Large calcium isotope fractionations by zeolite minerals from Iceland

Zeolites are secondary tectosilicates produced during the hydrothermal alteration of basalt. The minerals serve as major sinks of calcium, which readily exchanges with calcium from surrounding groundwater. However, no studies have specifically investigated the calcium isotope geochemistry (δ44/40Ca) of zeolites. Here, we report δ44/40Ca values for zeolites from East Iceland, where the minerals form during progressive burial of the lava pile. The zeolites show a δ44/40Ca range of 1.4‰, which strongly correlates with average mineral calcium-oxygen bond lengths. As this correlation appears most consistent with equilibrium isotope partitioning, our findings point toward developing a novel geothermometer for studying low-grade basalt metamorphism. The results also have significance for using calcium isotopes to trace basalt weathering, including its role in long-term climate regulation and application in carbon capture and storage, a leading strategy for mitigating anthropogenic climate change. Calcium isotope ratios of Icelandic zeolites bracket those for host basalt and appear to control the Ca ratios of hydrothermal fluids and calcite, which could indicate their potential for use as a low-grade geothermometer

C alcium (Ca), the fifth most abundant element in the Earth's crust 1 , plays a key role in regulating climate over geologic timescales 2,3 and is essential for biological processes, such as biomineralization, plant growth, and cellular regulation 4,5 . Due to the ubiquitous occurrence of Ca in Earth and extraterrestrial materials, as well as major geochemical cycles, stable Ca isotope ratios have emerged as a promising tool for investigating processes in geochemistry, cosmochemistry, biology, and archaeology 6,7 . Calcium isotope ratios are reported in delta notation as δ 44/40 Ca smp (‰) = [( 44 Ca /40 Ca) smp /( 44 Ca /40 Ca) std − 1] × 1000, where smp refers to the sample and std refers to the normalizing standard, which in this study is OSIL Atlantic Seawater or ASW (δ 44/40 Ca ASW = 0‰).
In the ongoing effort to develop and apply the δ 44/40 Ca tracer, research has focused on quantifying mechanisms that fractionate isotopes according to their masses and produce isotopic offsets (Δ) between related Ca-bearing reservoirs, i.e., Δ 44/40 Ca a − b = δ 44/40 Ca a − δ 44/40 Ca b . Differentiating between kinetic and equilibrium isotope effects during mineral formation is particularly essential for implementing Ca isotopes as paleoenvironmental or temperature proxies [8][9][10] . Most studies aimed at understanding Ca isotope fractionation during mineral precipitation have focused on calcite (CaCO 3 ) formation at low temperatures (<30°C) characterizing the Earth's surface. Here, kinetic isotope effects [11][12][13][14][15][16][17] cause calcite to preferentially incorporate lighter Ca isotopes from solution with Δ 44/40 Ca cal-sol on the order of -1‰ to -2‰ 6 . Theory predicts that higher temperatures should promote equilibrium effects and minimize isotopic offsets (Δ 44/ 40 Ca cal-sol ≈ 0‰) during calcite formation 13,16,18 ; however, only a handful of natural calcites precipitated at elevated temperatures have been measured [19][20][21][22] . In parallel, some studies examining silicate mineral formation at high temperatures characterizing the solid Earth have attributed δ 44/40 Ca variability to equilibrium isotope partitioning 23,24 , driven by differences in Ca-O bonding conditions 9,10 . However, discrepancies between measured intermineral Δ 44/40 Ca of high-temperature silicates and ab initio model predictions of equilibrium Ca isotope offsets have been interpreted as evidence for mostly kinetic control 25,26 .
Missing from Ca isotope fractionation theory is an understanding of mechanisms that produce δ 44/40 Ca variability during mineral formation at temperatures bridging the surface and solid Earth. Intermediate temperatures in the range of~30-200°C characterize many hydrothermal systems, which represent key interfaces linking surficial geochemical cycles and solid Earth processes. Studies have used Ca isotopes to examine mid-ocean ridge hydrothermal systems 19,27,28 , seafloor weathering and oceanic lithosphere subduction 22 , continental hydrothermal systems 20 , and water-rock interactions in pilot studies of mineral carbonation of basalt, which is a leading carbon capture and storage (CCS) strategy 29,30 . Application of the Ca isotope tracer to these and other intermediate temperature systems requires a thorough examination of all secondary minerals that may fractionate Ca isotopes and contribute to the δ 44/40 Ca values of circulating waters. In addition, a better understanding of both equilibrium and kinetic effects on Ca isotope fractionation at intermediate temperatures is essential for improving knowledge about Ca isotope cycling and identifying novel applications for the δ 44/40 Ca tracer.
