Systematic measurement of the intrinsic losses in

X

i

v

:g r

-

q

c

/

4

4

2

7v

2

4

M

a

y

2

4

Systematic measurement of the intrinsic losses in various kinds of bulk fused silica Kenji Numata,1,2,∗Kazuhiro Yamamoto,3Hidehiko Ishimoto,4Shigemi Otsuka,1Keita Kawabe,1Masaki Ando,1and Kimio Tsubono 11Department of Physics,University of Tokyo,7-3-1Hongo,Bunkyo-ku,Tokyo 113-0033,Japan 2NASA Goddard Space Flight Center,Code 661,8800Greenbelt Rd.,Greenbelt,Maryland,20771,USA 3The Institute for Cosmic Ray Research,University of Tokyo,5-1-5Kashiwa-no-Ha,Kashiwa,Chiba 277-8582,Japan 4The Institute for Solid State Physics,University of Tokyo,5-1-5Kashiwa-no-Ha,Kashiwa,Chiba 277-8581,Japan (Dated:February 5,2008)Abstract We systematically measured and compared the mechanical losses of various kinds of bulk fused silica.Their quality factors ranged widely from 7×105to 4×107,the latter being one of the highest reported among bulk fused silica.We observed frequency-dependent losses and a decrease in the losses upon annealing.PACS numbers:05.40.Jc;04.80.Nn

Fused silica is used for many optical applications because of its extremely low optical losses between ultraviolet and infrared wavelengths.One of the uses of fused silica is as substrate of mirrors in interferometric gravitational wave(GW)detectors which are starting observation runs[1,2,3,4].The mirrors in these detectors require not only low optical losses, but also low mechanical losses in order to reduce the amplitude of thermal noise in their observation band(a few100Hz)[5].Fused silica has been chosen for the current detectors, because it satisfies the requirements of low mechanical loss.However,mechanical losses in fused silica have not been well understood compared with their optical counterparts.This is due to the difficulty of performing low-mechanical-loss measurements.The loss due to the support for the measurement usually dominates the measured loss,when the mechanical loss of the sample is small.The measured losses,if obscured by the support loss,can be used only as upper limits.As a result,many of the previous reports have been comparisons of the measured maxima that were more or less accidentally obtained at certain frequencies.

In this paper,we report on comparative measurements of the quality factors(Q,the inverse of the mechanical-loss angle,φ)in various kinds of bulk fused silica from30kHz to100kHz.(Here,we define a“bulk”sample as a sufficiently massive sample that can be used as a mirror substrate.)These samples differ in their production processes or in their mechanical and optical properties.By adopting a nodal support technique[6,7],the support loss was effectively eliminated.This technique enabled us to systematically compare the samples with one another.The measured Qs were observed to vary between different kinds of fused silica.The values ranged from7×105to4×107,one of the highest reported among fused-silica bulk samples[8].The Qs were found to be not simply correlated to one specific property,such as the amount of OH content.These results suggest that the loss mechanism has origins that have not been well understood.We also found that an annealing process improved the Qs of bulk samples.In most samples,the Qs were observed to be higher at lower frequencies.At∼10kHz region,this is one of thefirst observations of the frequency-dependence of loss in fused silica,which has been thought to have similar frequency-dependent loss at very high frequencies(>∼1GHz).These results will help the choice of materials for advanced detectors and the general understanding of loss in fused silica.

II.FUSED-SILICA SAMPLES

We prepared13samples of commercial fused silica from Heraeus[9],Corning[10],Tosoh [11],and Shin-etsu[12].Table I lists the properties of each sample,as reported by the providers.Some of them have actually been adopted as mirror substrates in GW detectors [2,13,14,15],as listed in the last column.Fused silica has been mainly classified into four types(TYPE I,II,III,and IV)according to its production process[16,17].Many of the fused-silica samples measured here were TYPE III,which is synthetic fused silica produced by the hydrolyzation of silicon chloride in an oxygen-hydrogenflame.Every sample had a cylindrical shape with6-cm height.Most of the samples had a7-cm diameter.Only the Shin-etsu samples had a10-cm diameter.All surfaces of the samples were commercially polished to the same level by the same company for this round of tests.Their surfacefigure is on the order ofλ/10.Their detailed specifications are as follows:•Heraeus

