1.  Introduction

The triple point of water (TPW) is the unique physical state of water in which all three phases (solid, liquid and vapour) coexist at thermodynamic equilibrium. The TPW is realized in practice by using TPW cells in sealed borosilicate glass- or fused-silica-envelopes containing from $400{\mathrm{cm}}^3$ to $500{\mathrm{cm}}^3$ of high-purity water. A re-entrant well, located along the axis of the cell, allows for insertion of the Standard Platinum Resistance Thermometer (SPRT) to be calibrated. An ice mantle is produced around the thermometer well by one of the methods described in Subsection 5.1. After creating the ice mantle, the cell is accommodated in a water maintenance bath controlled at a temperature close to $0.01\mathrm{°C}$ (typically within few $\mathrm{mK}$) or in a Dewar flask containing crushed ice, and the equilibrium between the three phases is automatically established within the cell and can be maintained for many weeks.

2.  Manufacture of a triple point of water cell

The main steps in the manufacture of a TPW cell cover:

• The cell envelope (borosilicate or fused-silica) which is annealed to release strains and leak-tested to ensure that it is vacuum tight.

• A thoroughly cleaned and pre-conditioned cell-envelope to prevent its inner surface from dissolution into the water.

• A high-purity source water which is distilled, degassed and transferred into the cell envelope by distillation or by gravity.

• Flame-sealing of the cell at a constricted section of the filling tube.

• An isotopic and chemical analysis of a sample of the same water sealed in the cell.

Details of the manufacturing process of TPW cells can be found in [Barber et al. 1954, de Groot et al. 2002, Ya et al. 2005, Uytun et al. 2003]. Though some NMIs, mainly for research purposes, still manufacture TPW cells (CENAM, NIM, NMIJ, UME, VNIIM and VSL), nowadays the common choice for most users is to purchase TPW cells commercially available from different suppliers.

3.  Isotopic composition of the cell water

Natural water is a mixture of four main isotopologues: ¹H₂¹⁶O, ¹H₂¹⁷O, ¹H₂¹⁸O and ²H¹H¹⁶O. The Mise en Pratique for the definition of the kelvin, MeP-K [BIPM 2011] requires the water in the TPW cell to have the isotopic composition:

$\mathrm{0.000 155 76}$ mole of ²H per mole of ¹H,

$\mathrm{0.000 379 9}$ mole of ¹⁷O per mole of ¹⁶O, and

$\mathrm{0.002 005 2}$ mole of ¹⁸O per mole of ¹⁶O,

which are the amount-of-substance ratios of Vienna Standard Mean Ocean Water (VSMOW), based on the best measurement available [De Laeter et al. 2003].

Natural fractionation effects ensure that most of the continental surface (fresh) water, from which cells are made, is depleted in the heavy isotope ²H (indicated with $\text{D}$ in the following) and, to a lesser extent, ¹⁸O and ¹⁷O, with a strong dependence on the latitude, altitude and season at the location of the precipitation [Bowen and Revenaugh 2003]. During the distillation and degassing processes in the manufacture of the cells, the water may be further depleted or enriched [Nicholas et al. 1997, Peruzzi et al. 2007]. The combination of these effects leads to cells that allow realizing temperatures typically ranging between $110\mathrm{\mu K}$ below to $10\mathrm{\mu K}$ above the temperature realized with VSMOW water. Because of the dependence on source water and processing, the isotopic depression in cells is highly dependent on the cell manufacturer. Recently some manufacturers have adapted their manufacturing processes to obtain cells with water close to the VSMOW definition. The best of these cells may have an isotopic composition within $10\mathrm{\mu K}$ temperature equivalent of the ideal [Strouse and Zhao 2007, Tavener 2007].

Ideally, the isotopic composition of the cell water should be measured by taking a sample after the cell has been sealed [Nicholas et al. 1997, Strouse and Zhao 2007], and a correction $\Delta T_{\text{iso}}$ should be applied, that takes into account the deviation of the cell water from the VSMOW isotopic composition.

