1
Measurements of Thermal Conductivity and Kapitza Conductance of Niobium for SRF Cavities for Various Treatments Ahmad Aizaz1, Pierre Bauer2, Terry L. Grimm1, Neil T. Wright3 and Claire Z. Antoine2
I.
S
INTRODUCTION
uperconducting radio frequency (SRF) cavities are used to accelerate charged particles near the speed of light. These cavities have much lower losses than those made of copper, which allows much higher average fields. SRF cavities used for acceleration of particles near the speed of light are fabricated from bulk niobium. The thermal conductivity of Nb plays an important role in the stability of the applied RF fields in the cavity. The thermal break down of a Nb-made SRF cavity from a temperature rise on a single defect is governed primarily by Nb’s thermal conductivity due to localized heating [1]. This problem is addressed by using high purity Nb and limiting the quantity and size of defects. The purity of Nb is quantified by measuring its residual resistance ratio (RRR), which is proportional to thermal conductivity at temperatures near ~4 This work was supported by Fermi National Accelerator Laboratory and Michigan State University. 1 National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 USA. 2 Fermi National Accelerator Laboratory, Bataiva, IL, USA 3 Department of Mechanical Engineering Michigan State University, East Lansing, MI 48824 USA A. Aizaz (Phone: 517-333-6317; e-mail:
[email protected]).
200 180 160 140 120 100 80 60 40 20 0
Bcritical
1.0E+00 1.0E-01 1.0E-02
k=.28;h=.24
1.0E-03
k=.06;h=.08
1.0E-04
Rs (Ohms)
Index Terms— thermal conductivity, Kapitza conductance, phonon peak, niobium, plastic deformations, superconducting accelerator cavities, superconducting materials, surface treatment
K [1]. However, the situation is quite different when the heating is uniform over an area with dimensions comparable to the material thickness, i.e. a case for “defect free” cavities, causing global thermal instability (GTI) [1]. Under these circumstances, losses, such as BCS surface resistance, which has exponential temperature dependence, or electron heating from field emission, ultimately limit the maximum achievable gradients in the SRF cavity. In this limit for defect free cavities the phonon thermal conductivity, k, and the Kapitza conductance, h, play a vital role in determining the initiation of GTI. Thermal-magnetic simulations for defect free cavities, as shown in Fig. 1 and also by Amrit et al. [2], have revealed that the temperature rise on the RF surface may only be a few hundred milli-kelvin, but is sufficient to limit the maximum allowable magnetic fields in the cavities.
B (mT)
Abstract— Niobium is the material of choice for making the superconducting radio frequency cavities used in present-day accelerators for the acceleration of charged particles. In order to achieve high accelerating gradients for future accelerators such as the Linear Collider, thermal limitations in Nb cavities play an important role. The effects of plastic deformations due to applied strains on thermal conductivity of Nb in phonon transmission regime as well as on its kapitza conductance have been studied. The study reveals absence of the phonon peak due to applied strains beyond the elastic limits of the Nb metal as well as reduced Kapitza conductance. This resulted in almost 80% reduction in thermal conductivity of the niobium at 2 K. Low temperature annealing did not recover the phonon peak as was seen before the application of plastic deformations.
Units:
1.0E-05
k: (W/cm/K) h: (W/cm2/K)
1.0E-06 1.0E-07
Rs
1.0E-08
1.5
2
2.5
3
3.5
4
Ts (K) Fig. 1. Quench field as a function of the surface temperature for Nb cavity with two sets of values of k and h. About five times increase in k and three times increase in h resulted in almost 50% improvement in applied magnetic fields. Parameters used for these simulations are Rres = 5 nohms, t = 3 mm, Tb = 2 K, f = 1.3 GHz, RRR = 230. The right side scale is for surface resistance
While the thermal conductivity above ~4 K is well known and correlated with RRR, for temperatures below ~3 K the correlation is lost due to phonon conduction. In this regime, the microstructure of the material plays an important role in determining its phonon thermal conductivity. Significant changes in microstructure take place when the SRF cavities are routinely fabricated through plastically deforming the metal during the deep drawing process. The effect of plastic deformation on the thermal conductivity of Nb and on its Kapitza conductance is the focus of the present study.