We measured four samples of TYPE III from Heraeus Corp.:Suprasil-1,2,311,and 312;one sample of TYPE II,called Herasil-1.Suprasil-1and2,contain a relatively large amount of OH(1000ppm).In contrast,Suprasil-311and312contain the lowest level of OH(200ppm)among the TYPE-III fused silica measured here.Herasil-1, which is made of natural quartz powder byflame fusion,has a lower OH content (150ppm)than does TYPE-III silica.(A glass made from natural quartz is usually referred as“fused quartz”.)

•Corning

Corning currently produces fused silica called the7980series.Their productions are rated in size of bubbles and homogeneity of the refraction index.We measured three samples called7980-0A,0F,and5F(standard grade).The7980-0A type has the best-rated optical quality among them according to the company.The nominal chemical contents of these three samples are the same.

•Tosoh

We measured three samples from Tosoh Quartz Corp.:ES,ED-A,and ED-C.ES is TYPE-III fused silica.It includes the largest amount of OH content(1300ppm).

ED-A and ED-C are produced by the VAD(Vapor-phase Axial Deposition)method, which is a relatively new technique.The method involves three processes:1)the production of silicon-oxide powder from synthetic silicon-chloride,2)the reduction of OH by halogen compounds,and3)glass-forming by high-temperature hardening in helium gas.The method introduces less OH than TYPE III.Additionally,a dehydration process is performed on ED-C,thus achieving an extremely low OH level (1ppm).Unfortunately,Tosoh does not publish any detailed characterization of their production,such as bubble class.

•Shin-etsu

Shin-etsu Quartz Products Co.Ltd.is a Japanese company affiliated with Heraeus, which produces its own synthetic fused silica,called Suprasil P series.Suprasil P-10 and P-30contain a large amount of OH(1200ppm).The latter has the worst striae grade among our samples.

III.EXPERIMENTAL METHOD

The samples were supported at the cylindrical axis,according to a nodal-support tech-nique established by us[6].The internal modes of cylindrical isotropic samples have no displacement along the cylindrical axis if the number of nodal lines(order n)with respect to the rotation around the cylindrical axis is larger than unity[18,19].By supporting the sample at the centers of its twoflat surfaces with two small ruby balls with a diameter of2mm,the sample was effectively isolated from the support system for all higher order modes(n≥2).We measured the resonance quality factors of the samples in a vacuum at room temperature with the ring-down method.The resonance mode vibration between30kHz and100kHz was excited by a retractable piezoelectric actuator,and the decay of the displacement was measured on the lateral surface by a Michelson interferometer.The mode shapes were identified by comparing the calculated resonant frequencies with the measured ones.The repeatability of the Q by reloading the sample was less than10%.

Some of the samples were annealed in a vacuum electric furnace to observe the annealing effect on the Qs.The Heraeus Suprasil-2,311,Herasil-1,and Corning7980-5F were annealed at900◦C.Also,Heraeus Suprasil-312and Corning7980-0F were annealed at980◦C.The 5F sample was annealed at this temperature once again.In every case,the samples were annealed for24hours,and cooled down in the furnace within24hours.

IV.RESULTS

We summarize the measured quality factors of the higher order modes,which are consid-ered to be independent of the support loss(see also Table II).

•Heraeus

Figure1shows the measured Qs of Heraeus silica.The Qs of Suprasil-1and2 were similar,showing a weak tendency to decrease with increasing frequency.The maximum values measured were about1×107.Suprasil-311and312also showed similar Qs having a frequency-dependence.The maximum Qs of these two samples were3.4×107.After annealing,311and312showed maximum Qs of4.1×107and

4.3×107,respectively at the lowest mode.Herasil-1is by far the worse material,10

to40-times worse than Suprasils.Its Qs were almost constant across the entire wide frequency range.

