09.-13.09.2013 Microkelvin Workshop 2013 1. 09.-13.09.2013 Microkelvin Workshop 2013 2 Mise en pratique for the definition of the kelvin updated version,

09.-13.09.2013 Microkelvin Workshop 2013 1

Thermometry and temperature scales below 1 KJ. Engert, PTB Berlin

• Traceable thermometry

• PLTS-2000 - Realization, Dissemination

• Ultra-low temperatures T < 0.001 K

• Conclusions, Outlook


Mise en pratique for the definition of the kelvin updated version, Comité consultatif de thermométrie (CCT), 2011

http://www.bipm.org/en/publications/mep_kelvin/

Scope:“This document provides the information needed to perform a practical measurement of temperature in accord with the International System of Units (SI).”

The mise en pratique serves as a reference for:

the text of the ITS-90 and PLTS-2000

a Technical Annex of material deemed essential to realisation of the ITS-90

or PLTS-2000, but not included in the scale definitions themselves

descriptions of primary thermometers for direct measurement of

thermodynamic temperature

assessments of the uncertainty of the ITS-90, PLTS-2000, and

measurements made by primary thermometry

Traceable thermometry


Mise en pratique for the definition of the kelvin updated version, Comité consultatif de thermométrie (CCT), 2011

http://www.bipm.org/en/publications/mep_kelvin/

fundamental change in the practice of traceable temperature measurement

direct measurements by primary thermometersmore flexible approach → user no longer will be tied to the ITS

removes the short-term need for establishing a new unified international temperature scale from the lowest to the highest temperatures

Traceable thermometry


Temperature scales

10-3 10-2 10-1 100 101 102 103 104

1958 4He

1962 3He

n-H2 (1887)

IPTS-27 / IPTS-48

IPTS-68

EPT-76

TPW

ITS-90

T / K

PLTS-2000

tim

e


Temperature scales

3He vapour pressure scale PTB-2006 PTB-2006 ≡ ITS-90 2 K ≤ T ≤ 3.2 KPTB-2006 ≡ PLTS-2000 0.65 K ≤ T ≤ 1 K

Schuster G. et al.,Temperature, its Measurement and Control in Science and Industry,Vol. 6, (Edited by J.F. Schooley), New York, American Institute of Physics,pp. 97-100 (1992)

Fogle W.E. et al., ibid. pp. 85-90

ITS-90 ↔ PLTS-2000 ?

1 2 3

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

(T90

-T20

06)

/ mK

T90

/ K

PTB-2006

Engert et al., Metrologia, 44, 40 (2007)


pm / MPa = S ai (T2000 / K)i (i = -3···9)

T range: 0.9 mK to 1 K p range: 2.9 MPa to 4 MPa fixed points p3He / MPa T2000 / mK

Minimum 2.93113 315.24A 3.43407 2.444A-B 3.43609 1.896Néel 3.43934 0.902

0.001 0.010 0.100 1.0002.8

3.0

3.2

3.4

3.6

3.8

4.0

dp

/dT

/ (M

Pa/

K)

TA

TNéel

TMin

p3 H

e / M

Pa

T2000

/ K

TA-B

PLTS-2000

1

2

3

4

Temperature scales


Uncertainty for the realization of the PLTS-2000 in comparison to an approximation using a pressure calibration of the MPT adjusted to the 3He melting pressure minimum, calibrated superconductive reference point samples (W, Mo) and an interpolating resistance thermometer for the region around the minimum.

Red lines show the uncertainty of the PLTS-2000 in terms of thermodynamic temperature.

PLTS-2000 - Realization

1 10 100 1000

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

U(T2000

, k=2)

PTB:U(T

2000 realization, k=2)

T2000

/ mK

U /

mK

PTB:U(T

2000 approximation, k=2)

1 10 100 1000

-6

-4

-2

0

2

4

6

U(T2000

, k=2)

PTB:U(T

2000 approximation, k=2)

PTB:U(T

2000 realization, k=2)

Ure

l / %

T2000

/ mK


PLTS-2000 - Dissemination

10 100 1000 100001E-12

1E-11

1E-10

1E-9

1E-8

1E-7

T20

00 /

90 /

K

SV /

(V2 / H

z)

f / Hz

1E-4

1E-3

0.01

0.1

1

Resistance thermometers

Superconductive reference point samples

MFFTs, CSNTs

0.001 0.010 0.100 1.0002.8

3.0

3.2

3.4

3.6

3.8

4.0

dp

/dT

/ (M

Pa/

K)

TA

TNéel

TMin

p3 H

e / M

Pa

T2000

/ K

TA-B

PLTS-2000

1

2

3

4


Practical noise thermometry → Nyquist relation dc-SQUID based detection of thermal magnetic flux noise generated by noise

currents in a metallic temperature sensor Measurement of power spectral density (PSD): S(f,T)

fTRkU D= B2 4


Magnetic Field Fluctuation Thermometer (MFFT)

“Low-pass-like” spectral shape depends on geometry.If R = const(T): SF(f = 0 Hz, T) ~ T

spectral shape is independent of T

Current Sensing Noise Thermometer (CSNT)

1st order low-pass spectrum with fall-off frequency fc = R/(2πL).

