Indium joints for cryogenic gravitational wave detectors

A viable technique for the preparation of highly thermal conductive joints between sapphire components in gravitational wave detectors is presented. The mechanical loss of such a joint was determined to be as low as 2 × 10−3 at 20 K and 2 × 10−2 at 300 K. The thermal noise performance of a typical joint is compared to the requirements of the Japanese gravitational wave detector, KAGRA. It is shown that using such an indium joint in the suspension system allows it to operate with low thermal noise. Additionally, results on the maximum amount of heat which can be extracted via indium joints are presented. It is found that sapphire parts, joined by means of indium, are able to remove the residual heat load in the mirrors of KAGRA.


Introduction
The detection of gravitational waves is one of the most challenging tasks in astrophysics today. Although they have already been verified indirectly, the direct detection of these waves has still not been achieved. Today's most promising detectors are based on a Michelson interferometer using optical components in pendulum suspensions as free falling test masses. These instruments have already reached a sensitivity for length changes of better than 10 −18 m [1][2][3][4]. Several science runs have been made, taking data in joint operation schemes over many weeks. However, a direct detection of a gravitational wave has so far not been possible though upper limits on astrophysical parameters of possible sources could be given [5][6][7][8][9]. Currently, these detectors have been, or are about to be, upgraded to the so-called second or advanced generation. Advanced detectors, like Advanced LIGO [2] and Advanced Virgo [10], use quasi-monolithic suspensions based on fused silica elements joined by welding [11][12][13] and hydroxide catalysis bonding [14] to reduce suspension thermal noise which limits the sensitivity in the low frequency band. Additionally, novel techniques like signal recycling [15,16], higher laser power [17] or squeezed light [18] are being used to reduce further the noise limit throughout the whole detection band. Many of these techniques have been demonstrated already in GEO600 [19][20][21]. The design sensitivity of the advanced detectors aims to produce a tenfold reduction of noise throughout the detection band compared to the first generation.
The Japanese gravitational wave detection project KAGRA [22][23][24] adds two additional features to the list of improvements. It will be the first advanced detector being operated underground in order to reduce seismic disturbances and it will be the first km scale interferometric gravitational wave detector which will use optics cooled to cryogenic temperatures of about 20 K. Operating the detector at low temperatures will greatly reduce thermal noise [25,26] as well as thermal lensing problems [27]. Unfortunately, operating at cryogenic temperatures does not allow for the use of fused silica as a test mass or as a suspension material due to its large mechanical loss at low temperatures [28][29][30][31] and its poor thermal conductivity at cryogenic temperatures [32,33]. Both originate in the glassy structure of this material. An alternative is to use crystalline materials [25,34]. Several materials have been proposed and investigated in the past for future gravitational wave detectors, amongst them sapphire [35][36][37], calcium fluoride [38][39][40] and silicon [41][42][43]. Sapphire has been chosen to be the baseline material for the cryogenic operation of KAGRA while silicon is a potential candidate material for a third generation detector in Europe called the Einstein Telescope [23,44].
In order to construct a quasi-monolithic suspension from crystalline materials it is necessary to develop a fabrication technique for the fibres, a suitable jointing technique for the components, as well as to check if the techniques being used are compliant with the thermal noise and also the heat removal requirements. It was shown [45][46][47][48] that hydroxide catalysis bonding-developed initially for the Gravity Probe B mission [49] and successfully applied to room temperature suspensions [14,[50][51][52]-can be used to form strong bonds between sapphire pieces.
In case of a necessary repair, neither standard debonding routines nor welding techniques exist so far that could be used for the crystalline suspension elements. Strong research to overcome this issue is currently underway. Thus it has been proposed that thin indium layers be used as a jointing material between sapphire components which can be disassembled easily in the case of a failure in the suspension system. Depending on the joint strength, parts can be pulled apart with or without additional heating or an acid (e.g. nitric acid) can be used to dissolve the joints. Possible indium joints have been studied in the past for several applications and have been suggested for use in gravitational wave detectors [53,54]. In the case of the KAGRA detector, the suspension is proposed to be assembled using different bonding techniques (e.g. hydroxide catalysis bonding for attachments to the test mass, indium for compression joints between the fibres and the blade springs).
Here, techniques to join sapphire components by means of indium layers are presented. These techniques are straightforward and easy to use and therefore they can be used on site for KAGRA. The mechanical loss of such an indium joint is investigated and a first estimate of the overall thermal noise of a suspension using this technique is given. Additionally, a measurement is presented which confirms the capability of this jointing technique to produce highly thermal conductive components which are able to handle the heat load from residual optical absorption of the test masses in KAGRA.

