Loss measurements in bulk materials at low temperatures D. Heinert, C. Schwarz, R. Nawrodt, W. Vodel, A. Tuennermann and P. Seidel Institute of Solid State Physics, University of Jena Cascina, 24th November 2008

outline connection between direct detection of gravitational waves noise vs. losses measuring setup experimental data outline connection between direct detection of gravitational waves and dissipation of mechanical energy (losses) setup for the experimental determination of losses experimental data and theoretical loss models

fundamental noise sources noise vs. losses noise sources measuring setup fluctuation-dissipation-theorem experimental data standard anelastic solid fundamental noise sources seismic noise = limits for sensitivity of interferometric detectors noise level photon shot noise thermal noise frequency 10 Hz 1 kHz detection band

Why to investigate losses? noise vs. losses noise sources measuring setup fluctuation-dissipation-theorem experimental data standard anelastic solid Why to investigate losses?  fluctuation-dissipation-theorem (FDT) noise losses knowledge of losses as key for low detector‘s noise systematic investigation of loss mechanisms especially at low temperatures modeling of temperature and frequency dependence  working conditions for future detectors

approximation for losses noise vs. losses noise sources measuring setup fluctuation-dissipation-theorem experimental data standard anelastic solid approximation for losses model of standard anelastic solid phase lag between stress σ and strain ε within the solid  energy dissipation

possibilities of varying ωτ: noise vs. losses noise sources measuring setup fluctuation-dissipation-theorem experimental data standard anelastic solid definition of losses Φ ω – applied frequency τ – relaxation time possibilities of varying ωτ: changing frequency ω changing τ via temperature

+ - measuring setup resonant excitation of cylindrical bulk samples noise vs. losses measuring setup experimental data measuring setup resonant excitation of cylindrical bulk samples formation of an eigenmode of the substrate interferometric measurement of oscillation‘s decay time elongation x/x0 suspension with tungsten wires - + time t/τ

cryostat probe chamber measuring setup noise vs. losses experimental data cryostat probe chamber

Crystalline quartz (Ø 76.2 mm x 12 mm, z-cut) noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon Crystalline quartz (Ø 76.2 mm x 12 mm, z-cut) quartz is well known test material (quartz resonators)  Identification of loss mechanisms

Na Al Si O defect induced losses defect geometry of quartz: noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon defect induced losses defect geometry of quartz: alkali atoms along c-axis Na Al Si O

theory of the running acoustic wave attenuation noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon theory of the running acoustic wave attenuation (T.O. Woodruff and H. Ehrenreich) sound wave induces change of the dispersion relation of phonons - Grüneisen constant - strain produced by sound wave every phonon branch has its own Grüneisen constant stress changes the phonon population: whole phonon system relaxes to new equlibirium via phonon-phonon-collisions  heat flow  energy dissipation

- thermal conductivity noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon - thermal conductivity - density - phonon lifetime - velocity of sound Temperaturshift erklären !!!

calcium fluoride (Ø 76.2 mm x 75 mm, 100) noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon calcium fluoride (Ø 76.2 mm x 75 mm, 100)

thermoelastic damping (TED) noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon thermoelastic damping (TED) thermal expansion α material constants: specific heat capacity C thermal conductivity κ [Braginsky] density ρ

TED as limitation for low temperature behaviour noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon TED as limitation for low temperature behaviour

silicon (Ø 76.2 mm x 75 mm, 100 and 111) very pure material noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon silicon (Ø 76.2 mm x 75 mm, 100 and 111) very pure material  low defect losses thermoelastic damping neglectible phonon losses most important beides sind Drummodes 111 bei 57kHz

noise vs. losses measuring setup experimental data summary mechanical spectroscopy allows studying properties of solids  modelling and prediction of mechanical losses  material and working parameters for future detectors  noise reduction outlook Übergang von Bulk- zu Schichtmessungen mirrors need dielectric coatings  new loss sources  investigation via cantilever measurements

Latest results on Si-cantilever (50mmx8mmx140µm, 100) noise vs. losses measuring setup experimental data Latest results on Si-cantilever (50mmx8mmx140µm, 100)

Wärmeleitungsgleichung: noise vs. losses crystalline quartz measuring setup calcium fluoride experimental data silicon Wärmeleitungsgleichung: Ansatz: Diffusionslänge – typischer Abstand zwischen Temperaturextrema Frequenzabhängigkeit nach Zener: h  geometrieabhängig

measuring setup noise vs. losses experimental data Bau und erste Messung