If R = const(T): SF(f = 0 Hz, T) ~ T

M

L

R

T

Cu, 5N83 mm

3 mm

M(f)

L(f)R(f)

b2a

c

0

1

),(

÷÷

ø

ö

çç

è

æ÷÷ø

öççè

æ+

=

ff

TsTfS

÷÷

ø

ö

çç

è

æ÷÷ø

öççè

æ+

=2

c

2b

1

4),(

ff

R

TMkTfS


MFFT-1 Noise Thermometer

Magnicon GmbH




Uncertainty of T measurement with a calibrated MFFT

Goal → temperature measurement with relative expanded uncertainty

Urel (TMFFT) ~ 1% (k = 2, 95%) within ~ 60 s

calibration of the MFFT at Tcal calibration temperature

fs sample rate Ns number of samples,Mavg number of averages for calibration

measurementNavg number of averages for temperature

measurement Df = fhigh - flow frequency range used for T

determinationNf number of frequency bins in Df


Parametric model:fit of PSD at Tcal → Θcal={s0, a, b, fc}fit of measured PSD with Θcal → Tp, u(Tp)

Non-parametric model:Tnp → may be affected by bias

Improved non-parametric model:

Bayesian approach:coherent uncertainty estimates using MCMC techniquesprobability density functionsV(t) → FFT → PSD → averaging

Wübbeler et al., Meas. Sci. Technol. 23, 125004 (2012), ibid. 2013


b2a

c

0

1

),(

÷÷

ø

ö

çç

è

æ÷÷ø

öççè

æ+

=

ff

TsTfS

calcal),(),(T

TfSTfS

T=

å=fN

ff TfS

TfS

NT

T),(

),(

cal

npcalnp

å-=fN

ff TfS

TfS

NT

MT

),(

),()

11(

cal

inpcal

avginp

ffcal

cal

NMNNTTu

T

Tu

×+

×+=

avgavg2

2

2inp

211)()(

inp

( )dTTpT Tò= y|B

dTTpTTTu T )|()-()( 2BB

2 yò=

1 10 100 1000 100001E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

PSD at Tcal

PSD at T

S /

V2/H

z

f / Hz



Temperature estimates and uncertainties obtained by the Bayesian treatment TB, by the parametric approach TP and by the two non-parametric approaches Tnp and Tinp. The error bars indicate 95 % credible intervals for the Bayesian treatment and 95 % coverage intervals for Tp, Tnp and Tinp

Wübbeler et al., Meas. Sci. Technol., to appear 2013

(a)Tcal = 850 mKMavg= 2400Navg= 10

(b)Tcal = 850 mKMavg= 10Navg= 2400

TB Tp Tnp Tinp TB Tp Tnp Tinp


1 10 100 1000 100001E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

PSD at Tcal

SQUID noise

S /

V2 /H

z

f / Hz

1 10 100 1000 100001E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

PSD at Tcal

PSD at 15 mK PSD scaled to T

min

SQUID noise f

low and f

high

S /

V2 /H

z

f / Hz


Urel (TMFFT) ≤ 1%


Calibration certificate

parameters for SQUID setup parameters for DAQ box PSD at calibration temperature calibration parameters Tmin for U ≤ 1%



Ultra low-temperature 195Pt-NMR

On the way to a ultra low-temperature scale

T ≤ 1 mK


25 50 75 100 125

2

4

6

0

2.5

5

7.5

25 50 75 100 125

2

4

6

z (cm)

r (cm)

Bz (T)

Experimental set-up : Cu-Pt nuclear cooling stages

Pt-NMR #1 Pt-NMR #2 Pt-NMR #3Reference-point device

Heat switch Cu nuclear cooling stage Heat switch

Pt nuclear cooling stage



Ziele 2012Pulsed Pt-NMR thermometry is based on measurements of nuclear magnetisation of a high-purity bulk samples. The temperature fields and

result from the thermodynamic process of thermometry and are compared to the recorded free induction decay (FID).

equNNN nM ),( txTN

),(e txT


MHz/T 9.093/2 , 2

tanh2

, )/exp()sin()()(N

NN2

kTB

nMttfMtU zN


nuclear demagnetization cooling and magnetic thermometry = two aspects of one and the same thermodynamic process

, → solution of thermodynamic field equations

investigation of properties of Pt → susceptometer


),(e txT r ),(N txT r


PLTS-2000 - Background data

PTB- and NIST-Scale

T : 30 mK < T < 750 mK, D T/T < 0.3 %

p : D p = 110 Pa (at the minimum)

PTB- and UF-Scale

TN TUF - TPTB = 54 µK (6 %)

TB TUF - TPTB = 78 µK (4 %)

TA TUF - TPTB = 95 µK (4 %)

1 10 100 1000

-1.0

-0.5

0.0

0.5

1.0

U(T2000

, k=2, 95%)

