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Thermoelasticity in Crystalline Materials: A Deep Dive into Research Lines

Explore a detailed study on thermoelasticity in crystalline materials and other research lines conducted by E. Cesarini for the Virgo Coating R&D collaboration at Centro Studi e Ricerche Enrico Fermi, Roma (IT).

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Thermoelasticity in Crystalline Materials: A Deep Dive into Research Lines

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  1. The Virgo Coating Collaboration: a detailed study on thermoelasticityin crystalline materials and other research lines E. Cesarini1 for Virgo Coating R&D collaboration 1Centro Studi e Ricerche Enrico Fermi, Roma (IT)

  2. Overview • Crystallinematerials for future detectors • TED in silicon(in collaboration with PTB and University of Jena, Germany) • TED in sapphire(in collaboration with PTB and University of Jena, Germany) • TED aftercoatingdeposition • VCR&D objectives • The Virgo Coating Collaboration • VCR&D results so far GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  3. Whycrystallinematerials are interesting? • Futuregravitational wave detectors are proposed to be operated at cryogenic temperatures. • The focus is put on potential bulk materials that will be used in cryogenic detectors siliconand sapphire. • The knowledge of mechanical properties at low temperatures is strongly required to predict their thermal noise limited sensitivity • Coating losses are evaluated looking at their effect on the substrate loss. • Substrate is measured before coating deposition and substrate losses are supposed independent by the coating deposition process. • Energy stored in the coatingcan be evaluated by FEM or analytically or with a direct measurement (M. Granata et al. Archives of metallurgy and materials 60(1) 2015) GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  4. Thermoelasticity in Silicon The thermoelasticeffectis a relaxationprocesscaused by the heatexchangedwithin the vibrating body, betweencompressed and expandedregions. In thinsilicondiscs, atacousticfrequencies, the maincontribution to the substratelossisexpected to be due to thermoelasticloss(ref. Zener) • Rate of generation of heat: • The energydissipated per cycleisrelated to the temperature fieldthroughentropy: GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  5. Thermoelasticity in Silicon Study of the thermoelasitceffect in a cylinder (F. Martelli, F. Piergiovanni, 2009) The lossisrepresented by a convergingseries of Debyepeaks; The dissipationpeaks are centeredatangularfrequencieswmnkdeterminedas: In a disc, the heatfluxismainlyacross the thicknessh. It can be shownthatthisimpliesthat the onlyrelevantterms in the sum are those with k=1, and theyallhave an (almost) equalpeakfrequency. The sum converges to a single Debye curve GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  6. Thermoelasticity in Silicon The ratio between the dilatational and totalenergyisinfluenced by the mode sape: the thermoelasticloss must show a branching behaviour, depending on mode families. for crystallinematerials (cubic or bi-cubicstructure) must be obtainedusing FEM. (G. Cagnoli et al., Mode-dependent mechanical losses in disc resonators, Phys. Lett A, 2017) Si <100> wafer #7 (75,9 mm x 458 mm) BUTTERFLY MODE MIXED MODES Measured with GeNS @ LMA GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  7. Thermoelasticity in Sapphire Sapphiresample: 2 inchesdiameter, 1 mm thickness, double polished, crystalorientation: <0001> 0.25 degmisoriented (MeasuredwithGeNS @LMA) • Wecomparedexperimental data with thermoelasticdampingcalculation with the same formula used for siliconwafers • Dth,elhasbeenworked out through FEA simulation(Ansys @UToV/Comsol @PTB) GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  8. Thermoelasticityaftercoatingdeposition 2,2 mm SiO2coating on bothfaces of 468 mm thick Si disc GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  9. Thermoelasticityaftercoatingdeposition Evaluation of TED in coated substrates is started Thermoelasticlossevaluated for a slabusing the model in: Bishop J E and Kinra V K Mech. Comp. Mater. Struct. 3 83–95 (1996) b a Matlab Code checked with Cu/Si/Cu described in the paper Comparison of curves for bare Si and Si coated with SiO2 1 mm thickslab of Si + SiO2 film 4 um (Physicalparameterstaken from the table in the paper) GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  10. Thermoelasticityaftercoatingdeposition Study of sensitive parameters • Study with differentthicknesses • Mostsensitive thermalparametersare thermalexpansionand heatcapacity • Study with differentheatcapacities • No strong dependency on thermalconductivityobserved Effect of SiO2coating on Si, for differentvalues of heatcapacity Effect of SiO2coating on Si, for differentcoatingthicknesses (nominal1.5 in unit 1e6) GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  11. Thermoelasticityaftercoatingdeposition • The effect of SiO2coating seems to affect the thermoelastic loss in the adiabatic part (negative coating losses could be found?) • The effect increases with coating thickness (as expected) • The effect is strongly dependent on heat capacity (could be significantly different in films?) GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  12. Thermoelasticityaftercoatingdeposition W13014 silicon disc 0.468 mm thick, 2.22 micron SiO2coating on bothsurfacesmeasuredat LMA Computedlossangle iscompared with the measuredvaluesdivided by the dilutionfactorDth.el. of familiymodes (ratio betweendilatation and totalenergy) and multiplied by R0=Y/9K (Y is set to 160 GPa for siliconand K=97.6 GPa ) assuming a SiO2coatingloss angle of 510-5 GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  13. VCR&D objectives Collaborations • Developing new coating materials for the AdVirgo upgrades • Ready for the next upgrade on 2022 • For the upgrades beyond 2022 and for cryogenic operations • Understanding the losses in amorphous materials • Let growing the research on coating in the more general context of physics of glasses and amorphous materials • Cryogenic measurements are necessary to understand the physics of amorphous materials • ViSIONs: origin of relaxations • Virgo Coating R&D +Jena U.+PTB • GAST: FR, D, UK, IT, crystalline coatings on sapphire GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  14. VCR&D objectives Metrology: Materials: Deposition Parameters: • Interpretation of loss measurements is not always clear (modeling of mechanical losses, studying of ageing, barrel surface losses) • Different setups need to be validated (GeNS, cantilever, direct measurements) • New oxides • Nitrides • Fluorides • New mixing • Nanolayered composites • What is the effect ofdeposition parameterson the mechanical loss ? GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  15. VCR&D collaboration LYON • URBINO • GeNSCryo • FEA GENOVA • GENOVA • Ellipsometry • AFM, XPS • Raman • ROMA 2 • Laser Polishing • GeNS 300K 1’’ • FEA • Annealingtreatment • LYON/LMA • IBS HT, IAD • GeNS 300K • FEA • Optical metrology • LYON/ILM • Raman, Brillouin • Physics of Glasses • Molecular Dynamics • PERUGIA • Cantilevers • Physics of Glasses URBINO VIRGO PERUGIA • SALERNO/SANNIO • Plasma assisted e-BD • SEM,TEM,AFM and XRD • nanolayered composites and Mie-metamaterials ROMA 2 GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

  16. VCR&D results so far • Paper (PLA) on mode families in silicon • First positive results on optical and mechanical properties of Nb2O5 and SiNx • TiO2::Nb2O5 mixture under test • Evolution of SiO2: loss decreases 8 times after 900°C annealing • The Salerno/Sannio coating facility is already producing samples (see M. Principe talk) • Validation of loss measurement setups has started (GeNS to GeNS Lyon/ToV/Caltech) • First CO2 polishing of silica disc barrel surface • New laboratory in Urbino equipped with Cryo-GeNS and annealing furnace GRAvitational-wave Science&technology Symposium - Padova (Italy), March 1st and 2nd, 2018

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