1. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 1/28 SFB TR 7 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 Interpretation of bulk material measurements 1 Institute of Solid State Physics 2 Institute of Applied Physics 3 Department of Bioinformatics Friedrich-Schiller-University Jena, Germany http://www.physik.uni-jena.de/~cryoq/ 4th ILIAS-GW Annual General Meeting

2. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 2/28 Single anelastic process: Analysis of Q data resonant frequency

3. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 3/28 relaxation time relaxation constant activation energy Boltzmann constant EaEa Free energy distance Especially for stress induced transitions between states of minimum energy: Relaxation time

4. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 4/28 Total damping Sum of anelastic processes Background damping (suspension, residual gas damping…) Transition requires consideration of the anisotropy of and Analysis of Q data and transition requirements

5. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 5/28 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. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 6/28 Distribution is linearly related to, as is linearly related to the activation energy. Fused silica - Ø 3‘‘ x 12 mm Mechanical loss due to a superposition of loss processes with varying relaxation time with normalized distribution function Assuming Gaussian distribution of barrier heights in asymmetric double-well potential 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 most likely value of

7. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 7/28 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. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 8/28 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. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 9/28 Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) Relax. Peak 1 2 1 1 2 2 35 4600 48x10 6 53 3 170 900 43x10 6 50 8

10. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 10/28 Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) Relax. Peak 1 2 35 4600 48x10 6 53 3 170 900 43x10 6 50 8 Interaction of acoustic wave with thermal phonons 1 1 2 2

11. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 11/28 Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) Relax. Peak 1 2 35 4600 48x10 6 53 3 170 900 43x10 6 50 8 Interaction of acoustic wave with alkali ions 1 1 2 2

12. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 12/28 Dissipation due to stress induced hopping of alkali-ions in alpha-quartz W. P. Mason in Physical Acoustics, edited by W. P. Mason (Academic Press Inc., New York, 1965), vol. 3B, p. 247. O Si

13. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 13/28 Crystalline quartz – Ø 3‘‘ x 12 mm (z-cut) Relax. Peak 3 4 3 3 4 4 8 12 735 72 10 2 1 955 99 7

14. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 14/28 Crystalline quartz – Ø 3‘‘ x 12 mm (x-cut)

15. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 15/28 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. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 16/28 Crystalline silicon – Ø 3‘‘ x 12 mm (100)

17. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 17/28 1 1 2 2 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 1 2 50 2.592 12 38 600 3.39 12.7 20

18. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 18/28 1 1 2 2 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 1 2 50 2.592 12 38 600 3.39 12.7 20 Interaction of acoustic wave with thermal phonons

19. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 19/28 1 1 2 2 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 1 2 50 2.592 12 38 600 3.39 12.7 20 Presumably due to doping with phosphorus Pomerantz M 1970 Interaction of Microwave phonons with Donor Electrons in Ge and Si Phys. Rev. B 1 4029-36

20. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 20/28 3 3 4 4 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 3 4 13 21 20525 380 14 10 53 20030 380 28

21. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 21/28 3 3 4 4 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 3 4 13 21 20525 380 14 10 53 20030 380 28 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

22. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 22/28 3 3 4 4 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 3 4 13 21 20525 380 14 10 53 20030 380 28 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

23. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 23/28 5 5 6 6 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 5 6 5 5 14012 185 12 10 14 13860 183 6

24. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 24/28 5 5 6 6 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 5 6 5 5 14012 185 12 10 14 13860 183 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

25. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 25/28 5 5 6 6 Crystalline silicon – Ø 3‘‘ x 12 mm (100) Relax. Peak 5 6 5 5 14012 185 12 10 14 13860 183 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

26. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 26/28 Crystalline calcium fluoride – Ø 75 mm x 75 mm (100)

27. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 27/28 Crystalline calcium fluoride – Ø 75 mm x 75 mm (100) suspended with tungsten wire (50 µm in diameter) coupling of substrate motion to suspension

28. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 28/28 Crystalline calcium fluoride – Ø 75 mm x 75 mm (100) Relax. Peak 1 2 170 3.6 11.4 30 3 4 5 6 7 8 thermoelastic damping: (black line) Braginsky V B et al. 1985 Systems with Small Dissipation (Chicago: The University of Chicago Press) p.11 thermal conductivity volume therm. expansion coeff. density specific heat capacity 170 120 130 500 80 20 3 1 3 100 15 15.5 37 49 62 70 1 2 3 4 5 6 7 8

29. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 29/28 Crystalline silicon – Ø 3‘‘ x 12 mm (100) thermoelastic damping: Braginsky V B et al. 1985 Systems with Small Dissipation (Chicago: The University of Chicago Press) p.11 thermal conductivity volume therm. expansion coeff. density specific heat capacity

30. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 30/28 Crystalline quartz – work in progress Symmetrized stresses, strains and compliances of type I. The arrows indicate the relationships.

31. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 31/28 Crystalline quartz – work in progress Symmetrized stresses, strains and compliances of type II. The arrows indicate the relationships.

32. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 32/28 Crystalline quartz – work in progress The strain ellipsoid of the tensor for a particular defect orientation in the crystal.

33. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 33/28 Crystalline quartz – work in progress Selection rules for anelasticity. The numbers given (1, 2, or 3) indicate the number of distinct relaxation times. ’0’ means that no relaxation occurs. A dash indicates that the defect symmetry is not possible in the particular crystal system.

34. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 34/28 Crystalline quartz – work in progress

35. Interpretation of bulk material measurements Anja Schröter08.10.2007 Institute of Solid State Physics – Low Temperature Physics Friedrich-Schiller-University Jena 35/28 Landau-Rumer damping: Akhieser damping: Woodruff T O and Ehrenreich H 1961 Absorption of Sound in Insulators Phys. Rev. 123 1553-9