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A very high resolution thermometer for use below 7 K
Physica 107B (1981) 331-332 North-Holland Publishing Company
FD 3
A VERY NIGH RESOLUTION THERMOMETER FOR USE BELOW 7 K
*
J. A. Lipa, B. C. Leslie Physics Department,
+
and T. C. Wallstrom
Stanford University,
Stanford, CA
94305
We have developed a paramagnetic salt thermometer with a resolution A T / T z 3 x 1 0 -I0 at 4 K. We measure the temperature dependent magnetization of a paramagnetic salt in a fixed magnetic field by means of a SQUID magnetometer and a superconducting plck-up circuit. The device shows excellent operating characteristics over a temperature range of from 7 K to 2 K, the maximum that has been used so far. The temperature resolution is within a factor of three of that predicted from detector noise measurements.
INTRODUCTION One of the limiting factors in our ability to study the thermodynamic phenomena associated with cooperative phase transitions is the noise in temperature measurement. For the % - ~ a n s i t i o n of liquid helium, thls at present appears to be the only limitation. We have developed a thermometric device for application in this region which has a much lower noise figure than previous devices, and simultaneously avoids the dissipation of significant heat in the system due to the measuring process. The operating principle of the thermometer is the d.c. measurement of the temperature dependent magnetization of a parametric salt in a constant external field. The device is similar to one reported prevlously I for use in the milli-Kelvin temperature range, but operates in much higher magnetic fields, is better shielded, and does not appear to suffer from the same noise limitations. These differences have allowed us to achieve about three orders of magnitude higher resolution than has been previously reported for a paramagnetic salt thermometer, allowing us to resolve less than 10 -9 K at the l-point. The thermometer was also mechanized in the less sensitive a.c. mode to evaluate its null stability. Both outputs gave agreement to the limit of resolution of the a.c. system.
After crystallization the salt was ground into cylindrical form and a ten turn coil of .005 cm diameter niobium wire was wound directly on its surface. This coil had a self-inductance of about one micro-henry and formed the lower half of a pair of astatic windings. The leads from the windings were tightly twisted and passed through a small superconducting tube to a SQUID magnetometer located in the helium bath. The astatic coils were centrally located inside a niobium tube with a length-to-diameter ratio of 18, which provided a shielding factor against external noise in excess of 107 . Fields of up to 500 gauss were trapped in the niobium tube using a solenoid located in the helium bath. The complete assembly was suspended by low heat leak stainless steel supports inside a cryopumped vacuum chamber. All supports and electrical connections were thermally anchored at their mid-points to an actively controlled isolation stage maintained a few millidegrees above the bath temperature. The control loop for this stage used a conventional carbon thermometer/
~-SQUID iNPUT COIL
A STAT I C
THERMOMETER
~~
PICK-UP LOOP
The thermometer consists of crystals of Manganous Ammonium Sulphate tightly coupled to a superconducting pick-up coil connected to a SQUID magnetometer, and located within a long niobium tube which simultaneously maintains a constant applied field and shields effectively against external fluctuations. A cross-sectlon of the thermometer is shown in Figure i. The I00 mg salt plll was crystallized from aqueous solution onto a bundle of enameled copper wires to allow thermal contact to an experiment. The thermal relaxation time of the thermometer was less than 2 sec. at 2 K.
@ North-Holland PublishingCompany
~ j
SALT PILL
NIOBIUM FLUX TUBE
THERMAL~ CONTACT MATERIAL
Figure I:
0378.4363/81/0000-0000/$02.50
~
Schematic view of thermometer
331
332
lock-in amplifier detection system. In operation a magnetic field H, is trapped in the niobium tube and the temperature dependence of the current flowing in the sensing loop is monitored. The extra flux ~ , coupled to the s SQUID due to the presence of the salt can be written as ~s = x N A H x where X is the salt susceptibility, N and A are the number of turns and cross-sectional area of the pick-up loop, and x is a coupling constant less than unity. Replacing X with C/T where C is the Curie constant, we easily obtain d~ s -o where ~ is the quantum of magnetic flux, and o for our case the constant scale factor is as low as 1.9 x 10 -4 gauss/K. Since commercially available magnetometers 2 have a stability of the order of 10 -4 ~o over a number of hours, it can be seen that the thermometer has a very high potential resolution, approaching 2 x 10 -10 K at the h-point of helium, for fields of up to 5 0 0 gauss. dT
=
const.
