The International Temperature Scale of 1990 (ITS-90) defines a series of fixed reference points (temperature fixed points) at which thermometers – especially Standard Platinum Resistance Thermometers (SPRTs) – are calibrated. The relevant temperature fixed points are in the temperature range from about -190 °C to 1000 °C (83.8 K to 1235 K). Nine such official temperature fixed points are used in this temperature range.
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The temperature fixed points used for calibrating thermometers range from the triple point of argon (≈ -189.34 °C) as the lowest point to the freezing point of silver (≈ 961.78 °C) as the highest point in the contact thermometry range of the ITS-90. Each temperature fixed point corresponds to a clearly defined, reproducible temperature of a pure substance in phase transition (triple point or freezing/melting point), which serves as a calibration reference. The following table lists the relevant ITS-90 temperature fixed points and their temperatures:
| Substance (State) | Temperature ITS-90 |
|---|---|
| Argon (Triple Point) | -189.3442 °C |
| Mercury (Triple Point) | -38.8344 °C |
Water (Triple Point) | 0.01 °C |
| Gallium (Melting Point) | 29.7646 °C |
| Indium (Freezing Point) | 156.5985 °C |
| Tin (Freezing Point) | 231.928 °C |
| Zinc (Freezing Point) | 419.527 °C |
| Aluminum (Freezing Point) | 660.323 °C |
| Silver (Freezing Point) | 961.78 °C |
These temperature fixed points form the cornerstones for SPRT calibrations in the practically implementable range of the ITS-90. A Standard Platinum Resistance Thermometer (SPRT) is typically calibrated at several of these points, and the measured resistance ratios W(T) = R(T)/R(273.16 K) are used for interpolation between the temperature fixed points. The triple point of water (0.01 °C) plays a central role, as it is used for normalization (reference resistance at 273.16 K) and is included in every calibration. Depending on the target range, additional temperature fixed points are added – e.g., for a calibration up to 232 °C, the water triple point, indium, and tin points are usually used, while for calibrations up to 660 °C, zinc and aluminum are also included. The exact selection of required temperature fixed points is defined in the International Temperature Scale of 1990 (ITS-90). In the following, each temperature fixed point is explained in detail – with physical significance, practical realization, role in SPRT calibration, as well as aspects of uncertainties, apparatus, and impurities.
Triple Point of Argon (≈ -189.34 °C)
Physical Significance: The triple point of argon occurs at 83.8058 K (-189.3442 °C) and a pressure of about 0.68 atmospheres (≈ 69 kPa). At this point, solid, liquid, and gaseous phases of argon can coexist in equilibrium. It is the lowest defined temperature fixed point of the ITS-90 in the range considered here. It is used to calibrate thermometers at extremely low temperatures. Since liquid argon boils at ~-185.8 °C at normal pressure, setting the triple point requires pressure adjustment (slightly below 1 atm) or a closed system. The argon triple point is a cryo-reference point and allows the calibration of thermometers in the low temperature range at about -190 °C. In the ITS-90, it is used – along with the mercury and water triple points – to calibrate SPRTs from ~84 K to 273 K. For precision measurements in this low temperature range, the argon point is important as it provides a defined temperature reference to which measurements in liquid nitrogen (about 77 K) can be aligned, for example.
Practical Application and Realization: The realization of the argon triple point occurs in special cryogenic apparatus or triple point cells. Commercially available are, for example, argon triple point cells that work with liquid argon in a pressure-controlled Dewar. Typically, a corresponding pressure (≈0.68 atm) is set at which argon solidifies to its triple point. In practice, this often happens by putting liquid nitrogen in a closed vessel under pressure to raise the boiling point towards 83.8 K. Another method is using a standalone argon cell: One fills high-purity argon into a container, cools it under controlled conditions so that part of the argon solidifies and remains liquid, and adjusts the pressure until the temperature remains stable on the triple point plateau. Modern argon triple point systems can achieve plateaus of many hours (reported up to ~30 hours stability) and thus calibrate several thermometers in succession. Since liquid nitrogen at 1 atm is slightly colder (77.3 K), its boiling point was often used as a reference in the past. However, this is ~6 K below the argon triple point, which means extrapolation and increases uncertainty. By increasing the nitrogen pressure (or directly using argon as a cryogen), the temperature can be brought closer to 83.8 K, thus significantly reducing the calibration uncertainty.
Uncertainties and Influencing Factors: The reproducibility of an argon triple point realization is in the order of millikelvin or below. However, mastering this low temperature is challenging. Compared to metal temperature fixed points, the latent heat during the phase transition of a cryogenic gas is very low, and the thermal conductivity of solid/liquid argon is also small. This means that even the smallest heat leaks or environmental influences can noticeably affect the plateau temperature. To achieve uncertainties in the range of 0.1-1 mK, insulation, pressure stability, and temperature homogeneity must be optimized. Many metrology laboratories replace the argon triple point with calibration at the boiling point of nitrogen or argon due to lack of specialized equipment, which, however, is associated with higher uncertainties. – Impurities: The argon gas used must be extremely pure (typically 99.999% or better). Impurities such as air components (O₂, N₂) could disturb the equilibrium or slightly shift the observed triple point. After all, such foreign gases condense/sublimate at similar temperatures and could, for example, be present as a liquid phase. In high-quality cells, this is counteracted by gas purification and evacuation. Overall, the argon triple point is a very stable reference value when carefully realized; the biggest challenge lies in the technical implementation at ~84 K and not in the fundamental definition of this temperature fixed point.