•Corning

Figure2shows the results of Corning silica.All of them showed very similar Qs, slowly degrading at higher frequencies.The maximum value of these three samples were about1×107before annealing.The5F sample annealed at900◦C and the 0F sample annealed at980◦C showed marked improvements of Qs:50%at high frequency,growing to100%at the lowest frequencies.The second annealing at980◦C for5F improved its Qs further.

•Tosoh

Figure3shows the Qs of Tosoh silica.The ES sample showed lower Qs(∼5×106) that were almost constant with frequency.The Qs of ED-A and ED-C were observed to degrade with increasing frequencies,with the maximum values being1.9×107and

8.8×106,respectively.The dependence of the Qs on the frequency was similar in

both cases.

•Shin-etsu

The results of the Shin-etsu samples were reported in our previous paper[6].Their Qs were constant from20kHz to80kHz with values3.0×106for P-10and1.0×106 for P-30.The following facts became clear after examining these experimental results(Table II) by comparing with Table I:

•Higher Q samples show a stronger frequency dependence,namely a decrease in the Qs at higher frequency.

•TYPE-III fused silica tends to show higher Qs if the OH content is lower.However, this relationship does not hold with the other types of fused silica.

•Qs are not affected by the direction of high homogeneity.(Suprasil-1and2,Suprasil-311and312)

•Neither bubble grade nor homogeneity of the refraction index correlates with Qs.

(7980-0A,0F,and5F)

•Q could be degraded by poor striae grade.(Suprasil P-30)

•The annealing process improved the Qs of every sample.The degree of the improve-ment was dependent on the temperature and the samples.

V.DISCUSSION

In this section wefirst show that the loss due to the support and the loss concentrated on the surface are negligible.We then give a possible explanation for the frequency dependence of the measured losses.Finally,we consider the effect of annealing.

A.Support loss and surface loss

The support loss can hardly be responsible for the measured loss,including the observed uniform decrease in the Qs at high frequency,for the support system itself has a capability to measure Q of108[7].This is justified further under the following two assumptions[7]:1) the contribution from the support loss has a correlation only with a residual displacement at an actual support point,and2)the dissipating energy inside the support system has no frequency dependence.The former assumption is justified by the fact that the measured losses in lower order modes(n=0,1)are observed to be strongly dependent on the calculated displacements at the cylindrical center.The latter is also reasonable,because we found no evidence for a frequency-dependent support loss in the lower order modes.In our bulk sample,there is no obvious correlation between the resonant frequency and the displacement at the actual support point.Then,uniform decrease in Qs against increasing frequency should not be from the support loss,which has,by the assumptions,no correlation with frequencies.

Surface loss has been observed to be one of the sources of internal loss particularly when the sample has afiber-like shape[17,20,21].However,in our case,the contribution is considered to be less important by the similar consideration above.The contribution from the surface is expected to be proportional to the strain energy at the surface and to the surface-to-volume ratio[6].In our bulk sample,the former is strongly dependent on the modal shape rather than on the resonant frequency,and the latter is much smaller than in fibers.As a result,the measured Qs should be scattered according to the modal shape,if thesurface loss is dominant.Therefore,it is not responsible for the observed uniform increase in the loss at higher frequency.

B.Frequency-dependent intrinsic loss

Here,we offer some possible conclusions derived from the observed increase in losses at higher frequency.We presume that it does not originate from the external support or from the surface as discussed above.The remaining explanation would be that the intrinsic loss of the material itself has frequency dependence.

The frequency-dependent intrinsic loss is not in agreement with the frequency-independent structural-damping model,which is commonly applied to represent the intrinsic losses of materials[5,22].However,this explanation is not unnatural,for the structural-damping model is merely an experiential approximation within a certain frequency band. We compared our results with the results obtained in the other frequency ranges.Figure4 shows two examples of the measured loss angles here versus the frequency together with the results measured by the other groups(their references are written in thefigure caption).Our results do not contradict with the general tendency for the loss to increase along increasing frequency.To clarify the supposition of frequency-dependent losses,it is also useful to re-member that,in thefield of ultrasonic attenuation,the loss angle of fused silica is assumed to obey power laws of frequency[23].The theoretical model at the higher frequency may still hold to our frequency range.

