Synthesis of In‐House Produced Calibrated Silver Phosphate with a Large Range of Oxygen Isotope Compositions

The large range of stable oxygen isotope values of phosphate‐bearing minerals and dissolved phosphate of inorganic or organic origin requires the availability of in‐house produced calibrated silver phosphate of which isotopic ratios must closely bracket those of studied samples. We propose a simple protocol to synthesise Ag3PO4 in a wide range of oxygen isotope compositions based on the equilibrium isotopic fractionation factor and the kinetics and temperature of isotopic exchange in the phosphate–water system. Ag3PO4 crystals were obtained from KH2PO4 that was dissolved in water of known oxygen isotope composition. Isotopic exchange between dissolved phosphate and water took place at a desired and constant temperature into PYREX™ tubes that were placed in a high precision oven for defined run‐times. Samples were withdrawn at desired times, quenched in cold water and precipitated as Ag3PO4. We provide a calculation sheet that computes the δ18O of precipitated Ag3PO4 as a function of time, temperature and δ18O of both reactants KH2PO4 and H2O at t = 0. Predicted oxygen isotope compositions of synthesised silver phosphate range from −7 to +31‰ VSMOW for a temperature range comprised between 110 and 130 °C and a range of water δ18O from −20 to +15‰ VSMOW.