Nonetheless, despite the widespread occurrence and applicability of zeolites, their Ca isotope geochemistry has been neglected. Only one study has reported Ca isotope data for zeolites 21 . Coexisting heulandite and stilbite from Iceland are isotopically lighter and heavier, respectively, relative to basalt. Icelandic hydrothermal water and calcite also have δ 44/40 Ca values higher than basalt 21 . Heavy calcite is highly unusual because most carbonate minerals form kinetically and incorporate lighter isotopes relative to their Ca source reservoir 13,17,63 . Uptake of lighter Ca isotopes during zeolitization may elevate the relative abundance of heavier Ca isotopes in hydrothermal waters from which calcite precipitates 21 , but no systematic understanding has been established.
To better understand the Ca isotope geochemistry of zeolites, we used a high-precision thermal ionization mass spectrometry (TIMS) method to measure δ 44/40 Ca values of six zeolite mineral species. We also analyzed bulk basalt, primary mineral separates, and calcite. Specimens were collected from the Berufjörður-Breiðdalur region of East Iceland, which is a typelocality for the zeolitization of basaltic lava flows due to burial metamorphism 64 . Here, increasing temperature with depth below the surface of the lava pile has generated distinct zeolite zones where two zeolite mineral types, referred to as coindex mineral pairs 64 , distinctly form and thus are diagnostic of each depth zone (Fig. 1). Depth-controlled zeolite zones have been identified worldwide in active geothermal systems 37,44,65 , as well as extinct systems now exposed at the surface 32,38,41,66,67 . We report a large range of zeolite δ 44/40 Ca values, which is best explained by equilibrium isotope partitioning, given a strong observed correlation with Ca-O bond lengths. Our findings point the way for developing entirely new tools for investigating low-grade basalt alteration. They also broadly illustrate how future efforts focused on the Ca isotope geochemistry of zeolites could have implications for numerous other topics, such as understanding the compositional evolution of hydrothermal waters, quantifying elemental cycling in the oceans, and improving CCS strategies.

Geologic setting
Iceland is an exposed section of the Atlantic mid-ocean ridge overlying a mantle plume, which has caused extensive rifting and volcanism over the past 50-60 Myr 68 . Rocks increase in age away from the active rift zone, with the oldest rocks at the edges of Iceland dating to~16 Ma 69 . Samples analyzed in this study were collected from Berufjörður-Breiðdalur region described in detail by Walker (1960) (Fig. 1). Successive eruptions of a Tertiary volcano supplied lava that piled to a minimum total thickness of 2000 m at the eastern end 64,70,71 . The central volcano comprises highly altered rhyolite, while the flows are predominantly tholeiitic basalt, with lesser amounts of olivine basalt 64,71 . Within~1 Myr after the eruptions ceased, heat from burial, as well as the volcanic center and associated dike swarms, extensively zeolitized the lava pile, filling up to 90% of the primary porosity 38,64,70,72 . Pleistocene glacial erosion carved deep valleys and fjords into the lava pile and exposed the top~1000 m of the altered sequence, where the depth-controlled zeolite zones are clearly delineated and accessible above sea level (Fig. 1). The shallowest zone studied here is the chabazite-thomsonite zone (~30-70°C), followed by the mesolite-scolecite zone (~70-90°C) and the stilbite-heulandite zone (~90-150°C), which reaches a maximum depth of~1500 m below the top of the lava pile 31,39,64,73 .

Discussion
Controls on zeolite δ 44/40 Ca: kinetic isotope effects. A striking observation is that for each zeolite zone 64 , coindex pairs have contrasting δ 44/40 Ca that bracket basalt, with one mineral lower and the other higher (Fig. 2). Relative to basalt, the zeolites chabazite, mesolite, and heulandite have low δ 44/40 Ca, while their respective pairs (thomsonite, scolecite, and stilbite) have high δ 44/ 40 Ca. Chabazite, mesolite, and heulandite represent some of the isotopically lightest minerals thus far measured 6,26,74 , neglecting those that host appreciable 40 Ca additions from the radioactive decay of 40 K 75 . The data provide good evidence that zeolites fractionate Ca isotopes, as bulk basalt and primary mineral separates show effectively no isotopic variability (Fig. 3).
