JLAB-TN-08-025
Comparison of Heat Transfer Characteristics for “Pure”
and Brazed Niobium
Joshua Ballard, Robby Hicks, Ed Daly
Introduction
As part of the 12GeV upgrade, the helium vessels for the C100 cryomodules are fabricated from
Stainless Steel instead of Titanium. The interface between the Stainless Steel vessel and the Niobium
beam-tube components requires a 50/50 Gold-Copper Alloy braze joint instead of an arc weld.
Nb/SST Braze Joint
Figure 1: Nb/SST Braze Joint
The thermal conductivity of the Niobium at this interface must be high enough to transmit
incoming static and RF heat loads to the Helium bath without raising the temperature of the cavity. The
brazing process has the potential to lower the purity of the base metals by diffusion of the braze metals
into the bulk Niobium. The impurities could negatively affect the heat transport characteristics of the
Niobium.
1
Measurements of heat transport characteristics at 2 Kelvin were performed on both brazed and
unbrazed samples of RRR Niobium in order to verify that the thermal conductivity in this temperature
region is not adversely affected by the brazing process.
Apparatus
Two sets of four RRR Niobium samples each were machined for this analysis. One set was
brazed into a 316L Stainless Steel plate and then machined out (DWG# CRM-120-7020-0607). The other
set came from the same stock as the first, was machined to the sample dimensions and tested “as-is”. The
samples are .125” X .125” X 6” overall; the full dimensions, including temperature sensor locations, can
be seen in Figure 2 below.
.25
1.00
Figure 2: Sample Dimensions
The samples were clamped into a Copper heat sink with a .010” layer of indium foil between the
heat sink halves. The copper heat sink was brazed into a Stainless Steel flange. When mounted in the test
can and installed into a dewar, the heat sink is immersed in liquid Helium allowing the clamped end of the
Niobium samples to be anchored near 2 Kelvin.
A .25 Watt (50Ω) heater is installed in the .106” hole at the end of each sample and the
temperature sensors are installed per manufacturer instructions on the .125” X .125” section of the sample
as seen in Figure 2. The full test assembly can be seen below in Figure 3.
2
Figure 3: Assembled Test Fixture
Test Procedure
A LabView VI was written to record temperature, current and voltage measurements for use in
the analysis. Temperature at each location was measured with a calibrated Lakeshore Cernox resistor.
Heater voltage was measured with a Hewlett Packard multimeter and heater current was measured with
an Agilent multimeter.
While running the LabView VI for the experiment, one data point each for temperature, heater
voltage and heater current was taken every five seconds and written to a raw data file. The temperature
data was input into a running linear regression analysis. Once the linear regression analysis reported a
slope of 0.0005K/s or less for all three temperature sensors based on the last 60 data points, the system
was considered steady state and a separate steady state data set was written to file with the steady-state
temperature, the measured current, measured voltage and calculated power.
Data was taken for three nominal power settings, 65, 75 and 85 mW, one station at a time, for
both the brazed and unbrazed samples. Adequate time was allowed between testing of each station for all
samples to reach a steady state minimum temperature near 2K.
Raw Data
Results for the unbrazed and brazed samples can be seen in Table 1 and Table 2, respectively. T1
is the temperature closest to the heater, T2 is closest to the sink, T3 is the reference temperature taken
from the heat sink and T is the difference between T1 and T2.