Triple Point of Mercury (-38.8344 °C)
Physical Significance: The triple point of mercury (Hg) occurs at 234.3156 K (-38.8344 °C) and at an extremely low pressure of only about 0.2 mPa. Thus, it is practically in a vacuum – a tiny vapor pressure at which liquid, solid, and gaseous mercury coexist in equilibrium. This temperature is nearly identical to the normal freezing point of Hg (which also solidifies around -38.83 °C at 1 atm), but at the triple point, the gas phase is additionally involved, providing a unique, stable reference state. In the ITS-90, the Hg triple point is the only defined temperature fixed point in the subcooled range below 0 °C (besides argon). It represents the starting point for the negative Celsius scale and is needed to calibrate SPRTs below the freezing point of water. Typically, an SPRT for the range -39 °C to +30 °C is calibrated at the temperature fixed points of the mercury triple point, water triple point, and gallium point. This allows the thermometer interpolation to cover the entire range, including e.g., -38 °C (Hg) → 0 °C (H₂O) → 30 °C (Ga).
Realization and Apparatus: The practical implementation of the mercury triple point occurs in a closed cell containing a defined amount of high-purity mercury. Since the triple point is at ultra-low pressure, it is necessary to be able to evacuate the cell. Typically, a Hg triple point cell consists of a robust stainless steel vessel with a central thermometer measurement channel. First, the contained mercury is completely or partially frozen by cooling. Then, the system is allowed to warm towards -38.834 °C while the outer environment is well insulated, and the space above the Hg is pumped down to ~10^-3 Pa with a vacuum pump if necessary. Under these conditions, the mercury begins to melt, and a triple point mixture is established: Part of the Hg is solid, part liquid, with saturated Hg vapor above. The temperature remains constant at the triple point as long as solid/liquid phases are in contact. With good temperature fixed-point cells and techniques, very long plateau times can be achieved – reports mention freezing plateaus lasting up to 14 hours or more. One method for optimization is forming an “ice mantle”: A thin solid Hg layer is deliberately frozen on the inside of the sheath tube (around the immersion tube), and the cell is then insulated so that the interior slowly melts again from this solid mantle. This creates a stable internal solid/liquid equilibrium. It is important that the space above the mercury is truly free of foreign gases; often the cell is continuously evacuated during operation or packed in foam insulation to avoid pumping and minimize heat loss.
Uncertainty and Purity: The mercury triple point is one of the most precise temperature fixed points of the scale. Due to the clearly defined phase transition and good heat conduction in the metal, a reproducibility in the range of a few 10^ {-5}K is achieved. Experimental investigations show that with careful execution, the temperature of repeated triple points is identical within ±0.05 mK – an extremely low scatter. This often surpasses the stability of a controlled cold bath. The main uncertainty contributions result from the thermometer measurement itself (self-heating, resistance resolution, etc.) and possible pressure changes, rather than from the temperature fixed point. – Impurities: Mercury must be used in the highest purity (≥ 6N, i.e., 99.9999%). Even traces of foreign metals or gases can minimally shift the triple point. For example, dissolved gas (air) in Hg can cause small bubbles at the start of freezing and can cause local temperature disturbances. In high-quality cells, the mercury is pre-distilled and the cell is often purified several times by freezing/pumping. The isotopic composition of Hg can also theoretically have an influence – natural Hg consists of several isotopes, and a deviation from the average can change the triple point by a few 10^{-5} K. Therefore, in primary laboratories, special batches with known isotope distribution are sometimes used. Overall, however, it can be said that a correctly set up Hg triple point is one of the most reliable reference temperatures – it was already an important temperature fixed point in earlier scales (IPTS-68) and retains this significance in ITS-90.
Triple Point of Water (0.01 °C)
Physical Significance: The triple point of water is defined at 273.16 K, corresponding to 0.01 °C. At this point, ice, liquid water, and water vapor coexist in equilibrium. The water triple point is unique because it has been assigned exactly 273.16 Kelvin on the thermodynamic temperature scale by definition (this was formerly the basis of the Kelvin definition). Thus, it is by definition free from experimental uncertainty – in practice, of course, only in ideal realization. The TPW (“Triple Point of Water”) is the foundation of all temperature calibration: It forms the temperature fixed point to which all other measurements are traceable. In particular, for SPRTs, the resistance at 0.01 °C is taken as the reference value R(273{,}16\text{K}) to form the relative ratio W(T). This eliminates many systematic errors, achieving high precision. The water triple point is exactly at 0.01 °C on the Celsius scale, just slightly above the freezing point at normal pressure (0 °C). It is easily accessible yet extremely stable – ideal for laboratory use worldwide.
Practical Application and Realization: Triple point cells for water are standard equipment in metrology laboratories. A TPW cell consists of a glass or quartz vessel containing ultra-pure water (usually with a defined isotopic composition, e.g., VSMOW) and a vacuum above the water surface. The creation of a triple point state is achieved by forming an ice mantle layer in the water triple point cell: The “inner frozen mantle method” is common. In this method, the inner thermometer well of the cell is cooled, for example, with an insert chilled in liquid nitrogen or by a separate cooling insert, until an ice layer forms on the inside around the measurement channel. The aim is to create a closed ice ring along the inner tube. Afterwards, the cooling device is removed, and the cell is allowed to warm slowly at ambient temperature (TPW cells are usually kept in a thermostat or simply at room temperature). Due to the latent heat of the melting ice, the temperature at the water/ice interface settles exactly at 0.01 °C and remains constant as long as sufficient ice and water are present. A well-prepared cell can provide a stable plateau for hours, days, weeks, and months.
