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

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)]

Measured mechanical loss of sapphire Ø 3“ x 24mm At 20 K we achieved a loss of 10 −8 . Our measurements reveal a loss peak at 35 K for all the measured modes.

Akhiezer damping in bulk sapphire Loss peak at 35 K is linked to Akhiezer loss (interaction of acoustic and thermal phonons) as follows: 𝜙= 𝑇𝐶 𝛾 2 𝜈 2 𝜔 𝜏 𝑝 1+ 𝜔 𝜏 𝑝 2 where 𝜏 𝑝 = 3 𝜅 𝐶𝜌 𝜈 2 . [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)] 𝐶… heat capacity, 𝛾… Grüneisen‘s constant, 𝜈… solid‘s speed of sound, 𝜏 𝑝 … lifetime of thermal phonons, 𝜅… heat conductivity, and 𝜌… density of material.  Akhiezer loss can not be overcome thus it is an intrinsic limit. 𝛾 … Grüneisen‘s constant used to fit: 1.8, 2.1, 3.3

Sapphire fibers measured in Jena MolTech fibers (4 in total) single nail head with flat Ø 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 head Ø 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 shaddow sensor Ring down technique Liquid helium cryostat 𝑇=5…300 K Cone seems to be better suited for the measurement as we achieve lower losses.

MolTech fiber Ø 1.8 mm x 350 mm, clamped in cone Lowest obtained loss on sapphire fiber so far: 5× 10 −8 Thermo elastic damping (TED) above 60 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: 𝜙= 𝑌𝑇 𝜌𝐶 𝜔 𝜏 𝑇𝐸 1+ 𝜔𝜏 2 𝜏 𝑇𝐸 = 1 2.16×2𝜋 𝜌𝐶𝑑 𝜅 [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)] 𝑌… Young‘s Modulus, 𝜏 𝑇𝐸 …characteristic time, 𝑑… diamter of the fiber

Impex fiber No.3, attached head clamped in cone At low temperature we observe different behaviour for different modes. It is not clear why this happens. We take into account some week interaction with the support (recoil loss) or the influence of the surface (unlikely). This is under investigation right now and has to be taken as preliminary result. Again: TED above 60 K seems to limit the loss Low temperature behaviour is not cleared and under investigation

Thermal conductivity

Thermal conductivity measurement Measured with the broken piece of 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 THeater THeat Sink Distance: 10…200 mm 𝑃= 𝐴 𝐿 𝜅Δ𝑇 𝜅= 𝐿 𝐴 𝑑𝑃 𝑑𝑇 𝜅 … therm. conductivity L … temp-sensor distance A … cross section Δ𝑇 … temp. difference P … 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

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: 𝑄 = 𝐴 𝑤 𝐿 𝑘 𝑇 𝑇𝑀 − 𝑇 𝑈𝑀 ≈200𝑚𝑊 Around 1 W of extracted heat is desirable for KAGRA, but with fibers of Ø 1.6 mm Futher investigations are needed!

Nevertheless: Sapphire will fulfill the requirements for KAGRA 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 ( 𝜙 𝑏𝑢𝑙𝑘 ≈ 10 −8 ) Above 60 K TED limits the loss of sapphire fibers Losses of better than 𝜙 𝑓𝑖𝑏𝑒𝑟 ≈ 10 −7 are achieved below 10 K Heat extraction by suspension fibers needs to be slightly improved Nevertheless: Sapphire will fulfill the requirements for KAGRA