1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. + - 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

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

9. 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

10. 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

11. 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

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

13. 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)

14. 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

15. 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

16. 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

17. 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

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

19. 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

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