During the past decades, the rise of automated devices coupled to mass spectrometers operating in continuous flow or in dual-inlet mode have resulted in an explosive growth of the number of data published in scientific fields exploiting the stable isotope ratios of organic and inorganic compounds. Consequently, there is an increasing use and need for developing in-house produced materials calibrated against certified reference materials. Moreover, a large range of isotopic compositions is highly desirable to bracket the expected compositions of the studied sample collection as well as to be able to perform a two-point calibration, which is required for the acquisition of high-quality data.
In Earth and Archaeological Sciences, to only mention the most concerned research fields, the 18 O/ 16 O ratio of the phosphate radical  ) is now widely used to reconstruct the palaeoclimates of the Earth (Kolodny and Raab 1988, Fricke and O'Neil 1996, Amiot et al. 2004, Joachimski et al. 2012, Goedert et al. 2017, the thermophysiology and ecology of extinct vertebrates (Barrick and Showers 1994, Fricke and Rogers 2000, Amiot et al. 2006, T€ utken and Vennemann 2009, Bernard et al. 2010, Rey et al. 2018, the source and recycling of dissolved phosphate in natural waters (Markel et al. 1994, McLaughlin et al. 2006, Pistocchi et al. 2017) as well as the diet and living environment of past human populations (White et al. 1998, Evans et al. 2006, Lightfoot and O'Connell 2016, Pellegrini et al. 2016. The most common way to determine the 18 O/ 16 O ratio of the phosphate radical is to isolate it as silver phosphate (Ag 3 PO 4 ) crystals through a wet chemistry procedure (Crowson et al. 1991). Then, they are pyrolysed in the presence of graphite at high temperature to produce either CO 2 or CO measured either offline or online with an isotope ratio mass spectrometer (O'Neil et al. 1994, L ecuyer et al. 1998, 2007, Fourel et al. 2011. Fluorination has also been proved to be a precise and accurate technique that provided the first determination value of the d 18 O SMOW value of the Miocene Florida phosphorite NIST SRM 120c (L ecuyer et al. 1993). Whatever the research field, the d 18 O value of calcium phosphate minerals (e.g., biogenic, magmatic or hydrothermal apatite) and dissolved phosphate (H 2 PO -4 ,HPO 2-4 and PO 3-4 ) range world-wide from about a few per mil up to values close to 30‰. Indeed, high-temperature apatites of magmatic or hydrothermal origin have d 18 O ranging from 6‰ to 11‰ (Sun et al. 2016). With respect to soils and their connected aquatic environments (rivers, ponds and lakes), dissolved phosphate also displays a large range of oxygen isotope compositions between 8‰ and 25‰ (Markel et al. 1994, Gruau et al. 2005, Angert et al. 2012, Davies et al. 2014, Tamburini et al. 2014, Pistocchi et al. 2017, Granger et al. 2017, Bauke et al. 2018). In the case of dissolved phosphate being isotopically equilibrated with ambient water through biological recycling (Longinelli et al. 1976, Liang and Blake 2009, Chang and Blake 2015, von Sperber et al. 2017, it is expected to have d 18 O values that range from 6‰ (high-latitude freshwater environments) to ≈ 20‰ for seawater and to ≈ 22‰ for low-latitude freshwater environments in agreement with the available isotopic fractionation equations (Kolodny et al. 1983(Kolodny et al. , L ecuyer et al. 2013). In the case of biogenic apatites, their d 18 O values range from a few ‰ for vertebrates drinking highly 18 O-depleted waters (d 18 O as low as -20‰) relative to SMOW (high-altitude or highlatitude environments; e.g., Rey et al. 2018) up to about 30‰ for vertebrates living in arid environments (L ecuyer et al. 1999a).
To the present time researchers have used NIST SRM 120c, for which an agreed d 18 O SMOW value of 21.7 ± 0.2‰ (VSMOW) was only established in recent years. Indeed, Chenery et al. (2010) proposed a comparable value of 21.7 ± 0.7‰ after a 6-month period of repeated measurements of NIST SRM 120c calibrated against NBS 127 barium sulfate, which is consistent with the mean value of published data for NIST SRM 120c (21.5 ± 0.5‰) analysed in different laboratories (Chenery et al. 2010). Thereafter, Halas et al. (2011) confirmed the absence of any sizable isotopic fractionation effect during the conversion of Ag 3 PO 4 into CO, and proposed a mean d 18 O value of 21.8 ± 0.2‰ for NIST SRM 120c based on inter-laboratory calibrations. It is also worth noting that Vennemann et al. (2002) proposed a significantly higher value of 22.5‰ for NIST SRM 120c, although later Vennemann (2012) concluded that the most accurate value for NIST SRM 120c is likely close to 21.7‰. This value of 21.7 ± 0.2‰ for NIST SRM 120c is now widely accepted as exemplified by the recent study published by Huang et al. (2018). It has also to be pointed out that an isotopic ratio of 21.7 ± 0.16‰ for NIST SRM 120c was determined for the first time by using quantitative fluorination 25 years ago (L ecuyer et al. 1993). Nevertheless, it must be underlined that the Florida phosphorite NIST SRM 120c is a compositional, not an isotopic international reference material, and hence, its oxygen isotope ratio has never been officially certified. In order to comply with the IUPAC recommendations (Brandt et al. 2014), a two-point calibration can also be performed with NBS 127, which is a barium sulfate calibrated reference material for oxygen isotopes (d 18 O = 9.3‰ VSMOW), as was done by, for example, Rey et al. (2018) and Goedert et al. (2018). However, we underline that NBS 127 is a different matrix, (i.e., a barium sulfate instead of a silver phosphate)a chemical difference that needs to be taken into account during calibration procedures even though the recently developed 'purge-and-trap' technology was able to overcome this pitfall as shown by Fourel et al. (2011). Moreover, the stock of NBS 127 provided by the IAEA is now exhausted, thus seriously reducing the possibility of calibrating the oxygen isotope composition of solid matrices. Therefore, the need for alternative calibrated material is becoming critical.
Here, we propose a simple and inexpensive protocol to synthesise silver phosphate in a wide range (≈ 35‰) of oxygen isotope compositions based on the thermodynamic properties of the phosphate-water system, more specifically the equilibrium isotopic fractionation factor and the kinetics and temperature of isotopic exchange according to the data published by L ecuyer et al. (1999b). Beyond the theoretical considerations, an 'Excel calculation sheet' is provided (Table S1), which allows the d 18 O value of precipitated Ag 3 PO 4 to be predicted by tuning various parameters such as the temperature of oxygen isotope exchange, the duration of the reaction and the isotopic compositions of reactants.

Theoretical background
First-order kinetics of isotopic exchange between dissolved phosphate and water The most common pH-dependent speciation of phosphorus in aqueous solutions of low ionic strength are (a) the dihydrogen phosphate ion (H 2 PO -4 ), (b) the hydrogen phosphate ion (HPO 2-4 ) and (c) the phosphate ion (PO 3-4 ) according to the three following chemical equilibria at 25°C (Zeebe and Wolf-Gladrow 2001, Figure 1): For seawater (pH ≈ 7.6-8.4), the dominant species is HPO 2-4 while in the case of natural freshwater it is either H 2 PO -4 or HPO 2-4 . L ecuyer et al. (1999b) performed kinetic and isotopic experiments at a pH close to 5, for which H 2 PO -4 was almost the only species present in solution ( Figure 1). During first-order reaction kinetics, the rate of isotopic exchange can be quantified by considering f as follows, which is the mole fraction of exchanged isotopes between the phosphate ions and water molecules, while k is the rate constant (s -1 ) of the isotopic reaction: with A being the Arrhenius pre-exponential factor, E a the activation energy (kJ mol -1 ) of the isotopic reaction, R the universal gas constant, T the absolute temperature (K), t the time (