I
T2 -- • H
The use of d.c. magnetization measurements to determine relative temperature has a great sdvanrage over other common thermometric devices: low dissipation. For example, conventional carbon thermometry inevitably leads to heat inputs of the order 10 -8 W when micro-Kelvin resolution is obtained. In contrast, the largest source of intrinsic dissipation in the d.c. thermometer is less than 10 -17 W, due to losses in the salt from the 19 MHz drive signal to the SQUID. This is completely negligible in most experimental situations above i K. OBSERVATIONS Initial observations were made in the test chamber described above with the isolation stage thermally controlled to about 3 x 10 -6 K. The time constant for heat transfer between the thermometer and the isolation stage was about 30 minutes. Thus short term fluctuations of the temperature of this stage due to noise in the detection system were well filtered, but long peridd fluctuations could reach the test thermometer. Under these conditions it was possible to increase the gain of the magnetometer for periods of up to 5 minutes or so and observe the output as the thermometer passed through a temperature extremum. An example of such an output is shown in Figure 2. Noise measurements at such times were about a factor of three higher than the magnetometer noise observed with a shorted input. A 30% increase in noise is to be expected in the operating configuration due to the presence of a low pass filtering resistor shunting the input terminals. Measurements in the background field of 2 x 10 -2 gauss also show an excess noise close to but less than that observed in operation. With a trapped field of 500 gauss we obtained a sensitivity of 1.2 x 1 0 -9 K at 4 K using a i Hz bandwidth.
0
Figure 2:
lO 8 DEG
TEMP: 4K FIELD : 500 G
I I
I 2 TIME (MIN.)
I 3
4
High resolution noise measurements
Recently additional data has been obtained with a sample of 4He added to the system and with the thermometer mechanized simultaneously in both the d.c. and a.c. modes. In the latter case I an additional coil surrounding the pick-up loop is driven with an 80 Hz signal, while a phase-shifted component of adjustable amplitude is fed to a mutual inductance coupled to the pick-up circuit. The a.c. null stability is determined by geometric factors in the drive coil and mutual coil sections, and by the room temperature nulling electronics, but is completely independent of trapped field and SQUID drift. To date we have demonstrated that both outputs agree over periods of i to 3 hrs. to a resolution of about 5 x l 0 -7 K at 2 K, which is the limit of resolution of the a.c. system. Observations of the repeatability of the location of the h-transition as determined by heat capacity measurements indicates a null stability of 10 -7 K or better over periods of up to i hr. Tests are continuing in this area. In conclusion, we have demonstrated a temperature sensitivity of at least 3 x l 0 -I0 in AT/T in a device which has a very low power dissipation and can be used over a wide operating range. Also, the device can easily be calibrated against secondary thermometers. These properties make it ideally suited for many types of thermal measurement over its operating range, and in particular for very high resolution studies of phase transitions. This research was supported by NASA Contract No. 955057. FOOTNOTES *
Present address: Hewlett-Packard Company, Palo Alto, Ca. 94305 + Present address: Graduate College, Box 350, Princeton, New Jersey i. R.P. Giffard, R.A. Webb and J.C. Wheatley, J. Low Temp. Phys. 6, 533 (1972) 2. SQUID S y s t e m s C a t a l o g , SHE Corporation, San Diego, Ca., March, 1979.
FD 3
A VERY NIGH RESOLUTION THERMOMETER FOR USE BELOW 7 K
*
J. A. Lipa, B. C. Leslie Physics Department,
+
and T. C. Wallstrom
Stanford University,
Stanford, CA
94305
We have developed a paramagnetic salt thermometer with a resolution A T / T z 3 x 1 0 -I0 at 4 K. We measure the temperature dependent magnetization of a paramagnetic salt in a fixed magnetic field by means of a SQUID magnetometer and a superconducting plck-up circuit. The device shows excellent operating characteristics over a temperature range of from 7 K to 2 K, the maximum that has been used so far. The temperature resolution is within a factor of three of that predicted from detector noise measurements.
INTRODUCTION One of the limiting factors in our ability to study the thermodynamic phenomena associated with cooperative phase transitions is the noise in temperature measurement. For the % - ~ a n s i t i o n of liquid helium, thls at present appears to be the only limitation. We have developed a thermometric device for application in this region which has a much lower noise figure than previous devices, and simultaneously avoids the dissipation of significant heat in the system due to the measuring process. The operating principle of the thermometer is the d.c. measurement of the temperature dependent magnetization of a parametric salt in a constant external field. The device is similar to one reported prevlously I for use in the milli-Kelvin temperature range, but operates in much higher magnetic fields, is better shielded, and does not appear to suffer from the same noise limitations. These differences have allowed us to achieve about three orders of magnitude higher resolution than has been previously reported for a paramagnetic salt thermometer, allowing us to resolve less than 10 -9 K at the l-point. The thermometer was also mechanized in the less sensitive a.c. mode to evaluate its null stability. Both outputs gave agreement to the limit of resolution of the a.c. system.
After crystallization the salt was ground into cylindrical form and a ten turn coil of .005 cm diameter niobium wire was wound directly on its surface. This coil had a self-inductance of about one micro-henry and formed the lower half of a pair of astatic windings. The leads from the windings were tightly twisted and passed through a small superconducting tube to a SQUID magnetometer located in the helium bath. The astatic coils were centrally located inside a niobium tube with a length-to-diameter ratio of 18, which provided a shielding factor against external noise in excess of 107 . Fields of up to 500 gauss were trapped in the niobium tube using a solenoid located in the helium bath. The complete assembly was suspended by low heat leak stainless steel supports inside a cryopumped vacuum chamber. All supports and electrical connections were thermally anchored at their mid-points to an actively controlled isolation stage maintained a few millidegrees above the bath temperature. The control loop for this stage used a conventional carbon thermometer/
~-SQUID iNPUT COIL
A STAT I C
THERMOMETER
~~
PICK-UP LOOP
The thermometer consists of crystals of Manganous Ammonium Sulphate tightly coupled to a superconducting pick-up coil connected to a SQUID magnetometer, and located within a long niobium tube which simultaneously maintains a constant applied field and shields effectively against external fluctuations. A cross-sectlon of the thermometer is shown in Figure i. The I00 mg salt plll was crystallized from aqueous solution onto a bundle of enameled copper wires to allow thermal contact to an experiment. The thermal relaxation time of the thermometer was less than 2 sec. at 2 K.
