Uptake of trace elements by calcite (one the most abundant marine and terrestrial minerals) has a variety of applications in climate and environmental sciences. For example, element/Ca ratios (E/Ca) as measured in the calcite shell of foraminifera are widely used proxies to reconstruct the environmental conditions at the time the calcite was precipitated by the organism. Reconstructing of seawater temperature and composition in the past (paleoenvironmental proxies) through E/Ca in carbonate minerals is among of them (e.g., Elderfield et al., 1996; Nürnberg et al., 1996; Lea, 2003; Katz et al., 2010). Despite a wide use of trace element signatures in biogenic and abiogenic calcite, some complications are associated with the interpretation of calcite elemental composition. It was found that crystal growth rate (V) plays an important role in elemental uptake and the relationship between E/Ca and V is not universal (e.g., Lorens, 1981; Tesoriero and Pankow, 1996; Huang and Fairchild, 2001; Stoll et al., 2002; Nehrke et al., 2007; Tang et al., 2008; Mavromatis et al., 2013; Gabitov et al., 2014a). Furthermore, fluid chemistry sometimes affects elemental incorporation into calcite, as shown by the apparent partition coefficient of Mg between calcite and fluid (K^Mg = (Mg/Ca)_calcite/(Mg/Ca)_fluid), which decreases with increasing Mg/Ca in the solution (Mucci and Morse, 1983). In this scenario, it appears evident that studies with goals to decouple the effects of growth rate and fluid content on the elemental uptake by calcite, are of fundamental importance to improve our interpretation of palaeoceanographic proxies and our understanding of mineralization processes. In this study, we present microscale analyses on the uptake of Li, B, Mg, Sr, and Ba by Mg-bearing calcite grown slowly from artificial seawater (ASW) solution at laboratory conditions. This slow rate is lower than typical extension rates of coccolithophores and foraminifera, and therefore, should represent calcite growth conditions that are closer to equilibrium compared to many marine biominerals. Although physiological effect can play an important role in elemental uptake during calcite biomineralization, it is not discussed in this study as we focused on an inorganic system, which is far from being completely understood.

In the experiment with high initial saturation state (Ω_cc = 43.45, run OVG-1) abundant nucleation on the walls and the bottom of the containers were observed with naked eye and pH (NBS scale) decreased from 9.09 to 7.96 during experiment. The degree of visible nucleation decreased with decreasing of Ω values between experiments. Thus, only small amount of crystals (other than cleavage fragments) were observed in the runs OVG-3 (Ω_cc = 12.93) and OVG-3′ (Ω_cc = 13.03) where pH decreased from 8.55 to 7.95 (OVG-3) and from 8.54 to 8.13 (OVG-3′). Despite decrease of pH from 8.21 to 7.98, run OVG-4 (Ω_cc = 6.02) did not yield visible crystallization. Obtained crystals and cleavage fragments were examined with electron microscopy and Raman spectroscopy techniques.

Decrease in uptake of Li/Ca, B/Ca, Sr/Ca, and Ba/Ca by calcite overgrowth (Figure 3, distance from 3 to 0 μm) cannot entirely be explained by evolution of E/Ca in experimental fluid where Li/Ca, Mg/Ca, and Ba/Ca increased with time, Sr/Ca decreased with time, and B/Ca decrease is insignificant (Table 3). Similar trends for B/Ca and Sr/Ca were observed at large scales where those ratios decreased from the fast growth core (nucleation site) to the slow grown rim of crystals with the sizes of up to 1,500 μm (Gabitov and Watson, 2006; Gabitov et al., 2014a,b). Bulk precipitation experiments of calcite also found strong growth rate effect on Sr, Ba, and B uptake (e.g., Tesoriero and Pankow, 1996; Uchikawa et al., 2015; Mavromatis et al., 2018). In our study, growth rate can potentially control B, Sr, and Ba uptake because decrease in Ω with experimental duration should cause a decrease in growth rate (e.g., Zhong and Mucci, 1989) however, this was not confirmed by the growths rate calculated from LA-ICP-MS depth profiles. Therefore, the reason for decrease in Sr/Ca and Ba/Ca is not entirely clear. B/Ca trend could be caused by pH drop by 0.6 units during experiment OVG-3, however the observed decrease in calcite B/Ca (25%) is much smaller than B/Ca decrease (by a factor of 100) observed by Uchikawa et al. (2015) for pH decrease from 8.5 to 8.0. Observed trend in Li/Ca is much less pronounced due to larger scattering, which resulted from low concentration of Li.

Mg/Ca is the only ratio in the overgrowth that often correlates with evolution of fluid Mg/Ca, i.e., Mg/Ca increases in both calcite and fluid with the time of calcite growth. On the other hand, an increase of calcite Mg/Ca with time can be related to slow dehydration of Mg²⁺(H₂O)₆ compare to Ca²⁺(H₂O)₆ at the calcite surface (Pavlov et al., 1998; Rodriguez-Cruz et al., 1999a,b).

Pairs of apparent partition coefficients (K) were calculated for each element in the newly formed calcite overgrowth as E/Ca ratios between calcite and solutions (initial and final) (Table 5). Depth profiling data for calcite precipitated between the addition of La and the end of experiment (Δx_La−surface) were used in the calculation of K values as an average E/Ca for Δx_La−surface layer (Figure 3D). In the three profiles (run OVG-3), where locations of the increase in Mg/Ca were distinct from the increase in La/Ca, K were also calculated for Δx_La−surface and Δx_Mg−La. In the run OVG-3′ the width of calcite overgrowth was thinner that the overgrowth width in the run OVG-3, showing slower growth in the run OVG-3′. The small difference in saturation states (Ω_cc = 12.93 and 13.03) unlikely can explain this inconsistency. The most reasonable explanation is the difference between cleaning treatments of calcite cleavage fragments. The quick rinse of calcite with HCl caused surface etching and created higher potential for nucleation on the cleavage fragment in the run OVG-3 in comparison to the run OVG-3′ where calcite was rinsed with H₂O only.

