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A method for evaluation of the inhomogeneity of thermoelements

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A method for evaluation of the inhomogeneity of thermoelements
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2009 Meas. Sci. Technol. 20 055102
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IOP PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 20 (2009) 055102 (9pp)
doi:10.1088/0957-0233/20/5/055102
A method for evaluation of the
inhomogeneity of thermoelements
Y A Abdelaziz1 and F Edler2
1
2
National Institute for Standards, Tersa St, Elharam, 12211 Giza, Egypt
Physikalisch-Technische Bundesanstalt, Abbestraße 2-12, 10587 Berlin, Germany
E-mail: [email protected] and [email protected]
Received 12 December 2008, in final form 11 February 2009
Published 27 March 2009
Online at stacks.iop.org/MST/20/055102
Abstract
Thermoelectric inhomogeneity is the spatial variation of the Seebeck coefficient along a
thermoelement. It is often considered to be the largest contribution of an uncertainty budget in
thermocouple calibration. In this work, investigations of inhomogeneities were performed on
single thermoelements, using a heater with short movable heating zones (two-gradient
method). We chose platinum wires which are commonly used in noble metal thermocouples
and copper wires which are available in good homogeneity and which are commonly used in
base metal thermocouples. The results of different investigations of the thermoelements are
presented.
Keywords: thermoelements, thermoelectric inhomogeneity, Seebeck coefficient.
In addition to the temperature difference, the measured
emf is caused by the Seebeck effect only, and therefore,
the Seebeck inhomogeneity is of practical interest in
thermometry. The Seebeck inhomogeneity is defined in [1] by
equation (2):
1. Introduction
Thermocouples are the most widely used electrical sensors
in temperature measurements. They are characterized by
a simple construction. Two dissimilar wires electrically
insulated are joined at one end. A temperature difference
between this common junction (measuring junction) and the
open end (reference junction) causes a potential difference
which can be measured between the two dissimilar wires
at their open ends. This thermoelectric voltage is called
electromotive force (emf) and occurs in any conductor which
is located in a nonuniform temperature region. It can be
described by equation (1):
dE = S(T ) · dT ,
δS(T , x) = S(T , x) − SN (T ),
expressing the abnormal spatial variation of the Seebeck
coefficient along a thermoelement relative to a normal
reference function, SN (T ).
Inhomogeneity effects are measured by exposing
the thermocouple or a single thermoelement to defined
temperature gradients. Different methods can be applied.
The common method to investigate assembled thermocouples
is to submerge them slowly into a fixed-point cell during
melting or freezing or into a liquid bath maintaining the
temperatures of the measuring and reference junction constant
while monitoring the output emf. Thus, any deviation
of the measured emf is an indication of inhomogeneities.
Another method, the two-gradient method, can also be used to
investigate single thermoelements before they are assembled.
Most of the previous researches studied thermocouple
inhomogeneity at assembled thermocouples [2–8]. In this
work, the inhomogeneity tests were performed on single
thermoelements using short movable heating zones with two
temperature gradients.
(1)
where dE is the differential voltage generated by sections of the
wires in a temperature gradient, S(T ) is the Seebeck coefficient
and T is the temperature. As long as the Seebeck coefficient,
S(T ), is a function of only temperature and not of the position
x along the wires, dE depends on the end temperatures only.
Such wires are said to be homogeneous. Often most of the
thermoelements used are inhomogeneous because of thermal
and mechanical stresses and environmental influences. This
results in localized changes in the Seebeck coefficient and can
be considered as the most important uncertainty contribution
in measuring temperatures by using thermocouples.
0957-0233/09/055102+09$30.00
(2)
1
© 2009 IOP Publishing Ltd Printed in the UK
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
unchanged. The left-hand side of the heater completely covers
an inhomogeneous section and the right-hand side covers only
this inhomogeneous section between 217 ◦ C and TC (about
200 ◦ C). Therefore, the output emf remains constant.
