Introduction

Temperature is extremely difficult to measure directly, so most practical thermometry is performed with devices that have some temperature-dependent property (such as resistance or voltage). Such devices must be calibrated to establish the relationship between this property and the temperature.

The global temperature measurement infrastructure is essential for ensuring equivalence between temperature measurements worldwide. It is currently evolving in a way that will open up new opportunities for improved temperature measurement in process, through the move from a definition based on a physical artefact (the water triple point cell) to one based on a fundamental constant (1, 2). The current framework used for approximating temperature is provided by the International Temperature Scale of 1990 (ITS-90) (3). Specifically, the ITS-90 provides the framework for tracing temperature measurements back to the International System of Units (SI) unit of temperature, the kelvin, in a practical way. When calibration activities are accredited by a national accreditation body to ISO 17025:2017 (4) this provides assurance that the measurements are reliable and traceable to the SI. There are two key components (5).

The first component is a set of specific temperature values, called fixed points, based on highly reproducible phase changes of materials. These temperatures have been assigned a priori by international consortia using very accurate thermodynamic thermometry techniques to measure their temperature directly. The second component is a set of specified interpolating devices and associated equations which provide low interpolation uncertainties at temperatures between the fixed points.

A key drawback of this approach is that harsh environments can physically change the temperature sensor and hence the relationship between the thermometer output and temperature, which in turn causes a loss of calibration and therefore measurement traceability. In this article some solutions to this problem are outlined whereby traceability can be maintained in process.

This is linked to the ‘reproducibility crisis’ (6, 7) whereby two temperature measurements of the same phenomenon taken by two different groups differ, often by unacceptably large amounts. It is often impossible to know which one is more trustworthy, often because no clear record of measurement traceability is available.

In this article the problem of calibration drift is described, then some practical solutions to retain traceability in process are described, namely self-validating thermocouples, embedded temperature references and finally a paradigm shift in the form of practical ‘primary’ thermometry whereby temperature is measured directly.

Calibration Drift

When temperature sensors are used to monitor processes in harsh environments they can be subjected to contamination (for example in a jet engine or in a silicon processing plant), high temperatures (such as during casting of single crystal nickel alloy turbine blades or quartz manufacturing), vibration (during flight or launch of a spacecraft) or ionising radiation (mainly nuclear applications). The result is that the composition or microstructure of the sensor changes. This results in a change in the relationship between the sensor output (such as voltage or resistance) and the temperature, which is referred to as calibration drift. This in turn causes a progressive loss of knowledge of the process temperature by an unknown amount, resulting in a measurement error and an (often unnoticed) change in the process parameters.

It cannot be emphasised enough that in practice there is no indication of this calibration drift occurring. It causes inefficiency in terms of higher than necessary energy consumption, poor yield or unnecessarily large product rejection and waste, and in some cases inability to achieve the desired regions of the process envelope. It can also have safety implications necessitating suboptimal operation, for example in processes involving combustion, steam generation or other high temperature aspects which become more efficient as the temperature increases, but which are run at conservatively low temperatures to preserve a large safety margin. In many process control applications significant resources are spent on replacing sensors at considerable cost, in terms of expense and process down time.

Self-Validating Thermocouples

Thermocouples are very widely used in industry for process monitoring and control. They are particularly susceptible to calibration drift, because they tend to be used in environments which are harsh. This can be overcome by equipping the thermocouple with a miniature fixed point, which comprises of a metal (in a graphite container) with a known melting temperature. The fixed point is placed in contact with the thermocouple measurement junction, so that when the ambient temperature exceeds the melting temperature of the fixed point, a ‘hesitation’ is seen in the thermocouple output corresponding to the melting plateau arising from the absorption of heat from the surroundings during melting. Since the temperature during this hesitation is known a priori, the thermocouple can be recalibrated in situ, allowing the calibration drift to be determined.

The choice of phase-change material will depend on the operating temperature envisaged; it can be selected from the ITS-90 defining fixed point metals (3), or, for temperatures above about 1100°C, high temperature fixed points based on metal-carbon alloys can be used (8–14). These materials are summarised in Table I.