2 II. SAMPLE PREPARATION Test results from two sets of samples, i.e. cylinders and flat rectangular plates, are reported here. The cylindrical samples, S1 and S2, were taken from a long Nb rod supplied by Tokyo Denkai with an ingot RRR of 232. Measurements of both, the thermal conductivity and the Kapitza conductance are reported for these two cylindrical samples. Wah Chang supplied the two rectangular flat plate samples, F1 and F2, for thermal conductivity measurements to evaluate the possibility of partial recrystallization in the “as received” Nb. The supplier reported a RRR value for these samples of ~300. Cylindrical samples test configuration A series of tests were conducted on the two Nb cylindrical samples, to evaluate the effect of different surface conditions. Table I gives the details of the surface treatment of each test performed on these samples in chronological order. Described in the table I, surface index (SI) is defined as the ratio of exposed surface area to the projected area. TABLE I SURFACE PREPARATION OF THE TWO CYLINDRICAL NIOBIUM SAMPLES Date Sample Surface Process Nov S1 Flat surface Machine cut & light BCP etch (10-20 2005 µm) Nov S2 Flat surface Machine cut 2005 May S1 Flat smooth Mech. polish to mirror surface & light 2006 BCP etch (5-6 µm) May S2 Rough on Cut surface with stainless steel knife2006 the order of edge through mechanical hand press 1-2 mm deep enough for SI > 3. Light BCP etch (5-6 µm) June S1 Flat smooth ~3% of total length plastically 2006 deformed axially & mech. polish to mirror surface & light BCP etch June S2 Rough on BCP etch cleaning & heat treatment at 2006 the order of 750 °C for 2 hrs 1-2 mm
A. Flat plate rectangular samples test configuration The flat plate samples have the same size and have undergone the same heat treatment process as that for cylindrical sample S2 prior to its June 2006 test. Table II lists the preparation details of these samples prior to each test.
used to measure the temperature rise in the sample when a dc heat load is applied to one end through a thin foil heater. The other end of the sample is exposed to liquid helium (LHe) contained in a stainless steel tube, as shown in Fig. 2. This experimental arrangement has the advantage of measuring both the thermal conductivity as well as the Nb - LHe interface heat transfer coefficient in the same experimental run. The interface temperature is estimated by linear extrapolation. Additional details are presented in [3].
Fig. 2. Cylindrical Nb sample experimental setup. The sample holder assembly has a Nb sample with heater on the bottom side and stainless steel tube with knife-edge containing liquid helium on the other side.
For the flat plate samples, the sample holder assembly, as shown in Fig. 3, is simply a blank conflat flange. A right angle bend is made at one end of the flat plate sample to attach the sample to the flange using a brass screw. The heater on the other end of the sample provides the desired input heat load. Using the same evacuated chamber with the an arrangement of three collinear carbon sensors, similar to those for the cylindrical samples, the measurements for thermal conductivity of these flat plate rectangular samples are made. Total error in the measurements of thermal conductivity from both the experimental arrangements and the Kapitza conductance measurements is less than 10%.
TABLE II SURFACE PREPARATION OF TWO FLAT PLATE NIOBIUM SAMPLES Date Sample Surface Process Mar F1 Flat smooth Ordinary cleaning 2006 Mar F2 Flat smooth Ordinary cleaning 2006 Jul F1 Flat smooth BCP etch cleaning & heat treatment at 2006 750 °C for 2 hrs Jul F2 Flat smooth BCP etch cleaning & heat treatment at 2006 750 °C for 2 hrs
III. EXPERIMENTAL SETUP The cylindrical Nb samples (3 cm dia. by 3 cm long) are mounted on the sample holder, as shown in Fig. 2, and placed in an evacuated chamber assembly. Three in-situ calibrated carbon sensors, attached along the length of each sample, are
Fig. 3. Flat plate experimental setup. Nb sample of size 11 X 1.4 X 0.3 cm has a germanium sensor on one side and three carbon sensors on the other, for in– situ calibrations. Drawing not to the scale.
