Sodium incorporation into inorganic CaCO 3 and implications for biogenic carbonates

The sodium content of biogenic carbonates shows potential as a palaeoceanographic proxy for salinity and/or calcium concentration but the incorporation of Na + into inorganic and biogenic calcite is poorly understood. Taxonomic and conspeciﬁc variations in the sensitivity of carbonate Na/Ca to seawater Na + /Ca 2+ and salinity point to a biological inﬂuence on Na + partitioning and/or covariations with other environmental parameters. One major unknown of the biological control during calciﬁcation is the rate of mineral precipitation, which has a strong control on trace-element partitioning in inorganic carbonate systems. We conducted inorganic CaCO 3 precipitation experiments where the eﬀect of solution composition and crystal growth rate on Na + uptake by carbonate crystals are independently assessed. Calcite crystals were precipitated at rates varying from 10 (cid:1) 6.5 to 10 (cid:1) 4.5 mol/m 2 /s, while faster growth rate than 10 (cid:1) 4.5 mol/m 2 /s resulted in the coprecipitation of aragonite and vaterite. For a given crystal growth rate, calcite Na/Ca increases by 0.22% per % increase in solution (Na + ) 2 /Ca 2+ activity ratio. However, calcite Na/Ca increases up to ﬁvefold per order of magnitude increase in crystal growth rate, suggesting crystal growth rate and precursor phases are likely dominant controls on marine carbonate Na/Ca. We use these results in the framework of the DePaolo (2011) model for trace element uptake by calcite to assess the origin of variable (Na/Ca) foraminifer sensitivities to [Ca 2+ ] seawater and salinity. Last, maximum mineral growth rates are estimated for a range of marine carbonates based on known carbonate Na/Ca and the (Na + ) 2 /Ca 2+ activity ratio of seawater. Estimated rates vary from 10 (cid:1) 5.6 (planktic foraminifers) to above 10 (cid:1) 4 (sea urchins) mol/m 2 /s. Such high mineral growth rates imply high degrees of oversaturation with respect to calcite (10 to >100), supporting the idea that elemental partitioning and isotopic fractionation recorded in marine biogenic carbonates are controlled by kinetic rather than equilibrium exchanges.

However, the fundamental variables behind the 'salinity' and 'Ca 2+ concentration' effects have yet to be validated and the interplay of multiple driving variables could potentially complicate applications of the calcite Na/Ca proxy. Two significantly distinct models of Na + incorporation in calcite have been suggested based on inorganic calcite growth experiments: (1) crystal lattice incorporation of Na + where two Na + substitute for one Ca 2+ and calcite Na/Ca is a function of the solution (Na + ) 2 /Ca 2+ activity ratio (White, 1977(White, , 1978 and (2) interstitial occupation of Na + where calcite Na/Ca depends on the solution Na + concentration or activity and number of lattice defects (Kitano et al., 1975;Ishikawa and Ichikuni, 1984;Busenberg and Plummer, 1985;Okumura and Kitano, 1986). In addition, calcite Na/Ca has been shown to significantly increase with increasing crystal growth rate and the solution SO 4 2À concentration (Busenberg and Plummer, 1985) as well as with the solution citrate concentration (White, 1978). The effects of individual parameters on Na + uptake by calcite have not yet been integrated into a predictive model of calcite Na/Ca due to the absence of data on crystal growth rate (Kitano et al., 1975;White, 1978;Ishikawa and Ichikuni, 1984) and/or correlations between multiple parameters affecting Na + partitioning. For example, Busenberg and Plummer (1985) reported an increase in Na + incorporation into calcite with increasing crystal growth rate but variable concentrations of SO 4 2À in solution (and in calcite) interfered with the solution-crystal Na + exchange and prevented a clear assessment of the impact of crystal growth rate on calcite Na/Ca.
With regards to biogenic CaCO 3 , calcification commonly occurs in solutions with altered chemistries relative to the surrounding environment, contributing to elemental offsets between taxa that precipitated within the same environment (e.g. foraminifers: Erez, 2003;de Nooijer et al., 2014) and in heterogeneities within their shell walls (e.g. Spero et al., 2015;Branson et al., 2016;Fehrenbacher et al., 2017;Mezger et al., 2018Mezger et al., , 2019Bonnin et al., 2019;Geerken et al., 2019). For example, the precipitation of foraminifer tests involves selective ion transport (Bentov and Erez, 2006;Nehrke et al., 2013;de Nooijer et al., 2014), pH regulation (Bentov et al., 2009;de Nooijer et al., 2009ade Nooijer et al., , 2009bToyofuku et al., 2017), transport of (modified) seawater to the site of calcification (vacuolization; Erez, 2003;Bentov and Erez, 2006), and the synthesis of organic molecules (e.g. Branson et al., 2016). The tests of marine calcifiers may therefore form under variable solution [Na + ] and [Ca 2+ ] distinct from those of seawater, as well as under highly variable calcite saturation states and crystal growth rates. Lastly, the formation of precursor phases such as vaterite (e.g. Jacob et al., 2017) may have a significant effect on Na + partitioning. Investigating Na + partitioning over a wide range of ionic concentrations and calcite saturation state is therefore necessary to the development of models of Na + partitioning relevant to biogenic CaCO 3 .
Here we aim to identify and quantify the primary factors controlling Na + incorporation into calcite over a wide range of solution [Na + ] (0.001-1.4 M), [Ca 2+ ] (1.0-30 mM) and crystal growth rate (10 À6.5 -10 À3.3 mol/m 2 /s) without interferences from additional impurity ions (e.g. Mg 2+ , SO 4 2À ). Crystal growth rates are varied by changing the solution saturation state with respect to calcite  and the Ca 2+ /CO 3 2À activity ratio (0.3-5000). Our experimental results are used to develop a numerical model relating calcite Na/Ca to the solution (Na + ) 2 /Ca 2+ activity ratio and crystal growth rate. The effect of SO 4 2À ions on Na + partitioning is also investigated by reassessing previous work in light of our new results. Implications for the use of biogenic carbonate Na/Ca as a salinity and Ca 2+ concentration indicator are discussed and we provide first order approximations of crystal growth rates for a variety of marine calcifiers based on previously published biogenic calcite Na/Ca values.

Mechanism of Na + incorporation in CaCO 3
Past studies suggested an interstitial occupation of Na + in calcite and aragonite (Ishikawa and Ichikuni, 1984;Busenberg and Plummer, 1985;Okumura and Kitano, 1986), which involves the solution Na + concentration or activity as a main driver of carbonate Na/Ca. The Busenberg and Plummer (1985) model involves the substitution of two CaCO 3 groups by Na 2 SO 4 . However, synchrotron X-ray spectroscopy results from a range of calcite and aragonite samples indicate negligible presence of Na 2 SO 4 (Yoshimura et al., 2017) despite the nonnegligible presence of SO 4 2À in biogenic CaCO 3 . The Xray spectroscopy results show the presence of Na in calcite and aragonite is mainly in the form of Na 2 CO 3 . Yoshimura et al. (2017) suggest the incorporation of Na 2 CO 3 into the CaCO 3 lattice is accommodated by a CO 3 2À vacancy (i.e., replacement of two CaCO 3 groups by one Na 2 CO 3 group), similarly to the White (1977) model. This model can explain the presence of a significant amount of Na in CaCO 3 for carbonate minerals formed in solutions without the presence of additional impurity ions. According to this model of Na-incorporation, CaCO 3 growth in simple NaCl solutions can be viewed in terms of the following two reactions: With the equilibrium constants K 1 and K 2 expressed as follows: where a i is the free activity of the relevant ion or mineral phase. From (3) and (4), the equilibrium activities of CaCO 3 and Na 2 CO 3 are obtained: and from (5) and (6), the Na/Ca ratio of calcite near chemical equilibrium conditions is obtained: Na Ca This model involves a dependency of calcite Na/Ca on the solution (Na + ) 2 /Ca 2+ activity ratio. Hence, calcite Na/Ca is expected to be negatively correlated with the solution Ca 2+ concentration and, where the solution Na + /Ca 2+ concentration ratio remains constant, positively correlated with salinity.