The deviation of the cell water from VSMOW is conventionally expressed in terms of $\mathrm{\delta }$D, $\mathrm{\delta }$¹⁸O and $\mathrm{\delta }$¹⁷O (called “$\mathrm{\delta }$-values”):

and similarly for $\mathrm{\delta }$D and $\mathrm{\delta }$¹⁷O. The subscription CAL emphasizes that the $\mathrm{\delta }$-value has been determined with respect to VSMOW. For all natural waters, the $\mathrm{\delta }$-values are in the parts-per-thousand range, so are expressed in permil (‰, per thousand); they are usually negative for most cells.

Besides VSMOW, to further improve the inter-laboratory reproducibility of the water isotopic composition measurements, Standard Light Antarctic Precipitation (SLAP) water [Gonfiantini 1978, Li et al. 1988] is also used to define the scale. The $\mathrm{\delta }$-values of SLAP have been defined based on consensus between expert laboratories taking part in a large international intercomparison [Gonfiantini, 1984]. They are $\mathrm{\delta }$D = -428 ‰ and $\mathrm{\delta }$¹⁸O = -55.5 ‰ with respect to VSMOW. These consensus values are used in the definition of the so-called normalized VSMOW-SLAP scale:

and similarly for D, with the value $-0.428$ in the nominator. All isotope laboratories usually report their isotope $\mathrm{\delta }$-values for water in this normalized way. It should be noted that the original reference VSMOW and SLAP waters are exhausted. Their successors, VSMOW2 and SLAP2 have been prepared with utmost care to resemble the originals to within the uncertainties. Only for SLAP2 the $\mathrm{\delta }$D value is -427.5 ‰ instead of -428 ‰.

For all naturally occurring surface waters, the isotopic composition is sufficiently close to that of VSMOW, and the correlation between the ¹⁸O and the ¹⁷O contents is so strong [Meijer and Li 1998] that the correction $\Delta T_{\text{iso}}$ to be applied to the triple-point temperature realized by a sample water can be specified by a linear function of only the $\mathrm{\delta }$D and $\mathrm{\delta }$¹⁸O values:

where the last term on the right accounts for both the $\mathrm{\delta }$¹⁷O and the $\mathrm{\delta }$¹⁸O effects, but requires only the knowledge of the $\mathrm{\delta }$¹⁸O.

The most precise set of isotopic depression constants presently available, and those specified for use with the ITS-90, are by Faghihi et al. (2015a and 2015b). These values are: $A_{\text{D}}=673\mathrm{\mu K}$ and $A_{\text{O}}=630\mathrm{\mu K}$, with estimated standard uncertainties of $4\mathrm{\mu K}$ and $10\mathrm{\mu K}$, respectively.

The uncertainty in the isotope correction is usually dominated by the uncertainties in $\mathrm{\delta }$D and $A_{\text{D}}$. For cells not more than $100\mathrm{\mu K}$ different from VSMOW, the uncertainties in the corrections are less than $2\mathrm{\mu K}$ at most, so are generally negligible.

The practice by some TPW cell manufacturers of adding un-natural, isotope-enriched waters to the initial source waters, to compensate for isotope depletion taking place during the purification process, is not recommended. After adding such enriched waters, the isotopic correction cannot be calculated using the recommended formula above and must be evaluated with the following instead:

which requires full isotopic analysis ($\mathrm{\delta }$D, $\mathrm{\delta }$¹⁸O and $\mathrm{\delta }$¹⁷O) and the use of a third depression coefficient $A_{17}=60\mathrm{\mu K}$, with estimated standard uncertainty of $1\mathrm{\mu K}$ [White and Tew 2010].

Most TPW cells made from continental fresh water can be expected to be within the temperature equivalents $-110\mathrm{\mu K}$ and $+10\mathrm{\mu K}$ of VSMOW, so a correction of $+50\mathrm{\mu K}$ and a standard uncertainty of $35\mathrm{\mu K}$ will account for typical variations in isotopic composition. Such a simple alternative is acceptable where no isotopic information is available.