Sample preparation and indium jointing process
Several techniques are discussed in the literature for jointing parts by means of indium [55]. One of the major obstacles is the formation of a thin protective oxide layer on the indium surface. This oxide layer lowers the adhesion of the indium on sapphire and supports the dewetting process. Thus weakening of the joint will be unavoidable. However, the joints which were prepared for the experimental determination of the mechanical loss were revealed to be strong enough for handling and measuring. In the case of KAGRA, a purely compressive design for the indium joint has been proposed so the strength of the joint plays a role only during the handling and assembling of the system and is not seen as an issue during operation.

Sample overview
All the single crystal sapphire samples were obtained from Impex [56]. Two cylindrical shaped samples, each 30 mm in diameter and 50 mm and 70 mm in length, respectively, are used for the mechanical loss measurement of the indium joint (figure 1). Another sapphire cylinder of the same diameter but of 120 mm length serves as the non-jointed reference and is used for comparison ( figure 1). The axis of all the cylinders is coincident with the crystallographic c-axis. The surfaces are inspection polished, except the two surfaces of the shorter cylinders intended for jointing which are polished to a global peak to valley flatness of λ/10 (λ=632.8 nm).
The bar shaped samples used to check the heat extraction measure 50 mm in length and have a cross section of 5 mm×5 mm. One end of each bar was polished to λ/10 to allow for a proper jointing while all the remaining surfaces were left ground. Again the c-axis is aligned along the bar.

Cleaning of samples
In general, all samples have been cleaned in several steps. In the first step nitric acid (typically 25 % solution to avoid hazardous reactions with possible organic contaminants) was used to remove any possible remaining indium from previous tests. In the second step a mixture of sulphuric acid and hydrogen peroxide solution has been used to remove organic contamination (finger prints, vacuum grease from previous measurements, etc.). After that a common RCA clean was applied [57,58] (for details see appendix C). Finally the samples were blown dry by means of high purity nitrogen.
Initial steps also involved different acids (e.g. formic acid, nitric acid, hydrochloric acid) to remove the oxide layer from the indium before the jointing process. This procedure was done in a glove box using argon or nitrogen as a protective atmosphere. However, any remaining small amounts of oxygen resulted in the oxide layer quickly forming again. Therefore it was not even possible to produce pure indium surfaces which could be handled for a few minutes in order to form the indium joint. For the formation of the joints on site at the KAGRA detector, in particular, it will not be possible to avoid the natural growth of indium oxide at the surface. Thus all jointing tests presented here were done using indium with a native oxide layer.

Indium jointing techniques
Indium foils of 100 μm thickness and a purity of 99.999% were obtained from Advent Research Materials. The foil was prepared in diluted hydrochloric acid to remove the old oxide layer prior to being placed between the samples. This ensures that only a thin and fresh native oxide layer of a few nm is incorporated in the jointing process. The indium foil was placed between the two cylinders which were aligned visually along the axis while any further crystal orientation was left unconsidered.
Additional weight of 1.5 kg was put on top of the cylinder stack, giving a total weight of 1.7 kg, equivalent to a pressure of 23.6 kPa on the joint. In previous test runs this pressure turned out to ensure the layer became thin enough without squeezing out all the indium during heating. Heat was applied from the bottom using a hot plate at a temperature of 200°C. A temperature sensor was fixed on the upper sample to ensure a reasonable temperature to melt  figure 2). The beaker was purged with high purity nitrogen to avoid a further oxidation of the indium during the jointing process. The temperature was kept constant for 2 h before the hot plate was switched off and the whole setup was allowed to cool down to room temperature overnight. Indium protruding around the joint was removed. The whole process was carried out in a dust-free environment but nonclean-room conditions. The indium layer between both samples turned out to be semi-transparent and porous but still mechanically robust. The photograph of the indium layer shown in figure 3(a) was converted into a black and white image. The ratio of black and white pixels was used to determine the surface coverage to be (40 ± 10) %. The thickness of the indium layer was obtained in a side view via comparison with a micrometer stage, using a microscope. It was determined to be (8.4 ± 2.0) μm. This error occurs due to a variation of the layer thickness around the circumference.
A second bonding was carried out exactly as described above except that both sapphire surfaces intended for bonding were covered by 0.5 μm of indium via thermal evaporation prior to the indium foil being inserted. This helped to reduce the effect of dewetting and thus, with previously coated surfaces, the bond layer appears quite dense with a coverage of about A hot plate was used to melt the indium foil between the sapphire cylinders. A temperature sensor was fixed on the upper sample to control the temperature. A weight was put on top to obtain a thin indium layer.
For the heat removal experiment, two bar samples were joined using a 100 μm thick indium foil. The two samples were placed onto each other with a small external force to keep the samples together. The indium joint region was then heated by means of the radiation of a halogen lamp (see figure 4). Thus a joint of (77.4 ± 2.0) μm was measured as described above. After measuring, the joint was separated which allowed a visual inspection of the  dense indium layer to take place (see figure 8) as well as allowing it to be peeled it off to measure its weight of (0.015 ± 0.001) g for comparison. The thickness was calculated to be (82 ± 22) μm (for ρ=7310 kg m −3 ) which is in good agreement with the previous result.
The thicker indium film was suitable for the heat removal measurement, as discussed in section 4.