METHODOLOGY
Three sets of inorganic CaCO 3 growth experiments were conducted to investigate the effect of solution (Na + ) 2 /Ca 2+ activity ratio (a 2 Na þ =a Ca 2þ ), Na + activity (a Na þ ), crystal growth rate (R c ), and CaCO 3 polymorphism on calcium carbonate Na/Ca ((Na/Ca) c ). Calcite growth experiments lasting several days (LogR c < -6 mol/m 2 /s, from here on called 'slow growth') were carried with a CO 2 bubbling system at the University of Oregon (Section 2.1, Fig. 1a, b and c; Watkins et al., 2013) while experiments with higher crystal growth rates (LogR c = -6.0 to -3.3 mol/m 2 /s; from here on called 'fast growth') were carried out using a Metrohm chemostat at the Royal Netherlands Institute for Sea Research (Section 2.2 and 2.3, Fig. 1d, e and f; Kaczmarek et al., 2016). The use of two experimental setups was necessary to achieve a wide range of crystal growth rates (10 -6.5 -10 -3.3 mol/m 2 / s) and solution a 2 Na þ =a Ca 2þ (~10 -4 to 650). Prior to each experiment, plastic and glassware were acid-washed, rinsed with deionised water (18.2 MO) three times and all solutions were left to equilibrate with the laboratory's controlled temperature for a minimum of 12 hours (25.0 ± 0.5°C). The solution ionic strengths and ionic free activities were calculated using the PHREEQc R-package (version 3.6.0, Charlton and Parkhurst, 2011) with the Pitzer database. The use of PHREEQc databases other than Pitzer resulted in erroneous ionic activity coefficients at ionic strength higher than 0.5 (Fig. A1) and are therefore not recommended for solutions with salinities close to or above the ionic strength of seawater. Calcite saturation states (X calcite = a Ca 2þ Â a CO 2À 3 =K sp ) were calculated from the activities of free Ca + and CO 3 2À and the activitybased solubility product for calcite at 25°C (K sp = 10 À8.42 , Jacobson and Langmuir, 1974 Na þ =a Ca 2þ on (Na/Ca) c . Crystal growth rates (R c ) were very similar within this set of experiments because solutions with higher ionic strength had higher steady state dissolved inorganic carbon concentrations ([DIC] w ; i.e. the activity product of CO 3 2À and Ca 2+ remained similar among these experiments). These experiments were conducted following a similar protocol as described in Watkins et al. (2013) whereby CO 2 gas (200 ppm) was bubbled throughout experiment durations of 41 to 93 hours into a stirred solution (1.7 L), containing 30 mM CaCl 2 2H 2 O, 5 mM NH 4 -Cl and 0 to 1.37 M NaCl (Fig. 1a). The pH was monitored and controlled at 8.30 ± 0.07 using an autotitrator (Jensen systems) with 1 M NaOH solution, combined with Titronic universal burettes and an NBS-calibrated BlueLine pH combination electrode (Schott Instruments). The small addition of NaOH (2.3-5.7 mM) and decrease of [Ca 2+ ] w (~8%) during the course of the experiments were taken into account for calculating the average a 2 Na þ =a Ca 2þ values of each experiment. Calcite nucleation and precipitation occurred after O calcite reached 7.5 ± 1.5. Following nucleation, O calcite decreased to 3.3 ± 1.2 until the system reached steady state conditions (Fig. 1b). Estimation of O calcite during the course of an experiment was achieved by regular solution sampling (3.5 mL) and subsequent [DIC] w analyses.
For [DIC] w analyses, 3.5 mL of solution reacted with 0.1 mL of 85% orthophosphoric acid in He-flushed exetainers. After equilibrating for 4 hours, the gas headspace was analysed by continuous-flow mass spectrometry on a GasBench-DeltaV system. A known concentration of inhouse NaHCO 3 standard was analysed with the samples, from which a calibration curve was determined.
At the end of each experiment, the solution and any suspended crystals were discarded. The remaining crystals ( Fig. 1c) attached to the bottom and sides of the beaker were rinsed at least three times with de-ionised water, airdried, and then gently detached from the walls of the beaker using a plastic spatula. Average R c (mol/m 2 /s) were determined from the decrease in [Ca 2+ ] w (as estimated from the difference between the NaOH added and the final solution total alkalinity) and the estimated average surface area of calcite crystals (Tang et al., 2008): where the 0.5 factor accounts for Ca 2+ having 2 equivalents per mole, NaOH f is the total NaOH (Eq/L) titrated into solution at the end of the experiment, TA f is the solution total alkalinity (Eq/L) at the end of the experiment as measured by Gran titration, V is the solution volume (L), t is the duration of calcite precipitation (s), and SA* is the estimated average geometric surface area during an experiment: where Sp is the specific surface area of calcite crystals at the end of an experiment (0.3 ± 0.1 m 2 /g for an average particle size of~10 lm determined from SEM images, Figs. 1c and A1, Tang et al., 2008), m CaCO 3 is the total mass (g) of calcite precipitated and the denominator value of 2 applies to obtain the average geometric surface area during an experiment knowing that initial SA* is 0 m 2 /g. Reported average R c and O calcite values for each experiment are representative of steady state growth conditions rather than conditions during the initial and brief nucleation stage (see the 'Stage 2' period of near-constant rate of CaCO 3 formation under near-constant alkalinity on Fig. 1b).