A further, smaller, isotopic effect occurs with isotopic fractionation between water and ice when the cell is in use [Nicholas et al. 1997]. In theory, the effect causes the temperature to be dependent on the frozen fraction and ranges from no effect for zero frozen fraction to about $-15\mathrm{\mu K}$ for a cell nearly fully frozen. In practice, the freezing rates for cells are sufficiently fast and the isotopic equilibration process is so slow that significant fractionation does not occur during the initial freezing of the mantle [Ferrick et al. 2002]. Measurements of the composition of the water and ice from partly frozen cells support the theory: cell frozen normally over a period of a few hours exhibit isotopic fractionation of no more than $2\mathrm{\mu K}$ [Nicholas et al. 1997, Renaot et al. 2005]. One cell frozen slowly over a few days exhibitedfractionation of $7\mathrm{\mu K}$ [Tavener 2006]. However, additional fractionation occurs with freezing at the ice-water interface around the thermometer well. Detailed understanding of the effect of repeated freezing and melting is not known, but it could be responsible for a depression of several microkelvin and some of the observed non-repeatability of cells.

4.  Impurities

The temperature realized by a TPW cell is exactly $273.16\mathrm{K}$ only for ideally pure VSMOW water. Though extreme care in water purification is taken during the manufacture, the water enclosed within a TPW cell is never completely free of impurities.

Impurities in the water of TPW cells give rise to the most significant source of uncertainty and constitute the most difficult effect to assess. Recent TPW comparisons [Stock et al. 2006, Peruzzi et al. 2009] exhibited results dispersed over ranges exceeding $200\mathrm{\mu K}$, largely due to impurities.

There are four main sources of impurity in the water of a TPW cell:

1. Chemicals used in the cleaning and pre-conditioning of the cell may be a source of contamination. These may include HF, HCl and NH4. Most of these materials have a high dissociation constant, so are detectable from measurements of electrical conductivity [Ballico 1999].

2. Borosilicate glass, from which most cells and their manufacturing plant are made, is weakly soluble in water resulting in a temperature depression at the time of manufacture and additional drift with time. In high quality cells, actual depressions at the time of manufacture can be as low as a few microkelvin [Peruzzi et al. 2007, Strouse and Zhao 2007]. The drift rates range up to $-20\mathrm{\mu K}/\text{year}$ with a mean rate of $-4\mathrm{\mu K}/\text{year}$, although the variation between the cells is very large [Hill 2001]. With borosilicate cells, the drift rate is likely to increase with time and is very dependent on the treatment of the glass prior to the manufacture of the cells [White et al. 2005]. Storage of the cells near $0\mathrm{°C}$ and manufacture of the cells from fused silica both reduce the drift rate [Zief and Speights 1972, Strouse and Zhao 2007]. The use of fused silica cells may, depending on the manufacturing process, result in a higher level of particular impurities and a higher initial impurity level due to the higher temperature required to melt pure silica and seal the cell.

3. Low-volatility compounds in the source water: for example, light hydrocarbons have a similar boiling point to water so distillation may not remove them. The typical magnitude of this impurity effect is unknown, but anecdotal evidence suggests that cells subjected to a prolonged degassing during manufacture (approximately 2 days) can be $20\mathrm{\mu K}$ higher than other cells, after isotope corrections have been applied.

4. Residual gases in the cell water. However, since one quarter of the difference between the temperature of the ice point and the TPW is due to dissolved gasses [Ancsin 1982], it can be inferred that any impurity effect due to dissolved gasses is smaller than the residual-gas-pressure effect, which is generally negligible.

The preferred method for estimating the influence of impurities and the resulting uncertainties is the “Sum of Individual Estimates” (SIE), see Guide Section 2.1 Influence of impurities, which requires the determination of the concentrations of allthe relevant impurity species by applying an appropriate analysis technique to a representative sample of the cell water.

Inductively-Coupled Plasma Mass Spectrometry (ICPMS), applied to water samples separated from the cell, showed that the total impurity concentration in high-quality TPW cells can be as low as $0.1\mathrm{\mu mol}\cdot {\mathrm{mol}}^{-1}$ [Peruzzi et al. 2007]. ICPMS performed on water from old borosilicate cells resulted in a total impurity concentration of up to $4\mathrm{\mu mol}\cdot {\mathrm{mol}}^{-1}$ [Hill 1999]. Nevertheless, the results of ICPMS are regarded as semi-quantitative due to intrinsic features of the technique and of the sample preparation. Moreover, ICPMS analysis can detect only a limited number (about 60) of elemental impurities and no organic impurities.

