ABSTRACT
Secondary fixed points, such as the ice point and palladium melting point in thermometry and saturated salt solutions in hygrometry, may be more reproducible than the interpolating instruments (PRTs, thermocouples and relative humidity hygrometers) with which they are used. For this reason, they are good starting points for metrological traceability in mid-level calibration laboratories.
However, the traceability chain becomes less clear in such cases, as they are neither (i) direct realisations of an SI unit, nor (ii) artefacts that may be sent to an NMI for calibration. (Such fixed points are often generated/realised when needed and thereafter disposed of.) In fact, traceability is to a method of preparation/realisation, often one which is internationally recognised and codified in a documentary standard.
However, the process of proving and maintaining traceability is similar for secondary and primary fixed points, as
(i) primary fixed points and their realisation are subject to the same sources of uncertainty, error or drift that affect secondary fixed points, and
(ii) primary fixed points (as well as interpolating standards such as PRTs) require both a) interlaboratory comparisons (ILCs) to validate the user’s ability to realise/use them, and b) intermediate checks to confirm their continuing accuracy between ILCs, in the same way that secondary fixed point realisations do.
Hence, it is argued that metrological traceability may be as reliably (and often more accurately) maintained using secondary fixed point standards (periodically benchmarked against other laboratories via ILCs using suitable transfer instruments, and subject to intermediate checks between such ILCs) as using more “traditional” thermometry and hygrometry measurement standards.
Considering the typical drift of interpolating instruments and fixed points over time, a hybrid calibration/fixed point approach is recommended for PRT thermometry, and a fully fixed point-based approach is recommended for relative humidity hygrometry.

INTRODUCTION

Metrological traceability in a mid-level Temperature or Humidity calibration laboratory is most simply achieved by periodically submitting an interpolating instrument (such as a PRT, thermocouple or hygrometer) for calibration at a more accurate laboratory, such as a National Metrology Institute (NMI) with Calibration and Measurement Capabilities (CMCs) published in Appendix C of the BIPM Key Comparison Database (KCDB) [ILAC-P10:2020, ISO/IEC 17025:2017 Annex A].
(High-level laboratories may maintain primary standards, such as ITS-90 defining fixed points in Temperature or Josephson voltage and quantum Hall resistance standards in the Electrical field, but there are no such commercial labs in South Africa.)

Traceability via periodic calibration is reasonable, if the drift of the calibrated reference standard is sufficiently small in the interval between calibrations. For the purposes of this article, we will consider drift up to one-third of the typical expanded uncertainty to be tolerable. (An uncertainty component smaller than 1/3 of the combined uncertainty is effectively negligible.)
In this article, it will be shown that
(i) while high-quality industrial (“semi-standard”) PRTs may drift little enough to rely only on periodic calibration, improved accuracy is achieved by “re-zeroing” the PRT against the ice point (i.e., applying a fresh R0 or Rtp value) between calibrations;
(ii) PRTs of moderate quality drift sufficiently that intermediate checks are essential and re-zeroing is highly recommended;
(iii) high-quality RH hygrometers are often stable enough to get by with a two-year calibration interval, but reference salt solutions may only need benchmarking every three to four years;
(iv) RH hygrometers of moderate quality may drift so much that a one-year calibration interval is barely frequent enough.

On the basis of this analysis of drift, it will be recommended that mid-level Thermometry laboratories use the ice point together with calibrated PRTs as the basis of their traceability, and that Hygrometry laboratories without access to dewpoint standards use reference salt solutions as their starting point for traceability.

DRIFT/REPRODUCIBILITY OF IPRTs AND THE ICE POINT

Let’s assume that a mid-level Thermometry laboratory wishes to achieve an expanded uncertainty of 0.1 K with its industrial PRT (IPRT) reference standard. So, they tolerate drift up to 0.033 K before recalibrating: how long may the calibration interval be?

At 0.0035 K/year, the calibration interval of this high-quality IPRT may be as long as nine years.

Is the ice point reproducible enough to improve this IPRT’s performance?

Yes, 2015, 2017 and 2024 ILCs show agreement with NMISA within ~0.01 K (and the less accurate 2020 ILC shows agreement with the reference lab within 0.02 K), so re-zeroing the PRT’s calibration function every three years by applying a fresh R0 value may be beneficial.

The author has experience of a moderate-quality IPRT, subjected to unknown usage, where R0 dropped by 0.06 K over three years. If the drift was uniform at 0.02 K/year, an intermediate check at the ice point (and possible re-zeroing) at least every six months would be highly recommended for such a reference standard.

DRIFT/REPRODUCIBILITY OF RH HYGROMETERS AND SATURATED SALT SOLUTIONS

Let’s assume that a mid-level Hygrometry laboratory wishes to achieve an expanded uncertainty of 1.5 %rh with its relative humidity (RH) hygrometer reference standard. So, they tolerate drift up to 0.5 %rh before recalibrating: how long may the calibration interval be? First, we consider two high-quality RH hygrometers:
(Note: The data series graphed below are offset from each other for greater clarity, so only the change/variation in each series should be considered.)

At 0.2 %rh/year, these high-quality RH hygrometers may be used for around two years before recalibration.

Are saturated salt solutions more stable or reproducible than this?

Yes, at 0.1 %rh/year, salt solutions appear to be at least twice as reproducible or stable as high-quality RH hygrometers.

Here are reproducibility data of home-made saturated salt solutions:

Estimating the achievable uncertainty from the spread of ILC results (LV-RV) over nine years, U(k=2) = (max-min)/√3 = 1.0 to 1.5 %rh. (Remember that the series are offset from each other in the graph: in fact, (LV-RV) is within ±1.5 %rh for all but one result over the nine years.)
(Note that the NMISA salt solutions in the preceding graph are “sealed” in capsules with a semi-permeable membrane, while the home-made ones are open. While the former may be more stable as long as a saturated solution persists, the latter are more easily refreshed by adding or removing solid or liquid. A salt solution capsule requires careful storage in an appropriate humidity-controlled environment, for a long operating life.)

How do moderate-quality RH hygrometers compare to salt solutions?

At 0.4 to 1 %rh/year, these moderate-quality RH hygrometers would need recalibration every 6 to 12 months to meet the drift requirement. Considering these drift rates, it would be preferable to base a mid-level Hygrometry laboratory’s traceability on saturated salt solutions (such as those studied by Greenspan), with verification of the salt standards by RH hygrometers (check hygrometers).

CONCLUSIONS

∙Measurement data over periods of five to nine years demonstrate that:
– the ice point may be reproducible to 0.01 K, equivalent to three years of drift for a high-quality IPRT, or six months of drift for a moderate-quality IPRT,
– a saturated salt solution may be stable or reproducible to 0.1 %rh/year, while an RH hygrometer may drift 0.2 to 1 %rh/year.
∙Based on these drift data, it is recommended that
– an IPRT reference standard be checked periodically at the ice point, and its calibration data be adjusted using a new value of R0, when observed drift at the ice point reaches 0.01 K,
– salt solutions be used as reference standards in preference over RH hygrometers, unless RH hygrometers of the highest quality are available,
– any fixed point, but particularly a salt solution, should be subject to intermediate checks, typically using one or more check hygrometers (or a check PRT for a thermometric fixed point).

Contact the author at LMC-Solutions.co.za.