Accuracy and Influencing Factors: As the water triple point is the basis of the scale, it has been subject to intensive investigations for decades. New, high-quality cells show deviations from the ideal value of less than 10 µK (microkelvin) due to minimal impurities. Older or less pure cells may exhibit a drift of ~50 µK, which is still extremely low. The reproducibility between different cells and laboratories is in the range of a few tens of microkelvin – international comparison measurements found standard deviations around 0.00005 °C. This makes the TPW the most stable temperature fixed point of all. However, in practical application, a correction must be considered: the hydrostatic pressure effect. Since the thermometer is usually immersed ~25 cm deep in the cell, there is a slightly higher hydrostatic pressure at the sensor than at the ice/water surface. The equilibrium temperature decreases by about 7.3∙10^-5 K per cm of water column. At ~25 cm height, this results in a correction of about -0.18 mK. This is either calculated and added or already accounted for in the calibration certificate. The uncertainty of this correction is very small (a few µK) as long as the height and coefficient are known. – Impurities: Purity is crucial for the TPW. Distilled, degassed water is used, ideally with a defined isotopic composition (e.g., VSMOW, “Vienna Standard Mean Ocean Water”). Deviations in the isotopic composition (proportion of deuterium or ^18O) can shift the triple point by a few 0.1 mK; therefore, commercially available distilled water can easily cause measurable differences from the ideal 273.16 K. The purity of the container material is equally important: quartz glass cells are preferred, as normal borosilicate glass can release tiny amounts of alkali ions into the water over time, lowering the triple point. Furthermore, no exchange of foreign gases should occur – therefore, cells are usually permanently sealed, often with a small residual gas pressure of their own water vapor phase. When carefully considering all these factors, the water triple point provides an unparalleled precise reference.
Melting Point of Gallium (29.7646 °C)
Physical Significance: Pure gallium melts at 29.7646 °C (approx. 302.9146 K). This relatively low melting point (slightly above room temperature) is a defined temperature fixed point of the ITS-90. Gallium has the special property that it expands when solidifying (similar to water) and that its triple point is practically at the same temperature value, as the vapor pressure of gallium at ~30 °C is extremely low. For calibration purposes, usually the melting point (MP) is used, i.e., the transition from solid to liquid under slight overpressure or atmospheric pressure. (NIST, for example, realizes gallium at a minimally increased pressure as a “triple point” at 29.7666 °C to further reduce uncertainty, but the difference to the melting point at 1 atm is in the microkelvin range.) The gallium fixed point fills a gap in the temperature range of the scale: It provides a precise reference value near 30 °C. This allows for significantly more accurate interpolation of SPRTs in the range from 0 °C to ~30 °C than if one only had 0 °C and, for example, 156 °C (indium). Thus, ITS-90 specifies for the range 0 °C to 30 °C that calibration should be performed at 29.7646 °C – in simple cases, the water triple point and gallium melting point are sufficient for calibrating this segment.
Realization and Typical Apparatus: The gallium melting point is relatively easy to realize. Typically, a cylindrical “fixed-point cell” (made of stainless steel or with PTFE lining) filled with several hundred grams of high-purity gallium (at least 6N) is used. Due to its proximity to room temperature, no elaborate high-temperature furnaces are required; a simple thermostatic bath or a small heating/cooling apparatus suffices. However, gallium tends to supercool significantly: Liquid Ga can be cooled far below 29.7646 °C without solidifying if no crystal nuclei are present. Therefore, the temperature fixed point is usually approached as a melting plateau, not as a freezing plateau. In practice, the procedure is as follows: First, allow all the gallium to solidify (e.g., by cooling the cell to ~20 °C). Then, place the cell in a slightly warmed bath (approx. 30.5 °C) and observe the temperature inside. As soon as the gallium begins to melt, the temperature stabilizes at the melting point and remains there as long as a solid gallium core is present. The thermometer is immersed in the liquid portion (through a central measuring channel). Due to the heat of fusion, the temperature remains exactly at 29.7646 °C until the last piece of solid Ga has melted. This process creates an extended plateau at a constant temperature. Alternatively, one can controllably melt only a part (by keeping the cell just below MP) to obtain longer plateaus. In all cases, it is important to avoid mechanical shocks, as these could generate crystal nuclei (less critical for the melting plateau than for freezing). Gallium fixed-point cells are also commercially available; some have a slight overpressure of argon to ensure no foreign air enters and to realize the triple point instead of the pure melting point – however, this difference is negligibly small.