@ North-Holland PublishingCompany
~ j
SALT PILL
NIOBIUM FLUX TUBE
THERMAL~ CONTACT MATERIAL
Figure I:
0378.4363/81/0000-0000/$02.50
~
Schematic view of thermometer
331
332
lock-in amplifier detection system. In operation a magnetic field H, is trapped in the niobium tube and the temperature dependence of the current flowing in the sensing loop is monitored. The extra flux ~ , coupled to the s SQUID due to the presence of the salt can be written as ~s = x N A H x where X is the salt susceptibility, N and A are the number of turns and cross-sectional area of the pick-up loop, and x is a coupling constant less than unity. Replacing X with C/T where C is the Curie constant, we easily obtain d~ s -o where ~ is the quantum of magnetic flux, and o for our case the constant scale factor is as low as 1.9 x 10 -4 gauss/K. Since commercially available magnetometers 2 have a stability of the order of 10 -4 ~o over a number of hours, it can be seen that the thermometer has a very high potential resolution, approaching 2 x 10 -10 K at the h-point of helium, for fields of up to 5 0 0 gauss. dT
=
const.
I
T2 -- • H
The use of d.c. magnetization measurements to determine relative temperature has a great sdvanrage over other common thermometric devices: low dissipation. For example, conventional carbon thermometry inevitably leads to heat inputs of the order 10 -8 W when micro-Kelvin resolution is obtained. In contrast, the largest source of intrinsic dissipation in the d.c. thermometer is less than 10 -17 W, due to losses in the salt from the 19 MHz drive signal to the SQUID. This is completely negligible in most experimental situations above i K. OBSERVATIONS Initial observations were made in the test chamber described above with the isolation stage thermally controlled to about 3 x 10 -6 K. The time constant for heat transfer between the thermometer and the isolation stage was about 30 minutes. Thus short term fluctuations of the temperature of this stage due to noise in the detection system were well filtered, but long peridd fluctuations could reach the test thermometer. Under these conditions it was possible to increase the gain of the magnetometer for periods of up to 5 minutes or so and observe the output as the thermometer passed through a temperature extremum. An example of such an output is shown in Figure 2. Noise measurements at such times were about a factor of three higher than the magnetometer noise observed with a shorted input. A 30% increase in noise is to be expected in the operating configuration due to the presence of a low pass filtering resistor shunting the input terminals. Measurements in the background field of 2 x 10 -2 gauss also show an excess noise close to but less than that observed in operation. With a trapped field of 500 gauss we obtained a sensitivity of 1.2 x 1 0 -9 K at 4 K using a i Hz bandwidth.
0
Figure 2:
lO 8 DEG
TEMP: 4K FIELD : 500 G
I I
I 2 TIME (MIN.)
I 3
4
High resolution noise measurements
Recently additional data has been obtained with a sample of 4He added to the system and with the thermometer mechanized simultaneously in both the d.c. and a.c. modes. In the latter case I an additional coil surrounding the pick-up loop is driven with an 80 Hz signal, while a phase-shifted component of adjustable amplitude is fed to a mutual inductance coupled to the pick-up circuit. The a.c. null stability is determined by geometric factors in the drive coil and mutual coil sections, and by the room temperature nulling electronics, but is completely independent of trapped field and SQUID drift. To date we have demonstrated that both outputs agree over periods of i to 3 hrs. to a resolution of about 5 x l 0 -7 K at 2 K, which is the limit of resolution of the a.c. system. Observations of the repeatability of the location of the h-transition as determined by heat capacity measurements indicates a null stability of 10 -7 K or better over periods of up to i hr. Tests are continuing in this area. In conclusion, we have demonstrated a temperature sensitivity of at least 3 x l 0 -I0 in AT/T in a device which has a very low power dissipation and can be used over a wide operating range. Also, the device can easily be calibrated against secondary thermometers. These properties make it ideally suited for many types of thermal measurement over its operating range, and in particular for very high resolution studies of phase transitions. This research was supported by NASA Contract No. 955057. FOOTNOTES *
Present address: Hewlett-Packard Company, Palo Alto, Ca. 94305 + Present address: Graduate College, Box 350, Princeton, New Jersey i. R.P. Giffard, R.A. Webb and J.C. Wheatley, J. Low Temp. Phys. 6, 533 (1972) 2. SQUID S y s t e m s C a t a l o g , SHE Corporation, San Diego, Ca., March, 1979.