2. Two-gradient method
The two-gradient method in which a movable heater is
used is a simple and precise method to assess qualitatively
and quantitatively inhomogeneities in thermoelements. A
movable heater or furnace with known temperature gradients
is moved along the thermoelement (or thermocouple) under
investigation with a known and uniform velocity. In this way
the thermoelement is exposed to two temperature gradients,
one on each side of the heated zone. Both temperature
gradients are reversed left to right. Therefore, the two
emfs generated at the positions of the gradients will be of
opposite sign but of the same magnitude as long as there are
no inhomogeneities in the thermoelement. In this case, the
resulting emf measured at the two ends of the thermoelement
will be zero. On the other hand, a spatial variation of the
Seebeck coefficient caused by inhomogeneities will result in
an emf that deviates from zero if such inhomogeneous sections
of the thermoelement are exposed to the temperature gradients.
This emf measured using the two-gradient method will not
directly give a quantitative indication of the inhomogeneity
as obtained using a one-gradient measurement. With the twogradient method, the resulting emf as a function of the position
of the heating zone is actually a measure of the derivative
of the corresponding emf measured by using the onegradient method [9]. Because of the compensating effect of
the two oppositely directed temperature gradients, a direct
reading of the emf differences would result in a quantitative
underestimation of inhomogeneity-caused uncertainties.
Figure 1 shows a model of scanning a thermoelement by
using a movable heater (top) and a corresponding experimental
scanning curve of a copper wire (bottom). In this case, the
maximum temperature of the heater is higher than a critical
temperature TC , at which inhomogeneities will be induced.
Part (a) of figure 1 shows the output emf at different positions
of the heater. Part (b) shows the thermoelement containing
a homogeneous section ‘white’, an inhomogeneous section
induced by the movable heater ‘black’ and a third section
which becomes inhomogeneous by the movable heater during
scanning. The temperature profiles of the movable heater at
different positions (1, 2, 3 and 4) are shown in part (c) of
figure 1. The resultant emf can be described as follows.
3. Experimental set-up
Figure 2 shows the schematic diagram of the experimental
set-up. Both ends of the investigated thermoelement were
maintained at the same temperature in an electrically shielded
box. Therefore, any deviation of the measured emf from
zero is an indication of inhomogeneity when the short, welldefined heating zone is moved along the wire. The heater
was moved with a constant velocity of 2 mm min−1 . The
measured emfs using a nanovoltmeter Keithley model 2182
were recorded, displayed and stored automatically using a
R
program. The measurement uncertainty of the
LabVIEW
emfs was estimated to a value of about ±0.1 μV, mainly
caused by the short-time stability of the nanovoltmeter during
the scans. The stability of the heater temperature can
be neglected because of the applied two-gradient method
(difference measurement). Environmental influences were
minimized by using the shielded terminal box and would
influence both junctions equally. Therefore, almost no
parasitic emfs have to be considered.
The temperature profiles of the movable heater used
to perform the inhomogeneity tests were measured using a
sheathed type J thermocouple. The thermocouple was inserted
into an alumina tube and maintained at a fixed position. A
second sheathed thermocouple identical to it in geometry was
inserted into the alumina tube from the other side to adjust
a symmetrical condition concerning heat flux effects along
the alumina tube during the measurement of the temperature
profiles. The heater was moved along the type J thermocouple.
For example, two different temperature profiles, but of the
same maximum temperature (about 227 ◦ C), are shown in
figure 3. The profile with the wider heating zone was achieved
by inserting a small aluminum tube into the heater coil. The
width of the heater is dg .
4. Investigation of a copper wire
Position 1. The inhomogeneous part of the thermoelement
induced by the heater itself is exposed to two symmetrical
temperature gradients on both sides of the movable heater. The
output emf is zero because the temperature gradients generate
two emfs of the same amount but of opposite signs.