K-values vs. calcite growth rate are plotted together with those from previous studies (Figure 4). There, most of the growth rates were originally reported as bulk precipitation rates (R) (amount of CaCO₃ precipitated per calcite area per time); except studies of Gabitov et al. (2014a,b), where velocities of advancing crystal surface (V) were evaluated (extension per time). Bulk precipitation rates were converted to extension rates using molar volume of calcite (V_m = 3.69·10⁻⁵ m³/mol); for example: V = R·V_m = 3.98·10⁻⁹ mol/(m²·s)·3.69·10⁻⁵ m³/mol = 1.47·10⁻⁴ nm/s.

All of the data shown on Figure 4 are for low-Mg and Mg-free calcite except for the data from Mucci and Morse (1983) and our study. It was found that high Mg content of the fluid affects incorporation of elements into calcite. The strongest effect was observed for Sr and Ba (Figure 4), where K^Sr and especially K^Ba of Mg-bearing calcite are much higher than those of low-Mg or Mg-free calcite precipitated at similar rates (see Lorens, 1981; Tesoriero and Pankow, 1996). This effect was explained previously by coupled substitution of Ca in calcite due to the differences in ion radii of Mg, Ca, Sr, Ba (r_Mg < r_Ca < r_Sr < r_Ba), where the distortion of crystal lattice due to incorporation of small Mg (relative to Ca) is compensated by involvement of large Sr (e.g., Mucci and Morse, 1983). This explanation is consistent with our data where deviation of K^Ba (Ba is the largest cation) from the literature data is stronger than of K^Sr: K^Ba of Mg-bearing calcite is two orders of magnitude higher than K^Ba of Mg-free calcite precipitated at similar rates (10⁻⁴-10⁻³ nm/s) whereas our K^Sr is higher than literature values by one order of magnitude (Lorens, 1981; Tesoriero and Pankow, 1996; Mavromatis et al., 2018). Sr incorporation into Mg-bearing calcite demonstrates much lower dependence on growth rate in comparison to Sr in low-Mg or Mg-free calcite, which corroborate the dominance of substitution of Ca with Mg and Sr over the growth rate of Mg-bearing calcite.

In contrast to K^Sr and K^Ba, K^Mg is similar to previously reported data for slowly grown low-Mg calcite (Gabitov et al., 2014a) demonstrating near-equilibrium partitioning of Mg in our study. The similarity between K^Mg values from our study (where Mg/Ca_fluid = 5.2–5.8 mol/mol) and those reported by Gabitov et al. (2014a) (where Mg/Ca_fluid = 0.08–0.2 mol/mol) suggest that fluid Mg/Ca does not significantly affect K^Mg at growth rates between 10⁻⁴ and 0.1 nm/s (Figure 4). The potential explanation is that at a slow growth rate, Mg incorporation is not limited by its dehydration rate of hydrated Mg molecules. K^B is much higher than previously reported data for calcite slowly grown from solutions having pH values within the range of pH in our experiments. Our partition coefficients overlap only with those for calcite grown at higher rates from the study of Uchikawa et al. (2015). We hesitate to interpret obtained data as boron incorporation into calcite is different from divalent cations and strongly depends on pH and carbonate chemistry of the solution (e.g., Uchikawa et al., 2017). Lithium unlikely substitutes Ca in calcite lattice as was considered for divalent cations, but rather incorporates interstitially (discussed in Marriott et al., 2004a). The recent study shows increase of KLi with increasing of growth rate (Füger et al., 2019). However, even at relatively high growth rates their K^Li are lower than ours by an order of magnitude, whereas our data partially overlaps with the data of Marriott et al. (2004a) for calcite precipitated at unknown rate. It was shown that salinity has positive effect on K^Li (Marriott et al., 2004b), however it is cannot entirely explain the difference between our data (salinity ~25 psu) and those of Füger et al. (2019) (salinity ~18 psu).

This study shows that elemental entrapment by Mg-bearing calcite could be very different from entrapment by low-Mg calcite, suggesting non-equilibrium elemental partitioning between calcite and seawater even when crystal growth rate is very slow. This finding corroborates an importance in the development of empirical K-V relationships for calcite precipitated from seawater and suggests that existed K-V trends for B, Sr, Ba, and possibly Li in low-Mg and Mg-free calcite cannot be directly applied for growth rate correction in geochemical proxies based on marine Mg-bearing calcite samples.

The recent study shows increase of K^Li with increasing of growth rate and decreasing of pH (Füger et al., 2019). However, even at relatively high growth rates their K^Li are lower than ours by an order of magnitude (at similar pH range), whereas our data partially overlaps with the data of Marriott et al. (2004a) for calcite precipitated at unknown rate. It was shown that salinity has positive effect on K^Li (Marriott et al., 2004b), however the higher salinity in our experiments cannot entirely explain the difference between our data (salinity ~25 psu) and those of Füger et al. (2019) (salinity ~18 psu).

RG and AS conceived the project. RG conducted experiments with assistance of KS. VY, AB, and RG collected the SEM data. AS collected LA-ICP-MS and ICP-MS data on calcite and final fluids. CB conducted ICP-MS analysis of initial fluid. RG wrote the first draft of the manuscript. RG, CB, AP-H, VY, AB, AS, and KS participated to the interpretation of the data and participated to the subsequent stages of preparation of the manuscript.