Experiment group 2: various R c with constant [Na] w (chemostat)
Calcium carbonate crystals were precipitated for 2-24 hours using a modified version of the protocol described in Kaczmarek et al. (2016). This experimental setup consists of a titrator (Stat 902 Titrando, Metrohm, 2.902.0010), three burettes (800 Dosino, Metrohm, 2.800.0010), a combined polymer calcium electrode (6.0510.100) and a pH electrode (6.0262.100; Fig. 1d). All devices are connected to the titrator and controlled via the Tiamo 2.5 software. This equipment allows for keeping the solution pH, [Ca 2+ ] w and [CO 3 2À ] w constant during the course of an experiment by additions of burette solutions, which compensate for Ca 2+ and CO 3 2À loss by CaCO 3 precipitation. It was found that the calcium-electrode reading drifted significantly (>7 mV, equivalent to > 50% change in [Ca 2+ ] w ) during the first 1-2 hours of measurement. Such a large drift in the signal of the calcium electrode was most likely caused by the high ionic strengths of the solution used in this study since stable readings were obtained in dilute solutions (Kaczmarek et al., 2016). To minimize the drift of the calcium reading, the electrode was conditioned for~2-3 hours before the start of each experiment (Fig. 1e) using a solution with [Ca 2+ ] w and [Na + ] w identical to that of the growth solution but without added DIC to keep the solution undersaturated with respect to calcite. Although a conditioning step greatly reduced the drift of the calcium electrode reading for experiments lasting less than~24 h, it did not permit us to conduct stable experiments lasting several days. Hence, slow growth experiments were conducted with a different experimental setup (see previous Section 2.1).
Following stabilization of the calcium electrode signal, 100 mL of CaCl 2 solution was mixed with 100 mL of Na 2 -CO 3 solution to form a 200 mL oversaturated solution [Ca 2+ ] w = [DIC] w = 0.7-5 mM, pH = 9.90 ± 0.15; LogR c = -6.0 to -3.5 mol/m 2 /s) and a constant [Na + ] w of 0.47 M to evaluate the effect of R c and a 2 Na þ =a Ca 2þ on (Na/Ca) c at seawater [Na + ] w . The oversaturated solution was kept in an air-tight glass beaker connected to the  Watkins et al., 2013) used for slow calcite growth experiments lasting several days. (b) Example of an experimental run (S13) using the CO 2 bubbling system. The alkalinity increase due to NaOH addition (red curve) is offset by alkalinity removal to CaCO 3 , leading to a total alkalinity (black squares) that is nearly constant during the crystal growth period. (c) Calcite crystals recovered at the end of an experiment carried out with the CO 2 bubbling system. (d) Chemostat system (similar to Kaczmarek et al., 2016) used in a temperaturecontrolled room (25 ± 0.5°C) for experiments lasting less than 24 h. (e) Example of an experimental run (40_2) using the chemostat system. Potential drift of the calcium electrode reading was monitored before and after each experimental run (step 1 and 3). The small increase in the rate of CaCl 2 and Na 2 CO 3 additions during the course of an experiment (step 2) reflects an increase in the reactive surface area. (f) Calcite seed crystals and overgrown calcite crystals recovered at the end of an experiment carried out with the chemostat system. 1: 14 mM CaCl 2 , burette 2: 14 mM Na 2 CO 3 , burette 3: 50 mM NaOH, Fig. 1d). Shortly after solution mixing, calcite seeds (Alfa Aesar, 10-32 mm diameter, (Na/Ca) c < 0. 01 mmol/mol) were immersed in 1-2 mL of the oversaturated solution, then immediately transferred to the 200 mL oversaturated solution to initiate calcite growth. CaCl 2 and Na 2 CO 3 addition rates typically increased during the course of an experiment (Fig. 1e), due to the increase in reactive surface area of the growing crystals. At the end of each experiment, the solution and detached crystals ( Fig. 1f) were immediately vacuumed-filtered (0.45 mm), then rinsed three times with de-ionised water. Potential drift of the calcium electrode reading during the course of an experiment was estimated by remeasuring the conditioning solution (matrix-matched but undersaturated) with the calcium electrode at the end of each experiment. Typical drift of the calcium electrode reading was 0-10% and remained below 20% with respect to the initial growth solution [Ca 2+ ] w . The amount of CaCO 3 accumulated during each experiment was inferred from the total amount of CaCl 2 added and accounts for any small decrease in [Ca 2+ ] w during the course of an experiment caused by a drift of the calcium electrode reading (n CaCO 3 = n CaCl 2 _added + n Ca_initialn Ca_final ). The mean R c value for each experiment was calculated from: where t is the duration of calcite precipitation in seconds and SA is the average geometric surface area: where Sp seeds is the specific surface area of calcite seeds (0.35 ± 0.02 m 2 /g, determined with a TriStar 3000 Brunauer-Emmett-Teller analyser using N 2 , Utrecht University), m seeds is the mass of calcite seeds added ($5 mg) and g is the relative increase in the reactive surface area between the start and end of an experiment (determined from the increase in CaCl 2 addition rates, Fig. 1e). The 0.5 factor applies to obtain the average geometric surface area during an experiment. Experiments with O calcite values above 18 (n = 5, CV and CAV samples) were conducted without the addition of calcite seeds due to the coprecipitation of aragonite and vaterite (Fig. A2). The R c values for unseeded experiments were estimated from the empirical relationship between total crystal surface area and total crystal weight obtained from the seeded experiments (r 2 = 0.85, p-value <0.01; Fig. A3). The latter method is justified by the fact that the average diameter of individual crystals was similar for seeded and unseeded experiments (i.e. 20-40 lm, Fig. A2). We note however that the estimated R c values for the unseeded experiments are less precise compared to the seeded experiments due to coprecipitation of aragonite and vaterite and the absence of accurate constraints on the specific surface area of these crystals. To account for this, uncertainties of ±50% of the value of estimated R c values were applied for the unseeded experiments but this does not compromise the overall patterns and conclusions reached in this study.

Experiment group 3: fast R c with variable [Na + ] w (chemostat)
Calcite crystals were precipitated following the same protocol described in Section 2.2 but under different [Na + ] w (0.4 to 0.6 M) and very similar O calcite of 11.5 ± 0.5 ([Ca 2+ ] w = [DIC] w = 1.3-1.5 mM) to investigate the effect of a 2 Na þ =a Ca 2þ (250 to 500) on (Na/Ca) c in conditions far from chemical equilibrium and for solutions with [Na + ] w similar to the range of variability of natural seawater. The pH of these experiments was 10.0 ± 0.3. This resulted in similar crystal growth rates for all experiments ranging from 10 À5.3 to 10 À4.9 mol/m 2 /s. Scanning electron microphotographs of the CaCO 3 samples (Fig. A2) show all samples are made of 100% calcite crystals of similar size, suggesting spontaneous nucleation did not occur or was insignificant relative to the accumulated calcite on seed material.

Cleaning of CaCO 3 samples and trace-element analysis
Following drying and weighing, the CaCO 3 samples were transferred to 0.2 mL Eppendorf vials, sonicated in deionised water for two minutes, centrifuged for 60 seconds at 2000 rpm after which the supernatant was removed. This cleaning procedure was repeated twice and was necessary to remove NaCl from the CaCO 3 samples (Fig. A4). Repeating the cleaning step up to five times for a sample did not improve the reproducibility of results and did not reduce the (Na/Ca) c ratios further (i.e. no indication of Na + leaching). A similar cleaning procedure but using Milli-Q saturated with respect to calcite instead of pure Milli-Q also resulted in very similar (Na/Ca) c ratios ( Fig. A4), further confirming the cleaning procedure with pure Milli-Q is adequate and does not lead to preferential Na + leaching from the calcite crystals. Following cleaning and drying, the samples were dissolved in 0.1 M ultrapure HNO 3 . The elemental composition of the CaCO 3 samples was measured on a Thermo Fisher Scientific iCAP-Q-ICP-MS at the Royal Netherlands Institute for Sea Research (Texel). The isotopes of 23 Na, 43 Ca and 44 Ca were measured in a cycle of 1.5 minutes. Samples were measured against 4 ratio calibration standards with a similar matrix, with a drift standard measured every third sample and converting isotope counts into elemental ratios. The monitor standards JCt-1 and NFHS-1 (Okai et al., 2002) were included for quality control. Elemental values were drift-corrected, even though drift was low (~1%). Accuracy based on the two quality control standards was 99 ± 2%. All reported (Na/Ca) c ratios were corrected for the contribution of calcite seeds (if any) based on the estimated amount of total CaCO 3 precipitated during each experiment (Sections 2.2).

XRD analysis
Samples for XRD were crushed to a fine powder under ethanol with a mortar and pestle. XRD samples were measured on a Bruker D8 Discover at Utrecht University, and scanned at 2°per minute for a 2h range of 4-70°. The percent calcite/aragonite/vaterite in each sample was estimated using TOPAS version 4.2 software (Rietveld refinement method) for analysing diffraction peaks.