Many studies have shown that kinetic fractionation during mineral precipitation causes preferential uptake of lighter Ca isotopes relative to the main Ca reservoir 11,74 . Other minerals measured thus far with low δ 44/40 Ca values similar to zeolites are mainly carbonates, which have experienced kinetic fractionation due to either variable precipitation rates 13,14 or biogenic vital effects during mineral growth 74 . Kinetic effects resulting in low δ 44/40 Ca have also been observed in some high-temperature silicate minerals 25,76,77 . However, unlike carbonates and primary rockforming silicate minerals, all Ca in zeolites is exchangeable 34 ; therefore, it cannot be assumed a priori that kinetic fractionation mechanisms identified for the former minerals apply to zeolites. Kinetic isotope fractionation during mineral precipitation from solution mainly occurs due to incomplete exchange of ions or molecules, when transfer from solution to the solid proceeds more quickly than the reverse reaction 9,11,78 . Calcium ion exchange in zeolite minerals is equilibrium-controlled 34,43 , thus implying that forward and backward reaction rates are equal. Nevertheless, we consider below potential transport-related kinetic isotope effects.
Zeolites consist of an aluminosilicate tetrahedral framework, where cations occupy specific exchange sites within void channels 33 . Isomorphic substitution of Al 3+ for Si 4+ in the tetrahedra creates a net negative charge in the zeolite framework, which is balanced by the uptake of mono-and divalent cations,   including Ca 2+ , from the coexisting solution 33 . Thus, coulombic forces related to charge density could in theory kinetically fractionate Ca isotopes due to variable mass-dependent diffusion rates occurring at the mineral-fluid interface or within the zeolite framework itself 11,[79][80][81] . Charge density and distribution, as well as framework topology, control the ease and rate of Ca uptake and diffusion through zeolite frameworks 34,58,82 . Commonly a proxy for charge density, and thus cation-exchange capacity, zeolite Si/Al ratios reflect the anionic field strength that attracts cations into the structure. In general, zeolites with lower Si/Al ratios have higher charge densities and more readily take up cations relative to those with higher Si/Al ratios and lower charge densities 34,83 . If kinetic effects related to rates of Ca uptake or diffusion fractionated Ca isotopes, then a trend between zeolite Si/Al ratios and δ 44/40 Ca values should exist. However, we observe no trend for the present dataset, suggesting that charge density does not elicit kinetic isotope effects for these minerals (see Fig. S1).
One key point is that basalt represents the initial source of Ca in this system 37,38 . If the occurrence of zeolites with δ 44/40 Ca higher than basalt was the result of a kinetic fractionation mechanism during mineral formation, then this would require that zeolites with lower δ 44/40 Ca either precipitate faster or form first, thereby creating an isotopically enriched solution from which zeolites with higher δ 44/40 Ca later precipitate, as no kinetic fractionation mechanism could result in the preferential uptake of heavier Ca isotopes. Calculations and experiments employing solution chemistry and thermodynamic conditions have been used to predict the progression of zeolitization [84][85][86][87] , and while petrographic evidence in some locations points to possible chronologic sequences of zeolites 32,40,88,89 , studies in Iceland indicate that the coindex pairs form simultaneously under similar conditions 37,38,41,90 . Furthermore, some coindex zeolite pairs analyzed here were intergrown and collected from a single amygdule, suggesting simultaneous precipitation. The absence of clear evidence for kinetically controlled reservoir effects is unsurprising, as all zeolite-bound Ca is extra-framework, with ion-exchange reactions between zeolites and fluids continuing after initial growth of the aluminosilicate frameworks 43,66 . Calculated equilibrium elemental compositions of zeolites, as well as those produced experimentally under equilibrium conditions, agree with geochemical analyses of natural Icelandic zeolites, which strongly indicates that the ion-exchange reactions are equilibrium-controlled 43,44,66 . Because zeolites with identical formation conditions have contrasting δ 44/40 Ca and the ionexchange processes governing Ca uptake are equilibrium-controlled, kinetic effects are unlikely to contribute to the δ 44/40 Ca variations observed here.