A number of approaches to self-validating thermometers have been made. One of the first well-characterised self-validating thermocouples was developed by Tischler et al. (15) and other effective ones were subsequently demonstrated (16–19), including one which was trialled in a power generation application (20). The concept was extended to higher temperatures using high temperature metal-carbon fixed points (21) and ultimately to 2300°C (22). A phase-change cell based on the Curie point (the temperature above which some materials lose their permanent magnetic properties, associated with a detectable hesitation in the temperature) was recently incorporated with a resistance thermometer to provide assurance in hygiene critical applications; this is now commercially available (23).

The challenge is to make these devices small enough to fit inside typical protective sheaths used in industrial thermocouples, so that the self-validating thermocouples are, from a practical point of view, indistinguishable from regular process control thermocouples in terms of incorporation in the process environment.

A practical self-validating thermocouple concept has been developed by the National Physical Laboratory (NPL), UK, and is now being commercialised by UK thermocouple manufacturer CCPI Europe Ltd (24, 25) with the trade name INSEVA. Such a device is shown in Figure 1. The long-term uncertainty achievable with the self-validating thermocouple is approximately 0.5°C (25). It is currently being trialled in heat treatment applications where the process temperature must remain within a very tight process control envelope. Some example melting curves obtained with the INSEVA device (using the silver melting point, 961.78°C and the gold melting point, 1064.18°C) are shown in Figure 2.

Current development activity is focused on proving the technology in industrial trials, so far in heat treatment applications in the UK and Europe, and on the development of algorithms for real-time automatic detection and characterisation of the melting plateau to facilitate recalibration in software. Early results with trials at process temperatures up to around 1200°C with the silver, gold and copper fixed points are promising, with the NPL algorithm reliably detecting and characterising a wide range of melting plateaus of different shapes; these all rely on characterising the density of points to produce a histogram in terms of temperature which can then be characterised to determine the melting point (26). A hybrid approach is taken due to the wide variation of the shape of melting plateaus (Figure 2) depending on the ambient temperature conditions (for example, the shape of the melting curve will vary depending on whether the ambient temperature is subjected to constant ramp rate, or held constant, or other condition), so that in some cases the histogram approach is combined with a correctional algorithm based on detection of points rising above the noise (27). Further development is currently underway, with efforts focusing on machine learning for fully autonomous detection and characterisation of the melting plateau.

Embedded Reference Phase-Change Cells

A similar concept has been developed for instrumentation used on board spacecraft (28, 29). The concept of using small phase-change cells for SI traceable calibrations on board spacecraft was discussed by Sapritsky (30). Devices based on gallium and gallium-based alloys have been developed by Sun et al. and Hao et al. (31, 32) with a length and diameter of 25 mm and 80 mm respectively. Similar size (containing about 100 g of phase-change material) gallium and gallium alloy cells for space applications have been developed by Burdakin et al. (33, 34) and by Gero et al. (35) for both contact and non-contact thermometry which claimed a realisation uncertainty of about 5 mK. All these cells are still too large for the RAL Space (Science and Technology Facilities Council, UK) application. Topham et al. developed feasible miniature references (36) containing about 4 g of gallium and stainless steel bellows to accommodate expansion and contraction of the phase-change material, and showed during tests on the International Space Station that the melting and freezing of gallium is not affected by weightless conditions (37). During those tests the device worked well although a number of potential improvements were identified.

NPL and RAL Space have collaborated on the development of a robust miniature phase-change cell which is robust and can operate autonomously. This makes use of the melting point of gallium, 29.7646°C, which is a convenient reference temperature for applications in Earth observations. The miniature phase-change cell contains about 2 g of gallium. The cell, which is made of stainless steel (Figure 3), is embedded in a prototype calibration blackbody structure adjacent to the platinum resistance thermometers used for measuring the temperature of the blackbody. The blackbody is used for calibrating radiometric instrumentation for climate monitoring, so errors arising from calibration drift have serious implications for these measurements, which feed into datasets used for high profile applications such as environmental policy development.