Experimental determination of thermodynamic variables (k, E a and a)
The rate constant k: L ecuyer et al. (1999b) performed a best fit of their data with the Arrhenius law and found a strong temperature dependence of the rate constant k: A convenient way to report graphically the rate of isotopic exchange against time is to rewrite Equation (4) as follows: The absolute value of the slope of the straight line for a given temperature T is the rate constant k of the reaction. Equation (7) also allows the half-time (t 1/2 ) of the isotopic reaction to be determined by solving it for f = 0.5 as follows: The activation energy E a of the reaction: Due to the tetrahedral architecture and covalent bonds (P-O) of the phosphate ion, the activation energy E a necessary to promote oxygen isotope exchange between phosphate and water molecules is very high, with a value of 133.6 ± 4.6 kJ mol -1 at pH = 5 (L ecuyer et al. 1999b). The activation energy E a is calculated from the slope of the straight line defined by Equation (6) combined with Equation (5).
The fractionation coefficient a between H 2 PO -4 and H 2 O: At thermodynamic equilibrium, and according to the Mass Action Law, we can write the following isotopic exchange equation: Rearranging the terms in Equation (9), the equilibrium constant or isotopic fractionation factor called a, which is determined for a given temperature T, is expressed as follows: It is important to note that this temperature-dependent fractionation factor a must be independent from the isotopic compositions of both reactants according to Northrop and  Application to the synthesis of silver phosphate of known oxygen isotope ratio Experimental protocol of silver phosphate precipitation We present a protocol of silver phosphate precipitation from a highly soluble salt in water (solubility = 25 g 100 ml -1 at 25°C, Lide 2005) such as potassium dihydrogen phosphate KH 2 PO 4 (L ecuyer et al. 1999b). An aliquot of 50 mg of pure high-grade (> 99.5% m/m) Sigma-Aldrich TM synthetic KH 2 PO 4 was dissolved in 35 ml of de-ionised water of known oxygen isotope composition. The resulting aqueous solutions had a concentration of 1 g l -1 (10.6 mmol l -1 ) of phosphate ions with a pH of 5 at ambient temperature. It is important to note that the amount of oxygen in water is much higher than in the pool of dissolved phosphate (oxygen molar ratio between H 2 O and KH 2 PO 4 ≈ 5000) and, consequently, the change in the oxygen isotope composition before and after equilibrium is not detectable with respect to the analytical uncertainties (1s = 0.05‰ for the d 18 O value of H 2 O). The solutions were transferred into Ace Glass TM PYREX tubes and sealed with threaded Teflon plugs. Each set of tubes for a given temperature was placed in a high precision oven for runtimes defined by the user. Samples were withdrawn at desired times and quenched in cold water to room temperature within a few minutes. Each sample of dissolved phosphate was quantitatively precipitated as silver phosphate (chemical yields were close to 100%) according to the protocol determined by Firsching (1961), which means that all the dissolved phosphate species (≈ H 2 PO -4 ) were converted into Ag 3 PO 4 . For a chemical yield of 100%, the expected amount of silver phosphate is close to 150 mg. Running an experiment batch with ten Ace Glass TM PYREX tubes at the same time ensures the production of about 1.5 g of silver phosphate crystals of predicted oxygen isotope composition.