RESULTS
A summary of results from all the experiments carried out in this study is presented in Table 1. For a more complete description of the experimental conditions and results, the reader is referred to the electronic database (Table A1).
3.1. Experiment group 1: slow R c with variable [Na + ] w (CO 2 bubbling) Calcite crystals precipitated slowly (logR c = À6.5 to À6.1 mol/m 2 /s) with the CO 2 bubbling system have (Na/Ca) c spanning 0.13-1.55 mmol/mol over the 10 À4 -125 range in a 2 Na þ =a Ca 2þ ( Fig. 2a; [Na + ] w = 0.001-1.4 M, [Ca 2+ ] w = 30 mM, pH = 8.3). The relationship between (Na/Ca) c and a 2 Na þ =a Ca 2þ is not linear and is welldescribed by a power function (r 2 = 0.96): where D and k are best-fit parameters (D = 4.2 Â 10 À4 and k = 0.22 at logR c~-6.3 mol/m 2 /s). The (Na/Ca) c values from this set of experiments is also well-fitted by a model using the explanatory variables a Na þ (not shown) instead of a 2 Na þ =a Ca 2þ since the same [Ca 2+ ] w was used for all experiments. However, results presented in Section 3.2 suggest (Na/Ca) c is controlled by a 2 Na þ =a Ca 2þ (White, 1977(White, , 1978 rather than a Na þ (Busenberg and Plummer, 1985).
Small variations in crystal growth rate between these experiments could not be evaluated accurately because of uncertainties in the reactive surface areas during each experiment (calcite seeds were not used for this set of experiments). Instead, the solution mean X calcite (2.2-5.3, Table 1) was used as a proxy for relative difference in crystal growth rate since X calcite values are strongly correlated with R c over the entire dataset presented in this study (Fig. A5). For these experiments, no significant X calcite effect on (Na/Ca) c was resolved (Fig. 2a), except perhaps for the comparatively high (Na/Ca) c of experiment S15 ((Na/Ca) c = 1.55 mmol/mol, X calcite = 5.3), which may have been caused by the higher X calcite in comparison to the other experiments. Experiment S15 was therefore excluded when fitting equation (13) to the data.
Measurements of 11 different aliquots taken from the same calcite sample (Fig. 2a, a 2 Na þ =a Ca 2þ = 18.5, sample S3) resulted in a relative standard deviation (RSD) in (Na/Ca) c of 6.4%, which is significantly higher than the analytical precision of 0.8% (1 RSD) but does not compromise the reported trends in this study. The cause of sample heterogeneity in (Na/Ca) c may be due to minor refractory NaCl fractions and/or small variations in R c during the course of an experiment (cf. Section 3.2).  Fig. A6 for typical XRD spectrums) carried out on these samples indicates the aragonite fraction represents~40% of the sample masses (n = 2, Fig. A2, Table A2) while the vaterite fraction ranges from~1% to 14% (n = 5, Fig. A2, Table A2). The polymorph fractions were also assessed based on the % surface occupied by each polymorph on SEM microphotographs (Fig. A2) and yielded results compatible with the XRD analyses (Table A2).

Experiment
Crystal growth rates were significantly faster when using the chemostat than the CO 2 bubbling apparatus (Section 3.1) despite some experiments having similar solution O calcite (Fig. A5). This can be attributed to differences in the solution a Ca 2þ =a CO 2À 3 (0.6-3.3 vs. >3900; Nehrke et al., 2007).
Variations in (Na/Ca) c ratios for all the CaCO 3 samples range from 3.4 to 33.2 mmol/mol and are strongly corre- Fig. 2. Sodium content of inorganic calcite as function of the solution (Na + ) 2 /Ca 2+ activity ratios (a 2 Na þ =a Ca 2þ ) for slow growth experiments (group 1, CO 2 bubbling system). (a) Calcite Na/Ca ((Na/Ca) c ) vs a 2 Na þ =a Ca 2þ and (b) solution-calcite Na + partitioning (D Na ) vs a 2 Na þ =a Ca 2þ . These experiments were caried under very similar solution [Ca 2+ ] (~30 mM) but different [Na + ] (~10 À3 to 1.4 M). The within-sample variability in (Na/Ca) c and D Na was assessed for experiment S3 (±2 RSD = 12.8%, n = 11) and is represented by the error bars in both panels. The calcite saturation state and mineral growth rate of these experiments remained within relatively small ranges (2.2 < X calcite < 4.2; À6.5 < LogR c < À6.1 mol/m 2 /s) except for one experiment (smaller circle: S15 excluded from the model fitting). Best fits with Eq. (13) (panel a) and Eq. (14) (panel b) are represented by the black curves.  (Charlton and Parkhurst, 2011) with the Pitzer database. c Computed with a calcite solubility product K sp of 10 À8.42 at 25°C (Jacobson and Langmuir, 1974).
lated with crystal growth rates (r 2 = 0.97, p-value <10 À3 , Fig. 3), while the solution a 2 Na þ =a Ca 2þ (90 to 650), and crystal polymorphism seem to influence (Na/Ca) c to a lesser degree. Nevertheless, two pairs of experiments which resulted in 100% calcite (35_17 and 35_18 vs 35_4 and 35_7) and with almost identical a Na þ (0.335 ± 0.001 M) and R c (logR c = À5.14 ± 0.07 mol/m 2 /s) but distinct solution a 2 Na þ =a Ca 2þ (325 vs 650) resulted in higher (Na/Ca) c values for the calcite grown in solution with the highest a 2 Na þ =a Ca 2þ (14.3 and 15.8 vs 12.2 and 13.1 mmol/mol, Fig. 3). At near-constant R c , a doubling in a 2 Na þ =a Ca 2þ therefore resulted in a~19.0% increase in (Na/Ca) c , which is fairly consistent with the 16.4% increase in (Na/Ca) c predicted for a doubling in a 2 Na þ =a Ca 2þ by Eq. (13). The highest (Na/Ca) c ratios were obtained for CaCO 3 samples that contained vaterite despite these samples having formed in solutions with comparatively low a 2 Na þ =a Ca 2þ , indicating enhanced incorporation of Na + in vaterite than in calcite.

Experiment group 3: fast R c with variable [Na + ] w (chemostat)
Calcite crystals precipitated rapidly (logR c = À5.3 to À4.9 mol/m 2 /s) with the chemostat system but under variable [Na + ] w (0.4-0.6 M, range of natural seawater variation) have (Na/Ca) c ratios ranging from 10.8 to 15.6 mmol/mol. For these experiments, (Na/Ca) c is correlated with a 2 Na þ =a Ca 2þ (r 2 = 0.74, p-value = 0.002, Fig. 4a) and with logR c (r 2 = 0.72, p-value = 0.005, Fig. 4b), indicating that both solution chemistry and crystal growth rate affected (Na/Ca) c for this set of experiments. These results contrast with the slow growth experiments of Section 3.1, where the (Na/Ca) c results appear insensitive to small variations in solution X calcite (and presumably R c ). Hence, where logR c is close to À5.0 mol/m 2 /s, small variations in crystal growth rate have a significant effect on Na + partitioning between calcite and solution.

Summary of results
Results from experiment 1 indicate that (Na/Ca) c is positively correlated with either a 2 Na þ =a Ca 2þ or a Na þ and small variations in R c do not significantly affect (Na/Ca) c where R c is on the order of 10 À6 mol/m 2 /s or lower.
Results from experiments 2 and 3 indicate (Na/Ca) c is strongly correlated with R c where R c > 10 À6 mol/m 2 /s. Rapid precipitation of CaCO 3 with R c > 10 À4.5 mol/m 2 /s resulted in samples containing a small fraction of vaterite; these samples have the highest (Na/Ca) c reported in this study. Experiment 2 also indicates (Na/Ca) c increases with higher a 2 Na þ =a Ca 2þ where a Na þ and R c are constant.

Controls on inorganic calcium carbonate Na/Ca
Variations in the Na/Ca ratio of inorganic calcium carbonate crystals have been related to the solution a 2 Na þ =a Ca 2þ (White, 1977;1978), a Na þ (Ishikawa and Ichikuni, 1984;Busenberg and Plummer, 1985), the crystal growth rate (Busenberg and Plummer, 1985;Fü ger et al., 2019), the carbonate sulphate content (Kitano et al., 1975;Busenberg and Plummer, 1985) and the polymorph (Kitano et al., 1975). In the following sections, the effect of each of the above parameters on (Na/Ca) c is evaluated based on results of this study as well as from previous work.

