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new large interferometric detectors of gravitational waves , such as ligo  @xcite , virgo  @xcite , geo  600  @xcite and tama  @xcite are now coming on line . to reach their design sensitivities ,
many noise sources will need to be understood and controlled .
one of the most fundamental noise sources that limits sensitivity is internal vibration of the test masses due to thermal noise . to reduce the thermal noise resulting from the test masses
, these masses must be made from low loss material and must have low dissipation in the fundamental modes of the mass and its suspension .
there are many dissipation processes in materials that could limit the quality factor ; including thermoelastic dissipation , surface dissipation and dissipation due to lattice defects@xcite . for fused silica fibers with diameter less than a few mm ,
the dissipation in the surface is much more important than losses in the bulk material ; in this regime the dissipation decreases with increasing the diameter of the fiber  @xcite .
the surface loss in fused silica has not been fully explained by any single loss mechanism , although hypotheses have been proposed for several contributing processes , including adsorbed water @xcite , surface bond oscillations @xcite , microcracking @xcite , and absorbed alkali molecules@xcite .
a vacuum annealing treatment was shown by numata and collaborators to improve the quality factors of fused silica for all resonance frequencies  @xcite .
annealing in air also improves the quality factor , but can cause surface defects and increase surface losses  @xcite .    in the work presented here , we measured the quality factor of the transverse vibrations of fused silica rods , with large diameters ( up to 12 mm ) to reduce dissipation from the surface .
we were especially interested in exploring the effects of an annealing treatment , which we performed in an argon atmosphere .
the measurement method was the same as with previous experiments performed in our laboratory at syracuse university  @xcite .
the quality factor of the rod was measured using the ringdown method .
the sample was suspended in a vacuum chamber by an all silica isolation chain of fine fibers and massive isolation bobs , as shown in fig .
[ setup ] .
our samples were made of suprasil  2 , suprasil  312 and suprasil  312  sv fused silica from heraeus amersil , inc .
the material was supplied as cylindrical rods about 20 mm in diameter .
each of our samples was made in the syracuse university glass shop using a glass lathe and a natural gas flame .
the section of the sample that was to be measured was drawn to the required diameter and length from the original material .
the length of the measurement rod for all samples was between 24 and 29  cm ; diameters were 3  mm , 8  mm or 12  mm .
the end result of the fabrication process was a structure made from one piece of material , consisting of the measurement rod , an isolation bob 10  cm in length and 20  mm in diameter and a smoothly tapering section between these two rods @xmath2 to @xmath3  cm in length .
the process of preparing the sample took about 2  hours .
the subsequent annealing treatment was performed in a continuous flow of high purity argon gas to remove any expelled impurities and prevent the adsorption of impurities .
samples were heat treated for 10  days : 3  days were devoted to slowly heating the sample , which was then held at the annealing temperature of 950  @xmath4c for 1  day .
finally , the sample was cooled over 6  days to room temperature .
we chose the long annealing period and long cooling period in order to decrease internal density fluctuations that could be responsible for additional dissipation .
as shown in papers  @xcite , annealed silica samples have decreased levels of density fluctuations , as shown by a lower level of rayleigh scattering .
the rayleigh scattering intensity is also lower in slowly cooled samples , for a given annealing temperature .
flexural modes of the measurement rod were excited by the gradient of an applied electric field oscillating at the resonance frequency .
the source of electric field was a comb capacitor placed near the end of the rod .
after excitation the capacitor was grounded and the mode was allowed to ring down .
we used the shadow method for measurement of the vibration of the sample .
a light beam from a diode laser cast a shadow of the sample on a split photodiode .
the photocurrents from the two halves of the detector were fed through a differential amplifier , whose output in turn went to a bandpass filter , a lock - in amplifier and computer data acquisition system .
the signal of the detector contains the spectral component corresponding to the oscillation of the sample . for extraction of the amplitude of the oscillation
, we applied a reference sinusoidal signal to the lock - in amplifier , with frequency slightly offset from that of the resonance .
hence , our data was a damped time series with frequency @xmath5 hz .
the amplitude decay time @xmath6 was fitted from the recorded time series .
the quality factor was calculated using the formula @xmath7 , where @xmath8 is the mode frequency .
the time of each measurement was about 5  @xmath6 , ranging for different modes from 3 hours to 8 days .
all measurements were made at room temperature , at a working pressure of @xmath9  torr .
for each sample , we measured the quality factor of three or four modes .
the quality factor of each mode was measured three times ; repeated results had a difference not higher than  @xmath10 .
the statistical error of the fits was less than  @xmath11 .
