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SFB TR 7

4th ILIAS-GW Annual General Meeting. Interpretation of bulk material measurements. A. Schröter 1,3 , R. Nawrodt 1 , D. Heinert 1 , C. Schwarz 1 , M. Hudl 1 , T. Köttig 1 , W. Vodel 1 , A. Tünnermann 2 , P. Seidel 1. 1 Institute of Solid State Physics 2 Institute of Applied Physics

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SFB TR 7

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  1. 4th ILIAS-GW Annual General Meeting Interpretation of bulk material measurements A. Schröter1,3, R. Nawrodt1, D. Heinert1, C. Schwarz1, M. Hudl1, T. Köttig1, W. Vodel1, A. Tünnermann2, P. Seidel1 1 Institute of Solid State Physics 2 Institute of Applied Physics 3 Department of Bioinformatics http://www.physik.uni-jena.de/~cryoq/ SFB TR 7 Friedrich-Schiller-University Jena, Germany

  2. Single anelastic process: Analysis of Q data resonant frequency

  3. Ea relaxation time relaxation constant activation energy Boltzmann constant Free energy distance Relaxation time Especially for stress induced transitions between states of minimum energy:

  4. Transition requires consideration of the anisotropy of and Analysis of Q data and transition requirements Sum of anelastic processes Background damping (suspension, residual gas damping…) Total damping

  5. Fused silica - Ø 3‘‘ x 12 mm Mode shape: A. Schroeter, R. Nawrodt, R. Schnabel, S. Reid, I. Martin, S. Rowan, C. Schwarz, T. Koettig, R. Neubert, M. Thürk, W. Vodel, A. Tünnermann, K. Danzmann and P. Seidel, On the mechanical quality factors of cryogenic test masses from fused silica and crystalline quartz, arXiv:0709.4359v1 [gr-qc], submitted to Class. Quantum Grav.

  6. Fused silica - Ø 3‘‘ x 12 mm Mechanical loss due to a superposition of loss processes with varying relaxation time with normalized distribution function Distribution is linearly related to , as is linearly related to the activation energy. Assuming Gaussian distribution of barrier heights in asymmetric double-well potential most likely value of half-width of Gaussian distribution at point where falls to 1/e of its max. value Solely variation in activation energies and not in relaxation constant: constant

  7. Fused silica - Ø 3‘‘ x 12 mm Fitting parameters: similar to that reported by Hunklinger Hunklinger S 1974 Ultrasonics in amorphous materials Proceedings IEEE Ultrasonics Symposium 493-501

  8. Probably useful description for losses in the amorphous coatings? Met people from the group Glasses physics and spectroscopy, Laboratory of colloids, glasses and nanomaterials, University of Montpellier, France at the conference PHONONS2007, Paris, France

  9. Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) 2 1 1 2 Relax. Peak 170 3x106 4 1 35 8x106 4 50 2 53 900 8 4600 3

  10. Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) 2 1 1 2 Interaction of acoustic wave with thermal phonons Relax. Peak 170 3x106 4 1 35 8x106 4 50 2 53 900 8 4600 3

  11. Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) 2 1 1 2 Interaction of acoustic wave with alkali ions Relax. Peak 170 3x106 4 1 35 8x106 4 50 2 53 900 8 4600 3

  12. Dissipation due to stress induced hopping of alkali-ions in alpha-quartz Si O W. P. Mason in Physical Acoustics, edited by W. P. Mason (Academic Press Inc., New York, 1965), vol. 3B, p. 247.

  13. Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) 3 3 4 4 Relax. Peak 2 5 95 3 8 5 73 99 4 72 1 7 12 10

  14. Crystalline quartz – Ø 3‘‘ x 12 mm (x-cut)

  15. Crystalline quartz – work in progress Work in progress: • mechanical losses are related to changes in moduli • concept of symmetrized stresses and strains, only certain combinations of stresses give rise to relaxation • appearance of relaxation also depends on defect symmetry • elastic dipole: a point defect introduced into a crystal produces local distortions • selection rules M: modulus of elasticity J: modulus of compliance A. S. Nowick and B. S. Berry, Anelastic Relaxation in Crystalline Solids (New York & London: Academic Press, 1972).

  16. Crystalline silicon – Ø 3‘‘ x 12 mm (100)

  17. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 2 1 1 2 Relax. Peak 9 3.3 1 92 2.5 12.7 2 12 600 20 50 38

  18. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 2 1 1 2 Interaction of acoustic wave with thermal phonons Relax. Peak 9 3.3 1 92 2.5 12.7 2 12 600 20 50 38

  19. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 2 1 1 2 Presumably due to doping with phosphorus Pomerantz M 1970 Interaction of Microwave phonons with Donor Electrons in Ge and SiPhys. Rev. B 1 4029-36 Relax. Peak 9 3.3 1 92 2.5 12.7 2 12 600 20 50 38

  20. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 4 4 3 3 Relax. Peak 10 30 200 3 13 25 205 380 4 380 53 28 21 14

  21. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 4 4 3 3 Presumably due to electronic redistribution in vacancy-oxygen complex Watkins G D and Corbett J W 1961 Defects in Irradiated Silicon. I. Electron Spin Resonance of the Si-A Center Phys. Rev. 121 1001-14 Relax. Peak 10 30 200 3 13 25 205 380 4 380 53 28 21 14

  22. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 4 4 3 3 Presumably due to reorientation of vacancy-oxygen complex Watkins G D and Corbett J W 1961 Defects in Irradiated Silicon. I. Electron Spin Resonance of the Si-A Center Phys. Rev. 121 1001-14 Relax. Peak 10 30 200 3 13 25 205 380 4 380 53 28 21 14

  23. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 6 5 5 6 Relax. Peak 10 60 138 5 5 12 140 183 6 185 14 6 5 12

  24. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 6 5 5 6 Presumably due to vibrations of Si-O-Si complexes Lam C C and Douglass D H 1981 Observation of Oxygen Impurities in Single-Crystal Silicon by Means of Internal Friction J. Low Temp. Phys. 44 259-264 Relax. Peak 10 60 138 5 5 12 140 183 6 185 14 6 5 12

  25. Crystalline silicon – Ø 3‘‘ x 12 mm (100) 6 5 5 6 Presumably due to vacancy-oxygen-hydrogen complexes Coutinho J et al. 2003 Effect of stress on the energy levels of the vacancy-oxygen-hydrogen complex in Si Phys. Rev. B 68 184106-1 - 184106-11 Relax. Peak 10 60 138 5 5 12 140 183 6 185 14 6 5 12

  26. Crystalline calcium fluoride – Ø 75 mm x 75 mm (100)

  27. Crystalline calcium fluoride – Ø 75 mm x 75 mm (100) coupling of substrate motion to suspension suspended with tungsten wire (50 µm in diameter)

  28. Crystalline calcium fluoride – Ø 75 mm x 75 mm (100) Relax. Peak 6 1 3.6 1 3 2 2 11.4 170 30 7 4 5 15 3 100 170 8 4 15.5 120 37 5 130 20 thermoelastic damping: (black line) 49 6 3 500 80 1 7 62 3 70 20 thermal conductivity volume therm. expansion coeff. 8 density specific heat capacity Braginsky V B et al. 1985 Systems with Small Dissipation (Chicago: The University of Chicago Press) p.11

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