Calcite-solution Na + partitioning
Early work showed Na + uptake in calcite and aragonite becomes significantly less sensitive to the solution [Na + ] w with increasing [Na + ] w (i.e. Freundlich isotherm behaviour; Kitano et al., 1975;Ishikawa and Ichikuni, 1984). These early results were interpreted as Na + occupying interstitial lattice positions, suggesting (Na/Ca) c should be controlled by a Na þ (Kitano et al., 1975;Ishikawa and Ichikuni, 1984) rather than a 2 Na þ =a Ca 2þ (as in White, 1977;1978). However, covariations between a Na þ and a 2 Na þ =a Ca 2þ during the Kitano et al. (1975) and Ishikawa and Ichikuni (1984) experiments, along with the absence of information on crystal growth rates, did not allow them to assess the effects of a Na þ and a 2 Na þ =a Ca 2þ on (Na/Ca) c independently. Results from experiment 2 suggest a a 2 Na þ =a Ca 2þ control (rather than a Na þ ) on (Na/Ca) c since Na/Ca ratios are 19% higher for calcite formed with a 2 Na þ =a Ca 2þ doubled but near-constant a Na þ and crystal growth rates (Fig. 3, logR c = À5.25 to À5.11 mol/m 2 /s). Overall, our inorganic calcite results indicate a 0.22% increase in (Na/Ca) c per % increase in a 2 Na þ =a Ca 2þ ( Fig. 2a; Eq. (13)). A a 2 Na þ =a Ca 2þ control on (Na/Ca) c is also consistent with recent results from synchrotron X-ray spectroscopy analyses of biogenic calcite and aragonite minerals showing that Na + is bound to CO 3 2À in the calcite lattice in the form of Na 2 CO 3 , implying a substitution of Ca 2+ by Na + (Yoshimura et al., 2017). Although the exact substitution mechanism remains to be elucidated, a a 2 Na þ =a Ca 2þ control on (Na/Ca) c makes it sensible to express the results on Na + partitioning in terms of the distribution coefficient D Na : Here D Na is expressed using free ionic activities following Lippmann (1980). Using ionic concentrations instead of free activities results in a similar level of data-model agreement (not shown). Combining Eq. (13) with Eq. (14), the following power law is obtained for D Na (Fig. 2b): The decrease in D Na (2.8 Â 10 À4 -1.5 Â 10 À5 ) as a 2 Na þ =a Ca 2þ increases from 2.0 to 125 (Fig. 2b) is reminiscent of the partitioning behaviour of Mg 2+ in calcite, with D Mg decreasing with increasing a Mg 2þ =a Ca 2þ (e.g. Mucci and Morse, 1983) but contrasts with the behaviour of Sr 2+ and Ba 2+ , which display constant partitioning coefficients with respect to the solution a Sr 2þ =a Ca 2þ and a Ba 2þ =a Ca 2þ , respectively (e.g. Tesoriero and Pankow, 1996). We speculate that the negative covariation between D Na and a 2 Na þ =a Ca 2þ may be caused by a decreasing availability of CO 3 2À vacancies as more Na + is incorporated.

Crystal growth rate
Calcite and aragonite crystal growth rates affect the incorporation of trace-elements into the crystal lattice (McIntire, 1963). Early work on sodium incorporation into inorganic calcite by Busenberg and Plummer (1985) showed a doubling in (Na/Ca) c per order of magnitude change in crystal growth rate. However, variable amounts of sulphate-bearing ions in their calcite samples did not allow for assessing the effect of crystal growth rate independently of the effect of sulphates. Recent work by Fü ger et al. (2019) also demonstrated a strong crystal growth rate effect on calcite D Na but the effect of a 2 Na þ =a Ca 2þ on D Na was not assessed, limiting the quantification of crystal growth rate effects.
The results from this study confirm that Na + incorporation into calcite greatly increases with higher R c values (Fig. 3). Four of the chemostat experiments (35_10, 11, 17, 18) were conducted under a very similar a 2 Na þ =a Ca 2þ of 643 ± 8 but with variable calcite growth rate (Fig. 3, logR c = À6.0 to À5.2 mol/m 2 /s, Table 1). From this set of experiments, a fivefold increase in (Na/Ca) c per order of magnitude increase in R c is inferred (Fig. 3). This result suggests a much stronger crystal growth rate effect on (Na/Ca) c than previously reported by Busenberg and Plummer (1985), suggesting that the relation between (Na/Ca) c and R c may not be linear. Calcite growth rate effects on the partitioning of a cation substituting for Ca 2+ have been explained by surface kinetic models (Watson, 2004;DePaolo, 2011). These models successfully reproduce the rate dependence observed for doublycharged ions (e.g. Sr 2+ , Mn 2+ , DePaolo, 2011) but have not been applied to monovalent ions like Na + because the mode of incorporation into calcite remained unclear. Results from recent work on inorganic and biogenic CaCO 3 (Yoshimura et al., 2017;Hauzer et al., 2018;Zhou et al., 2021) suggest Na + substitutes for Ca 2+ in calcite and aragonite. The DePaolo (2011) model predicts that the incorporation of impurity ions substituting for Ca 2+ into calcite is controlled by the calcite dissolution/precipitation ratio (R b / R f ). Following DePaolo (2011), the partitioning of Na + between calcite and solution may be described as follows: where D f Na and D eq Na are Na + distribution coefficients for the kinetic and equilibrium limits, respectively, and R b /R f is the CaCO 3 dissolution/precipitation reaction rate ratio.
Our results indicate D Na is not a constant at a given R c but depends on a 2 Na þ =a Ca 2þ (Fig. 2b, Eq. (15)). To accommodate for the a 2 Na þ =a Ca 2þ dependence of D Na , we express D f Na and D eq Na as functions of a 2 Na þ =a Ca 2þ by substituting Eq. (15) into (16) and obtain the following relation for D Na : where D f , k f and D eq , k eq are best-fit parameters for the dependence of D Na on a 2 Na þ =a Ca 2þ at the kinetic and equilibrium limits respectively. We note that the introduction of an empirical term to the DePaolo (2011) model may limit the predictive power of the model outside the range of conditions described in this study. Results from this study indicate that the relative sensitivity of (Na/Ca) c to a 2 Na þ =a Ca 2þ is not strongly altered by R c . At R c~1 0 À6.3 mol/m 2 /s, (Na/Ca) c increases by 0.22% per % in a 2 Na þ =a Ca 2þ while at R c~1 0 À5.2 , (Na/Ca) c increases by~0.25% per % in a 2 Na þ =a Ca 2þ (Section 3.2). Hence, it is assumed the k exponents are mostly independent of R c (i.e. k f~keq~k = 0.22) and Eq. (17) simplifies to: Multiplying Eq. (18) by a 2 Na þ =a Ca 2þ , a relation is obtained for (Na/Ca) c : To solve for (Na/Ca) c , the values of D f , D eq and R b /R f must be known. Here, they are inferred from all the experiments of this study that resulted in the precipitation of 100% calcite (n = 29, Table 1). The D eq term must be lower than 4.2 Â 10 À4 (i.e. the value of D for the slow-growth experiments, Section 3.1). The R b /R f ratio is estimated from the calcite dissolution rate R b in NaCl solution at pH 8-10 and 25°C (10 À7.2 to 10 À6.2 mol/m 2 /s, Chou et al., 1989;Ruiz-Agudo et al., 2010) and the forward rate is derived from the measured net precipitation rate R c and the backward rate R b (i.e. R f = R c + R b , DePaolo, 2011). A best fit is obtained with R b~1 0 À7.2 , D eq = 6.3 Â 10 À5 and D f = 7.4 Â 10 À3 (average data-model difference = 17%, r 2 = 0.99, Table 2). Using an R b value closer to 10 À6.2 mol/m 2 /s (as in Chou et al., 1989) results in a similar D f value but a higher D eq value and an overall worse fit with the data (average data-model difference = 34%, r 2 = 0.98).
To investigate the effect of crystal growth rate on (Na/ Ca) c independent of a 2 Na þ =a Ca 2þ , we introduce the term F Rc : where ðNa=CaÞ c;eq is the expected value of (Na/Ca) c under near chemical equilibrium conditions. Following the formulation of Eq. (13) for (Na/Ca) c , ðNa=CaÞ c;eq is expressed as follows: Substituting Eqs. (19) and (21) into (20), the following relation is obtained for F Rc :  The value of F Rc represents the increase in Na + uptake into CaCO 3 caused by crystal growth rate relative to Na + uptake at near-equilibrium conditions. By definition F Rc equals 1 at chemical equilibrium and increases up to a value equal to D f Deq at the kinetic limit of Na partitioning. Computed F Rc values from measured (Na/Ca) c display a clear relationship with R c with little scatter and no discernible a 2 Na þ =a Ca 2þ effect (Fig. 5a). Data obtained from the calcite samples show F Rc increases~14 fold over the À6.5 to À4.7 mol/m 2 /s range in logR c (Fig. 5a), representing more than an order of magnitude increase in (Na/Ca) c induced by crystal growth rate effects. The inferred increase in (Na/Ca) c from calcite samples likely does not cover the full range of the crystal growth rate effect. Modelled F Rc using Eq. (22) agree well with calcite data (Fig. 5a, r 2 = 0.99) and could potentially suggest a~100 fold increase in (Na/Ca) c from equilibrium (R c < 10 À7 mol/m 2 /s) to the kinetic limit (R c > 10 À3 mol/m 2 /s).