Impurity fractionation effects (or segregation) between water and ice, similar to those described in the previous subsection (isotopic fractionation), may occur during the preparation of the ice mantle and consequent storage of the cell in the maintenance bath. The size of such effects depends on

1. the amount of impurities species,

2. the equilibrium distribution coefficient $k_0^i$ of the impurities and

3. the details of freezing (freezing rate, diffusion coefficient of the impurities in the solid and in the liquid, presence of convection during freezing e.g. stirring of the liquid).

Ice was reported not to be able to dissolve any compound, e.g. $k_0^i=0$ for any water impurity, except for HCl, HF, NH3, NH4F, LiF, NaF and KF having $k_0^i\ne 0$ [Lliboutry 1964, Workman and Reynolds 1950, Zaromb and Brill 1956, Jaccard and Levi 1961, Brill 1957, Granicher 1963, Gross 1967]. Even for such impurities, $k_0^i<<1$ is fulfilled (for example, $k_0^{\text{HF}}=0.01$ [Jaccard 1963] and $k_0^{\text{HC1}}=0.003$ [Leviand Lubart 1961]), so it is reasonable to assume $k_0^i<<1$ for any impurity in water and apply Raoult’s law and the Overall Maximum Estimate (OME) method, see again Guide Section 2.1 Influence of impurities, to TPW cells. This means that a plot of themeasured TPW temperature versus the inverse liquid fraction $1/F$ allows the determination of the impurity level and temperature depression [Mendez-Lango 2002].

During freezing, the impurities are rejected into the liquid by the solid-liquid interface or trapped in the ice at grain boundaries. When the first ice-water interface is formed around the thermometer well, the ice so formed is pure. Measuring the temperature realized by the cell in this state and again after the cell has been (gently) inverted several times to mix the inner melt with the main body of water, may give an indication of the impurity level [ASTM 2002]. This test must be carried out with the first formation of the ice-water and measurements must be corrected for self heating. A similar effect occurs with extended use of a cell over a week or longer. The water around the well and the main body appear to mix slowly causing a gradual depression of the observed temperature with time [Stock et al. 2006].

The smallest uncertainty component due to impurities is achieved in recently manufactured high-quality cells and is probably below $10\mathrm{\mu K}$ [Nguyen and Ballico 2007, Strouse and Zhao 2007, Tavener 2007]. The dispersion of results in recent international comparisons [Stock et al. 2006, Peruzzi et al. 2009] suggests that a depression and uncertainty due to impurities of about $50\mathrm{\mu K}$ is more typical for older cells.

5.  Hydrostatic pressure effect

The definition of triple point temperature is realized only at the liquid/solid surface in contact with the vapour of the TPW cell but the sensing element of the SPRT is located near the bottom of the thermometer well to provide for adequate immersion. The TPW temperature must therefore be corrected for the hydrostatic pressure difference between the liquid/solid surface and the thermal centre of the SPRT sensing element. The correction is:

where $\text{d}T/\text{d}h$ is the hydrostatic pressure coefficient defined by the ITS-90, i.e. $-0.73\cdot {10}^{-3}\mathrm{K}{\mathrm{m}}^{-1}$. The difference in vertical elevation between the liquid surface $h_{\text{1iq}}$ and the thermal centre of the SPRT sensing element $h_{\text{SPRT}}$ amounts to $200$ to $300\mathrm{mm}$, depending on the size of the cell, translating into a hydrostatic pressure correction of $150\mathrm{\mu K}$ to $220\mathrm{\mu K}$.

The uncertainty related to the hydrostatic pressure correction is typically a few $\mathrm{\mu K}$ [Stock et al. 2006]. When a profile of the TPW temperature as a function of the SPRT immersion is measured (immersion profile, see [Stock et al. 2006]), the departure of the measured immersion curve from the expected hydrostatic pressure line provides an estimate of the uncertainty due to immersion and stray thermal effects, see [Stock et al. 2006].

6.  Realization of the TPW temperature in a TPW cell

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