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A carbon resistance thermometer with fast response below 10 mk
An electromagnetically shielded carbon thermometer is described. The unit has a response time shorter than the thermal equilibration time of the cryosystem at 5 mK: of the order of 5 min.
A carbon resistance thermometer with fast response below 10 mK G. Eska and K. Neumaier Key words: thermometers, response time, carbon resistance
Today, temperatures below 4 mK are commercially available, but thermometers of easy operation in this temperature range are not common. Suitable thermometers could be carbon resistors, but up to now there has been only one report 1'2 using carbon resistors down to 5 mK without saturation effects. The latter is due to overheating the resistors of bad thermal conductance by electrical and/or magnetic noise. Nobody has measured the thermal response time of such resistors around 5 mK, mainly because it was obvious that it would take hours to reach the saturation value of the resistor. In this paper we describe an experiment where the time behaviour of a carbon resistor below 10 mK was compared with a pulsed NMR-thermometer, both coupled to a copperrod which was linked to the mixing chamber of a dilution cryostat (Fig. 1). A magnetometer was used to measure the static nuclear susceptibility of copper of 5N purity by means of a SQUID (Fig. 1). In the next section we briefly describe the construction of the resistance thermometer and the experimental setup. The second paragraph covers the way in which the temperature scale was established and in the last section, the experimental results are presented. The carbon thermometer was made from a Speer grade 1002 100 ~2 1/4 W resistor similar to that described in Ref. 2. The resistor was ground to 0.15 mm thickness, and glued by Stycast 1266 into a slit o f a cylindrically shaped piece of copper. The resistor was then electrically isolated by cigarette paper. It was thought that the epoxy resin would penetrate the carbon matrix avoiding microcracks. This ruggedly designed resistor had a reproducibility better than 1% above 20 mK over years and it was recently recalibrated against the NBS standard down to 25 mK. The thermal connection to the copper body of the mixing chamber was made via two screw-contacts which connected two Cu-rods of 7 mm diameter and 200 mm length. A 1 mm diameter silver wire of 85 mm length was squeezed to the rod as well as to the resistor by screws as shown in Fig. 1. The resistor was centred inside the niobium shield of the SQUID magnetometer by means of epoxy spacers. The shield was kept at a constant temperature of 100 mK. The open end of the Nb-tube was closed by a lead disc. The resistance was measured by the two wire technique using a bridge (IT-VS-4). The bridge had a time constant of about one rain for low voltage excitation. The authors are at the Zentralinstitut fur Tieftemperaturforschung D-8046 Garching, FRG. Paper received 1 September 1982.
The wires were fed through a low pass filter which was made from ferrite inductances and mica capacitors and had a cut-off frequency of 0.2 MHz. The filter was thermally anchored to the mixing chamber and surrounded by a 0.2 mm lead sheet. The wires leading down to the resistor were shielded by a Pb-Sn-capillary. In this way the system was shielded electromagnetically as a whole. In a field of 58 mT at the centre of the NMR-sample, the remaining field at the corner of the Nb-shield was 19 mT which is well below the critical field of the Pb-Sn-capillary. For the NMR-sample a bulk Tl-rod (4 mm diameter, 25 mm length) was soldered directly to a Cu-screw which established the contact to the cold-finger. The construction of the NMR-thermometer is described elsewhere. 3 Thallium was chosen because of its small Korringa-constant ofT1 -T = 6 ms K only, combined with the good thermal conductance of a pure metal. Thus, changes in the temperature are detectable five times faster than with a Pt-NMR-thermometer, commonly used at these temperatures, at a sensitivity comparable to that of NMR on Cu nuclei in the same field and volume. The temperature calibration of the resistor for several different runs is shown in Fig. 2. The measuring power at T < 10 mK was less than 4 fW. For temperatures above 25 mK the resistor was calibrated in another cryostat against CMN and the NBS fixed point standard. Curve (a) of Fig. 2 was obtained using a slightly different system 4 from that described in Fig. 1. The Tl-thermometer was self-calibrated according to its Korringa- constant. For temperatures below 20 mK curve (b) and (c) were obtained in a field of 3 mT and the earth-field, respectively. The static Cu-susceptibility thermometer was used for calibration. It was calibrated at temperatures above 25 mK with the help of the resistor itself, which is believed to be accurately measured at those temperatures. Indeed, the Cu-thermometer calibrated in this way gave, within the experimental error, the same result as the Tl-thermometer at our lowest temperatures of 4.4 mK. There are two remarkable points in Fig. 2. First, there is no or only a weak saturation effect. This is believed to be due to the use of the cold filters and electromagnetic shielding of the wires and the resistor. All measurements which were done with resistors of similar type have shown the onset of saturation to be between 15 and 10 mK, if filters located at 4 K are used in connection with an unshielded twisted pair wiring. In a different experiment we compared two resistors made from Matsushita ERG 18 47 ~. The resistors ground to 0.15 mm thickness were glued between 0.1 mm silver foils