Carbonate sulphate content
Sodium concentration in calcite and aragonite has been shown to increase with the amount of sulphate ions incorporated in the crystal lattice (Kitano et al., 1975;Busenberg and Plummer, 1985) possibly due to the effect of sulphates on lattice parameters (e.g. Goetschl et al., 2019). Previously published (Na/Ca) c data from inorganic calcite samples with variable SO 4 /Ca ratios (Busenberg and Plummer, 1985) are compared to the data presented in this study in Fig. 5b. Overall, (Na/Ca) c increases with a sample's sulphate content, where (SO 4 /Ca) c > 20 mmol/mol. The Busenberg and Plummer (1985) samples with (SO 4 /Ca) c < 20 mmol/m ol are either in good agreement with the data presented in this study or have lower (Na/Ca) c ratios than expected from Eq. (22) with R b = 10 À7.2 (Fig. 5b). These lower (Na/Ca) c values (i.e. F Rc in Fig. 5b) could potentially be explained by higher and variable R b values (10 À6.2 < R b < 10 À7.2 ).

General model for calcite Na/Ca
For calcite samples with (SO 4 /Ca) c < 20 mmol/mol, (Na/Ca) c has been expressed as a function of the solution a 2 Na þ =a Ca 2þ and R c : Model outputs using Eq. (23) with the parameter values listed in Table 2 are compared to measured (Na/Ca) c for all inorganic CaCO 3 samples precipitated in this study and the calcite samples with (SO 4 /Ca) c < 20 mmol/mol from the study of Busenberg and Plummer (1985) (Fig. 6, r 2 = 0.91). The comparison of model outputs with the Busenberg and Plummer (1985) data provides an independent way of testing the predictive power of the model since these data were not used to derive model parameters. The model satisfactorily predicts the (Na/Ca) c data from the study of Busenberg and Plummer (1985), therefore encouraging model applications to other studies and calcite material. Overall, these results suggest the (Na/Ca) c of low Mg-calcite with (SO 4 /Ca) c < 20 mmol/mol could potentially be used as a proxy for crystal growth rate and the solution a 2 Na þ =a Ca 2þ .

Calcium carbonate polymorphs
Results from previously published inorganic CaCO 3 experiments suggest higher Na + uptake in aragonite than in calcite (Kitano et al., 1975) but similar Na + partitioning for low and high Mg-calcite (White, 1978). A few samples analysed in this study contained significant proportions of aragonite (~40%) and vaterite (up to 14-35%). These latter samples were all obtained from solutions having higher saturation levels with respect to calcite (45 < X calcite < 190, Table 1) and display significantly higher (Na/Ca) c values than the pure calcite samples despite the former precipitating from solutions with comparatively low a 2 Na þ =a Ca 2þ (Fig. 3).
Experiments carried out with a solution X calcite of 180-190 resulted in mixtures of calcite and vaterite (CV samples, Table 1). It is expected that amorphous calcium carbonate (ACC) precursors formed during these experiments since the ACC solubility product was attained during these experiments (K sp_ACC~4 Â 10 À7~1 20 K sp_calcite at 25°C, Brecevic and Nielsen, 1989). The (Na/Ca) c values of the CV samples (~29-33 mmol/mol) are the highest of all samples analysed in this study and cannot be explained Fig. 6. Combined effect of the solution (Na + ) 2 /Ca 2+ activity ratio and crystal growth rate (logR c ) on the sodium content of calcium carbonate minerals (Na/Ca) c . Measured (Na/Ca) c (coloured data points: this study and the Busenberg and Plummer (1985) experiments with (SO 4 /Ca) c < 20 mmol/mol) are compared to model outputs (coloured lines). Model outputs were obtained with Eq. (23) and R b = 10 À7.2 mol/m 2 /s, D eq = 6.3 Â 10 À5 and D f = 7.4 Â 10 À3 (i.e. same parameter values as in Fig. 5a). Data related to experiments with aragonite and/or vaterite co-precipitation (orange outline) and calcite data from the Busenberg and Plummer (1985) study were not used to derive model parameters but are shown for comparison. by the DePaolo (2011) kinetic model using the parameters derived with the calcite samples (Fig. 6). These high (Na/ Ca) c values are interpreted to reflect enhanced Na + uptake in vaterite and/or ACC compared to calcite.
Samples containing a mixture of calcite, aragonite and vaterite (CAV samples, Table 1) formed in solutions with X calcite of 45-50. Although the (Na/Ca) c results of the CAV samples are in good agreement with modelled (Na/Ca) c using the model parameters as derived from experiments with pure calcite samples (Fig. 6), the presence of three CaCO 3 polymorphs limits the interpretation of the (Na/Ca) c results for these samples.