Mechanical loss of indium joints
The mechanical loss f serves as a measure of the dissipation of vibrational energy in a system [59] and is defined as the ratio of dissipated energy ΔE per cycle to the maximum of the elastic energy E tot : It can be obtained by recording the specimen's free ring down of its resonant vibrations which are typically in the kHz range. For that purpose the cylinder-shaped samples were suspended using a single loop of 35 μm thin tungsten wire around their circumference. The samples then were excited to resonant mechanical vibrations by an electrical field of a driving plate. The plate is placed 1 mm from the sample and driven by an amplifier and a frequency generator providing up to 1.6 kV in a frequency range from several kHz to a few hundred kHz . The mechanical vibrations are read out by a laser vibrometer and acquired via LabView. Further details of the setup can be found in [60]. While scanning the excitation frequency, the resonant vibration at f 0 is reached. The excitation is switched off and the amplitude decays exponentially with the ring down time τ starting at an initial amplitude of A 0 : Then the mechanical loss of the system is given by f −1 =π f 0 τ. Figure 5 compares two ring downs of the indium joint and a reference sample at nearly the same frequency. It can be seen that the ring-down time of the joined sample is much shorter than the one of the reference sample. Thus, the mechanical loss of the joined sample is much higher than that of the reference sample. The measurement of the mechanical loss has been repeated at different resonant modes from 17 kHz to 132 kHz and at different temperatures in a range from 5 K to 300 K. These measurements have been repeated with the reference sample for comparison. The results are summarized in figure 6. ( ) As the indium layer is small compared to the sapphire, most of the energy is stored in the sapphire rather than in the indium layer and we have E tot ≈ E sub . Further, the mechanical loss of the single piece of sapphire was measured to be at least one order of magnitude lower than that of the joined sample f sub f meas (see figure 6). This allows us to make the following assumption: ( Thus to extract the mechanical loss of the pure indium layer from the measured data the ratio of elastic energy stored in the whole sample, E tot , to that in the layer, E layer , is needed. Therefore a numerical calculation using the finite element analysis Comsol 8 was used. All necessary material parameters, as well as temperature dependence, can be found in appendix B. When building models for finite element analysis it is necessary to set up a convenient mesh, especially in this case where two big cylinders of 30 mm diameter and lengths of 50 mm and 70 mm, respectively, are joined by an intermediate layer of only a few μm thickness. One way to overcome this problem is to start with a thicker layer in the mm range of the model. In a similar manner the energy ratio was calculated for a stepwise decreased thickness. Considering the overall deformation of the thin layer, a nearly linear relation of the stored elastic energy in the layer E layer on its thickness t layer is expected. This assumption still holds when the layer thickness becomes more and more reduced. It is also clear that E layer =0 for a vanishing layer (t layer =0).
An alternative approach is adopted from [61]. Some assumptions can be made regarding the elastic response of the layer to deformations under resonant vibrations of the whole sample. Deformations u and v of the sapphire surfaces parallel to the layer are carried forward directly to the indium. Also, forces acting perpendicular to the surface F z stay the same when changing from sapphire to indium. This allows the assumption that all stresses σ ij perpendicular as well as all strains ε ij parallel to the layer to be equal in both sapphire and indium. Then the remaining stresses and strains of the indium at the boundary can be calculated [62]. Due to the small thickness of the layer, these values can be assumed to be constant through the whole layer. Thus the stored elastic energy per layer thickness by the integral over the boundary surface A reads: For both of the above approximations the results of E tot and E layer are consistent. Thus the finite element analysis together with the measured thickness serves to extract the mechanical loss of the indium layer in this measurement. Figure 7 summarizes the extracted mechanical loss of the indium joint for different frequencies and at different temperatures. The measured losses for the porous indium layer are about a factor of ten larger than those for the compact indium layer. This can be correlated with intrinsic friction effects within the porous film. The compact layer resulted in mechanical losses of about 2×10 −3 to 3×10 −3 at 20 K. Within the errors of the measurement these values can be considered to be frequency independent.

