Thermocouple Inhomogeneity

The term inhomogeneity as related to thermocouples has the effect of opening Pandora's Box.

Equations 1-3.

Temperature may be the single most important processing parameter in the ceramic industry. Controlling the temperature of a process begins with accurately measuring the temperature in real time. Since most ceramics are processed in controlled atmospheres at relatively high temperature, only one real group of sensors emerges as a cost-effective choice: thermocouples.

The three major types of thermocouples discussed in this article are base metal, noble metal and refractory metal. Each group behaves differently in use over a period of time, but one thing is certain: they all initially have some degree of inhomogeneity, which will change as a function of time at temperature. The magnitude of electromotive force (EMF) for a given temperature varies greatly between these groups.1

Drift, error and every other term used to describe changes in a thermocouple’s output are simply a result of either physical or chemical inhomogeneity. Changes as a result of shorting, cold end error or shunting result in error, but they are not due to changes in the voltage produced as a result of temperature. The term inhomogeneity as related to thermocouples has the effect of opening Pandora’s Box; the ramifications of thermocouple inhomogeneity can be far-reaching and catastrophic. In fact, once inhomogeneity is understood, it is very difficult not to think about it when using thermocouples.

Figure 1. A typical or ideal thermocouple circuit (a), and the location of the temperature gradient relative to the reference and measurement junctions (b).

Understanding EMF

A rudimentary understanding of the operation of a thermocouple is needed to understand how and why there is great potential for erroneous readings when making measurements with thermocouples, especially with those that have apparently been calibrated. An effective assessment of uncertainty coupled with a comprehensive calibration program will help users achieve the best accuracy possible for a given thermocouple type and operating condition.

The output of a thermocouple is voltage, assuming a zero current condition; this is referred to as electromotive force (EMF). An example of a typical or ideal thermocouple circuit is illustrated in Figure 1a. Note that no consideration is given to the location of the thermal gradient in this type of circuit diagram. Ideally, the magnitude of EMF is proportional to the difference in temperature between the measurement junction and the reference junctions (see Equation 1).

In practice, the EMF depends on the average Seebeck coefficient of a segment of wire over a temperature difference between the reference and measuring junctions.2 No EMF is generated in the isothermal region. Figure 1b illustrates the location of the temperature gradient relative to the reference and measurement junctions. Since the EMF is generated in the region of the temperature gradient, the equation for EMF is better represented by Equation 2.

For a given temperature, the average Seebeck coefficient is a result of the material properties along the entire region that is exposed to a temperature gradient. If the material is chemically and structurally homogeneous in the region of the temperature gradient, then the Seebeck coefficient will be constant for a given temperature, regardless of the location of the temperature gradient along the wire. Equation 3 shows the idea in terms of deviation in the Seebeck coefficient.

This spatial non-uniformity of the Seebeck coefficient is the root cause of changes in the voltage-to-temperature relationship in thermocouples. Materials used for thermocouples have a unique Seebeck coefficient that is ideally defined by the normal reference function. No material matches those reference functions perfectly, however, and they all change depending on their inherent physical properties and how they are used.

A primary contributor to potential shifts in the Seebeck coefficient is related to the material itself; base metal thermocouples are most susceptible to changes in the Seebeck coefficient. Noble metals, especially a pure combination like Au/Pt, are the least susceptible.3 The refractory metal group, typically W/Re combinations, is likely to change due to its use at very high temperature where re-crystallization will cause structural changes in the material. But, depending on environment, all refractory metals can change significantly when exposed to temperature over time.

To better illustrate the idea in terms of real numbers, we can use a simplified linear example. For a type K thermocouple, the average Seebeck coefficient from 0 to 100°C is 40.962 µV/°C; therefore, at 100°C, the EMF will be 4096.2 µV. Let us assume that this is a new 40-cm-long thermocouple that is ideally homogeneous (having a Seebeck coefficient of 40.962 µV/°C over the entire length of wire). No matter where the temperature gradient is on the wire, the Seebeck coefficient remains constant.

If the sensor is then used at 1000°C but only protrudes into the oven 20 cm, the sensor is no longer homogeneous. The average Seebeck coefficient would then be expected to change if the temperature gradient covers part of the region exposed to 1000°C. The resulting error for a 3% change in the average Seebeck coefficient will be about 3°C at 100°C, and even higher as temperature increases.

Figure 2. Location of thermocouple inhomogeneity in use vs. during calibration.

Figure 2 illustrates this concept. A sensor is used at an immersion depth of 6 in., which exposes a specific section of the wire to high temperature, potentially causing changes in the Seebeck coefficient. The sensor is then removed for an annual calibration in the lab and is tested at an immersion of 12 in. In this case, the section of wire with potential degradation is within the isothermal region of the fluid, so no EMF is produced from this region of wire. It is very likely that the measurement data would be identical to that of its original or new values.

Nothing useful is produced by this calibration. In fact, a false sense of confidence is given for this thermocouple because the wrong section of wire has been calibrated. Inhomogeneity is a very likely reason that technicians and engineers end up chasing the process temperature; in other words, they adjust the process temperature to produce the best product and not to a known temperature where the process is optimized. Some gross estimates of inhomogeneity for base metal thermocouples are given by Bentley.4

Figure 3. Inhomogeneity effects in thermocouples.

