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Peter Murray

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  1. Measurement of the Mechanical Loss of Test Mass Materials for Advanced Gravitational Wave Detectors Peter Murray

  2. Q Peter Murray

  3. Summary • Thermal Noise • Measurement of Quality Factor • Calculation of Residual Coating Loss • Experimental Results • Silica • Silicon • Electron Energy Loss Spectroscopy • Cryogenics • Future Work • Conclusions IGR Lunchtime Talk

  4. Noise Sources • There are many sources of noise that can limit the sensitivity of interferometric detectors • Shot Noise • Radiation Pressure • Seismic Noise • Thermal Noise • Ground-based detectors high frequency limit of a few kHz, set by photon shot noise IGR Lunchtime Talk

  5. Thermal Noise • Random Brownian motion of atoms in test mass mirrors appears as thermally driven motion of the mechanical system • Thermal noise significant noise source at the lower operating frequency range • Low loss suspension materials ensure that thermal noise level over operating bandwidth of detectors is kept to a minimum IGR Lunchtime Talk

  6. Quality Factor • Q factor or Q, in resonant systems, is measurement of the effect of resistance to oscillation • Fusion energy gain factor, Q value or Q, the ratio of fusion power produced in a reactor to the power required to maintain the plasma in steady state • Q factor, in recumbent bicycle mechanics, refers to the width between the cranks and should be small when building a streamliner • Q factor, in marketing and pop culture commentary, sometimes used as a casual synonym for Q Score • The higher the Q Score, the more well-known and well thought of the item or person being scored is IGR Lunchtime Talk

  7. Measurement of Quality Factor • Larger Qs result in less off resonance loss by equipartition theorem • Levin approach proportional to f(w) at frequencies well below resonance • Apparatus being used to measure the mechanical dissipation of bulk samples at room temperature • Samples are suspended in loops of silk thread • Resonant modes exited using electrostatic actuator IGR Lunchtime Talk

  8. Measurement of Quality Factor IGR Lunchtime Talk

  9. Evaluating Quality Factor • Resonant mode modelled as freely decaying harmonic oscillator • Rate of decay of amplitude is measured • Q and mechanical dissipation can be determined • Many different suspensions are measured to obtain as high a Q as possible IGR Lunchtime Talk

  10. Calculation of Residual Coating Loss • Dielectric coatings formed from layers of Ta2O5 and SiO2 • Introduction of these coatings introduces another source of mechanical dissipation • Assuming all other losses have been reduced to a negligible level, total measured loss of a coated test mass can be expressed as • is the fraction of energy stored within the coating IGR Lunchtime Talk

  11. Calculation of Residual Coating Loss • The magnitude of the loss introduced by the dielectric coating can be calculated • Compare the losses of test mass before and after coating is applied • Subtracting the loss attributable to thermoelastic damping • The residual loss can be expressed as having a small frequency dependence IGR Lunchtime Talk

  12. Coating Split Analysis undertaken to calculate individual losses Masses produced coated with single layer of Silica or Tantala Reasonably consistent with above Suggests doping tantala reduces residual coating loss Un-doped tantala had small cracks which formed during annealing Could have introduced excess losses Control sample used in analysis had not gone through the same annealing process as the silica coated mass May attribute to difference between the two loss values for silica Single thick layer of silica may not have same structure as thinner silica in a multi-layer coating Experimental Results for Silica Samples IGR Lunchtime Talk

  13. LMA produced series of multi-layer tantala-silica coatings with increasing percentages of TiO2 30 alternating l/4 layers of Ta2O5 and SiO2 Adding any TiO2 to the Ta2O5 reduces the mechanical loss by ~30 to 50% Formula 4 has a residual loss higher than the first three formulae Originally unclear whether difference was due to the different coating chamber Formula 5 coating produced using this second chamber has a residual loss comparable to that of the first three Formula masses Suggests use of different chamber has no significant effect on coating losses Experimental Results for Silica Samples IGR Lunchtime Talk

  14. Electron Energy Loss Spectroscopy • Material is exposed to beam of electrons with a known, narrow range of kinetic energies • Some electrons will lose energy by inelastic scattering • Interaction of beam electron with an electron in sample • Results in both a loss of energy and a change in momentum • Interactions may be • Phonon excitations • Inter and intra band transitions • Inner shell ionisations • Latter are particularly useful for detecting elemental components of a material • Energy transferred is related to the ionization potential of atom • Therefore the spectrum can be compared to that of known samples IGR Lunchtime Talk