Another interesting observation is that zeolites with lower δ 44/ 40 Ca also have higher Sr/Ca (Fig. 3). During calcite precipitation, rate-dependent shifts in Ca isotope fractionation and Sr partitioning produce linear correlations between δ 44/40 Ca values and Sr/Ca ratios 13 ; however, the pattern observed in Fig. 3 for zeolites is nonlinear. In general, the understanding achieved for simple ionic solids does not immediately apply to more complex minerals, such as zeolites. Each zeolite studied here has a unique aluminosilicate framework. Incorporation of Sr into chabazite and heulandite, for example, is widely documented to reflect underlying structural characteristics, where zeolite framework topology and local bonding conditions give rise to larger exchange sites that prefer Sr relative to Ca 33,43,[91][92][93] . The trend shown in Fig. 3 provides evidence that structural properties known to control Sr incorporation may also discriminate Ca isotopes as well.
The CN of Ca in zeolites can vary widely within each mineral because the minerals support a variety of exchange sites with unique Ca-O bonding conditions 33 . For example, Ca in chabazite could have a CN of 6 or 12 depending on which exchange site Ca occupies (Table 3) 100 . Moreover, within a given zeolite exchange site, Ca can coordinate to either framework oxygens (O fmwk ), those composing molecular water also contained within the framework (O w ), or some combination thereof. In general, Ca-O fmwk bonds are considerably longer than Ca-O w bonds at a given site; thus, Ca-O bond lengths can vary greatly within one individual site, as well as between sites within a single mineral ( Table 3). The effect of CN on bond strength is documented for mineral systems where most of the bonds contributing to the CN of Ca have nearly equal lengths, relative to zeolites, which support highly different Ca-O bond lengths 25,[95][96][97] . As the average CN of Ca per zeolite cannot take into account nonuniform bond lengths, the average Ca-O bond length per zeolite likely better approximates bond strength for this particular mineralogical system. Therefore, we calculated an average Ca-O bond length for each unique Ca site and used this as a proxy for the average Ca-O bond length per mineral, assuming Ca is evenly distributed across all potential sites (Table 3).
When zeolite δ 44/40 Ca values are plotted versus average Ca-O bond length per mineral (Fig. 4), five of the six zeolites studied generate a significant correlation (R 2 = 0.93, p < 0.001). In general, zeolites with lower δ 44/40 Ca have longer approximate Ca-O bond lengths, while zeolites with higher δ 44/40 Ca have shorter approximate Ca-O bond lengths, consistent with equilibrium isotope fractionation theory 9,10 . While CN can adequately predict bond strength for many mineral systems 26,63,74,94,95,97 , the observation that stilbite (CN = 8) and scolecite (CN = 7) have nearly identical average Ca-O bond lengths and δ 44/40 Ca values supports our assumption that bond length better approximates the effect of bond strength on Ca isotope fractionation for zeolites. We suggest that differences in zeolite Ca-O bond energies underlie the trend between δ 44/40 Ca and bond length shown in Fig. 4, which we interpret as evidence for equilibrium isotope partitioning.
In the context of isotope fractionation between solution and mineral, it is important to consider Ca-O bonding dynamics in the surrounding fluid. Aqueous Ca 2+ coordinates to water O atoms in coordination or hydration spheres, which have shorter Ca-O bond lengths than zeolites 96 . Icelandic groundwater has higher δ 44/40 Ca values than zeolites (Fig. 4), consistent with predictions from equilibrium fractionation theory that stronger bonds preferentially concentrate heavier isotopes [8][9][10] . The exchange of Ca between groundwater and zeolite frameworks involves breaking a certain number of Ca-O w bonds in the hydration spheres (desolvation) to create Ca-O fmwk bonds 82 . Theoretical studies focusing on calcite have argued that desolvation can elicit kinetic isotope effects due to faster bond breaking of hydration spheres containing lighter Ca isotopes 80,101 . If such a mechanism is applied here, then minerals requiring more bond breaking of hydration spheres (i.e., those comprising fewer Ca-O w bonds) should preferentially incorporate lighter Ca isotopes. However, this pattern is not observed. For example, heulandite and thomsonite only need to break three to four hydration sphere bonds but show greater apparent fractionations than calcite, which must break at least six hydration sphere bonds, as the mineral supports no Ca-O w bonds. Stilbite has only Ca-O w bonds (Table 3), implying an absence of desolvation, yet Icelandic calcite and stilbite have similar δ 44/40 Ca (Table 2). In addition, chabazite has the least Ca-O w bonds of all zeolites studied here, but shows higher δ 44/ 40 Ca than heulandite. In parallel, heulandite and thomsonite have the same proportions of Ca-O w bonds relative to total Ca-O bonds, suggesting that these two minerals should desolvate hydration spheres identically, but heulandite has much lower δ 44/ 40 Ca values than thomsonite. While more research is needed to constrain relationships between zeolite structural characteristics, desolvation kinetics, and Ca isotope fractionation, our present observations better support an equilibrium isotope effect related to mineral Ca-O bond lengths.