Uncertainties and Purity: The gallium melting point is characterized by very low uncertainties. Firstly, the temperature is relatively low, making heat losses easy to control, and secondly, the plateau temperature is highly reproducible. In top metrological applications, a total deviation of <<1 mK is achieved; typical expanded uncertainties are in the range of 0.5 mK or below. For example, NIST prefers to realize gallium as a triple point to achieve a standard uncertainty of about 0.1 mK. For comparison: A high-quality water bath at 30 °C has fluctuations in the millikelvin range – a gallium fixed point is thus even more stable and is often used to check thermometers at ~30 °C or to validate adjustments of industrial sensors. – Impurities: Gallium must be used with very high purity. Metallic impurities (e.g., traces of indium, lead, etc.) would lower the melting point (freezing point depression). The ITS-90 guides recommend using at least 6N material and limiting the sum of impurities to a few ppm maximum. Fortunately, Ga is chemically relatively inert towards glass or quartz, so the container material hardly causes contamination. A possible source of interference is oxidation: Gallium quickly forms a thin oxide layer (Ga₂O₃) in air. This can make melting difficult and potentially lead to a slight hysteresis effect. To prevent this, a protective atmosphere (e.g., argon) is often used in the cell space, or the cell is sealed vacuum-tight after filling. Overall, gallium temperature fixed points can be operated in such a way that the influence of impurities remains well below 0.1 mK. The melting point of gallium has therefore established itself as a convenient, reliable calibration point just above room temperature.
Freezing Point of Indium (156.5985 °C)
Physical Significance: Pure indium has a freezing or melting point at 156.5985 °C (429.7485 K). (Freezing point = temperature at which liquid indium begins to solidify at normal pressure; corresponds to the melting point of solid indium when heating.) Indium is a relatively soft heavy metal whose melting temperature is moderately high, making it ideal as a calibratable temperature fixed point. Important: The indium point was newly introduced in the ITS-90 (there was no defining point at ~156 °C in the predecessor IPTS-68). This allows for more precise realization of the temperature scale in this range. The indium temperature fixed point fills the gap between gallium (30 °C) and tin (232 °C). For calibration up to ~230 °C, it is used to improve interpolation: e.g., for 0-232 °C, water, indium, and tin points are used. Also, for calibrations up to ~156 °C (e.g., for medical or laboratory thermometers), the indium point is typically used as the highest value alongside the TPW.
Realization: The indium freezing point can be realized in a metal fixed-point cell, similar to tin or other metals. A typical cell consists of a pure graphite crucible containing ~0.5-1 kg of indium, with a central well (measuring channel) for the thermometer. Graphite is used because it is inert at high temperatures and does not contaminate indium. The cell is operated in a temperature-controlled calibration furnace or heat pipe that can be heated to about 5-10 °C above the melting point. To perform the temperature fixed point, first, all the indium is melted (e.g., at ~161 °C for several hours to ensure no solid remains). Then the furnace is allowed to cool slowly. To achieve a reproducible plateau, the freezing process is deliberately induced: Often, slight undercooling is allowed (e.g., cooling to ~155 °C, one to two degrees below the FP), then a crystallization nucleus is created by a small disturbance – such as a super-cool. Indium then begins to freeze and releases heat of fusion. The temperature rises and settles exactly at 156.5985 °C. Now the furnace is kept just below this temperature, so that the indium continues to freeze very slowly. During this phase, the temperature remains constant as a plateau. The larger the amount of metal and the slower the cooling rate, the longer and flatter the plateau – several hours are achievable. The thermometer (SPRT) measures the temperature at the center of the crucible. Indium has relatively low thermal conductivity, but the graphite crucible and convection in the melt (if present) homogenize the temperature distribution.
Measurement Accuracy and Impurities: A cleanly realized indium fixed point offers excellent reproducibility, typically in the range of 1 mK or better. National metrology institutes assign very small uncertainties to the indium point, often dominated by systematic components such as purity correction. The latent heat during the indium transition (~28 J/g) is lower than for tin or zinc, but sufficient to ensure a stably flat plateau. It is important that there are no strong temperature gradients in the furnace; high-quality multi-zone furnaces or liquid baths ensure isothermal conditions within a few millimeters over the cell height. – Impurities: This is a central source of uncertainty. To derive the true freezing point of pure indium, the indium charge must be extremely pure (≥ 99.9999%). Foreign metals such as lead, tin, cadmium, etc. could form alloys and lower the freezing point. Metrologically, the purity is assessed in several ways: Chemical analysis (extent and type of impurities in ppm), sum formulas according to Raoult (to estimate a theoretical temperature depression), and most importantly, the analysis of the freezing curve. The latter means: The plateau temperature is recorded vs. time or vs. freezing progress. For absolutely pure material, the temperature remains constant until the end; for slightly impure material, it often shows a slight drop towards the end because the remaining liquid phase is increasingly enriched with impurities (which reduces the local melting point). By extrapolating to the time of freezing onset (or to “0% frozen”), one can determine the original temperature corresponding to the pure substance. In practice, indium fixed-point cells today are so pure that these corrections are very small, often less than 0.5 mK. The residual deviation is budgeted as uncertainty. Indium hardly reacts with graphite or quartz, and oxide formation (In₂O₃) is not pronounced at 156 °C – nevertheless, work is usually done under protective gas (e.g., argon) to exclude oxide and moisture. In summary, the indium point provides a reliable calibration value in the lower middle temperature range, significantly increasing measurement reliability between 30 °C and 232 °C.
