DOI 10.1007/s10909-012-0779-0
Thermal Properties of Two Materials Commonly Used in Low Temperature Laboratories
Angel Colin
Received: 9 August 2012 / Accepted: 28 September 2012 / Published online: 11 October 2012
© Springer Science+Business Media New York 2012
Abstract We carried out measurements of thermal conductance and thermal contact resistance of two materials commonly used in low temperature laboratories such as an Electro-Magnetic Interference (EMI) Filter and Stycast 2850 FT epoxy. Both samples were attached on a heat sink made of oxygen-free high thermal conductivity (OFHC) copper and characterized at temperatures between 0.3 K and 4.5 K, using a3He re- frigerator mounted on a pumped4He cryostat. For the EMI filter we applied a varied input power from 0.25 up to 50 µW to the heater which is soldered to its central pin, whereas for a thin layer of Stycast sandwiched between a copper strap and the heat sink we applied an input power from 10 up to 810 µW. The temperature dependences obtained in each case were K= 3 · 10−5T2.3 [WK], and RK= 8.4 · 10−3T1.7[cmW2K] respectively.
Keywords Heat conduction· Cryostats · Epoxy · RF filters
1 Introduction
The Electro-Magnetic Interference (EMI) Filters are commonly used in large number of microwave experiments. They are especially important in thermal detectors for as- tronomical applications in the millimeter and sub-millimeter range [1,2]. All thermal detectors need to be very well protected from extraneous thermal loads due to their sensitivity to any kind of energy that is deposited in them. Hence, the demands for thermal shielding with respect to both thermal conduction and radiation are extreme.
The use of radio frequency (RF) filters is necessary to avoid that RF radiation reaches the detectors via the signal wires.
A. Colin (
)Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Luis Enrique Erro No. 1, 72890 Santa María Tonanzintla, PUE, México
e-mail:[email protected]
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On the other hand, the choice of a bonding agent with high thermal conductivity and electrical insulation properties is not a simple task, because it depends on its ap- plication and the temperature range of operation. At low temperatures for example, the knowledge of the thermal contact resistance between two joined materials is es- sential to preserve as much as possible the properties of heat conduction through the solid surfaces of such materials.
In this paper, the thermal conductance through a #2-56 threaded miniature EMI Spec Spin Filter (Part Num. 54-874-013, operating from 1 MHz to 10 GHz,
®Spectrum Control Inc.), and the thermal contact resistance of Stycast 2850 FT epoxy (®Emerson & Cumming Inc.) are presented.
This kind of filters has been utilized in [1,2] for each one of the signal wires that enters the detectors. The filters are in direct contact with the metal mount which serves as heat sink, since the signal wires runs through different intermediate stages of the cryostat to reduce the heat load on the coldest stage. Each filter consists of ring capacitors soldered into a threaded metal tube filled within dielectric materials whose properties are specified by the manufacturer. For our convenience, this study is only focused to the thermal properties and considers the filter as a “black-box” in a whole device.
The Stycast epoxy is commonly used in most of low temperature laboratories. It has been well characterized before for several researchers [3,4]. Because of its ther- mal properties, it is applied in large variety of cryogenic experiments. Its main use is for mechanical attachment providing good heat conduction and electrical insulation.
In this study we have investigated its thermal contact resistance between a small cop- per strap and a copper heat sink; the results will be useful for studies of miniature Metal-Insulator-Metal joints.
2 Setup and Technique
All measurements were taken with a potentiometric conductance bridge (®S.H.E.
Corporation), applying the steady-state heat flow method and using a heat sink at- tached on the cold plate of a3He refrigerator which in turns is mounted on a pumped
4He cryostat, as is shown in Fig.1(a).
Referring to Figs.1(b) and (c), the Heater 1 and Heater 2 consist in a copper strap of 0.5× 2 × 15 mm3smoothed up to 10 µm on its contact surface. Each heater surrounds a metal film resistor (1 kOhm Mini-Melf MMA 0204-50; P70= 0.25 W,
®Beyschlag GmbH.) which is covered with cigarette paper and impregnated with IMI 7031 varnish (®GVL Cryoengineering) to get electrical insulation and good thermal contact. Both, the heat sink and the copper strap were made of oxygen-free high thermal conductivity (OFHC) copper. The Heater 1 is soldered to the central pin of the filter and provides the heat Q, which flows through this pin. The Heater 2 is in contact to the heat sink by an intermediate layer of Stycast of 50 µm of thickness onto a well defined geometry with a contact area AC= 0.2 cm2. This contact area of the heat sink was also smoothed up to 10 µm. The heat Q provided by Heater 2, flows thought the Stycast and is dissipated into the heat sink. The attachment was realized using an external clamp, which exerted a constant pressure of approximately
Fig. 1 Experimental arrangement (not to scale) for measuring thermal conductance and thermal contact resistance. (a) The3He refrigerator mounted on a pumped4He cryostat. (b) Setup, and (c) cross section of the setup (Color figure online)
150 N cm−2 during the cure of the epoxy. The cure was realized with catalyst 11 following the manufacturer instructions, after the cure the clamp was removed.