T1
T2
Heater
s
T3
Station 1
Station 2
Station 3
Station 4
Figure 4: Heater and Thermocouple Locations
3
T2
2.030
3.667
3.796
3.910
T3
2.027
2.188
2.216
2.244
T
0.433
4.096
4.337
4.569
Station 2
2.653
7.890
8.267
8.620
2.086
4.078
4.223
4.348
2.078
2.210
2.232
2.253
0.567
3.812
4.044
4.272
0.0018
1.9130
2.0490
2.1740
0.0000
0.0337
0.0365
0.0389
0.0000
0.0645
0.0748
0.0845
Station3
2.619
7.773
8.142
8.487
2.292
3.946
4.083
4.201
2.078
2.192
2.211
2.230
0.327
3.827
4.059
4.286
0.0018
1.9310
2.0620
2.1740
0.0001
0.0337
0.0363
0.0388
0.0000
0.0650
0.0749
0.0843
Station 4
2.672
7.813
8.183
8.530
2.058
3.504
3.627
3.738
2.078
2.169
2.184
2.199
0.614
4.309
4.556
4.792
0.0018
1.9380
2.0560
2.1860
0.0000
0.0337
0.0364
0.0389
0.0000
0.0652
0.0748
0.0850
Station 1
T1
2.463
7.763
8.133
8.479
htr Voltage htr Current
0.0032
0.0000
1.9250
0.0338
2.0740
0.0364
2.1980
0.0390
htr power (W)
0.0000
0.0650
0.0755
0.0857
T2
2.362
4.547
4.699
4.841
T3
2.123
2.255
2.287
2.320
T
0.287
3.28
3.5
3.707
Station 2
2.681
7.733
8.097
8.436
2.08
3.881
4.009
4.123
2.059
2.223
2.250
2.275
0.601
3.852
4.088
4.313
0.001
1.900
2.060
2.190
0.000
0.033
0.035
0.038
0.0000
0.0620
0.0724
0.0824
Station3
2.73
7.724
8.086
8.425
2.086
3.832
3.956
4.069
2.063
2.219
2.243
2.267
0.644
3.892
4.13
4.356
0.001
1.910
2.060
2.190
0.000
0.033
0.035
0.038
0.0000
0.0623
0.0725
0.0822
2.882
7.758
8.122
8.462
2.101
3.817
3.941
4.055
2.066
2.172
2.189
2.206
0.781
3.941
4.181
4.407
0.001
1.930
2.040
2.160
0.000
0.033
0.035
0.038
0.0000
0.0631
0.0722
0.0814
Station 1
T1
2.649
7.827
8.199
8.548
Station 4
Table 1: Unbrazed Sample Results
htr Voltage htr Current
0.001
0.000
1.900
0.035
2.050
0.037
2.170
0.040
Table 2: Brazed Sample results
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htr power (W)
0.0000
0.0659
0.0767
0.0870
Modified Data
For each sample, the distance between the resistors and the heat input into the sample is known.
This allows a thermal conductivity-like property1 to be determined and compared. The thermalconductivity-like property is determined the same way as true thermal conductivity and carries the same
units as thermal conductivity. From this point forward, “thermal conductivity” will refer to this thermalconductivity-like property. The heat transfer equation is shown below:
𝑞̇ =
𝑄̇ 𝑘
= ∆𝑇
𝐴 𝐿
Equation 1: Heat Transport Equation
Where, 𝑞̇ is the heat flux W/cm2, 𝑄̇ is the heat input in Watts, k is the “thermal conductivity” in
W/cm-K, A is the area in cm2, T is the temperature difference between the resistors in Kelvin, and L is
the distance between the resistors in cm.
Station 2
T
0.287
3.280
3.500
3.707
Brazed
Heat Flux, q, (W/cm^2)
2.61905E-07
0.653769841
0.760912698
0.863095238
0.567
3.812
4.044
4.272
6.91806E-07
0.640119048
0.74156746
0.838700397
0.601
3.852
4.088
4.313
1.74603E-07
0.615079365
0.718253968
0.817460317
Station3
T
0.433
4.096
4.337
4.569
Unbrazed
Heat Flux, q, (W/cm^2)
5.76915E-07
0.644771825
0.749126984
0.849910714
0.327
3.827
4.059
4.286
1.1699E-06
0.645009921
0.742956349
0.836547619
0.644
3.892
4.130
4.356
3.7996E-07
0.618055556
0.719246032
0.81547619
Station 4
Station 1
In Table 3, below, the data has been rearranged to show the heat flux and the temperature
difference across the brazed and unbrazed samples.
0.614
4.309
4.556
4.792
6.30169E-07
0.647003968
0.741835317
0.843630952
0.781
3.941
4.181
4.407
5.2381E-07
0.625992063
0.716269841
0.807539683
Table 3: Data rearranged for comparison between heat flux and T.
1
An accurate value for true thermal conductivity cannot be determined from this data as there are no considerations
made for the radiation heat input into the test assembly.