0011-2275/83/002084-03 $03.00 © 1983 Butterworth & Co (Publishers) Ltd. 84
CRYOGENICS. FEBRUARY 1983
ratios decreased with increasing temperatures to about 4% at 25 mK and less than 0.5% above 80 mK, showing the influence of the protection even in a case where no saturation effect was visible at lust glance (see Fig. 2). Second, there are large discrepancies at low temperatures between the different measurements in Fig. 2 which certainly are not due to the different magnetic fields acting on the Speer resistor in the specific experiment (for curve (a) and (c) the same field was applied). Regardless of careful earthing, these variations were produced by different use and earthing of the various pieces of electrical equipment around the experiment. Thus, we have to conclude that thermometry with a carbon resistor at temperatures around 5 mK can only be done if nothing is changed after establishing the calibration. Preserving this fact, the calibration can be reproduced as we have done repeatedly for curve (a) of Fig. 2. For T < 8 inK, the time response of the c'arbon resistor and the T1 -sample after applying a heat-pulse of 7.5/aJ is shown in Fig. 3. The repetition rate of the NMR-pulses was 30 s. Due to eddy current heating, only a small temperature gradient was established between the mixing chamber and the sample (see for example arrow in Fig. 3). The simultaneously measured values of the resistor are also plotted. The time dependence is analyzed in Fig. 4.
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Fig. 1 E x p e r i m e n t a l setup: a -- b o t t o m plate o f m i x i n g c h a m b e r , b -- screw c o n t a c t , c -- C u - l i n k , d - A g - l i n k , e - heater (1 k ~ metal f i l m resistor), f -- Nb-shield, g -- N b T i - c o i l , h -- astatic pair o f t h e C u - t h e r m o m e t e r , i -- c a r b o n resistor, j -- Pb-Sn c a p i l l a r y , k - TI N M R - t h e r m o m e t e r and I - lead shield
FEBRUARY
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which were, in turn, directly screwed to the mixing chamber. The resistance at 4 K was 599 g2 and 504 f2, respectively. The resistivity ratio was 0.825 and 0.828 between room temperature and 4 K. The former was protected in a similar way to that described above, the other one was used without a shield and with a f'dter located at room temperature only. The resistance at 7.5 mK was measured with a 10 ~V excitation yielding 31 k~2 and 21 kg2, respectively. This difference of about 20% in the resistivity
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Temperature, rnK Fig. 2 Carbon resistor vs t e m p e r a t u r e f o r d i f f e r e n t c a l i b r a t i o n - r u n s a - T I - N M R t h e r m o m e t e r , b -- and c -- C u - s u s c e p t i b i l i t y t h e r m o m e t e r (see t e x t ) . Curve a t o c are f o r t h e Speer resistor; f o r c o m p a r i son t h e dashed lines d a n d e s h o w a shielded a n d u n s h i e l d e d Matsushita resistor, respectively. (the c o n t r i b u t i o n o f t h e leads are n o t subtracted)
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Fig. 3 T i m e response of the T I - N M R - and the resistance-thermometer after applying a 7.5/~J heat pulse. The equilibrium temperature was 4.4 mK
Fig. 4 compares in a semi-log plot the time-behaviour of the difference between the equilibrium inverse temperature, just before applying the heat pulse, and the inverse temperature at time t after the pulse. The points shown are deduced from the smoothed data of Fig. 3. The temperature of the Tl-sample is illustrated just before and after the heat pulse was 4.4 mK and 7.6 mK, respectively. For times up to 5 rain after the heat pulse is applied both thermometers show the same time-constants. The faster one of 1.1 rain could not be resolved by the resistor due to the slow electronics. It is assumed to be the equilibration time of the metal part of the experimental setup. The second timeconstant of 5.5 min arose from removing the heat by the dilution unit of cooling power of about 0.1/2W at 6 mK. For times longer than 5 rain where the temperature had again reached a value only 5% higher than the final temperature of the system (4.4 mK), the time constants of both thermometers start to deviate and the time constant of the resistor becomes as long as 56 min. Whether this slow temperature decrease, indicated by the carbon resistor, is due to an excess of specific heat or due to bad thermal conductance of the carbon material could not be clarified. Nevertheless, the time response of the resistor just after the heat pulse is surprisingly fast at low temperatures indicated (Fig. 3) by the small jump in the