The observation that the loss angle decreases at low frequency is important for the GW detectionfield,because the amplitude of the mirror thermal noise in GW detectors is pro-portional to the square root of the mechanical-loss in the observation band(a few100Hz). The observation is important also for reducing pendulum thermal noise in GW detectors.In future ground-based GW interferometers,fused silica is the most promising material as test mass suspensionfiber[24].Because thermal noise of the pendulum is one of the serious noise sources at about1Hz to100Hz,the Q of thefiber has to be very high.Also in a develop-ment of a space-based GW interferometer(LISA),a torsion pendulum with fused silicafiber has been proposed to measure force noise acting on its proof mass[25].To measure LISA’s force noise requirement with the torsion pendulum,the Q of thefiber has to be larger than about108at around10mHz to lower the thermally induced motion below the force-noise induced motion.As the above-mentioned examples,there are several demands to have high Q at lower frequency ranges.Therefore,it is significant to perform further measurements at the ranges,to establish a method to produce silica with smaller loss,and to clear the loss mechanism,which seems to cover the frequency-dependent loss at the frequencies.

C.Effect of annealing

The quality factors of all of the samples were improved by the annealing process.We would like to emphasize that it is the bulk intrinsic loss itself that decreases,because the measured losses decreased uniformly to a lower level independently of the modal shape. Similar phenomena were observed in previous experiments using small silica samples[21,26]. Usually,the reduction of the loss in silica caused by a high-temperature treatment was attributed to a reduction of the surface loss.In our bulk sample,however,there is a smaller contribution from the surface compared to these smaller samples.The improvement of

the intrinsic loss by annealing might be derived from the release of residual strain and/or neutralizing several imperfections in the SiO2network.Annealing seems to increase the slope towards lower losses at low frequency.It is plausible to think that decreasing losses at decreasing frequencies is the fundamental behavior of fused silica,which is masked by a frequency-independent loss when imperfections are dominant.

We made an almost arbitrary choice of the annealing conditions.Our choice of the annealing parameters,such as temperature,duration,and cooling rate,is unlikely to be the best for each sample.Although annealing is a common process for glass production,it has not been optimized for minimizing the mechanical loss.One may expect to achieve an even higher Q for bulk fused silica with an optimized thermal treatment.In the process,we will have to make sure that the annealing does not degrade the other properties,such as the homogeneity of the refraction index,or the distribution of OH in the sample.

VI.CONCLUSION

We have reported on our systematic measurements of loss in13samples of bulk fused silica supported at the nodal point of their vibrational modes.The measured quality factor reached4.3×107,very high value as a bulk fused silica.We found that many of the samples showed frequency-dependent loss.Below∼1GHz frequency region,this is one of thefirst indications that the intrinsic loss of fused silica is frequency-dependent.We also showed the importance of a thermal treatment during/after its production for reducing the intrinsic loss in fused silica.

Further measurements above and below our frequency region will allow us to compare the results with ones in ultrasonic regions(>∼1GHz)and in GW observation bands,respec-tively.Clear explanation for the origins of the mechanical loss in fused silica still remains an open question,even with our systematic measurements.However,our results provide clues to answering the fundamental question of what determines the mechanical loss in sil-ica.We believe that it has significances not only for GW detectionfield but also for other communities.

VII.ACKNOWLEDGEMENTS

The authors would like to thank Dr.Riccardo DeSalvo(Caltech-LIGO)and Dr.Gregg Harry(MIT-LIGO)for commenting on our drafts and for their useful discussions.We also thank to Dr.Johannes Wiedersich(Technische Universit¨a t M¨u nchen)for commenting on our results.A part of this research is supported by the Japan Society for the Promotion of Science and a Grant-in-Aid for Scientific Research on Priority Areas(415)of the Ministry of Education,Culture,Sports,Science and Technology.[1] A.Abramovici et al.,Science256(1992)325.

[2]VIRGO Collaboration,VIRGO Final Design Report,1997.