IV.
RESULTS AND DISCUSSION
3
1
k (W/cm/K)
S1(1-2) S1(2-3)
(ΔL/L) of ~3% in the sample through plastic deformation. The absence of a phonon peak and the nearly 80% reduction in thermal conductivity at 2 K in the strained sample S1, in contrast with its May 2006 test, are considered to be the effect of plastic deformation on the thermal conductivity of Nb. 1
K (W/cm/K)
Thermal conductivity measurements of small grain Nb samples tested in November 2005, as shown in Fig. 4, clearly reveal the presence of a phonon peak at ~2 K in both of the cylindrical samples. As expected, there is no significant difference in the thermal conductivity measurements of the two samples as both are from the same bulk material. Here, values of thermal conductivity for each sample are given for each of two pair of sensors (i.e. pair 1 corresponds to sensor 1 and 2 and pair 2 corresponds to sensor 2 and 3). In this nomenclature, sensor 1 is closest to the heater.
S1(2-3)May 0.1
S1(1-2)May S1(1-2)Jun
S2(1-2)
S1(2-3)Jun
S2(2-3)
0.01 1
10
May: Unstrained sample June: 3% axially strained
0.1 1
Avg. Temp. (K)
10
Tb=2.0 K
Fig. 4. Phonon peak is seen at ~2 K in thermal conductivity measurements of both cylindrical samples in November 2005 tests. Error bars in the measurements are not bigger than the symbol size used in the Fig.
However, the BCP etched sample S1, having a cleaner surface, has Kapitza conductance at 2 K that is about twice that of S2, as shown in Fig. 5. The Kapitza conductance measurements of S1 are in good agreement with the values from the literature [4] for Nb from the same supplier, providing confidence in the validity of the current experimental results. 0 .2 0 .1 8
Fig. 6. The phonon peak is clearly absent in the thermal conductivity measurements of sample S1 in tests carried out after 3% strains induced in the sample (June 2006 test) as compared with its tests performed in May 2006.
For sample S2, the absence of a phonon peak in the measurements of May 2006, in contrast with those of November 2005, can be understood as surface roughness preparation protocol with the stainless steel blade pressing against the surface, causing inadvertent strains in the bulk niobium, similar to those induced intentionally in S1. Low temperature annealing (750 °C for 2 hrs) on S2, intended to recover the phonon peak in the Nb and shown in Fig. 7, is insufficient, although S2 showed a small increase (~30%) in thermal conductivity over the temperature range measured.
S1 S2 L it. D a ta [4 ]
0 .1 6 0 .1 4
10
0 .1 2
K (W/cm/K)
hk (W/cm^2 K)
Avg. Temp. (K)
0 .1 0 .0 8 0 .0 6 0 .0 4 0 .0 2 0 1 .6
1 .7
1 .8
1 .9
2
2 .1
1
S2(1-2)Jun S2(2-3)Jun
0.1
S2(1-2)May
2 .2
T b a th (K )
S2(2-3)May 0.01 1
Fig. 5. November 2005 Kapitza conductance measurements for the two cylindrical samples are compared with the one given by S. Bousson et Al. [4]. Refer to table I for surface finish differences between the two samples.
Measurements of thermal conductivity performed in May and June 2006 are compared in Fig. 6 for sample S1. As noted from Table I, before the June test, the sample S1 was intentionally axially compressed to induce nominal strain
Avg. Temp. (K)
10 May: Axially strained sample June: Heat treated
Fig. 7. Phonon peak did not reappear after it was lost during surface compression process to form rougher prior to May 2006 test. Low temperature heat treatment (June 2006 test) has small effect on the thermal conductivity of the niobium.