.dissipation of fused silica samples before and after annealing . [ cols="^,^,^,^,^",options="header " , ]     table 1 lists the minimum measured loss level for each sample before and after annealing . these loss levels are plotted against the samples volume - to - surface ratio in fig .  [ graph ] .
the line drawn in the figure was taken from the phenomenological model of gretarsson and harry  @xcite for suprasil  2 fused silica fibers with diameter less than about 1 mm .
the line shows the scaling of dissipation expected if it were limited by surface losses , without significant levels of bulk losses in the material .
every data point in the figure is the smallest dissipation measured for each sample ; usually this is seen in the second resonant mode .
we have not fitted the thermoelastic losses for our samples , because thermoelastic losses are negligibly low for samples of the diameters we used in the flexural modes that we measured .
the highest quality factor was obtained for an annealed sample  8 mm in diameter produced from suprasil  312 . before annealing the sample
had the best quality factor ( @xmath12 ) of any unannealed sample .
this sample was accidentally broken and then it was fixed ( we lost about 5 cm length at the end of the sample ) .
the best @xmath1 after the repair was @xmath13 .
the best value for the annealed sample was @xmath14 ( the loss angle @xmath15 ) at a resonant frequency of 384  hz .
note that we obtained rather different results with different brands of fused silica .
all of our best results were obtained with suprasil  312 .
samples of 312  sv showed substantially improved @xmath1 after annealing , but even then the quality factors were poorer than unannealed suprasil  312 .
we found the strongest effects from annealing in our thickest samples .
our 8 and 12  mm samples showed @xmath1 improvement of order a factor of 2 , while our thinnest sample showed only a small improvement .
this last observation is similar to what was seen by the moscow group  @xcite .
we can compare our results with the @xmath1 measured by numata and collaborators for modes in the range 30 to 100  khz on a fused silica cylinder sample  @xcite .
these results for suprasil  312 show frequency - dependent @xmath1s , with @xmath1 decreasing with increasing frequency .
( comparison of the pattern of @xmath1s to the mode shapes allowed a model to be made of contributions from bulk losses , surface losses , and suspension losses . )
notably , the @xmath1 values improved after annealing .
samples were annealed in a vacuum furnace for 24  hours at 980  @xmath4c .
the best @xmath1 from these experiment was @xmath16 before annealing ( improving after annealing to @xmath17 ) , at a frequency of about 33  khz .
our @xmath1 at lower frequencies is much higher , but fits with the frequency dependence seen in the numata experiments .
significant differences in values of the quality factors for samples from different material were noted in numata s work .
willems  @xcite has measured the quality factor of many modes of large unannealed samples of suprasil 312 and 311sv .
the gravest mode of the 312 sample had a @xmath1 of 120 million ( at a frequency of 11 khz ) , about 50% better than the best @xmath1 seen in our unannealed samples .
other modes had poorer @xmath1 , but there were many with @xmath1 within a factor of 4 of the best .
the best @xmath1 of the 311sv sample was 50 million , again about 50% better than the best @xmath1 seen in our unannealed 311sv samples .
the higher frequency modes of the two samples had quite comparable quality factors .
willems argues that this last fact demonstrates that the two samples have , in fact , similar dissipation levels overall , but it is also possible that the gap in best @xmath1 is consistent with differences between 312 and 312 sv like those seen in our own work .
further study will be required to untangle the comparison between 312 and 312sv .    in fig .
[ graph ] we drew the phenomenological law from gretarsson and harry  @xcite for comparison with the results of our measurements .
note that very few of our data points fall close to the line .
( perhaps this is because our data set is rather heterogeneous ; it includes measurement of annealed and unannealed samples of three different brands of silica . )
nevertheless , one can clearly see a trend to higher @xmath1 at larger diameters , in qualitative agreement with the prediction that losses are dominated by surface effects , as opposed to dissipation in the bulk .
our best result , @xmath14 , shows that the quality factor of fused silica after annealing has reached a value comparable to that of sapphire at room temperature  @xcite . this has led to renewed consideration of fused silica as a possible test mass material for advanced ligo@xcite .
however , it must be noted that advanced ligo would require silica with the low optical absorbtion of suprasil 312  sv , where mechanical dissipation is not quite as good .
research on this question is in progress  @xcite .
we thank john chabot , the glassblower at syracuse university , for his skill and care in drawing the fused silica samples . for useful discussions ,
we thank phil willems , kenji numata , gregg harry , and riccardo desalvo .
this work was support by syracuse university and by national science foundation grant no .
we present the results of quality factor measurements for rod samples made of fused silica . to decrease the dissipation we annealed our samples . 
 the highest quality factor that we observed was @xmath0 for a mode at 384  hz . 
 this is the highest published value of @xmath1 in fused silica measured to date .