Heat flow through indium joints
Besides low mechanical loss-and thus low thermal noise-the indium joint needs to fulfil a second task: it needs to be able to extract the residual heat in the mirror which originates from optical absorption. The cold side of the suspension fibre is kept at 16 K by means of a cold link to the cryocooler system [23,63]. The mirror side of the suspension should achieve a minimum temperature of 20 to 24 K during full optical power operation. The suspension fibres under discussion have been proven to provide enough cooling power [64].
Two sapphire pieces have been joined by means of indium as described in section 2.3 in order to check the heat extraction behaviour. The sample had an indium thickness of (77.4 ± 2.0) μm.
A schematic view of the setup and its realization can be found in figure 8(a). One end of the sample was mounted onto a temperature controlled cold plate inside a cryostat. Two calibrated temperature sensors (Lakeshore DT-670) were attached on both sides, 12 mm away from the joint. At the free end of the sample a resistive heater was attached, with a resistance of 100 Ω. The whole setup was enclosed by means of a heat shield that was kept to the average sample temperature in order to minimize heat radiation from the sample. Details of the setup can be found in [64].
After the desired temperature was reached at the cold plate and the sample different heating powers were applied to the sample, the temperatures at both sides of the indium joint were measured. The temperature difference between these two points is plotted against the heating power in figure 9 for the relevant temperature range of 16 to 24 K.
With increasing the heating power, the temperature difference between the two sensors increases as expected. At lower temperatures this temperature difference is bigger at a given heating power. At a given constant temperature difference, more heat gets extracted in the case of higher sample temperatures. Compared to a pure sapphire sample with the same geometry, the extractable heat is reduced by means of the thin indium layer. For example, the maximum temperature difference at 20 K with a pure sapphire sample in the same geometry would be around 10 mK at a heat flux of 200 mW.

