measurement of the mechanical loss of test mass materials for advanced gravitational wave detectors...

Measurement of the Mechanical Loss of

Test Mass Materials for Advanced Gravitational Wave Detectors

Peter Murray

QPeter Murray

10 April 2023 IGR Lunchtime Talk 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


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


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


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


Measurement of Quality Factor

Larger Qs result in less off resonance loss by

equipartition theorem Levin approach proportional

to () 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

lost/cycle

stored

00 2

1

E

EQ


Measurement of Quality Factor


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


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

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

Calculation of Residual Coating Loss


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

Experimental Results for Silica Samples

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

LMA produced series of multi-layer tantala-silica coatings with increasing percentages of TiO2

30 alternating /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


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


Electron Energy Loss Spectroscopy

LMA originally able to provide only approximate value of TiO2 in 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


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) th 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 th can be assumed to be negligible


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


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

Nodal Support


Finite Element Analysis of Mode Shapes


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


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


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


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

Thank You For Your Attention

Any Qs?


References [1]

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measurement of the mechanical loss of test mass materials for advanced gravitational wave detectors...

Documents

loss of energy

noise slide

q slide

resonance loss

loss values

loss attributable

residual loss higher

residual loss comparable