Mesolite is the only exception to the relationship shown in Fig. 4. This zeolite and scolecite support identical Ca-site structures, but the mesolite framework also comprises alternating channels of Ca and Na sites 102,103 . Our bond length estimate assumes that all Ca in mesolite resides in the Ca channel; however, Ca can substitute into the Na channel, where it coordinates to O fmwk with much longer bonds than in the Ca channel 104,105 . For this particular sample, it is possible that a substantial proportion of the Ca occupies the Na channel, where Ca-O fmwk bond lengths are longer than our calculation estimates. Thus, the accumulation of lighter Ca isotopes in the Na channel could explain the sample's lower δ 44 An alternative explanation is that mesolite experienced kinetic isotope effects. The Ca sites in mesolite and scolecite have identical framework topologies, Ca-O bond lengths, and CNs. Theory for this scenario dictates that contrasting Ca isotope ratios could reflect kinetic isotope effects 26 . However, because precipitation rate effects observed for other types of minerals do not apply to zeolites, which participate in equilibrium-controlled ion exchange after initial precipitation 43,44,66 , the exact mechanism that would produce kinetic isotope effects is uncertain. Nevertheless, the data imply that mesolite is the most likely candidate of all zeolites examined here to have experienced kinetic fractionation. If correct, then our observation that mesolite plots off the line in Fig. 4 only supports equilibrium isotope partitioning for the other minerals.
Barring the one mesolite sample, bulk zeolite δ 44/40 Ca values inversely vary with approximate Ca-O bond lengths. While we interpret this pattern to reflect inter-mineral equilibrium isotope partitioning, more research is needed to better constrain zeolite fractionation mechanisms. The correlation between zeolite Ca-O bond lengths and δ 44/40 Ca values reported here is consistent with theoretical 23,[96][97][98]107 , laboratory 63,95,108 , and field studies of other mineral types [24][25][26][27]109 . To the best of our knowledge, our study is the first to report such effects for zeolites, as few studies have investigated δ 44/40 Ca variability in minerals that form in nature at intermediate temperatures. Zeolites with low δ 44/40 Ca values incorporate more Sr relative to Ca (Fig. 3). As Sr 2+ has a larger ionic radius than Ca 2+ , these minerals presumably support larger exchange sites, consistent with Ca isotope evidence that the minerals have longer Ca-O bond lengths. We also note that zeolites appear to fractionate Sr isotopes, with heulandite and stilbite bracketing the composition for bulk basalt 50 . Our overall interpretation is further consistent with an early investigation reporting that fractionation of Li and K isotopes by zeolites during ion exchange is largely equilibrium-controlled 110 .
While structural differences between zeolite frameworks adequately explain δ 44/40 Ca variability, we do note that Ca isotope offsets between the coindex pairs increases with depth ( Fig. 2), which counters the expectation that higher temperatures diminish equilibrium isotope fractionation 10 . This only underscores the first-order control of the mineral structure. Each zeolite has a unique framework structure, which gives rise to the positive correlation between the magnitudes of isotopic contrast and Ca-O bond-length differences between the coindex pairs. Zeolite δ 44/40 Ca values may indirectly relate to formation temperature, as temperature determines which frameworks crystallize as a function of depth 38,64 and structural properties appear to control Ca isotope fractionation (Fig. 4). However, the Ca isotope geochemistry of the minerals could more directly relate to the temperature of coexisting groundwater, as zeolites participate in equilibrium-controlled ion-exchange reactions after formation 38,43,44 . Thus, calcium isotopes could be developed as a proxy for circulating fluid temperature; however, more studies are needed to better elucidate equilibrium versus kinetic controls on fractionation and fully quantify fractionation factors for each mineral relative to solution. Nevertheless, our present findings illustrate the potential for developing an entirely new geothermometer for investigating low-grade basalt metamorphism, as well as probing a diverse range of other environments where zeolites form 111,112 .