Implications for the KAGRA detector
In order to give a first estimate of the thermal noise performance of a cryogenic suspension which uses indium as its jointing material, a finite element analysis was carried out [65]. Following [66] a Gaussian pressure distribution with a sinusoidal oscillation with a frequency ω/2π was applied to a test mass model which contained the test mass as well as the relevant suspension elements. The total thermal noise read out by the laser beam at a temperature T is given by Figure 9. Temperature difference between two points which are 12 mm away from the indium joint, each at different heating powers and temperatures. In KAGRA 140 mW of heat needs to be extracted through an indium layer with a cross section of 350 mm 2 which corresponds to a power of 10 mW in our experiment with a 25 mm 2 cross section. This results in a temperature difference of less than 5 mK.
with F 0 being the maximum pressure applied to the surface and W diss the dissipated mechanical energy under this external oscillation. The dissipated mechanical energy is given by W x y z x y z r , , , , d 9 in the case of structural losses which are homogeneously distributed f(x, y, z) [66]. The mechanical energy density ò(x, y, z) is obtained from a finite element analysis using Ansys 9 or Comsol. The mechanical loss f is taken from the investigations above in the case of indium and from [67] and our reference measurements for the sapphire components. First results of the intrinsic loss of a hydroxide catalysis bond between sapphire pieces have been reported in [68]. Further details of the thermal noise analysis can be found in [65]. Figure 10 compares the obtained thermal noise level with the design goal for KAGRA. It can be seen that the mechanical losses obtained for the indium joints presented in this paper are sufficiently low to achieve the KAGRA thermal noise goals. Additionally, investigations of better indium layers fabricated by means of thermal evaporation have been reported [69].
Here, mechanical losses as low as 4×10 −4 could be achieved at 20 K which leads to a further reduction in thermal noise as shown in figure 10. However, this procedure is currently not available for a full-sized test mass and suspension for KAGRA and should be seen as a potential path for the future if the process of indium joints can be improved.
In the case of KAGRA, a total heating power of 550 mW needs to be extracted via four crystalline sapphire fibres [64] in the case of the input test mass. This corresponds to about 140 mW per fibre. A much smaller heat load will be experienced by the end test mass as no transmission through the bulk material occurs. The upper end of the fibre is kept at 16 K and the lower end should supply about 20 K operational temperature for the optical component. The sapphire fibres for KAGRA are equipped with square end pieces which are used for the necessary attachments. Thus, the cross section of the indium interface at these end pieces is approximately 350 mm 2 for the upper attachment as well as the lower attachment to the test Figure 10. The suspension thermal noise estimate calculated with a loss of 3×10 3 for the indium joints (red curve) is well below the requirements for bKAGRA (green curve). Further improvement is expected (dashed black curve), as explained in the text. mass. The increased interface area of the indium joint, as compared to the fibre cross section, converts the 140 mW that needs to be extracted to a 25 mm 2 equivalent of 10 mW. Measurements presented in figure 9 reveal that such a small heat flux through the indium joint will only cause an additional increase of temperature of about 10 mK for two joints per fibre. Compared to the temperature difference of 4 K between the upper and lower end of the fibre, this 10 mK can clearly be tolerated for KAGRA. Although these values are based on a rather thick layer of indium it can be taken as an upper limit. A thinner indium layer is expected to have at worst no larger thermal resistance than a thick layer. In the case that the dominating thermal resistance occurs from the interface between sapphire and indium, the overall thermal resistance would be independent of the thickness. If the main contribution arises from the indium material itself, a thinner indium layer would lead to a better thermal conductivity of the interface and thus even better values than those discussed here.

Summary
We investigated a jointing technique for cryogenic sapphire suspensions for KAGRA. The technique utilizes thin indium foil placed between the parts to be joined. Subsequent heating above the melting point, of around 156°C for indium, allows for the formation of a stable joint. A main advantage of these joints is the ease of disassembling in case of a failure. The mechanical loss f of the joints was found to be as low as 2×10 −3 at the desired temperature of 20 K. This ensures a low thermal noise of the suspension system well below the requirements of bKAGRA when indium joints are implemented. Additionally, it was demonstrated that the indium joints presented here are capable of extracting enough heat from the test masses in the KAGRA case. The temperature increase of the test masses is not more than 10 mK due to the heat resistance of the indium joints. In both cases, more investigations are needed in order to understand the origin of the intrinsic loss as well as the thermal resistance of the joint.

Appendix A. Boundary conditions used for the extraction of the indium layer mechanical loss
The boundary conditions in terms of stresses σ ij and strains ε ij are as follows:  Indium: the Young's modulus of polycrystalline indium increases by nearly a factor of two when cooled down to 5 K. The Poisson's ratio changes by just four percent. Elastic constants of indium can be found from [71]. At room temperature the Young's modulus is 12.74 GPa and the Poisson's ratio equals 0.4498. The temperature dependence can be found in [71] and is given by the equations: Y T K T  The RCA standard clean [58] applied to the samples consists of two solutions named SC-1 and SC-2. SC-1 is made of hydrogen peroxide (H 2 O 2 , 30%) and ammonium hydroxide (NH 4 OH, 25%) one parteach mixed with five parts of deionised water (H 2 O). The second mixture, SC-2, again uses the same amounts of hydrogen peroxide and hydrogen chloride (HCl 37%) diluted by six amounts of deionised water. Both solutions were heated to 75°C to 80°C prior to use. The samples are rinsed with deionised water, then put into SC-1 and kept inside an ultrasonic bath for 10 min. Afterwards they are rinsed again with deionised water before the procedure is repeated using the SC-2 solution. The samples are given a final rinse in deionised water and are blown dry by high purity nitrogen.