Freezing Point of Tin (231.928 °C)
Physical significance: Pure tin (Sn) has a freezing or melting point at 231.928 °C (505.078 K). This metal was already an important temperature fixed point in earlier temperature scales (e.g., IPTS-68) and was adopted as a defining point in the ITS-90. The tin point marks the transition from the “low” to the “medium” temperature range of the ITS-90. It is significantly above the boiling point of water and still below the red-hot limit (approx. 300 °C), which makes it easily manageable with liquid baths or simple furnaces. The tin fixed point is used for calibration of SPRTs up to ~232 °C. For example, for a 0-419 °C calibration, the tin point is used together with the TPW and the zinc point. But even in smaller ranges (0-232 °C), indium and tin are often used together to divide the scale into two segments. The advantage of including the tin point lies in improving the interpolation accuracy around the boiling point of water (100 °C) and beyond up to ~200 °C.
Realization: The tin fixed point is realized like other temperature fixed points in a graphite crucible cell with a central thermometer insert. High-purity tin (6N quality or better) is completely melted in the crucible by heating (e.g., to ~240-250 °C). Then the system is allowed to cool in a controlled manner. Tin has a fairly high latent heat of fusion (~60 J/g), which tends to produce very stable plateaus, as a lot of energy is released during solidification, slowing down the temperature drop. Usually, one waits until the temperature has fallen about 1-2 K below the nominal value (to achieve slight undercooling), and then triggers the solidification process: This can be done by a super-cool. As soon as solidification begins, the temperature rises to the freezing point and remains stable. The furnace is controlled to be a few tenths of a degree below 231.928 °C to neither add heat nor cool too strongly. In this equilibrium scenario, the tin slowly solidifies from the nucleation points. A plateau of several hours is achievable. During this time, the resistance is measured with the SPRT, which remains constant apart from minimal noise. The temperature of the environment (furnace) can be slightly modulated to extend the plateau (following the principle: if the temperature drops slightly, increase heating power minimally, etc.), with experienced users controlling this manually or using slow regulation.
Performance and Accuracy: Tin temperature fixed point cells have proven to be very robust and reproducible. The repeatability in well-constructed cells is 1-2 mK or better. In international comparisons and when used as a secondary standard, distributions in the single-digit millikelvin range can be expected. Larger uncertainties usually arise from the thermometer (self-heating, insulation errors) or from incomplete realization (e.g., too short plateau time, gradient in the cell). In primary laboratories, the standard uncertainty of the tin point is often stated as about 0.5-1 mK. Interestingly, the change from IPTS-68 to ITS-90 showed a small temperature offset at the tin point (the scales deviated by a few mK), but in ITS-90, the value 231.928 °C is considered the official reference value. – Impurities: As with all temperature fixed points, material purity plays a crucial role. Tin should be 99.999% pure or better. Common impurities in technical tin are, for example, lead, antimony, copper; even a few ppm of these can noticeably lower the freezing point. Therefore, temperature fixed point tin is either produced from chemically very pure material or purified by zone melting. The effect of impurities is assessed similarly to indium: through sum formulas or curve evaluation. In practice, an impurity is often recognized by a slightly inclined plateau (temperature decreasing over time). The angle of inclination can be used to infer the impurity mole fraction. However, typical temperature fixed point cells show hardly any inclination – an indication of negligible impurities. Another aspect is oxidation: Liquid tin immediately forms an oxide layer (SnO₂) on the surface when exposed to air. This can influence solidification (e.g., delayed nucleation, incomplete heat transfer). To counteract this, the cell is often provided with an argon protective atmosphere or the melt in the crucible is covered with a light graphite powder or glass lid. Graphite reduces tin oxide to a certain degree, which is also helpful. Such measures ensure that the effective freezing point corresponds as closely as possible to the ideal. Overall, the tin freezing point is a proven, comparatively easy-to-handle temperature fixed point with very low uncertainty in the medium temperature range.
Freezing Point of Zinc (419.527 °C)
Physical Significance: Pure zinc (Zn) has a freezing point at 419.527 °C (692.677 K). This is already a relatively high temperature range for resistance thermometers. The zinc point was chosen in the ITS-90 as a temperature fixed point instead of the previously used sulfur point (boiling point of sulfur ~444.6 °C in IPTS-68), as metal temperature fixed points are generally more reproducible and easier to handle. At ~419.5 °C, the zinc point covers the beginning of the upper temperature range for SPRTs. In calibrations, the zinc point is used, for example, when an SPRT is to be used up to ~420 °C: One typically calibrates at TPW (0.01 °C), tin (231.928 °C), and zinc (419.527 °C). Even for a calibration up to 660 °C, zinc is an intermediate point (TPW, Sn, Zn, Al). The value near 420 °C is particularly relevant for industrial temperature measurement technology (e.g., furnaces, thermocouples), making the zinc fixed point metrologically significant.
Realization: The zinc fixed point already requires a high-temperature furnace or a heat pipe that can reach ~430-440 °C. Three-zone vertical furnaces are often used to minimize temperature gradients. The cell itself is again made of graphite, as metals would react strongly with many materials at these temperatures. Graphite is inert under argon and can withstand the high temperatures. For realization, the zinc is first completely melted (held at ~430-450 °C to ensure homogenization). Then the system is cooled down. Zinc has a very large enthalpy of fusion (over 100 J/g), which means that an enormous amount of heat is released during solidification – an advantage for a long plateau. After a possible slight undercooling (1-2 K below FP), solidification is initiated, e.g., by touching the metal with a cold wire or slightly shaking the crucible. As a result, a solidification front forms, usually starting at the crucible wall, and the temperature rises to 419.527 °C. Due to the high latent heat, it remains there, even if the furnace is slightly cooler. A challenge with zinc, however, is that the ambient air and radiation losses at ~420 °C are considerable. To maintain the plateau, the furnace must therefore be controlled to supply exactly the right amount of heat – neither too much (then zinc would melt again and increase temperature) nor too little (then the plateau would end prematurely). In well-designed systems, plateaus lasting several hours can be achieved, providing enough time to perform multiple measurements with the SPRT.