Controls on hydrothermal water δ 44/40 Ca. Primary minerals display limited Ca isotope contrast and bracket δ 44/40 Ca values of bulk basalt (Fig. 3). This confirms previous suggestions that the limited Ca isotope variability of Icelandic basalt is due to a narrow range of primary mineral δ 44/40 Ca 21 . The source of fluid in the system studied here is meteoric 37 preferential Ca isotope release during primary silicate mineral dissolution for any silicate rock type. Therefore, hydrothermal waters and calcite in Iceland must be driven heavy as a byproduct of secondary light Ca sinks. During hydrothermal alteration of basalt, Ca-bearing zeolites and calcite are the two main sinks of aqueous Ca 2+ 45,113 , with zeolites forming distinctly prior to calcite 38,45,48,90,114 . Smectite and mixed layer clays form before zeolites, but they incorporate little Ca by comparison 38 29 , but no such calcite, whether anthropogenic or natural, has been measured in the Icelandic system. However, similar to natural hydrothermal waters 65,[116][117][118][119] , CCS waters are supersaturated with respect to zeolites after periods of CO 2 injection 45,48,90 . While some zeolites do show higher δ 44/40 Ca than basalt, the depth trend presented here is clearly asymmetric, where negative fractionations are larger (Fig. 2). Thus, it follows that progressive ion exchange with zeolites would elevate groundwater δ 44/40 Ca, supporting previous suggestions that uptake of lighter Ca isotopes by zeolites enriches hydrothermal waters in heavier isotopes 21,50,120 . Studies of other groundwater systems have suggested that preferential uptake of lighter Ca isotopes by anhydrite or calcite elevates water δ 44/40 Ca values relative to source rocks 19,20,121,122 . Zeolites form ubiquitously at temperatures ranging from~30 to 150°C during the hydrous alteration of silicates in many diverse environments 31,123 . Our results emphasize a need to consider Ca uptake by zeolites in studies aimed at understanding the geochemical evolution of natural groundwater, as well as CCS waters monitored during mineral carbonation of basalt 26,29,122,124 .
Controls on calcite δ 44/40 Ca. The overlapping range of calcite and hydrothermal water δ 44/40 Ca values in Iceland suggests that Δ 44/40 Ca cal-sol is close to 0‰ 21 , similar to patterns documented in other natural systems, where calcite slowly forms about the state of chemical equilibrium 125,126 . Equilibrium isotope effects appear to control the Ca isotope composition of zeolites, given the strong linear correlation between zeolite Ca-O bond lengths and δ 44/ 40 Ca (Fig. 4). Many hydrothermal calcite samples also have δ 44/ 40 Ca values that closely approach this line, suggesting a similar control by Ca-O bond length. We, therefore, propose that the unusually high δ 44/40 Ca of Icelandic hydrothermal calcite reflects the influence of zeolites on hydrothermal water δ 44/40 Ca. Because calcite samples display a range of δ 44/40 Ca values (Fig. 4), it is possible that the lighter calcite samples may have precipitated from hydrothermal waters that isotopically evolved to differing degrees. Alternatively, kinetic isotope effects due to variable precipitation rates may have contributed to the lower δ 44/40 Ca of some calcites relative to hydrothermal water. Regardless, it is likely that many Icelandic hydrothermal calcites have δ 44/40 Ca values consistent with equilibrium isotope control.