[3]K.Danzmann et al.,Proposal for a600m Laser-Interferometric Gravitational Wave Antenna,

Max-Planck-Institut f¨u r Quantenoptik Report190,Garching,Germany,1994.

[4]M.Ando et al.,Phys.Rev.Lett.86(2001)3950.

[5]P.R.Saulson,Phys.Rev.D42(1990)2437.

[6]K.Numata et al.,Phys.Lett.A276(2000)37.

[7]K.Numata et al.,Phys.Lett.A284(2001)162.

[8]To our knowledge,the reported highest Q of bulk silica is1.2×108,which can be found in

[32].It was measured in Suprasil-312SV at lower frequency than ours(11.202kHz).

[9]Heraeus-Amersil Corporation,3473Satellite Boulevard,Duluth,GA30136-5821.

[10]Corning Incorporated Advanced Material Division,334Country Route16Canton,NY13617.

[11]Tosoh Quartz Corporation,3-1435Tachiyagawa,Yamagata-shi,Yamagata,Japan990-2251.

[12]Shin-etsu Quartz Product Corporation,1-22-2Nishi-shinjyuku,Shinjyuku-ku,Tokyo,Japan

160-0023.

[13]Personal communication with Garilynn Billingsley(Caltech-LIGO).

[14] B.Willke et al.,The GEO600Gravitational Wave Detector,in:S.Kawamura,N.Mio(Eds.),

Proc.Second TAMA International Workshop,Oct.1999,Universal Academy Press,Japan, 2000,pp.33.

[15]M.Ando et al.,TAMA Project:Design and Current Status,in:S.Meshkov(Eds.),Proc.

Third Edoardo Amaldi Conference,July1999,American Institute of Physics,USA,2000, pp.130.

[16]R.Br¨u ckner,J.Non-Cryst.Solids5(1970)123.

[17]W.J.Startin,M.A.Beilby,P.R.Saulson,Rev.Sci.Instrum.69(1998)3681.

[18]G.W.McMahon,J.Acoust.Soc.Am.36(19)85.

[19]J.R.Hutchinson,J.Appl.Mech.47(1980)901.

[20] A.M.Gretarsson,G.M.Harry,Rev.Sci.Instrum.70(1999)4081.

[21]S.D.Penn et al.,Rev.Sci.Instrum.,72(2001)3670.

[22]P.R.Saulson et al.,Rev.Sci.Instrum.65(1994)182.

[23]See,for example,J.Wiedersich,S.V.Adichtchev,E.R¨o ssler,Phys.Rev.Lett.84(2000)2718,

and references therein.

[24]G.Cagnoli et al.,Phys.Rev.Lett.85(2000)2442.

[25]Personal communication with Jordan Camp(NASA/GSFC-LISA).

[26] D.B.Fraser,J.Appl.Phys.41(1970)6.

[27]S.Traeger,B.Willke,K.Danzmann,Phys.Lett.A225(1997)39.

[28]S.Rowan et al.,Phys.Lett.A246(1998)471.

[29]P.Amico et al.,Rev.Sci.Instrum.,73(2002)179.

[30]P.Sneddon et al.,LIGO document,G030194-00.pdf.

[31]S.Penn et al.,Class.Quantum.Grav.,20(2003)2917.

[32]P.Willems and D.Busby,LIGO document,T030087-00.pdf.

[33] C.K.Jones,P.G.Klemens,J.A.Rayne,Phys.Lett.8(19)31.

[34]R.Vacher,J.Pelous,Phys.Rev.B14(1976)823.

[35]R.Vacher et al.,J.Non-Cryst.Solids45(1981)397.[36]H.-N.Lin et al.,J.Appl.Phys.69(1991)3816.

[37]T.C.Zhu,H.J.Maris,J.Tauc,Phys.Rev.B44(1991)4281.