Alternative model for calcite Na/Ca
A significantly distinct model of Na + partitioning between calcite and solution involving a bicarbonate ion control on D Na has been postulated based on a reported correlation between D Na and the activity of HCO 3 À ions (Fü ger et al., 2019). According to this model, HCO 3 À compensates for the charge imbalance resulting from the assim-ilation of Na + into calcite, presumably by assimilation of the NaHCO 3 0 ion pair present in solution (Fü ger et al., 2019). Results from this study indicate variations in D Na at a given R c value are poorly explained by either the activity of HCO 3 À ions (Fig. 7a-c) or the HCO 3 À /Na + activity ratio (Fig. 7d-f). In fact, at a given R c value, experiments with the highest HCO 3 À activities have the lowest D Na values ( Fig. 7b and c), contradicting the Fü ger et al. (2019) model. Similarly, a high HCO 3 -/Na + activity ratio does not explain the scatter in D Na values at R c~1 0 À5.1 mol/m 2 /s (Fig. 7f).
As shown previously, variations in D Na at a given R c value are well explained by variations in a 2 Na þ =a Ca 2þ (Section 4.1.1). A low a 2 Na þ =a Ca 2þ promotes high D Na and a high a 2 Na þ =a Ca 2þ promotes low D Na (Fig. 8g-i). Careful examination of the Fü ger et al. (2019) data suggests solution Na + /Ca 2+ ratios and HCO 3 À activities covaried negatively, potentially explaining the positive relationship between calcite D Na and HCO 3 À activity reported by these authors. Fig. 7. Effect of crystal growth rate (LogR c ) and the solution HCO 3 activity (a, b, c), HCO 3 -/Na + activity ratio (d, e, f) and (Na + ) 2 /Ca 2+ activity ratio (g, h, i) on the partitioning of Na + between calcite and solution (D Na ). Panels on the left side (a, d, g) show all the calcite D Na values calculated from this study's experiments (except S7 and S8 with D Na > 2 Â 10 À4 due to very low solution (Na + ) 2 /Ca 2+ activity ratios). Panels in the middle (b, e, h) provide more details for experiments with LogR c = À6.4 to À6.0 mol/m 2 /s. Panels on the right side (c, f, i) provide more details for experiments with LogR c = À5.3 to À5.0 mol/m 2 /s. The error bars for logR c values represent the uncertainty in the surface area of calcite crystals during the course of an experiment. This figure shows D Na is not significantly affected by the activity of HCO 3 ions or the HCO 3 -/Na + activity ratio (a proxy for the NaHCO 3 0 /Na + ratio). The scatter in D Na at a given LogR c is explained by variations in the solution (Na + ) 2 /Ca 2+ activity ratio.

Biogenic (Na/Ca) c as an indicator of seawater calcium concentration
Fossil foraminifer and coral (Na/Ca) c values have been suggested to reflect past changes in seawater calcium concentrations because the (Na/Ca) c of these taxa is positively correlated with the environmental Na + /Ca 2+ concentration ratio (Gothmann et al., 2015;Hauzer et al., 2018;Zhou et al., 2021) and the residence time of Ca 2+ in the ocean is short (~1 My) relative to that of Na + (~100 My). In particular, foraminiferal (Na/Ca) c decreased with increasing [Ca 2+ ] w in studies where benthic (Hauzer et al., 2018) and planktic (Zhou et al., 2021) species were cultured in natural seawater with and without the addition of CaCl 2 . The present study shows that the (Na/Ca) c of inorganic calcite is positively correlated with the solution a 2 Na þ =a Ca 2þ and the crystal growth rate (Fig. 6) as well as the calcite sulphate content (Fig. 5b). Sulphate concentrations in low-Mg foraminiferal calcite are commonly below 20 mmol/mol (e.g. Busenberg and Plummer, 1985), a level which does not seem to increase (Na/Ca) c significantly (Fig. 5b). An increase in [Ca 2+ ] w is expected to decrease the a 2 Na þ =a Ca 2þ but increase the X calcite of the calcifying fluid (CF). For example, a~70% decrease in seawater a 2 Na þ =a Ca 2þ caused by the addition of CaCl 2 salt (as in the Hauzer et al., 2018 experiment) could be expected to result in a~70% increase in X calcite assuming [Ca 2+ ] in the CF is proportional to the environmental [Ca 2+ ] w . In turn, an increase in X calcite would lead to an increase in crystal growth rate and Na + uptake in the calcite lattice. Hence, it could be expected that a higher seawater [Ca 2+ ] w leads to competing and opposite effects on (Na/Ca) c , with a lower environmental a 2 Na þ =a Ca 2þ causing a lower (Na/Ca) c but a higher crystal growth rate causing a higher (Na/Ca) c . However, the sensitivity of low-Mg planktic foraminifer (Na/Ca) c to seawater a 2 Na þ =a Ca 2þ (+0.23 to +0.26% per % in a 2 Na þ =a Ca 2þ , Fig. 8) is similar that of inorganic calcite (Na/Ca) c (+0.22%, Fig. 8), suggesting that environmental [Ca 2+ ] w does not affect biomineral growth rates significantly for these taxa.
ter a 2 Na þ =a Ca 2þ but sits significantly higher than the range of (Na/Ca) c covered by low Mg-calcite planktic species as well as the range expected for low-Mg inorganic calcite (Fig. 8). The significantly higher (Na/Ca) O. ammonoides ratios suggest Na + partitioning for this species may reflect the formation of (a) precursor phase(s) (i.e. ACC and/or vaterite) and/or a possible enhanced Na + uptake in calcite with high Mg or SO 4 . Nevertheless, a 2 Na þ =a Ca 2þ appears to be the primary variable controlling (Na/Ca) O. ammonoides , with no evidence for a significant crystal growth rate effect caused by higher seawater [Ca 2+ ] w . Regardless of the potential causes for the absence of a positive [Ca 2+ ] w effect on foraminifer (Na/ Ca) c , the similar a 2 Na þ =a Ca 2þ sensitivities for foraminifer and inorganic calcite (Na/Ca) c are encouraging and should promote further development of this proxy. Further testing the sensitivity of foraminifer (Na/Ca) c to seawater [CO 3 2À ] w , [DIC] w and [Mg 2+ ] w is necessary since these variables have changed significantly in the geologic past (e.g. Zeebe, 2012) and could potentially impact biomineralization rates and Na + uptake in calcite.