  15. Electron Energy Loss Spectroscopy • LMA originally able to provide only approximate value of TiO2in Ta2O5 layers • EELS being used to produce a definitive composition of all these coatings • Formula 1 silica-tantala coating is uniformly doped with 8.5±1.2% titania • F3 doped with 22.5±2.9% TiO2 • F4 doped with 54±5% TiO2 • EELS analysis in agreement with LMA values Light layers are doped Ta2O5 layers Brighter the pixel, the more TiO2is present IGR Lunchtime Talk

  16. Empirical Model of Mechanical Losses in Silica • Previous models for substrate loss assumed a frequency independent loss. • Empirical model developed, by S. Penn et al, to model the mechanical loss in differing types of fused silica: • (V/S)−1 is the surface to volume ratio of a sample (in mm) • fth is thermoelastic loss • f is frequency • C1, C2, C3 and C4 constants related to specific type of fused silica • Resonant frequencies measured well away from frequency at which thermoelastic loss is maximum • Therefore fth can be assumed to be negligible IGR Lunchtime Talk

  17. Empirical Model of Mechanical Losses in Silica • Qs for a 65 mm diameter and 70 mm long Suprasil 311 silica test mass compared to the empirical model • Several Qs lie close to the empirical model • Some Q values however lie below the empirical model • Suggests some other factor limiting the quality factor • most likely frictional losses associated with the suspension IGR Lunchtime Talk

  18. Nodal Support • Nodal support being developed to improve Q values for suspension limited modes • Qs of 6.17x107 already achieved on Sapphire using “Super Noodle” • Ellie’s Talk (15th March) will discuss this in more detail IGR Lunchtime Talk

  19. Finite Element Analysis of Mode Shapes IGR Lunchtime Talk

  20. Future Work • Residual Coating Loss Measurements • Continue investigations into losses of different coatings applied to silica and sapphire masses • Introduction of Nodal support should improve Q values for suspension limited modes • EELS analysis will produce a definitive composition of coatings • Diffraction gratings etched onto test masses may be used as non-transmissive beam splitters in future detectors IGR Lunchtime Talk

  21. Future Work • Silicon at room temperature • Continue to investigate: • Losses of different aspect ratios of silicon • Losses of different orientations of silicon • The effects of doping silicon on losses • Begin to investigate losses introduced by applying coatings to silicon • Testing bulk samples at cryogenic temperatures IGR Lunchtime Talk

  22. Conclusions • Study of coating loses helping inform decisions towards upgrades for advanced gravitational wave detectors • Needs to also be investigated at cryogenic temperature • Intrinsic coating loss dominated by loss associated with tantala • Doping the tantala reduces this loss • EELS has helped to find the definitive composition of some of these coatings IGR Lunchtime Talk

  23. Conclusions • Current apparatus is capable of obtaining high quality factors • However, need to ensure not limited by suspension losses • Nodal Support may improve Qs of some resonance modes • Should allow better analysis of losses introduced by coating samples • Results suggest [111] silicon has lower loss than [100] silicon and work will continue to investigate this IGR Lunchtime Talk