A pure copper wire (99.999% purity, 0.5 mm diameter) of
high homogeneity was investigated. It was cleaned using pure
ethanol and distilled water to remove the layer of brown-black
copper oxide and surface traces. For the scanning process, the
copper wire was connected to the voltmeter directly. So, the
resulting emf of the nearly homogenous wire should be zero
and any deviation would indicate inhomogeneities, when the
gradients of the heating zone pass inhomogeneous sections
of the wire. In the next step, a well-directed inhomogeneity
induced in the copper wire was used to study and to quantify
local inhomogeneity effects. For this purpose, a small segment
of the copper wire was exposed briefly to a temperature of
about 350 ◦ C. In figure 4, the scanning results at 200 ◦ C before
and after inducing this inhomogeneity are presented. The
small emf changes along the copper wire before inducing the
inhomogeneity are within about ±0.1 μV, which indicates its
Positions 1 to 2. During the movement of the heater from
positions 1 to 2, the left-hand side of the temperature
profile of the movable heater covers an increasing range of
the inhomogeneous section of the thermoelement, but the
right-hand side covers only the inhomogeneous section of
the thermoelement which becomes inhomogeneous during
scanning, and it is exposed to a temperature higher than the
critical temperature TC . Therefore, during scanning the output
emf increases uniformly until the heater reaches position 2.
Positions 2 to 3 and 4. A further movement of the heater does
not change the output emf because the geometrical condition is
2
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
0.5
0.4
emf, μV
0.3
0.2
0.1
0
-0.1
-0.2
0
50
100
150
200
250
300
distance, mm
Figure 1. Scanning of a thermoelement using a movable heater.
Figure 2. Schematic diagram of the experimental set-up.
of the maximum of the inhomogeneity which corresponds to
the contact point of the copper wire with hot temperature.
Furthermore, the difference between the two emf curves along
the whole scanned length of the copper wire indicates that
not only a small localized inhomogeneity in the middle of the
copper wire was induced by the temperature of 350 ◦ C but also
extended parts of the thermoelement were influenced, which
resulted in abnormal variations of the Seebeck coefficient over
good homogeneity. The constant deviation of the measured
emf from zero (1.0–1.2 μV) was caused by the offset emf of the
voltmeter. The measured emfs of the manipulated wire differ
completely from that of the homogeneous one. A symmetrical
sine waveform was measured, with maximum and minimum
deviations from the original emf curve of about ±0.7 μV.
The intersection point between both the measurements before
and after introducing the inhomogeneity indicates the position
3
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
14000
small heating zone
wide heating zone
12000
emf, μV
10000
8000
6000
4000
2000
0
0
20
40
60
80
100
distance, mm
120
140
160
180
Figure 3. Temperature profiles of the movable heater at about 227 ◦ C.
2
before inducing inhomogeneity
1.8
after inducing inhomogeneity
1.6
emf, μV
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
20
40
60
80
100
distance, mm
120
140
160
180
Figure 4. Inhomogeneity scan at 200 ◦ C of the pure copper wire before and after inducing inhomogeneity.
12000
10000
emf, μV
8000
6000
4000
2000
0
0
1
2
3
4
5
6
7
8
distance, mm
9
10
11
12
13
14
Figure 5. Temperature profile of the movable heater at 200 ◦ C.
way, the compensation effect of the two oppositely directed
temperature gradients is considered. In general, at the position
xm of the heater, the measured emf corresponds to the emf
difference between positions x1 and x2 (figure 5). If the
emf at position x1 is known, the emf of position x2 can be
a range between 40 mm and 160 mm of the wire. Figure 5
shows the corresponding temperature profile of the movable
heater at 200 ◦ C.
For the quantitative estimation of the copper wire
inhomogeneity, the method proposed in [9] was used. In this
4
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
1.8
measured data
calculated data
1.6
emf, μV
1.4
1.2
1
0.8
0.6
0.4
0
20
40
60
80
100
120
140
160
180
distance, mm
Figure 6. Comparison of the measured and calculated emfs of the homogeneous copper wire.