Uncertainty and Special Features: The zinc point can be reproduced very precisely, but the practical uncertainties are usually somewhat larger here than at the lower points. This is due to factors such as: stronger thermal radiation (can affect thermometer or measuring bridge), higher sensitivity to furnace gradients, and slower diffusion if there are impurities. Nevertheless, primary laboratories report standard uncertainties of around ±1-2 mK for the zinc temperature fixed point. The measurement uncertainty of an SPRT at 420 °C is typically a few millikelvins, a good part of which already comes from the temperature fixed point realization. By overlapping the furnace zones (top and bottom heating), the axial temperature gradient in the cell area can be reduced to a few millikelvins/cm, ensuring uniformity in the ~10 cm high usable area of the crucible. – Impurities: Zinc must be used in very high purity, as it is a base metal that can dissolve many foreign metals. 5N or 6N zinc is used; typical impurities such as Pb, Cd, Fe must be in the ppm range or below in total. A peculiarity with zinc is the potential absorption of oxygen: Zinc melts at high temperature and can absorb oxygen from the crucible material or trapped air and form zinc oxide. Zinc oxide has a significantly higher melting point (~1975 °C) and precipitates as solid particles when cooled. These can act as nuclei or reduce the effective purity. Therefore, zinc cells are usually provided with a purified argon atmosphere. Graphite as a crucible additionally helps, as it binds oxygen (CO/CO₂ formation) and thus acts as a “getter”. As with indium and tin, the solidification process is also closely observed with zinc: A flat plateau over the entire duration indicates very low impurities; a plateau with noticeable slope could indicate ppm traces that slightly vary the melting point. In such cases, the beginning of the plateau is often extrapolated as the true temperature fixed point. All in all, however, the zinc point is well manageable and indispensable for calibrations in the upper PRT range.
Freezing Point of Aluminum (660.323 °C)
Physical Significance: Pure aluminum (Al) melts/solidifies at 660.323 °C (933.473 K). This is the highest defined temperature fixed point that most Standard Platinum Resistance Thermometers (SPRTs) can reach. Above this, so-called High-Temperature SPRTs are used (HTSPRTs), which typically have a much smaller nominal value than, for example, 25 ohms. The aluminum point is thus enormously important for calibrating the largest number of SPRTs used up to their operational limit (~660 °C). A typical calibration from 0 °C to 660 °C includes the water triple point, as well as the freezing points of tin, zinc, and aluminum. Many high-quality SPRTs are only designed for up to 660 °C, as beyond that, the platinum ages quickly. From an industrial perspective, 660 °C already covers wide fields (e.g., Al and Zn casting, laboratory furnaces, etc.), therefore the Al fixed point has considerable practical use.
Realization: The realization of the aluminum fixed point places increased demands on the apparatus. A high-temperature furnace is required, which can be held stable at ~660 °C. Usually, three-zone tube furnaces or heat pipes are used to create a uniform temperature profile along the length of the temperature fixed-point cell. The cell itself consists of a graphite crucible with pure aluminum (about 0.5-1 kg) and a central measurement tube. Graphite is essential here, as aluminum is very reactive: it would react with ceramic or metal crucibles (aluminum alloys with iron, for example) and draw oxygen from oxide-containing materials. Graphite, on the other hand, can slowly carbidize with aluminum, but for one-time or short-term uses this is negligible, especially since inert gas is present. The cell is typically operated under an argon atmosphere to prevent oxidation. The procedure: First, the Al is completely melted (at ~670-680 °C for some time, so that even the last crystal melts and the material becomes homogeneous). Then the furnace is slowly regulated down. Aluminum tends not to spontaneously solidify without strong supercooling, especially when there are no crystal nuclei present and the walls are well nucleation-free. Therefore, a nucleation trick is often used: When the temperature has fallen a few degrees below 660.3 °C (e.g., ~658 °C), a “cold” object is introduced – for example, a thin quartz rod (the so-called super-cool). This immediately creates a solidification nucleus and the aluminum begins to crystallize. The temperature rises to the freezing point. Now the furnace is kept just below this (~659 °C) to allow slow, controlled solidification. Due to the high heat of fusion (~400 J/g, one of the highest among the ITS-90 temperature fixed points), the temperature remains very stable. A well-created plateau can last for hours. Longer plateaus are difficult because at such high temperatures, losses inevitably occur and the temperature begins to fall again after complete solidification of the aluminum.