While several studies have identified how variable Ca coordination controls inter-mineral equilibrium isotope partitioning 63,108 , few have determined the effects of CN on mineral-fluid Ca isotope partitioning during natural calcite growth 127 . Calcite supports only one Ca site having Ca-O bonds of uniform length; 97,128-130 therefore, unlike zeolites, the CN for calcite adequately approximates bond strength and related isotopic effects. Calcium in calcite coordinates to six O atoms 128 . Thus, calcite has a lower CN than any of the zeolites examined in this study, as well as shorter Ca-O bond lengths. It follows that calcite should have higher δ 44/40 Ca than zeolites, which is the relationship observed in Fig. 4. Experimental results and calculations have demonstrated that Ca isotope fractionation during mineral precipitation depends on the CN of mineral Ca, as well as the CN of aqueous Ca 2+ , which can range from six to ten 80,[95][96][97]131 . Because Icelandic calcite appears to imprint the δ 44/40 Ca of hydrothermal waters and plot near the equilibriumcontrolled zeolite Ca-O bond-length line, we suggest that aqueous Ca 2+ in this system likely has a CN of six. Calcite, which has a known CN and a well-constrained Ca-O bond length, shows similar δ 44/40 Ca and bond length to Icelandic groundwater; thus, it follows that these reservoirs likely have similar CN. The isotopic offset between water and zeolites further implies that the CN of aqueous Ca 2+ must be lower than those of zeolites (lowest CN = 7) and more similar to that of calcite (CN = 6). The apparent offset between Ca-O bond lengths for calcite and hydrothermal water (Fig. 4) is likely a consequence of our assumptions, as bond lengths in calcite vary with impurities 97,98 , and bond lengths for sixfold coordinated aqueous Ca 2+ vary with temperature, ion pairing, and fluid ionic strength among other factors 80,95,96,131,132 .
Our results suggest that equilibrium-controlled calcite δ 44/ 40 Ca values could be used to identify the CN of aqueous Ca 2+ , and that laboratory studies able to control the CN of aqueous Ca 2+ could better constrain equilibrium isotope effects in synthesized calcites. In this context, the equilibrium isotopic offset between calcite and water (Δ 44/40 Ca cal-sol ), which is generally accepted to be~0‰ given small Δ 44/40 Ca cal-sol observed in natural settings where calcite precipitates at or near chemical equilibrium 15,125,126 , could be interpreted not only as an absence of kinetic isotope effects but also as an indication that aqueous Ca 2+ and calcite Ca both have a CN of six. This potentially has implications for various applications of the Ca isotope tracer, as the CN of aqueous Ca 2+ can vary with ionic strength and temperature 131,133 , which could theoretically impact the equilibrium isotope fractionation factor between calcite and water. For example, if fluid Ca 2+ was coordinated to eight oxygens instead of six (likely resulting in longer bond lengths in the hydration sphere 134 ), Δ 44/40 Ca cal-sol at equilibrium would be nonzero and positive, resulting in calcite that is enriched in heavier Ca isotopes [95][96][97] . Further work is needed to explore these ideas; however, our findings provide a valuable perspective on mineral-fluid isotope equilibrium, which could have implications for interpreting the δ 44/40 Ca values of marine carbonates deposited throughout geologic history.

Conclusions
This study reports Ca isotope data for natural zeolite minerals from Iceland, as well as hydrothermal calcite, bulk basalt, and primary mineral separates. Zeolite minerals display a δ 44/40 Ca range of~1.4‰, which is on the order of the range exhibited by all igneous rocks thus far measured 6,26 . Zeolite δ 44/40 Ca values strongly correlate with average Ca-O bond lengths, which we interpret to reflect equilibrium isotope partitioning. The bondlength hypothesis presented here also provides some evidence that equilibrium isotope effects control Δ 44/40 Ca between hydrothermal calcite and waters, given that these reservoirs support similar Ca-O bond lengths and display small isotopic offsets. As equilibrium isotope fractionation factors strongly depend on temperature 10 , our findings suggest that the Ca isotope geochemistry of zeolite minerals could be developed into an entirely new geothermometer for investigating low-grade basalt metamorphism. Moreover, zeolites should be considered in Ca isotope studies of other continental and oceanic hydrothermal systems where the minerals pervasively occur. Calcium isotopes hold particular promise for quantifying the mineralization of injected CO 2 during mineral carbonation of basalt, which is a leading CCS strategy 29,30 . Our study characterizes the composition of key mineral reservoirs necessary for interpreting and modeling Ca isotope variations in both field and theoretical CCS studies. More research dedicated to the Ca isotope geochemistry of zeolites could help improve numerous environmental, industrial, and medical applications of the minerals.

Methods
Field collection. During the summer of 2017, zeolites, bulk basalt, and calcite were collected from various outcrops in the Berufjörður-Breiðdalur region of East Iceland. No permissions were required for sampling in this location. Mineral types were identified in the field and later confirmed by X-ray diffraction (XRD), as described below. Where possible, coindex zeolite pairs were collected from a single outcrop for every depth-zone described by Walker (1960), and calcite samples were collected from all zones. Rock samples for primary mineral separates were collected from basaltic flows throughout Iceland (Fig. 1).