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Fig. 4 The difference between equilibrium-and actual inverse temperatures vs the time. The time constants shown by the dashed lines correspond to the thermal equilibrium within the metal end between metal and mixture, respectively. The dashed dotted line gives the behaviour of the carbon resistor after reaching 95% of the final temperature of 4,4 mK
resistance it the Tl-thermometer is switched off. This effect cannot be explained by overheating of the resistor by the rf-field because the duty cycle for the NMR-pulses was only 1.7 x 10-s . It must be due to the temperature step between the He 3-He a mixture and the sinter which vanished, shown by the immediate response of the resistor if the additional heating by eddy currents induced by the rf-field is removed. From our measurements we made two conclusions: first, carbon resistors can be used as fast thermometers even at 5 mK, as long as no better temperature resolution is needed than about 5%, an accuracy which is also the limit in the temperature calibration at these temperatures; secondly, reliable thermometry with carbon resistors can be accomplished below 10 mK if, after calibration of the resistor, no changes whatsoever in equipment and surroundings are made. We would like to acknowledge the experimental help of Professor K. Andres, U. Angerer, Dr Ch. Probst, Dr E. Schuberth and Mrs. M. Tuomisaari. References
1 2 3 4
Frossati, G., Schuhmacher, G., Thoulouze, D. EPS spring meeting, Freudenstadt (1972) Sanchez, J., Benoit, A., Flouquet, J., Frossati, G. J Phys 35-C1 (1974) 23 Amend, B., Andres, K., Eska, G., Neumaier, K., Ptobst, Ch., Sehubetth, E. to be published Angerer,U., Eska, G. to be published
C R Y O G E N I C S . F E B R U A R Y 1983
A carbon resistance thermometer with fast response below 10 mK G. Eska and K. Neumaier Key words: thermometers, response time, carbon resistance
Today, temperatures below 4 mK are commercially available, but thermometers of easy operation in this temperature range are not common. Suitable thermometers could be carbon resistors, but up to now there has been only one report 1'2 using carbon resistors down to 5 mK without saturation effects. The latter is due to overheating the resistors of bad thermal conductance by electrical and/or magnetic noise. Nobody has measured the thermal response time of such resistors around 5 mK, mainly because it was obvious that it would take hours to reach the saturation value of the resistor. In this paper we describe an experiment where the time behaviour of a carbon resistor below 10 mK was compared with a pulsed NMR-thermometer, both coupled to a copperrod which was linked to the mixing chamber of a dilution cryostat (Fig. 1). A magnetometer was used to measure the static nuclear susceptibility of copper of 5N purity by means of a SQUID (Fig. 1). In the next section we briefly describe the construction of the resistance thermometer and the experimental setup. The second paragraph covers the way in which the temperature scale was established and in the last section, the experimental results are presented. The carbon thermometer was made from a Speer grade 1002 100 ~2 1/4 W resistor similar to that described in Ref. 2. The resistor was ground to 0.15 mm thickness, and glued by Stycast 1266 into a slit o f a cylindrically shaped piece of copper. The resistor was then electrically isolated by cigarette paper. It was thought that the epoxy resin would penetrate the carbon matrix avoiding microcracks. This ruggedly designed resistor had a reproducibility better than 1% above 20 mK over years and it was recently recalibrated against the NBS standard down to 25 mK. The thermal connection to the copper body of the mixing chamber was made via two screw-contacts which connected two Cu-rods of 7 mm diameter and 200 mm length. A 1 mm diameter silver wire of 85 mm length was squeezed to the rod as well as to the resistor by screws as shown in Fig. 1. The resistor was centred inside the niobium shield of the SQUID magnetometer by means of epoxy spacers. The shield was kept at a constant temperature of 100 mK. The open end of the Nb-tube was closed by a lead disc. The resistance was measured by the two wire technique using a bridge (IT-VS-4). The bridge had a time constant of about one rain for low voltage excitation. The authors are at the Zentralinstitut fur Tieftemperaturforschung D-8046 Garching, FRG. Paper received 1 September 1982.