Key technical challenges in developing a practical device were: (a) to prevent a reaction between the gallium and the steel walls of the container (which could become a problem over the very long shelf-life of many years required for this instrumentation); and (b) to ensure reliable melting and freezing of the gallium (which has a pronounced tendency to remain liquid at temperatures many degrees below its freezing temperature). Another key part of the container is the weld which is essential to hermetically seal the cell and prevent any leakage of gallium, which could have a detrimental effect on the aluminium components of the spacecraft.

The cell yields very clearly defined melting curves (Figure 4), which last several hours, and which have a melting range of less than 0.01°C. This is remarkable performance given the tiny size of the phase-change cell, and that the thermometers are displaced from it rather than immersed in it (immersion of the thermometer in the phase-change cell being normal for general high precision temperature metrology applications), although it should be noted that the apparent (i.e. indicated) plateau temperature will have some dependence on the ambient temperature and its rate of change; this can be mitigated by characterising this dependence a priori, or by judicious selection of the part of the melting curve; the earlier stages of melting are the least susceptible to this influence, as can be seen in Figure 2. By calibrating the cell against NPL’s standard reference gallium cell, it can be used to calibrate the resistance thermometers on board the spacecraft with uncertainty of less than 0.01°C. Current work is focused on the development of additional fixed points between 0°C and 30°C.

Although this technique was developed for space applications, it is more widely applicable, for example for subsea temperature measurements where accuracy is of crucial importance. Deep ocean temperature measurements are extremely difficult and are heavily reliant on good reproducibility, as they need to be able to detect changes in ocean temperature over decades which amount to a few thousandths of a degree (38). This is very important because such a small temperature change of the ocean represents a vast change of the stored energy. Fixed points at the triple points of water (0.01°C) and mercury (–38.8344°C) would be useful for increasing confidence that the very small observed temperature changes reported are in fact real and not due to small calibration shifts of the sensors.

Practical Johnson Noise Thermometry

Another way to overcome the problem of calibration drift is to dispense with the need for calibration altogether by measuring temperature directly. This is referred to as practical primary thermometry, and the redefinition of the SI unit of temperature, the kelvin, in 2019 enables the kelvin to be realised in situ rather than relying on a traceability chain (1, 39).

If a property can be linked to temperature through fundamental physics, without recourse to a temperature scale or calibration, and if all parameters needed to work out the temperature are continuously measured, then a device can be used to measure this property which does not suffer from calibration drift, because any change or degradation of the sensor material is accounted for in the measurement. One such parameter is Johnson noise, which is the extremely small voltage arising from the random thermal motion of electrons in a resistor. A comprehensive review of Johnson noise thermometry is given in (40). The fact that the thermal motion of the electrons becomes more vigorous with increasing temperature results in the linkage between Johnson noise voltage and temperature via Nyquist’s equation, Equation (i) (41):

(i)

where is the mean squared Johnson noise voltage, k is the Boltzmann constant, R is the sensor resistance and Δf is the frequency bandwidth which depends on the properties of the sensing electronics and cables. A crucial point is that if the resistance R is measured continuously then all properties of the sensor and cabling which are affected by the harsh environment are characterised. This means that the thermometer can be used to measure temperature reliably at all times, independently of any calibration and, importantly, regardless of any sensor and cable deterioration.

The measurement of the Johnson noise voltage, which is miniscule (typically of the order of 1 μV root mean square even with a wide bandwidth of 1 MHz) is very challenging, especially in the presence of far larger external noise sources and has until recently been the preserve of large national laboratories concerned with measurement standards activities (42). Considerable design effort has been devoted to keeping external noise out of the system (43).

