A new facility forthermal conductivity

measurements

Filippo MartelliUniv. of Urbino and INFN Florence

GWADW 2006 – 27/5-02/06 2006 – La Biodola

GWADW 2006 2 of 16

Activities on thermal noiseActivities on thermal noisein Florencein Florence

• Modelling of thermal noise for Virgo optics and suspensions

• Measurements on crystalline silicon fibres

• Study of new materials for 3rd generation interferometric GW detectors (JRA3-STREGA collaboration)

GWADW 2006 3 of 16

Study of the thermo-mechanical properties of materials

for 3rd generation GW detectors

Cryogenic facility

Crystalline Silicon Samples

Measurements concern

Thermal conductivity

Thermal expansioncoefficient

Q measurements (possible, but our set up is not

optimized for this)

GWADW 2006 4 of 16

Thermoelastic properties

2

V

E Tc

Amplitudeof thermoelastic

peak

21

2.161p

Vf

c d

Position(cylindrical

sample)

• Knowledge of the thermoelastic peak is important for identification of the various contribution to the loss angle (study of bulk, surface, clamp….losses)

• Knowledge of thermal conductivity is crucial for suspensions to be used in cryogenic detectors (heat extraction)

GWADW 2006 5 of 16

100

1000

10000

1 10 100 1000

T (K)

Th

. co

nd

uct

ivit

y (W

/mK

)Thermal conductivity of Si

13 -3

n type P doped260 cm4 10 cm

12 -3

p type B doped5000 cm3 10 cm

14 -3

n type 15-25 cm5 10 cm

From Y.S. Touloukian, E.H. Buyco, “Thermo-physical properties of matter”, Plenum, NY, 1970

GWADW 2006 6 of 16

The cryostat

30 cm

A.S. Scientific cryostatExperimental volume: about 14 dm3

Inner cold shield

Outer cold shield

Optical windows

Optical windows

Inner tank Liquid He

Outer tank Liquid N2

Vacuum chamber

Experimental chamber

GWADW 2006 7 of 16

Thermal conductivity measurement

INSULATORBOX

HEATER

COPPERBOX

CLAMP

SAMPLE

THERMOMETERS

SAMPLEHEATER

P VIΔT = 100 mK

tr

LPS T

L=5.8 cmD=5 mm

GWADW 2006 8 of 16

Evaluation of the power loss

Heat loss is due mainly to radiation (small contribution by wire conduction)

INSULATORBOX

HEATER

COPPERBOX

CLAMP

SAMPLE

THERMOMETERS

SAMPLEHEATER

1mW of heating power

From the heating-cooling cycle at room T

Conductive losses through wires are negligible (0.1 % of radiative losses

at room temperature)

we evaluate the unknown parameterin radiative losses

3rad 4P T T

GWADW 2006 9 of 16

Power loss estimation

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02

1.E+04

0 50 100 150

T [K]

P [

mW

]

PP radPcond

100 mKT

GWADW 2006 10 of 16

Power loss estimation

0.0001

0.001

0.01

0.1

1

0 50 100 150

T [K]

P/P

loss

%

GWADW 2006 11 of 16

Results

100

1000

10000

0 50 100 150 200

T (K)

Th

. co

nd

uc

tiv

ity

(W

/mK

)

13 -3

= 260 cm4 10 cmn

12 -3

=5000 cm3 10 cmn

14 -3

=15-25 cm5 10 cmn

-6

Our sample:

purity 1042 cm (measured)

GWADW 2006 12 of 16

Thermal expansion measurement facility

-17 K10 10% 810LL

No hope with a simple Michelson !

Simple Fabry-Perot cavity

Problems from frequency stability !

if L=10 cm-9 L=10 m

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Thermal expansion measurement facility

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Measuring cavity

Sample

Mirrors Fixed clamp

Mobile clamp

Laser

Very soft elastic blades

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The reference cavity

Vacuum chamber hosting reference cavity

Heating wires for RC temperature control

Mirror Reference material: zerodur

Piezo actuator

Elastic Cu/Be blades

1 h

1 K

Result of the temperature stabilization

(Matteo Lorenzini)

T fluctuations muststay below 0.01 K

We now have a few mK stability

GWADW 2006 16 of 16

Conclusions

• We have a facility for direct measurements of thermal conductivity in samples shorter than 20 cm from 4 K up to room temperature

• First measurements on a Si sample down to 40 K show that the instrument is properly working (we need a better calibration)

• The setup for LHe should still be optimized

• We are studying the possibility of measuring the thermal expansion coefficient as well