Mechanical Loss and Thermal Conductivity of Materials for KAGRA and ET

1. Mechanical Loss andThermal Conductivityof 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, Germany 2Friedrich-Schiller-Universität Jena, Institute of Applied Physics, Albert-Einstein-Strasse 15, D-07745 Jena, Germany April 19th 2013 ELiTES Workshop, Tokyo

2. 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

3. Mechanicalloss

4. Basic layout of an interferometric GWD • Extremely sensitive Michelson interferometer, several noise sources • Main topic: Brownian thermal noise arising from themechanical loss of the materials (currently fused silica)for the optics, the test masses, and their suspensions.

5. 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.: CryogenicSetup forQ-factormeasurements on bulk materials for future gravitational wave detectors,in Proceedings of ICEC22-ICMC2008 (2009)]

6. 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.

7. 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)] … heatcapacity, … solid‘s speed ofsound … heatconductivity, and… densityof material. Akhiezerlosscan not beovercomethusitis an intrinsiclimit.

8. 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

9. Measurement setup • Use of massive coopersupportsandclamps: • Flat drill hole vs.Conedrill hole • Electrostaticdrivingplatesforexcitation • Optical readoutbyuseofshaddowsensor • Ring down technique • Liquid helium cryostat

10. MolTech fiber Ø 1.8 mm x 350 mm, clamped in cone • Lowest obtained loss on sapphire fiber so far: • Thermo elastic damping (TED) above

11. Thermo elastic damping in sapphire fibers Thermo elastic damping (TED) occurs from irreversible heat flow between compressed and strechted areasof 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

12. Impex fiber No.3, attached head clamped in cone • Again: TED aboveseemstolimittheloss • Low temperaturebehaviouris not clearedandunderinvestigation

13. Thermal conductivity

14. Thermal conductivity measurement • Measured with the broken pieceof MolTechfiber: • Ø 1.8 mm • 264 mm in length • Copper clamps to attach • the heater • the sensors • the heat sink

15. Setup and measurement procedure THeater T1 … therm. conductivityL … temp-sensor distance A … crosssection … temp. difference P … electr. power Distance: 10…200 mm 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 T2 THeat Sink

16. Thermal conductivityofsapphire • Thermal conductivityofthefiberisclearly different tothatofbulksapphire • Surfaceand also heattreatmentmightchangethe thermal conductivity

17. Heatextractionfromfibers • If weasume • L = 30 cm, Ø 1.8 mm • Test mass TM 20K • Uppermass UM 16K • Thermal conductivityof k 2 x 10^3 W/m/K • Heatextractionofonefiber: • Around 1 W ofextractedheatisdesirablefor KAGRA, but withfibersofØ 1.6 mm • Futher investigations are needed!

18. 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 fibersLosses 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