2.8
measured data
calculated data
2.4
emf, μV
2
1.6
1.2
0.8
0.4
0
0
20
40
60
80
100
120
140
160
180
distance, mm
Figure 7. Measured and calculated emfs of the copper wire containing the induced inhomogeneity at 200 ◦ C.
maximum emf difference of about 1.4 μV obtained from the
directly measured emf curve.
calculated easily. If we assume that the first part of the
thermoelement is homogeneous (see figure 4), the starting emf
for the calculation at x1 is zero. The distance dg between the
two temperature gradients must be known. For applying this
method, the incremental steps to calculate the absolute emf at
each position were 1 mm. Figure 6 shows the measured and
the calculated emfs of the nearly homogenous copper wire at
a heater temperature of 200 ◦ C, before the inhomogeneity was
induced. The calculated emfs were corrected by the offset emf
of 1.1 μV.
The measured and the calculated emfs of the copper wire
containing the induced inhomogeneity are shown in figure 7.
Both emf curves can be used as a qualitative evaluation of the
inhomogeneity but the calculated emf curve can also be used
as a quantitative estimation of the inhomogeneity. The peak of
the calculated curve at the position of about 90 mm from the
starting point of scanning corresponds to the inflection point
of the measured emf curve which indicates the position of the
induced inhomogeneity. The maximum emf difference of the
calculated curve as a measure of the inhomogeneity amounts
to about 1.8 μV, which is by about 0.4 μV higher than the
5. Investigation of a platinum wire
A new platinum wire was heated electrically at 1300 ◦ C for
5 h, and then assembled in a capillary tube and annealed
in a horizontal furnace at 1100 ◦ C for about 4 h to reach
a homogeneous state. Figure 8 shows the measured emf
curves of the Pt wire using the movable heater with different
temperature profiles (figure 3) at about 227 ◦ C. The measured
emf curves offer deviations from a constant emf value
indicating the presence of inhomogeneities in the platinum
wires in the order of about ±0.25 μV (heater with small
zone) and of about ±0.4 μV (heater with wide zone). These
differences indicate the influence of different heater profiles
which have to be considered for the quantitative estimation
of inhomogeneities by applying the method proposed in [9].
The lower emf changes using the heater with a smaller heating
zone are a result of the more distinctive compensating effect
caused by the two narrower temperature gradients of the
heater.
5
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
0.6
wide heating zone
small heating zone
0.4
0.2
emf, μV
0
-0.2
-0.4
-0.6
-0.8
-1
0
100
200
300
distance, mm
400
500
600
Figure 8. Scanned platinum wire using the movable heater with wide and small heating zones before inducing an inhomogeneity at 227 ◦ C.
0.3
before inducing inhomogeneity
after inducing inhomogeneity
0.2
0.1
emf, μV
0
-0.1
-0.2
-0.3
-0.4
-0.5
0
100
200
300
distance, mm
400
500
600
Figure 9. Scanned platinum wire using the movable heater with the small heating zone at 227 ◦ C before and after inducing inhomogeneity.
0.6
before inducing inhomogeneity
after inducing inhomogeneity
0.4
0.2
emf, μV
0
-0.2
-0.4
-0.6
-0.8
-1
0
100
200
300
distance, mm
400
500
600
Figure 10. Scanned platinum wire using the movable heater with the wide heating zone at 227 ◦ C before and after inducing inhomogeneity.
In the next step, an extra inhomogeneity was induced in the
platinum wire by cutting it at a distance of about 290 mm from
the starting point of scanning, and welding both ends together.
Figures 9 and 10 show the scanning results of the platinum
6
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
0.6
wide heating zone
small heating zone
0.4
0.2
emf, μV
0
-0.2
-0.4
-0.6
-0.8
-1
0
100
200
300
distance, mm
400
500
600
Figure 11. Scanned platinum wire using the movable heater with wide and small heating zones after inducing inhomogeneity at 227 ◦ C.
