790 296.4728 573 3.09106898 301.8857

524 2.92732969 296.5784 574 3.09438027 301.9968

525 2.93070027 296.6841 575 3.09769035 302.1080

526 2.93406966 296.7898 576 3.10099920 302.2193

527 2.93743785 296.8957 577 3.10430684 302.3308

528 2.94080483 297.0017 578 3.10761325 302.4423

529 2.94417061 297.1078 579 3.11091845 302.5540

530 2.94753519 297.2140 580 3.11422242 302.6658

531 2.95089857 297.3204 581 3.11752518 302.7776

532 2.95426074 297.4268 582 3.12082671 302.8896

533 2.95762171 297.5334 583 3.12412702 303.0018

534 2.96098147 297.6400 584 3.12742611 303.1140

535 2.96434003 297.7468 585 3.13072398 303.2263

536 2.96769738 297.8536 586 3.13402062 303.3388

537 2.97105353 297.9606 587 3.13731604 303.4513

538 2.97440847 298.0677 588 3.14061024 303.5640

539 2.97776221 298.1749 589 3.14390322 303.6768

540 2.98111474 298.2822 590 3.14719497 303.7897

541 2.98446606 298.3896 591 3.15048549 303.9027

542 2.98781618 298.4972 592 3.15377480 304.0158

543 2.99116509 298.6048 593 3.15706287 304.1291

544 2.99451279 298.7126 594 3.16034973 304.2424

545 2.99785928 298.8204 595 3.16363535 304.3559

546 3.00120456 298.9284 596 3.16691975 304.4695

547 3.00454863 299.0365 597 3.17020293 304.5832

548 3.00789150 299.1447 598 3.17348488 304.6970

549 3.01123315 299.2530 599 3.17676560 304.8109

550 3.01457360 299.3614 600 3.18004510 304.9249
79

 September 14, 2007 ITS-90 Table for SPRT S/N 4415 at 1 mA

t(°C) W(t) dt/dW(t) t(°C) W(t) dt/dW(t)

600 3.18004510 650 3.34244986

601 3.18332337 305.0390 651 3.34566645 310.8880

602 3.18660041 305.1533 652 3.34888180 311.0078

603 3.18987622 305.2677 653 3.35209592 311.1277

604 3.19315081 305.3821 654 3.35530879 311.2477

605 3.19642417 305.4967 655 3.35852043 311.3678

606 3.19969629 305.6114 656 3.36173082 311.4880

607 3.20296719 305.7262 657 3.36493998 311.6083

608 3.20623687 305.8412 658 3.36814790 311.7287

609 3.20950531 305.9562 659 3.37135458 311.8493

610 3.21277252 306.0714 660 3.37456001 311.9699

611 3.21603850 306.1866 661 3.37776421 312.0906

612 3.21930325 306.3020

613 3.22256677 306.4175

614 3.22582907 306.5331

615 3.22909013 306.6488

616 3.23234995 306.7646

617 3.23560855 306.8805

618 3.23886592 306.9966

619 3.24212205 307.1127

620 3.24537695 307.2290

621 3.24863062 307.3454

622 3.25188305 307.4619

623 3.25513426 307.5785

624 3.25838423 307.6952

625 3.26163296 307.8120

626 3.26488047 307.9289

627 3.26812673 308.0460

628 3.27137177 308.1631

629 3.27461557 308.2804

630 3.27785813 308.3978

631 3.28109946 308.5153

632 3.28433956 308.6329

633 3.28757842 308.7506

634 3.29081604 308.8684

635 3.29405243 308.9863

636 3.29728759 309.1044

637 3.30052150 309.2225

638 3.30375419 309.3408

639 3.30698563 309.4591

640 3.31021584 309.5776

641 3.31344481 309.6962

642 3.31667254 309.8149

643 3.31989904 309.9337

644 3.32312430 310.0526

645 3.32634832 310.1716

646 3.32957110 310.2908

647 3.33279265 310.4100

648 3.33601296 310.5293

649 3.33923202 310.6488

650 3.34244986 310.7684