Better Measurements

A few fundamental concepts must be understood to minimize error and improve measurement accuracy over time:
  • EMF is generated in any section of wire exposed to a temperature gradient.
  • EMF is proportional to the difference between the measuring junction and the reference junction.
  • The magnitude of EMF depends on the Seebeck coefficient for a given temperature difference.
Figure 3 reinforces the concept of error due to inhomogeneity. Considering the items above, a method for using and calibrating thermocouples should be established. For the sake of this discussion, the focus will remain specifically on the temperature/EMF relationship and how that is affected by inhomogeneity. (Other factors within the system that affect the measurement should be addressed in practice, but they are not part of the inhomogeneity issue. Poor connections, improper materials and EMI/RFI are a few of a very large number of possible error contributors.5)

Reducing error and improving reproducibility are critical to controlling or improving a process, and can be accomplished by following specific steps from the initial sensor purchase. Each step builds understanding of the measurement to be performed and continues to provide useful information about how the thermocouple may have changed during use.

Over time, the EMF footprint should be evaluated to assure that the measurement and associated process are in control and not drifting away from the target value. The primary concern is determining how much the thermocouple has changed as a result of its use. Begin by establishing a boundary for the system accuracy and for the thermocouple. This is typically achieved by determining the accuracy required to produce good product, and then performing an uncertainty analysis to isolate the allowable error contributions for each component of the measurement system. For example, how accurate is the controller vs. the sensor (and so on) considering all of the independent parts of the system?

Figure 4. Thermoelectric scanning apparatus.

Assuming it is a suitable device for the application, thermocouples should be purchased from a reputable manufacturer that has calibration and testing capabilities, preferably using ASTM standards.6 Many causes of inhomogeneity are related to production methods; poor closure welds and leaking end seals are always detrimental to performance. In addition, most thermocouple alloys are susceptible to preferential oxidation, grain boundary attack, and constituent depletion, and all of these cause inhomogeneity. Proper annealing after manufacture helps to restore the EMF and physical properties of the material changed during manufacture (remember, a change in the crystalline structure is also inhomogeneity).

Using EMF values from the original material tags is not recommended. Instead, a physical calibration should be performed. The resulting calibration data for a new thermocouple is vital to making judgments about how a thermocouple may have changed during use. Another safeguard is using referee sensors whenever the sensor is to be recalibrated. The referee sensor should be purchased with the original sensor lot and reserved for baseline comparisons at each calibration interval. It is recommended that the baseline comparisons be made at low temperature to avoid introducing shifts during the calibration process. High-temperature calibrations are not required to identify inhomogeneity.

If the calibration lab does not have the equipment necessary to perform thermoelectric scanning, then a profile immersion test should be performed. Such a test consists of reading the sensor output at 1-in. immersion increments in a stable liquid bath set to about 125°C. Once the sensor is past the point where stem conduction errors occur, the output should remain constant and a reference reading is relatively unimportant.

In situ comparison calibrations can also be performed using measurement devices that typically do not have issues of inhomogeneity. For low temperatures, a calibrated industrial resistance temperature device (IRTD) can be used, while noble metal thermocouples can be used for high temperatures. A word of caution is warranted here in regard to noble metal thermocouples: They may be less likely to have inhomogeneity, but a sensor that has been scanned is much more reliable. It is possible for these sensors to malfunction due to inhomogeneity.

Figure 5. Scan of a used thermocouple.

Advanced Methods

Methods have been developed to identify the location of inhomogeneity in the thermocouple wire of new and used sensors. Performing such a test requires specialized equipment and more time than conventional calibrations, but it is worth the effort in some cases.7 One of the main applications is to qualify a reference sensor to assure that inhomogeneity is minimized, especially in cases where profiling is the intended use of the sensor, or if the sensor will be used at various insertion depths.

Figure 4 shows a thermoelectric scanning apparatus developed for this purpose.8,9 Results of a scan taken from a sensor used at high temperature for one year are illustrated in Figure 5, while Figure 6 shows that of a type S reference sensor. The system operates by moving the sensor in a step-and-dwell increment through a narrow temperature gradient while recording the sensor’s output. Each scan is performed in two directions (immersion and withdrawal).

Figure 6. Scan of a type S reference thermocouple after use.

Much research has been done using this method, and results have shown that it is capable of identifying very small regions of inhomogeneity. Reversible and irreversible changes in EMF are avoided by using a low test temperature of 125°C. Originally, the fluid used was a gallium/indium/tin eutectic (GITE), but, considering the cost and hazardous nature of the material, other fluids are now used.

For more information regarding thermocouple inhomogeneity, contact Electronic Development Laboratories (EDL) Inc., 244 Oakland Dr., Danville, VA 24540; (800) 342-5335; fax (434) 799-0847; e-mail; or visit

Editor’s note: Graphics by Kristen Herndon, Marketing Director, Electronic Development Laboratories Inc.

SIDEBAR: Best Practices

  • Define the accuracy requirement and perform an uncertainty analysis for the measurement system.
  • Purchase high-quality thermocouples.
  • Always purchase a physical calibration; do not rely on tag values supplied from the mill.
  • Purchase a referee thermocouple for each lot of thermocouples purchased.
  • Send the referee for calibration with the unit under test (UUT).
  • If a thermocouple has been exposed to temperature, have an immersion profile performed at a single low temperature.
  • Consider using scanned noble metal reference thermocouples or calibrated IRTD to validate the process.


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