PTB

NISTUni Florida

Greywall

TX-T

2000

/ m

K

T2000

/ mK

1 10 100 1000-5

-4

-3

-2

-1

0

1

2

3

4

5

U(T2000

, k=2, 95%)

(TX-T

2000

)/T

2000

/ %

T2000

/ mK

Greywall

Uni Florida

NIST

PTB


InK - ProjectEuropean Metrology Research Programme (EMRP)

“Implementing the new Kelvin” - InK project 2012 – 2015→ T-T90, T-T2000

14 national metrological institutes, 3 res. Grants, NPL – coordinator http://projects.npl.co.uk/ink/

Work package 4 - “Primary thermometry for low temperatures”

development of primary thermometers → T-T2000 CSNT, CBT, MFFT

to resolve the long standing discrepancy between the background data on which PLTS-2000 is based

http://www.io.csic.es/

http://www.inrim.it/

http://www.lne.fr/

http://www.mikes.fi/

http://www.cem.es/

http://www.tubitak.gov.tr/

http://www.measurement.gov.au/Pages/default.aspx

http://en.nim.ac.cn/

http://www.uva.es/portal/paginas/portada

http://www.vniiofi.ru/





http://www.nrc-cnrc.gc.ca/

http://www.nist.gov/

http://www.kriss.re.kr/

http://www.unican.es/




Conclusions - Outlook

International Temperature Scales are essential for maintenance and dissemination of the Kelvin with low uncertainties

T ≥ 1mK

Dissemination of ITS-90 and PLTS-2000 down to 1 mK• sc. reference points, resistance thermometers • practical noise thermometers → MFFT, on-chip CSNT new calibration service, U(TMFFT)≤ 1%

Discrepancies in the background data of PLTS-2000 below 10 mK• EMRP-project→ “InK”

T ≤ 1mK

• ultra-low temperature scale - part of a follow-up project ?• choice of scale carrier - investigation of material properties• development and evaluation of primary thermometers• comparison measurements between different thermometers/laboratories• development of transfer standards


Acknowledgments

PTB J. Beyer, D. Drung, M. Schmidt, Th. SchurigD. Heyer, B. Fellmuth, J. FischerP. Strehlow, E. BorkG. Wübbeler, F. Schmähling, C. Elster

Magnicon GmbHH.-J. BarthelmessS. AliValiollahi

University of Heidelberg, Kirchhoff Institute of PhysicsCh. Enss et al.

Royal Holloway University of LondonJ. Saunders et al.



http://www.bipm.org/utils/en/pdf/Estimates_Differences_T-T90_2010.pdf

Estimates of the differences between thermodynamic temperature and the ITS-90

0 200 400 600 800 1000 1200 1400-40

-20

0

20

40

60

80

0 10 20 30-1.0

-0.5

0.0

0.5

1.0

T-T

90 /

m

K

T90

/ K

T-T

90 /

mK

T90

/ K

10 100 1000-100

-80

-60

-40

-20

0

20

40

60

80

100

(T-T

90)/

T90

/

pp

m

T90

/ K


Relative deviation of Tnoise from T2000/90 for different noise thermometers.

0.001 0.010 0.100 1.000-5

0

5

10 CSNT MFFT-1 MFFT-2 U(T

2000)

+/- 1%

(Tn

ois

e-T

2000

/90)

/T20

00/9

0 / %

T2000/90

/ K

0.001 0.010 0.100 1.000

0.001

0.010

0.100

1.000

CSNT MFFT-1 MFFT-2

Tn

ois

e / K

T2000/90

/ K

Linearity of Tnoise in terms of T2000/90 for different noise thermometers..


Both Nuclear Demagnetisation Cooling and Magnetic Thermometry are two aspects of one and the samethermodynamic process. It arises from solution of proper field equations for boundary and initial values that can be controlled in the demagnetisation experiment.

Thermodynamic field equations are derived from the Boltzmann equation for the phase density of metal electrons and the Master equation for the probability density to find a nuclei with z-spin.

energy density of metal electrons

energy density of nuclear spins

heat flux

magnetisation

caloric and thermal equations of state

Both the thermodynamic temperature and the spin temperature result from the numerical solution of field equations for a given demagnetisation process .

),(e txT

),(N txT

),( txBz


),,,( e txpmf

),,( n txmw

2/1

2/1

3B

e

2

e d2

smzss pfBgm

mp

e

I

ImzII

I

wBgme NN

2/1

2/1

3

eB

e

2

d2

sm

izssi pfmp

Bgmmp

q

I

ImII

mss

Is

wgmnMpfgmnM NNNN

2/1

2/1

3Beee d

N

NN

equN

2

F

e2

F

2Bequ

eN

NNN

equn

eque

2

F

e2

Feeque B ,

121

23

, B , 12

51

53

kTBIg

IgkTB

kTBIg

BIgneBkT

ne zIII

zzIIzIz

09.-13.09.2013 Microkelvin Workshop 2013 1. 09.-13.09.2013 Microkelvin Workshop 2013 2 Mise en pratique for the definition of the kelvin updated version,

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