0.8
measured data
calculated data
0.6
emf, μV
0.4
0.2
0
-0.2
-0.4
-0.6
0
100
200
300
distance, mm
400
500
600
Figure 12. Measured and calculated data of the scanned platinum wire at 227 ◦ C using the movable heater with the small zone.
one [9] by using the small heating zone. The same position of
the inhomogeneity (peak in the recalculated curve, inflection
point in the measured curve) was found at about 290 mm
from the starting point of the scanning. Also in figure 13,
the position of the inhomogeneity in both curves is the
same. Furthermore, comparing figures 12 and 13, independent
of the different geometries of the temperature profiles,
the same position of the inhomogeneity could be found.
Simultaneously, the maximum emf differences in both
calculated emf curves were found to have about the same value
of (1.0 ± 0.1) μV. It should be mentioned that the maximum
emf differences in the directly measured curves differ from
each other considerably, 0.6 μV and 1.0 μV for the heater
with the small and wide zones, respectively.
The results of several scanning runs of the inhomogeneous
platinum wire at 227 ◦ C and 410 ◦ C (two runs at each
temperature) are presented in figures 14(a) and (b) to prove the
reproducibility of the homogeneity tests. Here, the movable
heater with a small heating zone was used. Figure 14(a) shows
the measured emfs and figure 14(b) shows the calculated data
according to Holmsten.
wire before and after inducing the defined inhomogeneity by
using the movable heater with a small heating zone (figure 9)
and the one with a wide heating zone (figure 10) at about
227 ◦ C. A large additional emf having a sine waveform was
observed at the position of the induced inhomogeneity (about
290 mm from the starting point).
Figure 11 compares the measured emf curves of the
inhomogeneous platinum wire by using two different heater
profiles (small and wide heating zones) at a temperature of
227 ◦ C. In both cases, the intersection of the emf curves
with the x-axis (offset of about −0.2 μV) clearly indicates
the position of the localized inhomogeneity at about 290 mm
from the starting point. The maximum emf difference found
using the small heating zone was about 0.6 μV; the maximum
emf difference found using the wider heating zone amounts
to about 1.0 μV. This is, considered relatively, the same value
of the difference found in the former ‘homogeneous’ platinum
wire (figure 8) by using the two different heating zones.
The results of the qualitative assessment and the
quantitative estimation of the induced inhomogeneity of the
platinum wire are presented in figures 12 and 13. Figure 12
shows the measured emf curve compared with the recalculated
7
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
0.8
measured data
calculated data
0.6
0.4
emf, μV
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
100
200
300
distance, mm
400
500
600
Figure 13. Measured and calculated data of the scanned platinum wire at 227 ◦ C using the movable heater with the wide zone.
1
at
at
at
at
emf, μV
0.5
227°C
227°C
410°C
410°C
0
-0.5
-1
-1.5
0
100
200
300
400
500
600
distance, mm
(a)
2
at
at
at
at
1.5
227°C
227°C
410°C
410°C
emf, μV
1
0.5
0
-0.5
-1
-1.5
0
100
200
300
distance, mm
400
500
600
(b)
Figure 14. Reproducibility of the homogeneity tests for measured and calculated data of the scanned platinum wire at different temperatures.
(This figure is in colour only in the electronic version)
The temperature difference T in column 4 is the difference
between the heater temperature and the room temperature
which was constant at 23 ◦ C during the measurements. The
abnormal variations of the Seebeck coefficient were calculated
according to equation (3):
The results of the quantitative estimation of the induced
inhomogeneity of the platinum wire at different temperatures
(227 ◦ C, 303 ◦ C and 410 ◦ C, small heating zone) using the
same method of calculation [9] as was described previously are
given in table 1. The absolute Seebeck coefficients of platinum
at different heater temperatures are listed in column 2 [10].
δS(P t) = emf/T .
