Mechanical Loss and Thermal Conductivity of Materials for KAGRA and ET

Gerd Hofmann1, Julius Komma1, Christian Schwarz1, Daniel Heinert1, Paul Seidel1, Andreas Tünnermann2, and Ronny Nawrodt1

1Friedrich-Schiller-Universität Jena, Institute for Solid State Physics, Helmholtzweg 5, D-07743 Jena, Germany2Friedrich-Schiller-Universität Jena, Institute of Applied Physics, Albert-Einstein-Strasse 15, D-07745 Jena, Germany

April 19th 2013ELiTES Workshop, Tokyo

Mechanical Loss andThermal Conductivity

of Materials for KAGRA and ET

ELiTES Workshop, Tokyo, 19th April 2013Gerd Hofmann 2 / XX

Friedrich-Schiller-Universität Jena

Outline

• Test mass materials for future GWDs– Fused silica – state of the art, certainly at RT (optics & suspension)– Silicon ET– Sapphire KAGRA

• Bulk loss of silicon & sapphire vs. fused silica• Mechanical loss of sapphire fibers for suspension

– Different lengths, single vs. double head• Thermal conductivity of sapphire fibers• Summary & Outlook

MECHANICAL LOSS



Basic layout of an interferometric GWD

• Extremely sensitive Michelson interferometer, several noise sources• Main topic: Brownian thermal noise arising from the

mechanical loss of the materials (currently fused silica)for the optics, the test masses, and their suspensions.



Mechanical loss of fused silica vs. silicon & sapphire

The mechanical loss of fused silica strongly increases when being cooled down.Much more suitable are single crystalline materials like silicon or sapphire.For KAGRA, IMs and EMs will be made of sapphire.In ET-LF they will be made of silicon. [R. Nawrodt et al.: Cryogenic Setup for Q-factor measurements on bulk materials for

future gravitational wave detectors, in Proceedings of ICEC22-ICMC2008 (2009)]

0 30 60 90 120 150 180 210 240 270 30010-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

mec

hani

cal lo

ss

temperature in K

fused silica silicon sapphire



Measured mechanical loss of sapphire Ø 3“ x 24mm

At 20 K we achieved a loss of . Our measurements reveal a loss peak at 35 K for all the measured modes.

0 30 60 90 120 150 180 210 240 270 300 33010-9

10-8

10-7

2x10-7me

chanic

al los

s

temperature T in K

32.3 kHz 36.2 kHz 50.8 kHz



Akhiezer damping in bulk sapphire

Loss peak at 35 K is linked to Akhiezer loss (interaction of acoustic and thermal phonons) as follows:

where .[A. Akhieser: On the absorption of sound in solids. Journal of Physics (1939)][V. B. Braginskyet al.: Systems with Small Dissipation.The University of Chicago Press, Chicago and London (1985)]

… heat capacity, … solid‘s speed of sound

… heat conductivity, and … density of material.

Akhiezer loss can not be overcome thus it is an intrinsic limit.0 30 60 90 120 15010-9

10-8

10-7

10-6

mec

hani

cal l

oss

temperature T in K

32.3 kHz 36.2 kHz 50.8 kHz



Sapphire fibers measured in Jena

• MolTech fibers (4 in total)

– single nail head with flatØ 10 mm x 5 mm

– fiber Ø 1.8 mm– 1 unbroken (350 mm)– 1 broken (86 mm & 264 mm)

• Impex fibers (5 in total)

– double nail headØ 10 mm x 5 mm

– fiber Ø 1.6 mm– total lenght 100 mm



Measurement setup

• Use of massive cooper supports and clamps:• Flat drill hole vs.

Cone drill hole• Electrostatic driving

plates for excitation• Optical readout

by use of shaddowsensor

• Ring down technique

• Liquid helium cryostat



• Lowest obtained loss on sapphire fiber so far: • Thermo elastic damping (TED) above

MolTech fiber Ø 1.8 mm x 350 mm, clamped in cone

0 30 60 90 120 150 180 210 240 270 300 33010-8

10-7

10-6

10-5

10-4

1217 Hz TED

mec

hani

cal lo

ss

temperature T in K



Thermo elastic damping in sapphire fibers

Thermo elastic damping (TED) occurs from irreversible heat flow between compressed and strechted areas of the fiber.The loss is given by:

[C. Zener : Internal Friction in Solids: I. Theory of Internal Friction in Reeds. Physical Review 52 (1937)][C. Zener : Internal Friction of Solids: II.General Theory of Thermoelastic Internal Friction. Physical Review 53 (1938)]

… Young‘s Modulus,…characteristic time,… diamter of the fiber



Impex fiber No.3, attached head clamped in cone

• Again: TED above seems to limit the loss• Low temperature behaviour is not cleared and under investigation

0 30 60 90 120 150 180 210 240 270 30010-7

10-6

10-5

10-4

10-3Me

chan

ical l

oss

Temperature in K

87Hz 1240Hz 3676Hz 35132Hz

THERMAL CONDUCTIVITY



Thermal conductivity measurement

• Measured with the broken pieceof MolTech fiber:– Ø 1.8 mm– 264 mm in length

• Copper clamps to attach– the heater– the sensors– the heat sink



Setup and measurement procedure

T1

T2

THeater

THeat Sink

Dist

ance

: 10…

200

mm

𝑃=𝐴𝐿 𝜅 Δ𝑇 𝜅=

𝐿𝐴𝑑𝑃𝑑𝑇

… therm. conductivity L … temp-sensor distanceA … cross section … temp. differenceP … electr. power

Measurement Procedure:#1 – Wait until all sensors are in thermal equilibrium#2 – Set a given Heater Power and wait until all sensors reach thermal equilibrium again#3 – Repeat #2 until a maximum given temperature difference between T1 and T2 is reached#4 – Plot T1-T2 vs. PHeater + linear fit of the data



Thermal conductivity of sapphire

• Thermal conductivity of the fiber is clearly different to that of bulk sapphire• Surface and also heat treatment might change the thermal conductivity

1 10 100 100010

100

1000

10000

30000

1.8mm dia, 168mm length, MolTec-Fibre (Jena) 1.55mm dia, 60mm length, unpolished (Touloukian) 2.47mm dia, 60mm length, unpolished, annealed 2.52mm dia, 60mm length, polished, annealed recommended values for bulk sapphire

Th

erm

al C

ondu

ctiv

ity [W

/mK

]

Temperature [K]



Heat extraction from fibers

• If we asume – L = 30 cm, Ø 1.8 mm– Test mass TM 20K– Upper mass UM 16K– Thermal conductivity of k 2 x 10^3 W/m/K

• Heat extraction of one fiber:

• Around 1 W of extracted heat is desirable for KAGRA, but with fibers of Ø 1.6 mm

• Futher investigations are needed!



Summary

• Cooling of the test masses and suspensions will reduce brownian

thermal noise in future GWDs using silicon or sapphire

• Bulk sapphire is limited by phonon-phonon-interaction at the

desired temperature of 20 K ()

• Above 60 K TED limits the loss of sapphire fibers

Losses of better than are achieved below 10 K

• Heat extraction by suspension fibers needs to be slightly improved

Nevertheless: Sapphire will fulfill the requirements for KAGRA

Mechanical Loss and Thermal Conductivity of Materials for KAGRA and ET

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