4 prior to the heat treatment. However, one must consider the possible influence of the BCP process, done prior to the heat treatment of S2, on the increased Kapitza conductance. There is no significant change in Kapitza conductance of sample S1, before and after inducing 3% strain in the sample. 1
hk (W/cm^2K)
The same effect of low temperature annealing is also observed in thermal conductivity measurements done on the two flat plate samples. The initial measurements on flat samples done in March 2006 did not reveal a phonon peak in the as received material, possibly due to partial recrystallization in the material. After annealing them at 750 °C for 2 hours, no significant change in their thermal conductivities was observed for most of the temperature range measured. However, a slight improvement below ~ 3 K can still be observed due to the low temperature heat treatment. Since the results of the two flat samples are within experimental errors, only the ones for F2 are shown in Fig. 8. Based on these observations, it can be argued that the low temperature annealing is insufficient to recreate the lost phonon peak in the thermal conductivity curve of Nb with RRR in the range of 200 to 300.
S2 S1 S1 S2
June 06 M ay 06 June06 M ay 06
0 .1
10
k (W/cm/K)
0 .0 1 1 .5
1
July06 (2-3) Mar06 (1-2) Mar06 (2-3) 0.01 1
Avg. Temp. (K)
10
F2
2 .1
Fig. 9. Kapitza conductance of cylindrical samples S1 and S2 is compared with their measurements done in May and June 2006.
One plausible explanation for this observation comes from the surface preparations (smooth shiny surface with light BCP etch) for the two tests on the sample S1, being almost identical and thus removing any surface effect that might otherwise have affected Kapitza conductance.
Fig. 8. The low temperature heat treatment (July 2006) has only slightly increased the thermal conductivity of sample F2 from its previous test in March 2006 on as received sample.
To understand the effect of large surface roughness on Kapitza conductance, S2 was specially prepared having roughness on the order of 1-2 mm with a surface index (SI) greater than 3. In Kapitza heat transfer, nanometer-lengthscale surface roughnesses that are comparable in size to the dominant phonon wavelengths at the bath temperature of super fluid helium are primarily responsible for diffuse scattering of phonons at the interface [2]. This results in an increased Kapitza conductance across the interface. The increased interface surface area (SI>3) of S2 should result in a corresponding increase in the Kapitza conductance as compared with the flat and smooth surface. However, in the May 2006 test results, shown in Fig. 9, the difference between the Kapitza conductance values of the two samples is less than 10%. No simple explanation can be provided for this result other than assuming that somehow the induced surface strains on sample S2 during its surface roughness preparation might have affected in lowering its Kapitza conductance. This is more likely so, when the Kapitza conductance results for June 2006 test for the two samples (Fig. 9), are also examined. Here, some strain relieving due to heat treatment on the rough surface of S2 has resulted in a doubling in its Kapitza conductance as compared to its value
1 .9
T b (K )
July06 (1-2)
0.1
1 .7
V. CONCLUSION The effect of plastic deformations on thermal conductivity and Kapitza conductance of Nb has been studied. The disappearance of the phonon peak at 2 K causing an almost 80% reductions in thermal conductivity is attributed to the plastic deformations in the Nb. This may also have an effect on the phonon conduction in its Kapitza heat transfer. Further investigation and experimental research is planned to demonstrate this effect after subjecting the samples to high temperature heat treatment ~1400 °C as is usually done in the post purification process for SRF cavities.
REFERENCES [1] [2] [3]
[4]
H. Padamsee, J. Knobloch, T. Hays, “RF Superconductivity for Accelerators”, John Wiley & Sons, Inc. 1998. J. Amrit, C.Z. Antoine, M.X. Francois, and H. Safa, “On intrinsic thermal limitations of superconducting cavities: Kapitza resistance”, Adv. in Cryo. Eng.: Proc. of the Cryo. Eng. Conf., Vol 47. 2002. A. Aizaz and T.L. Grimm, “Thermal limitations in superconducting RF cavities: Improved heat transfer at niobium-helium interface”, Adv. In Cryo. Eng.: Trans. Of Cryo Eng. Conf., Vol 51B, pp 1179-1186, edited by J. Weisend II 2006. S. Bousson, M. Fouaidy, T. Junquea, N. Hammoudi, J.C. Le Scornet, J. Lesrel, “Kapitza conductance and thermal conductivity of materials used for SRF cavities fabrication”, Proc. of 9th Workshop on RF Superconductivity 1999.