Oxygen isotope analysis of silver phosphate
Oxygen isotope compositions were measured using a high-temperature pyrolysis technique involving a Var-ioPYROcube TM elemental analyser (EA) interfaced in continuous flow (CF) mode to an Isoprime TM isotope ratio mass spectrometer (IRMS; EA-Py-CF-IRMS technique (L ecuyer et al. 2007(L ecuyer et al. , Fourel et al. 2011 at the University Claude Bernard Lyon 1. For each sample, five aliquots of 300 lg of Ag 3 PO 4 were mixed with 300 lg of pure carbon black powder and loaded in silver foil capsules. Pyrolysis was performed at a temperature of 1450°C. Measurements were calibrated against NIST SRM 120c (natural Miocene phosphorite from Florida) and NBS 127 (barium sulfate, BaSO 4 : d 18 O = 9.3‰ VSMOW). The d 18 O value of NIST SRM 120c is fixed at 21.7‰ (VSMOW) according to L ecuyer et al. (1993) who determined this value by fluorinating silver phosphate crystals (n = 25, 1s = 0.16) at 600°C for 12 h, and calibrated the oxygen isotope ratios with the certified reference material NBS 28 quartz (9.5 ± 0.2‰), and measurement standards 'Snowbird' quartz (16.1 ± 0.1‰) and tholeiitic basaltic glass CIRCE 93 (5.6 ± 0.1‰).

Predicted oxygen isotope composition of synthesised silver phosphate
According to Equation (4) We emphasise that the recommended working temperature range is 110-130°C. Below a temperature of 110°C, the reaction kinetics are so slow that significant isotopic exchange takes months, or even years when the temperature is < 100°C. On the other hand, above a temperature of 130°C, the Ace Glass TM PYREX tubes sealed with a threaded Teflon TM plug could start to leak, leading to a shift of the initial oxygen isotope ratio of water. Finally, we provide an 'Excel calculation sheet' (Table S1) that automatically computes the oxygen isotope composition of the precipitated silver phosphate depending on time t and temperature T of isotopic exchange as well as the oxygen isotope compositions of reactants KH 2 PO 4 and H 2 O at t = 0. Predicted oxygen isotope compositions of synthesised silver phosphate ranged from -7 to +31‰ VSMOW for a temperature range between 110 and 130°C and a range of water d 18 O from -20 to +15‰ VSMOW (Figure 2). For example, Table S1 shows a possible tuning of the parameters described above to obtain silver phosphate crystals with a d 18 O value (‰ VSMOW) that mimics that certified for the barium sulfate international reference material NBS 127.
To further demonstrate the efficiency of this method, we measured the oxygen isotope compositions of three silver phosphates with expected d 18 O values ranging from about +10 to +22‰ VSMOW (Table 1), which cover the most common range of documented d 18 O values for natural dissolved phosphate and apatites. We report the measured d 18 O values as a function of the expected ones, and obtained a strong linear correlation with a slope close to 1 (a = 1.032 ± 0.029) and an intercept close to 0 (b = -0.794 ± 0.466) (Figure 3). Within this isotopic variation range of 12‰, the calculated standard error is 0.24‰, which is comparable to the error associated with the established d 18 O value of NIST SRM 120c. This shows that the method described is suitable to produce robust in-house produced calibrated Ag 3 PO 4 for oxygen isotope measurements in phosphatic compounds.

Potential application to the sulfate-water system
A similar protocol may be applied to the sulfatewater system to produce barium sulfate of known oxygen isotope composition. Indeed, the required thermodynamic properties such as the rate constant k, the activation E a and the T-dependent isotopic fractionation factor a have been determined by Chiba and Sakai (1985). The oxygen isotope measurement of sulfates, whatever their natural or anthropogenic origin, could be very useful in tracing their mechanisms of formation. For instance, sulfates may form in the atmosphere from the oxidation of sulfur dioxide by hydroxyl radicals, hydrogen peroxide or ozone. Sulfates may also result from a high-temperature oxidation to produce sulfur trioxide during combustion processes before being ultimately hydrated to form sulfuric acid. Various oxygen isotope fractionations could be associated with these chemical reactions, requiring the production of calibrated barium sulfate with different d 18 O VSMOW values.   (6) and (12)

Conclusions
The protocol developed in this study is based on the equilibrium isotopic fractionation factor a, the kinetics k and temperature T of isotopic exchange in the dissolved phosphate-water system. It offers the possibility to produce in a reasonable amount of time (a few days or a couple of weeks) about 1.5 g (the equivalent of 1000 measurements) of silver phosphate of known oxygen isotope composition. Moreover, the tuning of some parameters (time and temperature of isotopic exchange and the compositions of reactants) allows the synthesis of silver phosphate within a large range (≈ 35‰) of oxygen isotope ratios that match the documented natural variability for both phosphatebearing minerals and dissolved phosphate of organic or inorganic origin.