Biogenic (Na/Ca) c as an indicator of seawater salinity
The sodium content of the calcium carbonate shells or skeletons of marine calcifiers has been shown to increase with the salinity of the environment in which biomineralization occurs (Ishikawa and Ichikuni, 1984). In particular, foraminiferal calcite (Na/Ca) c is significantly correlated with seawater salinity (Wit et al., 2013;Mezger et al., 2016Mezger et al., , 2018Mezger et al., , 2019Allen et al., 2016;Bertlich et al., 2018;Geerken et al., 2018) but the cause(s) of this covariation has not been determined. Planktic foraminifers cultured in seawater of various salinity (26 to 45 g/kg) display (Na/Ca) c ratios with enhanced sensitivity to a 2 Na þ =a Ca 2þ (e.g. T. sacculifer: +0.48% per % in a 2 Na þ =a Ca 2þ , Fig. 8) compared to the (Na/Ca) c of inorganic calcite precipitated under constant R c (+0.22%) and the (Na/Ca) c of the same taxa cultured in seawater with altered [Ca 2+ ] w (T. sacculifer: +0.26%). This suggests more than half of the salinity effect on T. sacculifer (Na/Ca) c is caused by a variable other than a 2 Na þ =a Ca 2þ . An increase in seawater salinity from 26 to 45 g/ kg (as in Bertlich et al., 2018) with a constant Na + /Ca 2+ concentration ratio results in a 2 Na þ =a Ca 2þ increasing almost proportionally from 34 to 61 (Fig. 9a). Model results suggest this would lead to a +14% increase in (Na/Ca) c , which is significantly lower than the +47% to +100% increase in (Na/Ca) c reported for T. sacculifer (Mezger et al., 2016;Bertlich et al., 2018). We postulate that higher salinities lead to higher X calcite in the calcifying fluid of foraminifers, which in turns leads to higher crystal growth rates and Na + uptake by calcite. Over the 26-45 g/kg salinity range, X calcite of a foraminifer CF could potentially double (Fig. 9b) assuming a CF composition similar to environmental seawater but with an elevated pH (i.e. pH = 8.6-9.0, Bentov et al., 2009;de Nooijer et al., 2009ade Nooijer et al., , 2009bToyofuku et al., 2017). A doubling of X calcite in seawater at 25°C results in a~fourfold increase in crystal growth rate (Lopez et al., 2009;Wolthers et al., 2012), which in turns leads to an approximate doubling in (Na/Ca) c for LogR c values above À5.7 mol/m 2 /s (Figs. 5a and 8). Thus, the expected impact of X calcite on (Na/Ca) c caused by increasing salinity is potentially stronger than the effect caused by seawater a 2 Na þ =a Ca 2þ discussed earlier. We therefore postulate that reported increases in foraminiferal (Na/Ca) c with increasing seawater salinities are caused in large part by a covariation between salinity and the biomineral growth rate. Taxonomic and between-studies differences in foraminiferal '(Na/Ca) c vs salinity' relationships may therefore indicate a variable response of internal carbonate chemistry and/or pH (and therefore X calcite ) to changes in salinity. Modelled results suggest the reported increase in (Na/Ca) T. sacculifer with salinity (~4.1 to 6.4 mmol/mol, Bertlich et al., 2018) could correspond to a salinity-induced increase in crystal growth rate from 10 À5.6 to 10 À5.4 mol/m 2 /s (Fig. 8). Extrapolating this reasoning to other element-to-calcium ratios suggests foraminiferal Sr/Ca, Ba/Ca, B/Ca and Li/Ca should also be positively correlated with salinity since the incorporations of these trace elements in calcite are positively affected by crystal growth rates (e.g. Gabitov et al., 2019). Evidence for positive correlations between foraminiferal calcite Fig. 9. Simulated chemical conditions in the calcifying fluid of a foraminifer as a function of salinity assuming a calcifying fluid pH of 8.6-9.0 (de Nooijer et al., 2009a(de Nooijer et al., , 2009b and [Na + ] and [Ca 2+ ] identical to the environmental seawater. (a) Effect of salinity on the (Na + ) 2 /Ca 2+ activity ratio (a 2 Na þ =a Ca 2þ ). (b) Effect of salinity on X calcite . This figure suggests that variations in (Na/Ca) foraminifer caused by variations in salinity originate from positive covariations between salinity and a foraminifer calcifying fluid's a 2 Na þ =a Ca 2þ and X calcite . Small variations in a foraminifer calcifying fluid's pH likely impact X calcite and (Na/Ca) foraminifer .
These assessments depend somewhat on whether Na + and Ca 2+ concentrations in the foraminifer CF are similar to seawater, which may not be the case due to the role of selective ion transport (Bentov and Erez, 2006;Nehrke et al., 2013;de Nooijer et al., 2014) and the uptake of Ca 2+ during calcification. However, active Ca 2+ transport and calcification are unlikely to alter the concentrations of Na + and Ca 2+ in the CF by more than a few percent (e.g. Furla et al., 2000) because Na + is highly concentrated in seawater (~0.47 M) and Ca 2+ is not expected to be the limiting factor for biomineralization (as opposed to CO 3 2À ions which are significantly less concentrated than Ca 2+ in seawater).

Crystal growth rates of biogenic calcium carbonate minerals
The strong positive covariation between inorganic calcite Na/Ca and crystal growth rate (Fig. 3) and the moderate (Na/Ca) c sensitivity to changes in a 2 Na þ =a Ca 2þ (Figs. 6 and 8) suggest calcite Na/Ca may provide some constraints on crystal growth rates for natural calcite with SO 4 /Ca lower than~20 mmol/mol (cf. Fig. 5b). Maximum crystal growth rates for a selection of marine calcifiers were estimated based on published (Na/Ca) c data (Fig. 10, Table 3) and assuming the calcifying fluid a 2 Na þ =a Ca 2þ reflects the modern seawater value of 47 (DOE, 1994). It is also assumed that the involvement of Mg 2+ at the site of calcification does not alter the effect of growth rate on Na + incorporation considerably. Overall, inferred crystal growth rates for marine calcifiers vary from 10 À5.6 to above 10 À4.0 mol/m 2 /s. This range in crystal growth rate is consistent with the idea that kinetic rather than equilibrium processes determine trace-element partitioning and isotopic fractionation between biominerals and seawater (Watson, 2004;DePaolo, 2011;Watkins et al., 2013Watkins et al., , 2014Devriendt et al., 2017aDevriendt et al., , 2017b. Among marine calcifiers, sea pens, sea urchins, sand dollar and green spine are expected to exhibit some of the highest growth rates (logR c > À4.0 mol/m 2 /s), followed by calcitic corals (gorgonians), bivalves, red algae, high-Mg benthic foraminifers, coraline algae and oysters (logR c > À5.0 mol/m 2 /s) while slowest crystal growth rate are inferred for coccoliths and low-Mg foraminifers (À5.6 < logR c < À5.2 mol/m 2 /s). The inferred precipitation rates for sea urchins, which are beyond the limit of Na + kinetic partitioning for calcite, are consistent with observations that show ACC as a precursor (Beniash et al., 1997;Politi et al., 2004). The Na/Ca of foraminifers generally suggest lower crystal growth rates, although the benthic species Operculina ammonoides has (Na/Ca) c values that could suggest relatively high precipitation rates (logR c > À4.0 mol/m 2 /s). This particular species has a shell made of high Mg-calcite suggesting a different biomineralization pathway (e.g. precipitation of vaterite or ACC in a highly saturated environment) than low-Mg-calcite taxa. Overall, the large (Na/Ca) c range observed in benthic foraminifera may be explained by the different biomineralization path-ways used by these organisms in contrast to the rather narrow (Na/Ca) c range in planktic foraminifera.
Within-shell variability in foraminiferal (Na/Ca) c are characterised by alternating bands of high and low Na/Ca ratios varying by up to 3 fold (Branson et al., 2016;Geerken et al., 2018Geerken et al., , 2019Bonnin et al., 2019). Variations in calcite crystal growth rate of~one order of magnitude (e.g. 10 À6 < R c < 10 À5 mol/m 2 /s) could potentially explain the Na/Ca banding pattern. In addition, the formation of precursor phases such as vaterite during biomineralization (Jacob et al., 2017) could also affect foraminiferal (Na/Ca) c since vaterite has a significantly higher Na/Ca than calcite when formed under similar a 2 Na þ =a Ca 2þ (Fig. 6). For example, high Na/Ca ratios above 20 mmol/mol reported in parts of foraminiferal shells such as the spines and spine base of spinose foraminifers (Mezger et al., , 2019Bonnin et al., 2019) could be explained by the formation of vaterite and/or ACC. Taxonomic and temporal variations in the calcifying fluid a 2 Na þ =a Ca 2þ may also contribute to within-and between-shell Na/Ca variability but these effects are less likely to be causing the large differences in Na/Ca between species and within a single shell due to the relatively moderate response of calcite Na/Ca to changes in environmental a 2 Na þ =a Ca 2þ (Fig. 8). Besides the concentrations of Na + , Ca 2+ and SO 4 2À in the CF and crystal growth rate effects, additional factors such as the Mg 2+ concentration, the Mg/Ca ratio and/or Fig. 10. Maximum calcite growth rate for a range of marine calcifiers inferred from published bulk calcite Na/Ca ratios using Eq. (19) and assuming a constant calcifying fluid (Na + ) 2 /Ca 2+ activity ratio of 47 (i.e. standard seawater, DOE, 1994). Rates were calculated using R b = 10 À7.2 mol/m 2 /s, D eq = 6.3 Â 10 À5 and D f = 7.4 Â 10 À3 (i.e. same parameter values as in Fig. 5a, Fig. 6 and Fig. 8) and with calcite Na/Ca data from Lorens and Bender, 1980;Busenberg and Plummer (1985)