  24. Thank You For Your Attention Any Qs?

  25. References [1] • [1] P. Fr´e, “Introduction to General Relativity”, SIGRAV Summer School (Cascina, Italy), (May 2004). • [2] M. Francaviglia, “Black Holes Solutions and Their Properties”, SIGRAV Summer School (Cascina, Italy), (May 2004). • [3] I. Bombaci, “Neutron Stars’ Structure and Nuclear Equation of State”, SIGRAV Summer School (Cascina, Italy), (May 2004). • [4] A. Abramovici et al. Science, 256 (1992) 325-333. • [5] J. Hough et al. “Proposal for a Joint German-British Interferometric Gravitational Wave Detector”, Technical report, Max-Planck-Institut F¨ur Quantenoptic, (Sept 1989). • [6] F. Acernese et al. Class. Quantum Grav. 21 (2004) 385-394. • [7] R. Tsunesada, Class. Quantum Grav. 21 (2002) S403-S408. • [8] H. B. Callen, T. A. Welton, Physical Review, 83:34, (1951). • [9] H. B. Callen, R. F. Greene, Physical Review, 86:702, (1952). • [10] P. R. Saulson, Phys. Rev. D, 42 (1990) 2437-2445. • [11] P. H. Sneddon, “Investigations of Internal Mechanical Loss Factors of Test Mass Materials for Interferometric Gravitational Wave Detectors”, PhD thesis, University of Glasgow, (2001). • [12] A. P. French, “Vibrations and Waves”, M. I. T. Introductory Physics Series, Van Nostrand International, (1965). • [13] Yu. Levin, Phys. Lett D, 57 (1998) 659-663. • [14] K. Numata, Class. Quantum Grav. 19 (2002) 1697-1702. • [15] P. Willems, D. Busby, “Report to the April 25th 2003 Core Optics Down-Select Committee Meeting”, http://www.ligo.caltech.edu/docs/T/T030087-00.pdf. • [16] S. Penn, “Lowering Mechanical Loss in Fused Silica Optics with Annealing”, http://www.ligo.caltech.edu/docs/G/G040160-00/G040160-00.ppt. • [17] S. Rowan, G. Cagnoli, P. Sneddon, J. Hough, R. Route, E, Gustafson, M. Feyer, V. Mitrafanov, Phys. Lett. A, 265 (2000) 5-11. • [18] V. B. Brasinsky, V. P. Mitrafanov, V. I. Panovo, “Systems with Small Dissipations”, University of Chicago Press, (1986). • [19] S. Rowan et al. “Test Mass Materials for a New Generation of Gravitational Wave Detectors”, Proceedings of SPIE - Vol. 4856 (2003) 292-297. IGR Lunchtime Talk

  26. References [2] • [20] V. B. Brasinsky, M. L. Gorodetsky, S. P. Vyatchanin, Phys. Lett. A, 271 (2000) 303-307. • [21] LIGO Scientific Collaboration, “Test Mass Material Down-select Plan”, http://ligo.caltech.edu/gari/LIGOII/Downselect/index.html. • [22] H. J. Pain, “The Physics of Waves and Vibrations 5th Edition”, J. Wiley and Sons, (1998). • [23] G. W. McMahon, Journal of Accoustical Society of America, 36:85, (1964). • [24] D. R. M. Crooks, “Mechanical Loss and its Significance in Test Mass Mirrors of Gravitational Wave Detectors”, PhD thesis, University of Glasgow, (May 2003). • [25] D. R. M. Crooks, P. Sneddon et al. Class. Quantum Grav. 19 (2002) 883-896. • [26] S. D. Penn et al. Class. Quantum Grav. 20 (2003) 2917-2928. • [27] D. R. M. Crooks, P. Sneddon et al. Class. Quantum Grav. 21 (2004) S1059-S1065. • [28] G. Harry, “Thermal Noise from Optical Coatings”, http://www.ligo.caltech.edu/docs/G/G030337-00/G030337-00.pdf. • [29] http://lma.in2p3.fr/Lmagb.htm. • [30] http://www.ssp.gla.ac.uk/ResSum/Nanocharacterisation.htm. • [31] I. MacLaren, “Characterisation of Multilayer Mirror Coatings”, http://emvogil-3.mit.edu/gharry/meeting/MacLaren.pdf. • [32] http://www.tip.csiro.au/IMP/Optical/coatingsindex.htm. • [33] E. J. Elliffe et al. Class. Quantum Grav. 20 (2003) 5025-5037. • [34] S. Penn et al. “Frequency and Surface Dependence of the Mechanical Loss in Fused Silica”, http://www.ligo.org/pdf public/techpapers penn.pdf. • [35] D. F. McGuigan, C. C. Lam et al. “Measurements of the Mechanical Q of Single- Crystal Silicon at Low Temperature”, Journal of Low Temperature Physics, 30 (1978) 621. • [36] http://www.asscientific.co.uk. • [37] A. Giazotto, “Preliminary Studies on an Advanced Interferometer for Gravitational Wave Detection”, SIGRAV Summer School (Cascina, Italy), (May 2004). IGR Lunchtime Talk