8
(3)
Meas. Sci. Technol. 20 (2009) 055102
Y A Abdelaziz and F Edler
Table 1. Quantitative estimation of the induced inhomogeneity of the platinum wire at different temperatures.
Temperature of
heater TH (◦ C)
227
303
410
SN (Pt) at TH
(μV K−1 )
−9.53
−10.83
−12.46
Maximum emf
difference (μV)
T (K)
δS(Pt) (μV K−1 )
δS(Pt)/SN (Pt)
0.9
1.3
2.2
204
280
387
4.41 × 10−3
4.64 × 10−3
5.68 × 10−3
4.63 × 10−4
4.29 × 10−4
4.56 × 10−4
The nearly constant ratio of the abnormal Seebeck coefficient
and the absolute Seebeck coefficient of platinum of about 4.5 ×
10−4 at different temperatures confirms the correlation found
in [4] that the inhomogeneity measured at one temperature
can be expressed as a percentage of the total emf at this
temperature. A similar expression f = S/S, a so-called
inhomogeneity factor, was introduced in [5] for characterizing
thermoelements.
References
[1] Reed R P 1992 Thermoelectric inhomogeneity testing: Part I.
Principles Temperature: Its Measurement and Control in
Science and Industry vol 6 ed J F Schooley (New York:
American Institute of Physics) pp 519–24
[2] Bentley R E 2000 A thermoelectric scanning facility for the
study of elemental thermocouples Meas. Sci. Technol.
11 538–46
[3] Jonathan V P 2007 Quantitative determination of the
uncertainty arising from the inhomogeneity of
thermocouples Meas. Sci. Technol. 18 3489–95
[4] Jahan F and Ballico M 2003 A study of the temperature
dependence of inhomogeneity in platinum-based
thermocouples Temperature: Its Measurement and Control
in Science and Industry (Chicago, IL, 2002) (AIP Conf.
Proc.) pp 469–74
[5] Kim Y-G, Gam K S and Lee J H 1997 The thermoelectric
inhomogeneity of palladium wires Meas. Sci. Technol.
8 317–21
[6] Kim Y-G, Gam K S and Kang K H 1998 Thermoelectric
properties of the Au/Pt thermocouple Rev. Sci. Instrum.
69 3577–82
[7] Reed R P 1992 Thermoelectric inhomogeneity testing:
Part II. Advanced methods Temperature: Its
Measurement and Control in Science and Industry vol 6
ed J F Schooley (New York: American Institute of Physics)
pp 525–30
[8] Zvizdic D and Veliki T 2006 Testing of thermocouples for
inhomogeneity XVIII Imeko World Congress: Metrology for
a Sustainable Development (Brazil)
[9] Holmsten M, Ivarsson J, Falk R, Lidbeck M and Josefson L-E
2007 Inhomogeneity measurements of long thermocouples
using a short movable heating zone Int. J. Thermophys.
29 915–25
[10] Roberts R B 1981 The absolute scale of thermoelectricity II
Phil. Mag. B 43 1125–35
6. Summary
Two thermoelements (a copper wire and a platinum wire) were
investigated for inhomogeneity by using a movable heater with
two symmetrical temperature gradients. In the case of the
copper wire the investigation technique was demonstrated.
The main benefit of the two-gradient method is the simple
local verification of inhomogeneities in thermoelements,
independent of the shape and magnitude of the heating
zone.
The quantitative estimation of inhomogeneities
concerning their influence on the uncertainty of a temperature
measurement requires a numerical recalculation of the directly
measured emf curve, which is a measure of the derivative of
the corresponding emf measured by using the one-gradient
method. It was found that the magnitude of the directly
measured emf depends on the temperature and on the shape of
the heating zone, i.e. on the temperature gradients T and on
the width dg of the zone. Applying the method of Holmsten
[9], the recalculated emf was found to be independent of the
shape of the heating zone but proportional to its temperature,
i.e. directly proportional to the value of the Seebeck coefficient
of the thermoelement.
9
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