Uncertainty and Challenges: The measurement uncertainties at the aluminum point are generally somewhat larger than at the lower metal points. Top laboratories still achieve remarkable precision (a few mK), but the reproducibility between different realizations or cells can be, for example, ±2-5 mK. Main reasons: Impurity effects have a greater impact here (because a few ppm of foreign substances can cause several mK, and at 660 °C materials diffuse or react faster), and thermal gradients are more difficult to completely eliminate. Nevertheless, the Al point can be very well used as a calibration reference, as the deviation from the ideal value can usually be captured by known corrections. In practice, an purity correction is often applied: The sum of impurities in the aluminum is determined from the manufacturer’s certificate or through subsequent analyses, and the temperature reduction is estimated from this. For example, silicon or iron in aluminum has significant effects (several mK per ppm). Another method is to take the beginning of the freezing plateau as a reference, as at this time most impurity elements are still evenly distributed. In the middle or towards the end of the plateau, impurities can accumulate in the remaining melt and slightly pull the plateau downwards. For instance, Widiatmo et al. (PTB) reported on analytical methods to derive the effective purity from the plateau progression. – Impurities and Material Issues: High purity aluminum (usually 5N5 to 6N, i.e., 99.9995% or more) is necessary. Typical impurities include Cu, Si, Fe, Ga. Especially Si and Fe dissolve well in liquid Al and significantly shift the freezing point. Hydrogen also poses a problem: Liquid Al can dissolve hydrogen from residual moisture or organic substances (similar to how silver dissolves O₂). During solidification, the hydrogen is expelled (pore formation), which can cause temperature effects and disruptions in crystallization. Therefore, care is taken to ensure that all components are dry and clean; often the cell is heated in a vacuum before filling. Graphite crucibles can react with Al over time (formation of Al_4C_3), which consumes the Al and theoretically changes the FP; however, this usually only happens with prolonged holding time or multiple reuse. Fresh graphite crucibles sometimes have loose particles that could act as impurities – therefore they are pre-annealed and blown out. Oxidation: Aluminum immediately forms an Al₂O₃ layer in air, which is very stable. In the melt, this can float on top as slag. If this oxide “skin” forms a hollow sphere during solidification, it can happen that the aluminum solidifies simultaneously at the wall and in the core, creating a so-called double-front plateau – two phase transitions that occur one after the other, visible as a slight plateau step. This is, of course, undesirable. This is countered by carefully stirring before solidification (to break up oxide) or by adding a small “sacrificial platelet” of Al, which preferentially oxidizes. Overall, the aluminum fixed point requires a great deal of care but provides a clearly defined reference value for the highest temperatures of an SPRT.
Silver Freezing Point (961.78 °C)
Physical Significance: Pure silver (Ag) has a freezing point at 961.78 °C (1234.93 K). This is the highest defined temperature fixed point of the ITS-90 that is realized using contact thermometry. Above this, the scale transitions into the optical range: From the silver point onwards, T{90} is defined by applying Planck’s radiation law to a blackbody, where the silver, gold, or copper point can serve as a reference. In other words: At ~962 °C, the range that can be fully covered with SPRTs ends; above this, pyrometers are used (e.g., the gold point ~1064 °C and the copper point ~1084 °C are used as calibration references for radiation thermometers). The silver fixed point is thus the transition point and allows SPRTs or other sensors to be calibrated up to just under 1000 °C. In calibration procedures, it is rarely used for standard SPRTs (many SPRTs only go up to 660 °C), but for special high-temperature SPRTs, calibration up to 961.78 °C can be performed. A complete ITS-90 calibration sequence up to the silver point would include temperature fixed points at 0.01 °C, 231 °C (Sn), 419 °C (Zn), 660 °C (Al), and 961 °C (Ag).
Realization: The realization of the silver fixed point requires sophisticated apparatus. Typically, a three-zone vertical furnace or an isothermal block furnace with excellent temperature uniformity is used. Some laboratories also employ so-called heat pipe ovens – these use, for example, sodium as a working medium to create a very homogeneous temperature zone at ~1000 °C. The silver fixed point cell consists of a graphite crucible containing high-purity silver (often ~1 kg to ensure a long plateau time). The crucible has a central graphite thermometer well. Graphite is essential because silver can be reactive at high temperatures (e.g., it strongly dissolves oxygen) and would interact with other materials (ceramics, metal). Graphite, on the other hand, can absorb a small amount of carbon from liquid silver, but this is minimal. The cell is usually operated under protective gas (argon) or possibly evacuated to avoid oxidation – silver eagerly absorbs oxygen from the air, which can lead to disturbances. For the procedure, the silver is first melted (~970-980 °C to ensure that everything is truly liquid). Then it is cooled. To obtain an initial nucleus, the “cold rod” method (super-cool) is often used: The thermometer is briefly removed and a cooled quartz rod is inserted into the well, which rapidly undercools the liquid silver at one point and creates a solidification crystal. Alternatively, the cell is removed from the furnace and blown on the surface – the main thing is to create a solid silver nucleus. Immediately after, the cell is placed back in the furnace (or the rod is removed and the thermometer reinserted) and the temperature is maintained just below the FP. The silver now slowly solidifies from the nucleation point. The temperature rises to 961.78 °C and remains there. Through appropriate furnace control, measurements can be taken during this phase. However, with the silver point, there is the problem that the resistance thermometers themselves drift when exposed to such high temperatures for so long. Therefore, in practice, a short measurement cycle is often preferred: e.g., allowing only 50% of the metal mass to solidify (plateau duration perhaps 1-2 hours) and then quickly terminating to avoid unnecessarily stressing the SPRT. The significance is still given, as the plateau value remains identical as long as solid and liquid phases coexist.