There have been many attempts to develop a practical Johnson noise thermometer. Brixy et al. (44) developed a thermometer which comprised of a thermocouple for rapid response and a Johnson noise thermometer for long-term stability, with the four wires used for Johnson noise thermometer consisting of two thermocouples. This was successfully tested in nuclear environments, hot isostatic pressing, glass manufacturing and petrochemical applications, operating up to 2200°C (45). Other types of dual probes were developed by Soulen et al. for cryogenic applications (46), Blalock et al. for nuclear applications at 300°C (47), de Groot et al. for high temperature applications up to 1500°C (48) (although stability was a problem in the latter application) and Borkowski et al. (49). Extensive work has been performed on Johnson noise thermometer for nuclear applications at Forschungszentrum Jülich in Germany (45, 50) although this is now discontinued, and at Oak Ridge National Laboratory in the USA (see for example (51)). Most recently, a new approach has been applied to develop a practical high accuracy Johnson noise thermometer using a range of completely new techniques to overcome lead wire effects and amplifier noise (52).

However, so far no practical Johnson noise thermometer has reached the market. A current collaboration between Metrosol Ltd (a UK instrumentation electronics specialist) and NPL has overcome this challenge and developed a prototype thermometer which employs completely new approaches using analysis in the frequency domain rather than the more conventional time domain. This enables simultaneous measurement of the resistance of the sensing element and the thermal noise power, as well as calibration of the noise power measurement and enabling a wider bandwidth (and hence higher signal to noise ratio) by compensating for the frequency dependent effect of the cables.

The device has unprecedented immunity to external electrical interference (53, 54), passing the most stringent heavy industrial immunity standard test required by IEC 61000-4-3:2020 (55). The accuracy achieved is about ±0.5°C in a few seconds (54). The current prototype is shown in Figure 5.

Figure 5 also shows the standard deviation of the temperature measured with the practical Johnson noise thermometer prototype up to 1000°C, compared with the limit given by Rice’s equation (56, 57), which represents the noise ‘floor’ below which the standard deviation of no measurement can go. It can be seen that the measurements are already quite close to the noise floor; the principal way of improving the statistical quality (and hence the measurement uncertainty) further is by averaging the measurement over a longer duration, so Johnson noise thermometer measurements always represent a compromise between accuracy and response time.

For Johnson noise thermometry, the traceability is transferred from temperature to electrical standards, i.e. the noise voltage is traceable to the SI ampere, but any calibration drift in the sensing electronics used to measure this voltage is expected to have a negligible effect on the inferred temperature.

With an achievable uncertainty of about ±0.5°C (54) when the measurement is averaged over a few seconds, the most obvious application of practical Johnson noise thermometry is as a replacement for thermocouples. As the uncertainty can be decreased by measuring over a longer time period (it decreases with the square root of the time over which measurements are averaged) it may also have applications in temperature standards and calibration applications. The current prototype operates between room temperature and about 1000°C. Development is currently focusing on increasing the upper temperature by exploring new probe designs, and also different sensing materials which are sufficiently robust to withstand temperatures up to around 1200°C and whose resistance can be tuned. Experiments with a range of exotic sensing element materials are currently underway.

There are other types of temperature sensor which could, in time, be used for practical primary thermometry. Examples of these include Doppler broadening thermometry (58) which links thermal energy to the optical frequency of an atomic or molecular spectral line, and acoustic gas thermometry (59) which measures the speed of sound in a gas, and which was used to determine the Boltzmann constant for the redefinition of the kelvin with unprecedented accuracy (60). Practical implementations of these devices are in varying stages of development. The ultimate goal is to enable users to measure temperature directly, dispensing with the need for calibration and eliminating the problem of calibration drift.

Conclusion

The problem of calibration drift and its effects on process control, and the consequent impact on factors such as efficiency, product yield and safety have been described. Some new techniques to overcome it and retain traceability to national temperature standards have also been described, specifically self-validating thermocouples and embedded miniature reference cells for in situ traceable recalibration. In addition, a paradigm shift in the form of practical primary thermometry has been introduced by means of a practical Johnson noise thermometer, which enables direct measurement of temperature which does not rely on calibrations and does not exhibit calibration drift. Many of these developments are at the advanced prototype stage and are expected to enter the market in the next few years, offering the possibility of greatly improved process measurement and control.