Sample preparation. Heavy liquids (Apatite-to-Zircon Inc., Viola, ID, USA) were used to separate mostly pure fractions of plagioclase, clinopyroxene, olivine, and apatite from three basalt samples with different ages and geologic histories. Intergrown zeolite samples from the same amygdule were physically separated. All basalt and mineral specimens, including primary minerals, calcite, and zeolites, were washed with MilliQ water and sonicated to remove excess sediment and impurities. Samples were dried in an oven at 50°C and powdered by hand using a Diamonite mortar and pestle. Zeolites fundamentally differ from typical rockforming silicate minerals, as their frameworks only comprise Al, Si, and O, that is, the minerals do not contain structurally bound Ca. All Ca is extra-framework, as it occurs in voids and channels created by the frameworks. Therefore, bulk measurements are most appropriate for characterizing the Ca isotope geochemistry of zeolites. Subsamples of basalt, primary mineral, and zeolite powders were completely digested using HF and HNO 3 acids. No insoluble residues were observed. Calcite powders were completely dissolved in 5% HNO 3 . To further interrogate the Ca isotope geochemistry of zeolites, a sequential leaching and digestion procedure was applied. Supplementary information (S2) more completely describes this experiment, and the results are summarized in Table S3 and Fig. S2. The leaching solution clearly fractionated Ca isotopes, as indicated by correlations between δ 44/ 40 Ca values and elemental ratios (Fig. S3), as well as fractions of Ca leached (Fig. S4); therefore, leachate and residual digest δ 44/40 Ca values were excluded from the main interpretations of this study.
X-ray diffraction. The identities of zeolite specimens collected in the field were confirmed by XRD in the Integrated Molecular Structure Education and Research Center at Northwestern University. Powder XRD data were collected at room temperature on an STOE-STADI-P powder diffractometer equipped with an asymmetrically curved germanium monochromator (CuKα1 radiation, λ = 1.54056 Å) and a one-dimensional silicon strip detector (MYTHEN2 1K from DECTRIS). The line focused Cu X-ray tube was operated at 40 kV and 40 mA. Intensity data from 2θ ranges of 1°-100°were collected over a period of 30 min. The instrument was calibrated against a NIST Si standard (640d) prior to measurement.
Elemental analysis. Sample solutions were diluted with 5% HNO 3 and analyzed for concentrations of Ca, Na, Mg, K, and Sr using a Thermo Scientific iCAP 6500 ICP-OES at Northwestern University. The concentrations have an uncertainty of ±5% (relative standard deviation), as determined by repeated analyses of NIST SRM 1643f. Concentrations of Si and Al were measured using a lithium metaborate fusion procedure and an Enviro II ICP-AES (Activation Laboratories, Ancaster, ON). These data have an uncertainty of ±5%.
Bond-length calculation. The weighted average bond length per zeolite mineral (L) was approximated by compiling published data on lengths for the two types of bonds (either Ca-O w or Ca-O fmwk ) specific to each exchange site containing Ca (Table S2). For some zeolites, Ca occupying a given exchange site can coordinate to both water O atoms and framework O atoms (Table 3). Because, in general, bond lengths differ depending on whether Ca coordinates to water O or framework O atoms, we calculated weighted average, site-specific bond lengths (l s ), which account for differences in Ca-O w bond lengths (l w ) and Ca-O fmwk bond lengths (l fmwk ) according to the number of water O atoms (N w ) and framework O atoms (N fmwk ) available for coordination. The equations are: where L is the estimated bond length per mineral (Å), f Ca is the fraction of Ca occupying each site (1, 2,…i), l s is the weighted average site-specific bond length (Å), l w is the average Ca-O w bond length in a given site (Å), l fmwk is the average Ca-O fmwk bond length in a given site (Å), N w is the number of Ca-O w bonds in a given site, N fmwk is the number of Ca-O fmwk bonds in a given site, and CN s is the coordination number of Ca in a given site. The calculations adopted for Fig. 4 assume even distribution of Ca across all potential Ca-bearing sites (Table 3). Sensitivity to this assumption was tested by changing f Ca to values that produce the minimum and maximum possible estimates of L for each mineral. The correlation remains significant for all scenarios (R 2 > 0.80, p < 0.001). See Supplementary information (S1) for more details on statistical analysis (Table S1).