Uncertainties and SPRT Drift: The silver fixed point itself is as definable as the other metal points, but the achievable overall uncertainty is usually the highest. A significant limiting factor is – as mentioned – the behavior of the thermometers: Standard platinum resistance thermometers tend to age from ~660 °C onwards (grain boundary migration, stress relaxation in the wire, outgassing of the sheath atmosphere). At ~962 °C, these effects accelerate. It has been observed that a high-temperature SPRT can experience a drift of e.g., ≈10 mK within 24 hours at 961 °C. If such a thermometer is abruptly removed from the hot temperature fixed point, its properties change suddenly (mechanical stresses discharge); reports mention, for example, a jump of +35 mK in the triple point of water resistance after shock cooling from 961 °C to room temperature. Therefore, calibration laboratories proceed very cautiously: They limit the plateau time (often max. 4-6 hours at the silver point), does not cool the thermometer too quickly and subsequently subjects them to targeted temperature relaxation/annealing (e.g., 24 h at 450-650 °C, slow cooling) to restore the original state. Despite these difficulties, the silver point can be realized with a standard uncertainty of a few millikelvins. The reproducibility between different institutes is perhaps ±5 mK, which, when referring to 962 °C, is still extremely accurate (~5 ppm relative). Calibration certificates for SPRTs up to 960 °C often state an expanded uncertainty of a few tenths of a °C, which includes the long-term stability of the thermometer and other contributions. The temperature fixed point itself is significantly more precise. – Impurities: Silver must be of highest purity (6N) for the freezing point to be correct. Base impurities (Pb, Cu, etc.) lower it, but this is hardly significant with 6N-Ag. A more significant role is played, as mentioned, by dissolved oxygen: Liquid silver dissolves about 20 cm³ O₂ per 100 g Ag at 962 °C – which is considerable. As the melt cools, the solubility decreases and the oxygen escapes, which can lead to so-called “spitters” (the silver can literally pop up). To prevent this, the cell is kept under argon (O₂-free) and, if possible, under slight overpressure, so that no oxygen enters the metal at all. Graphite also helps here as it binds O₂. Another phenomenon is the phase transition behavior in the presence of wall reactions: Graphite can minimally dissolve in silver; during solidification, a thin carbide layer can form, potentially creating two simultaneous solidification fronts (one on the outside at the crucible wall, one inside at the insert). This would cause a not entirely flat plateau. However, modern cells have design features to avoid this (e.g., special coatings or defined cooling points). Finally, the plateau is also monitored for slope at the silver point to detect any impurities. Overall, despite its challenges, the silver fixed point is a clearly defined and reproducible temperature fixed point – it just requires significantly more experience and care in handling.
Note: Above the silver point, one leaves the domain of resistance thermometry. The ITS-90 defines temperatures for T > 961.78 °C using radiation pyrometry – for this, a blackbody is referenced to, for example, silver, gold, or copper fixed point temperatures, and then higher temperatures are measured using Planck’s law. Thus, silver (961 °C), gold (1064 °C), and copper (1084 °C) are also temperature fixed points, but they primarily serve as reference points for the optical scale (for high temperatures), while in the range up to silver, all temperature fixed points are used for contact thermometers (SPRTs). The procedures described here also apply in principle to gold and copper, but in practice, SPRTs are not operated up to those temperatures. Instead, from ~962 °C onwards, thermocouples or pyrometers are preferably calibrated using these temperature fixed points.
Summary
The temperature fixed points of the ITS-90 from -190 °C to ~1000 °C form a continuous network of defined temperatures. Each temperature fixed point is characterized by a specific phase transition of a pure substance and is uniformly established worldwide. By calibrating Standard Platinum Resistance Thermometers (SPRTs) at several of these points, the ITS-90 can be approximated over the entire range, allowing for high-precision temperature measurements. The achievable uncertainties are impressive: from the microkelvin range (water triple point) to a few 0.1 mK (gallium, mercury) to a few mK (aluminum, silver). However, it is important to note that this accuracy is only realized with sophisticated technology, pure materials, and experienced users. Factors such as hydrostatic pressure, self-heating of the SPRT, heat conduction, impurities, or isotope effects must be considered and corrected to achieve the nominal values of the temperature fixed points. The ITS-90 provides detailed guides and correction formulas for this purpose, ensuring good results under standard conditions. The described temperature fixed point cells and calibration procedures are now the standard for precise temperature metrology – from national standards to calibration laboratories to high-quality industrial measurement facilities, they ensure a uniform temperature scale with high reliability and accuracy.
Sources
- CCT Guidebooks: Guides to Thermometry – Bureau International des Poids et Mesures
Guide to the Realization of the ITS-90:
Part 1 – Introduction (2018)
Part 2.1 – Fixed Points: Influence of Impurities (2018)
Part 2.2 – Triple Point of Water (2018)
Part 2.3 – Cryogenic Fixed Points (2018)
Part 2.4 – Metal Fixed Points for Contact Thermometry (2021)
Part 5 – Platinum Resistance Thermometry (2021)
- Walter Blanke: The International Temperature Scale of 1990: ITS-90
- Thomas Klasmeier: Table Book “Temperature”, Edition 3
- G. F. Strouse: NIST Special Publication 250-81, Standard Platinum Resistance Thermometer Calibrations from the Ar TP to the Ag FP
- Henry E. Sostmann and John P. Tavener: FUNDAMENTALS OF THERMOMETRY – PART II – FIXED POINTS OF THE ITS-90 – CONFIDENCE IN THE METAL FREEZING POINTS OF ITS-90