The wires were fed through a low pass filter which was made from ferrite inductances and mica capacitors and had a cut-off frequency of 0.2 MHz. The filter was thermally anchored to the mixing chamber and surrounded by a 0.2 mm lead sheet. The wires leading down to the resistor were shielded by a Pb-Sn-capillary. In this way the system was shielded electromagnetically as a whole. In a field of 58 mT at the centre of the NMR-sample, the remaining field at the corner of the Nb-shield was 19 mT which is well below the critical field of the Pb-Sn-capillary. For the NMR-sample a bulk Tl-rod (4 mm diameter, 25 mm length) was soldered directly to a Cu-screw which established the contact to the cold-finger. The construction of the NMR-thermometer is described elsewhere. 3 Thallium was chosen because of its small Korringa-constant ofT1 -T = 6 ms K only, combined with the good thermal conductance of a pure metal. Thus, changes in the temperature are detectable five times faster than with a Pt-NMR-thermometer, commonly used at these temperatures, at a sensitivity comparable to that of NMR on Cu nuclei in the same field and volume. The temperature calibration of the resistor for several different runs is shown in Fig. 2. The measuring power at T < 10 mK was less than 4 fW. For temperatures above 25 mK the resistor was calibrated in another cryostat against CMN and the NBS fixed point standard. Curve (a) of Fig. 2 was obtained using a slightly different system 4 from that described in Fig. 1. The Tl-thermometer was self-calibrated according to its Korringa- constant. For temperatures below 20 mK curve (b) and (c) were obtained in a field of 3 mT and the earth-field, respectively. The static Cu-susceptibility thermometer was used for calibration. It was calibrated at temperatures above 25 mK with the help of the resistor itself, which is believed to be accurately measured at those temperatures. Indeed, the Cu-thermometer calibrated in this way gave, within the experimental error, the same result as the Tl-thermometer at our lowest temperatures of 4.4 mK. There are two remarkable points in Fig. 2. First, there is no or only a weak saturation effect. This is believed to be due to the use of the cold filters and electromagnetic shielding of the wires and the resistor. All measurements which were done with resistors of similar type have shown the onset of saturation to be between 15 and 10 mK, if filters located at 4 K are used in connection with an unshielded twisted pair wiring. In a different experiment we compared two resistors made from Matsushita ERG 18 47 ~. The resistors ground to 0.15 mm thickness were glued between 0.1 mm silver foils
0011-2275/83/002084-03 $03.00 © 1983 Butterworth & Co (Publishers) Ltd. 84
CRYOGENICS. FEBRUARY 1983
ratios decreased with increasing temperatures to about 4% at 25 mK and less than 0.5% above 80 mK, showing the influence of the protection even in a case where no saturation effect was visible at lust glance (see Fig. 2). Second, there are large discrepancies at low temperatures between the different measurements in Fig. 2 which certainly are not due to the different magnetic fields acting on the Speer resistor in the specific experiment (for curve (a) and (c) the same field was applied). Regardless of careful earthing, these variations were produced by different use and earthing of the various pieces of electrical equipment around the experiment. Thus, we have to conclude that thermometry with a carbon resistor at temperatures around 5 mK can only be done if nothing is changed after establishing the calibration. Preserving this fact, the calibration can be reproduced as we have done repeatedly for curve (a) of Fig. 2. For T < 8 inK, the time response of the c'arbon resistor and the T1 -sample after applying a heat-pulse of 7.5/aJ is shown in Fig. 3. The repetition rate of the NMR-pulses was 30 s. Due to eddy current heating, only a small temperature gradient was established between the mixing chamber and the sample (see for example arrow in Fig. 3). The simultaneously measured values of the resistor are also plotted. The time dependence is analyzed in Fig. 4.