The heat sink is a copper block with a threaded cylindrical cavity to hold the filter, which is in direct contact and tightened manually. A piece of PC board with gold printed microstrips is attached in the same way as the Heater 2 in order to provide electrical leads [5]. Note that in Fig.1(c), the PC board and the Heater 2 are omitted for clarity. The heat sink is designed to hold a commercially calibrated Ge resistance thermometer (®Lake Shore Cryotronics Inc.) for monitoring temperatures, but for our purposes it was not used in this experiment since it was replaced by the ther- mometer T2. The thermometers T1, T2, and T3(100 kOhms TMi-A1 CCS/F2 carbon- ceramic resistor,®IDB Ingenierburo, Dietmar Budzylek) were previously calibrated in the manner of Clement and Quinell [6] with an accuracy of 1 % and glued with IMI varnish, having four lead connections of manganin wire to minimize the effects of lead resistance. Finally the full device was mounted using a copper screw and an intermediate layer of varnish between the heat sink and the cold plate of the cryostat to get thermal contact.
The temperature gradients are given by
T1= T1− T2 and T2= T3− T2 (1) were T1and T3measure the temperature of the straps and T2measures the temper- ature of the heat sink. Therefore, the thermal conductance K estimated for the EMI filter is given by
K= Q
T1 (2)
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and the thermal contact resistance RK for the Stycast is given by the known for- mula [7]
RK= T2
(AQ
C) (3)
where ACis the contact area.
In each run, we stabilized T1, T2 and T3 first within 100 mK and wait for each applied heat load until the steady state condition was reached.
For Heater 1, we applied a varied input power Q, from 0.25 up to 50 µW. T1
was typically about 160 mK. For Heater 2, we applied an input power Q from 10 to 810 µW. Here, T2was typically about 130 mK.
3 Results and Discussion
Our main interest was focused only in the low input power applied to the samples at the lowest temperatures, but taking care that the input power be enough to obtain temperature gradients greater than 100 mK, since during the measurements we ob- served that for Q < 0.25 µW applied to the filter, we obtain T1<100 mK, giving in consequence uncertainties of about 30–35 %. In the same way for the Stycast, for Q < 10 µW, we obtain T2<80 mK, resulting uncertainties of about 40–50 %.
Therefore, for values of Q > 0.25 µW and Q > 10 µW, the uncertainties can be reduced down to 1 % and 3 % respectively.
In order to check the linearity of the temperature dependence, the measurements were taken in three runs at three different cold stages in the cryostat (0.3 K, 1.3 K, and 4.2 K). The results of our measurements are depicted in Figs.2and3. For each plot, the temperature was considered as the average of T1 and T2, and T3 and T2, respectively.
The data were approximated to a form x= aTb, giving a= 3 · 10−5[WK], b = 2.3 for the EMI filter, and a= 8.4 · 10−3[cmW2K], b = 1.7 for the Stycast.
The low thermal conductance of the EMI filter may be due to the different contrac- tion coefficients of the metal and its internal insulating materials that do not guarantee a good thermal contact between the threaded filter and the heat sink at low tempera- tures.
It must be taking into account that we have considered the filter assembly as a
“black-box” in this experiment, thus discarding its internal and unknown manufac- turing properties. A separated characterization of its internal components could be useful to complete this experiment.
According to our results at these low temperatures, one may assume that most of the low power applied on the central pin of the filter is dissipated to the heat sink.
Hence, the thermal contribution from these filters connected to thermal detectors via the signal wires can be considered negligible.
On the other hand, the thermal contact resistance presented by the Stycast may be attributable to several factors, the most notable being the arbitrary distribution of small glass beads contained into the unknown chemical formula of this epoxy. These glass beads have been seeing under microscope with different sizes and irregular
Fig. 2 Thermal conductance of an EMI Filter as a function of temperature
Fig. 3 Thermal contact resistance of Stycast as a function of temperature
forms, whose average size is around 50 µm. In addition, it is well known that at low temperatures the acoustic mismatch in crystalline and none crystalline solids limit the transmission of thermal phonons between the different materials forming the contact, hence their thermal conductivity is notably reduced [8].
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The data obtained in this experiment converted to thermal conductivity units, show that the temperature dependence coefficient is consistent with the quasi linear behav- ior between 2 and 10 K already observed with the same catalyst 11 reported in [3]
where b= 1.8, but in contrast with those reported in [4] where b= 2.65 between 0.05 and 2 K with an unknown catalyst, our thermal conductivity values are 35 % lower than this work.
4 Conclusion
We built a simple but efficient device to characterize this kind of RF EMI filters at low temperatures. These filters are commonly used by threading into metals to facil- itate the mounting and demounting process. But it is important to know their ther- mal behavior, since at low temperatures the different contraction coefficients of their internal components and their metal case do not guarantee a good thermal contact with metal mounts. The miniature heater devices also present an efficient low power supply, minimizing the heat losses as may occur with the bulky heater devices. The miniature devices are essential for characterization of materials, especially when the space is reduced into the cryostats.
The results presented in this paper provided useful information that can be applica- ble to a wide variety of cryogenic experiments where small heat leaks are permitted.
Acknowledgements The author is grateful to Dr. Ernst Kreysa for his assistance during the experimental runs.
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