Johnson Noise Thermometry at High Pressure
Ivan C. Getting (CIRES) and John L. Hall (JILA)
University of Colorado at Boulder
a COMPRES member institution
June 2004
A Johnson Noise Thermometer has been developed which makes it possible
to measure temperature accurately at high pressure. All effects of pressure,
deformation, chemical reaction, etc., which normally plague thermocouples,
are accounted for with a simple measurement of resistance each time
temperature is to be measured. Thermocouples and other temperature
sensors can be calibrated against this absolute thermometer in each specific
type of apparatus and cell design of interest. Such calibration studies need
be made only once for each experimental configuration with the results
applicable to subsequent runs.
This electronic thermometer requires a ~100 ohm probe with four leads
which also serve as two thermocouples. For each temperature determination
both the electric noise across the resistor and the resistance of the resistor are
measured.
Slight non-idealities in the electronic amplifiers and the imprecise definition
of the band width make it rather difficult to build a Johnson noise
thermometer with intrinsic calibration at the ~1 Kelvin level. The
thermometer we have built will be calibrated against NIST traceable
thermocouples at one atmosphere where the thermocouples are known to be
correct. It is anticipated that ITS-90 can be realized to 1 K by this
procedure.
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Figure 1. Layout of the Johnson noise thermometer. A set of low noise relays directs
signals from the resistive probe and other calibration resistors to the amplifiers, for noise
measurements, or to a commercial LCR meter, for resistance measurements. The
digitized noise signals, thermocouple voltages, and resistance values are directed to a
computer for analysis.
2
NC Normalized Output vs. RT
N.C.
Poly. (N.C.)
16
14
NC Normalized Output
12
10
8
6
4
2
0
0
50
100
150
200
250
Sensor RT (ohm*kelvins)
300
350
400
Thousands
Figure 2. Johnson noise thermometer output vs. the sensor RT product, where R = sensor
resistance, T = sensor temperature. Each point is actually 100 separate measurements. In
this room temperature study, the sensor resistance is changed in 200 ohm intervals
simulating the RT range intended with a nearly constant 100 ohm sensor over a wide
temperature range. With the intended sensor, room temperature corresponds to RT = ~50
thousand. RT = ~350 thousand corresponds to ~2000 K. Amplifier voltage noise is
eliminated from the data by taking the correlated output of two amplifier systems in
parallel. The data show a slight upward curvature due to current noise in the preamplifier.
3
NC Gain Factor vs. Time
0.990
0.985
NC Gain Factor
0.980
0.975
0.970
0.965
0.960
0.955
2/26/04
2/25/04
2/24/04
2/23/04
2/22/04
2/21/04
0.950
Date
Figure 3. Amplifier gain vs. time. The amplifier gain and zero can be checked for each
temperature measurement. The gain has recently been made very stable. The drift rate in
these data is ~0.01 % per day. This stability permits us to make temperature
measurements over several days without checking the gain.
4
Raw Zero Outputs vs. Time
N.C.
A.C.
Linear (A.C.)
Linear (N.C.)
0.050
0.040
Output
0.030
0.020
0.010
0.000
2/26/04
2/25/04
2/24/04
2/23/04
2/22/04
2/21/04
-0.010
Date
Figure 4. Amplifier zero vs. time. The amplifier zero is now also extremely stable. The
drift rate corresponds to 0.003 % of full scale per day. Thus temperature measurements
can be made for days without checking the amplifier zero as well. With these recent
improvements in stability, each temperature measurement can now be made in about 30
seconds, 15 seconds for the measurements and a similar time for data reduction.
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N.C. 4
std dev +
tol tol +
N.C. 4 ave
std dev Poly. (N.C. 4 ave)
N.C. Norm. Output Fit Residuals vs. RT
0.100
0.080
0.060
Output Residuals
0.040
0.020
0.000
-0.020
-0.040
-0.060
-0.080
-0.100
0
50
100
150
200
250
Sensor RT (ohm*kelvins)
300
350
400
Thousands
Figure 5. Thermometer output fit residuals. The output data shown in Figure 2 are fit
with a 4th degree polynomial. At each RT value 100 determinations of the Johnson noise
are made using one million measurements of each of two amplifier outputs. Three such
determinations are shown at each value of RT, blue squares. The plot above represents
over four billion samples of Johnson noise. The standard deviation of each group of 100
determinations is shown by the orange squares. The original design Type A standard
uncertainty is shown by the dashed black lines. The instrument performs as designed.
The Type A relative standard uncertainty of a single measurement, sampling over a 10 s
period, is ~0.15 % which corresponds to ~1.5 K at 1000 K. This precision can be
improved by making multiple measurement. The red diamonds show the average of each
set of 100 measurements. The standard deviation of these means is ~0.015 % or ~0.15 K
at 1000 K.
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NC Relative Std. Dev. of Fit Residuals vs. RT
0.0050
Ave. Z & G
meas. Z & G
Relative Std. Dev. of Residuals
0.0045
0.0040
0.0035
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
0
50
100
150
200
250
Sensor RT (ohm*kelvins)
300
350
400
Thousands
Figure 6. Relative standard deviation of the output fit residuals. This plot shows
explicitly the precision of the temperature determinations. Measurement of the amplifier
gain and zero contain scatter as do the temperature determinations. The precision with
gain and zero measurements is shown in the dashed line. With the newly won stability
these two parameters no longer need to be determined for each measurement. The heavy
blue lines shows the ~0.15 % precision over the entire measurement range without gain
and zero measurements. Having to make gain and zero checks for each measurement
would increase uncertainty by a factor of 1.7 and the measurement time by a factor of 3.
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Planned Testing:
The Johnson Noise Thermometer will be migrated to a large volume multianvil device during the winter of 2004/2005. A collaborative program is
under development with Yanbin Wang and Mark Rivers of GSECARS at
APS, Argonne National Laboratory. We plan to implement the thermometer
in a multi-anvil cell in my laboratory in Colorado where we know the
electrical ambient is sufficiently quiet and then to migrate the instrument to
GSECARS where is will be available to the high pressure community.
Uncertainty in temperature measurements made with this thermometer
decreases as the number of measurements is increased. It operates at a
resolution of ~1.5 K at 1000 K for a single measurement over 10 s. It is thus
practical to achieve fractional Kelvin resolution in a few minutes. This is
better than the temperature stability in typical large volume high pressure
devices. This instrument is capable of resolution higher than the definition
of the practical temperature scale, ITS-90, above ~1000 K.
The application of Johnson noise thermometry to specific solid medium cells
and apparatus type stands to solve the problem of temperature measurement
at high pressure, a problem which has been with us for 100 years.
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