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Fig. 1 E x p e r i m e n t a l setup: a -- b o t t o m plate o f m i x i n g c h a m b e r , b -- screw c o n t a c t , c -- C u - l i n k , d - A g - l i n k , e - heater (1 k ~ metal f i l m resistor), f -- Nb-shield, g -- N b T i - c o i l , h -- astatic pair o f t h e C u - t h e r m o m e t e r , i -- c a r b o n resistor, j -- Pb-Sn c a p i l l a r y , k - TI N M R - t h e r m o m e t e r and I - lead shield
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which were, in turn, directly screwed to the mixing chamber. The resistance at 4 K was 599 g2 and 504 f2, respectively. The resistivity ratio was 0.825 and 0.828 between room temperature and 4 K. The former was protected in a similar way to that described above, the other one was used without a shield and with a f'dter located at room temperature only. The resistance at 7.5 mK was measured with a 10 ~V excitation yielding 31 k~2 and 21 kg2, respectively. This difference of about 20% in the resistivity
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Temperature, rnK Fig. 2 Carbon resistor vs t e m p e r a t u r e f o r d i f f e r e n t c a l i b r a t i o n - r u n s a - T I - N M R t h e r m o m e t e r , b -- and c -- C u - s u s c e p t i b i l i t y t h e r m o m e t e r (see t e x t ) . Curve a t o c are f o r t h e Speer resistor; f o r c o m p a r i son t h e dashed lines d a n d e s h o w a shielded a n d u n s h i e l d e d Matsushita resistor, respectively. (the c o n t r i b u t i o n o f t h e leads are n o t subtracted)
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Fig. 3 T i m e response of the T I - N M R - and the resistance-thermometer after applying a 7.5/~J heat pulse. The equilibrium temperature was 4.4 mK
Fig. 4 compares in a semi-log plot the time-behaviour of the difference between the equilibrium inverse temperature, just before applying the heat pulse, and the inverse temperature at time t after the pulse. The points shown are deduced from the smoothed data of Fig. 3. The temperature of the Tl-sample is illustrated just before and after the heat pulse was 4.4 mK and 7.6 mK, respectively. For times up to 5 rain after the heat pulse is applied both thermometers show the same time-constants. The faster one of 1.1 rain could not be resolved by the resistor due to the slow electronics. It is assumed to be the equilibration time of the metal part of the experimental setup. The second timeconstant of 5.5 min arose from removing the heat by the dilution unit of cooling power of about 0.1/2W at 6 mK. For times longer than 5 rain where the temperature had again reached a value only 5% higher than the final temperature of the system (4.4 mK), the time constants of both thermometers start to deviate and the time constant of the resistor becomes as long as 56 min. Whether this slow temperature decrease, indicated by the carbon resistor, is due to an excess of specific heat or due to bad thermal conductance of the carbon material could not be clarified. Nevertheless, the time response of the resistor just after the heat pulse is surprisingly fast at low temperatures indicated (Fig. 3) by the small jump in the
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Fig. 4 The difference between equilibrium-and actual inverse temperatures vs the time. The time constants shown by the dashed lines correspond to the thermal equilibrium within the metal end between metal and mixture, respectively. The dashed dotted line gives the behaviour of the carbon resistor after reaching 95% of the final temperature of 4,4 mK
resistance it the Tl-thermometer is switched off. This effect cannot be explained by overheating of the resistor by the rf-field because the duty cycle for the NMR-pulses was only 1.7 x 10-s . It must be due to the temperature step between the He 3-He a mixture and the sinter which vanished, shown by the immediate response of the resistor if the additional heating by eddy currents induced by the rf-field is removed. From our measurements we made two conclusions: first, carbon resistors can be used as fast thermometers even at 5 mK, as long as no better temperature resolution is needed than about 5%, an accuracy which is also the limit in the temperature calibration at these temperatures; secondly, reliable thermometry with carbon resistors can be accomplished below 10 mK if, after calibration of the resistor, no changes whatsoever in equipment and surroundings are made. We would like to acknowledge the experimental help of Professor K. Andres, U. Angerer, Dr Ch. Probst, Dr E. Schuberth and Mrs. M. Tuomisaari. References
1 2 3 4
Frossati, G., Schuhmacher, G., Thoulouze, D. EPS spring meeting, Freudenstadt (1972) Sanchez, J., Benoit, A., Flouquet, J., Frossati, G. J Phys 35-C1 (1974) 23 Amend, B., Andres, K., Eska, G., Neumaier, K., Ptobst, Ch., Sehubetth, E. to be published Angerer,U., Eska, G. to be published
C R Y O G E N I C S . F E B R U A R Y 1983