5
When 𝑞̇ is plotted against T, the slope of a least-squares straight line through the data is k/L.
The average “thermal conductivity” can be determined by multiplying the resulting slope by L (12.7cm),
the distance between the resistors. Table 5, below, displays the average “thermal conductivity” for each
sample based on the least-squares fit of the data displayed graphically in Figure 5 and tabulated in Table
4.
Figure 5: Heat flux vs. T. Slope is k/L by Equation 1.
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Brazed
Station 1
Station 2
Station 3
Station 4
Unbrazed
Station 1
Station 2
Station 3
Station 4
Slope
Intercept
0.49
-0.954
0.454
-1.095
0.425
-1.037
0.389
-0.909
0.433
0.431
0.417
0.406
-1.131
-1.005
-0.951
-1.108
R2
1
1
1
0.999
1
0.999
1
0.998
Table 4: Least-Squares Fit of Data from Figure 5
Station 1
Station 2
Station 3
Station 4
Average
STDEV
Unbrazed
5.4991
5.4737
5.2959
5.1562
5.3562
0.1611
Brazed
6.2230
5.7658
5.3975
4.9403
5.5817
0.5448
Table 5: Comparison of “Thermal Conductivity” Values for Unbrazed and Brazed RRR Niobium in W/cm-K
Discussion
The thermal performance of the Niobium subjected to brazing with 50/50 Gold-Copper
brazing alloy is not significantly or adversely affected. The results from this analysis show that the
thermal performance of the brazed Niobium is actually slightly improved (about 4%) over the unbrazed
Niobium.
Overall, the “thermal conductivity” determined is higher than published data2. A significant
cause of this difference comes in the form of static heat input into the system. A line-of-sight between the
300K dewar lid and the 2K samples could allow a significant amount of radiative heat transfer to take
place. Estimates of the magnitude of this systematic error range from 17% to as much as 50%. Reducing
the error could lower the “thermal conductivity” measurements by a factor of 2, which would bring the
data much closer to the published data. This systematic error is the same for both sets of samples and
does not invalidate the comparison of “thermal conductivity”.
2
Data was provided by Gigi Ciovati from thermal conductivity measurements of single crystal niobium hollow rod
(RRR=288).
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It is also possible that the RRR value for the samples tested is much higher than expected. RRR
in the range of interest is proportional to thermal conductivity, so a higher than expected RRR would
provide for a higher than expected thermal conductivity measurement. An independent measurement of
the RRR value for the brazed and unbrazed samples would allow a good comparison of the “thermal
conductivity” to previously referenced published data to take place.
In order to improve the accuracy of the “thermal conductivity” measurement, the experiment
could be performed again. Eliminating, or minimizing, the systematic error and performing the analysis
with smaller T’s would provide a much more accurate measurement of thermal conductivity for these
samples. Smaller T’s would provide a greater quantity of useful data to analyze and would allow the
thermal conductivity at 4.2K to be compared to the RRR value to further verify the accuracy of the
measurements.
There are random uncertainties introduced by the instrumentation and dimensional
measurements. For the “thermal conductivity”, k, the uncertainty is calculated to be approximately
1.17%, which accounts for a variation of approximately ±0.065 W/cm-K.
Contact resistance is also a possible cause of uncertainty introduced in this experiment. Three
points where contact resistance comes into play are the mounting of the heaters, installation of the RTD’s
and clamping of the test specimen in the copper heat sink. All efforts were made to ensure that the
procedure to assemble the experimental setup was the same for both the brazed and unbrazed samples. It
can safely be assumed that contact resistance is negligible and the same for both sets of samples and,
therefore, does not invalidate the comparison.
Conclusion
In conclusion, this experimental comparison shows that the heat transport characteristics of the
brazed Niobium are not adversely affected. Further measurements must be performed in order to get an
accurate measurement of the true thermal conductivity for the brazed Niobium.
Operational testing of two cavities constructed with this braze joint show no degradation of
thermal or RF performance due to the newly incorporated braze joint. Based on the conclusions of this
experiment and the successful operational testing of the ccavities in the HTB, it is safe to say that the SST
to Niobium braze joint will not adversely affect thermal or RF performance of the C100 cryomodules.
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