[38] D.Tielb¨u rger et al.,Phys.Rev.B45(1992)2750.TABLE I:Properties of fused silica.†1Bubble grade(high,0;low,8);†2Striae grade(high,A; low,C);†3Homogeneity of refraction index(∆n,×10−6);†4Direction of homogeneity for the speci-fied value(3D,all three directions;1D,specific one direction).*:NM,near mirror;EM,end mirror; BS,beam splitter;RM,recycling mirror.**:LIGO,VIRGO,and GEO use custom made311and 312called SV grade that include less OH than our commercial grade samples.

Company Trade name TYPE†1†2†3†4OH(ppm)Used in project

Heraeus Suprasil1III0A53D1000GEO(NM∗,EM)

Suprasil2III0A51D1000GEO(RM)

Suprasil311∗∗III0A33D200LIGO,VIRGO,GEO(BS)

Suprasil312∗∗III0A41D200LIGO(NM),VIRGO(NM,RM) Herasil1II0A41D150VIRGO(EM)

Tosoh ES III-A-1D1300

ED-A VAD-A-3D100

ED-C VAD-A-3D1

Corning79800A1.1×1070.4±0.04

79800F1.1×1072.1×107(980◦C)0.3±0.03(0.6±0.1)

79805F1.0×1072.1×107(900◦C)0.3±0.04(0.5±0.1)

3.3×107(980◦C)(0.7±0.04)

Shin-etsu Suprasil P-103.0×106−0.03±0.04

Suprasil P-301.0×106−0.02±0.04

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90

80

70

60

50

40

30

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

10090807060504030

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030

Frequency[kHz]

FIG.1:Quality factors of Heraeus fused silica;the vertical axis shows the measured Q and the

horizontal axis shows the resonant frequency.The filled markers represent the higher order modes,in other words,nodal supported modes.Large excess loss occurred in these modes,only if there was a lower order mode near by.Suprasil-1and 2showed similar Qs.Qs of Suprasil-311and 312also showed a similar Qs and the tendency to degrade with higher frequency.The maximum values exceeded 3×107.Herasil-1showed the lowest Qs and no frequency dependence in this frequency range.The annealing process improved every Q,reaching 4×107in Suprasil-311and 312.

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

10090807060504030

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030Frequency[kHz]

FIG.2:Quality factors of Corning fused silica;every sample showed quite similar Qs before

annealing,having the highest value of about 1×107.After annealing at 980◦C for 0F and at 900◦C for 5F,the Qs increased by 50%to 100%.A second annealing at 980◦C improved the Qs of 5F further.(On graph 5F,only the result of this second annealing is shown.)A lower Qs at higher frequency was observed in every case.

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90

80

70

60

50

40

30

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030

Frequency[kHz]

10

5

10

6

10

7

10

8

Q u a l i t y F a c t o r

100

90807060504030

Frequency[kHz]

FIG.3:Quality factors of Tosoh fused silica;ED-A showed the highest Qs,1.9×107.ED-C,which contains less OH,showed lower Qs.Both of them showed obvious frequency dependence.They were made by a relatively new technique.ES,which was produced by a traditional technique,showed lower Qs.

10

101010101010

1010L o s s A n g l e : φ

10

10

10

10

10

10

10

10

10

10

10

Frequency[Hz]

FIG.4:Comparison of the measured loss angle of fused silica versus the frequency;the vertical axis represents the loss angle,φ(=1/Q ),and the horizontal axis shows the frequency (log scale).Our results measured in Heraeus Suprasil-2and Suprasil-311are shown as filled markers along with its power law fits (after the annealing,higher order modes only).Other’s results measured in fused silica are also plotted.Every measurement was done at room temperature.Their references are as follows:Fraser(1970):[26],Traeger(1997):[27],Startin(1998):[17],Rowan(1998):[28],Gretarsson(1999):[20],Penn(2001):[21],Amico(2002):[29],Sneddon(2003):[30],Penn(2003):[31],Willems(2003):[32],Jones(19):[33],Vacher(1976):[34],Vacher(1981):[35],Lin(1991):[36],Zhu(1991):[37],Tielb¨u rger(1992):[38],Wiedersich(2000):[23].The acoustic attenuation αwas converted to the loss angle φby using a relationship of φ=αv/(πf ).Here,v is the sound velocity.