A New Method for Silicon Triple Isotope Analysis With Application to Siliceous Sponge Spicules

Multiple isotope ratios of elements disclose information on the fractionation mechanism that cannot be obtained from a single isotope ratio alone. We describe a laser fluorination technique in combination with gas source mass spectrometry for the measurement of triple Si isotope ratios with high precision that allows resolving ppm‐level variability in triple silicon isotope ratios (29Si/28Si, 30Si/28Si) Δ‘29Si due to purely mass‐dependent fractionation in Si isotopes. We demonstrate how the triple silicon isotope ratios can be used to characterize different mass‐dependent processes that fractionate silicon isotopes. We report new data on reference materials (NBS‐28 [RM8546], Diatomite, BigBatch) and on siliceous sponges. Our triple silicon isotope data resolve that kinetic fractionation, possibly related to breaking Si(OH)4 molecules, causes the low δ30Si of sponges. The data further suggest that the cause for fractionation may be the same for the groups of Demospongiae, Homoscleromorpha, and Hexactinellida and that triple silicon isotope ratios of sponges have potential as seawater silicon isotope proxy.


Introduction
Stable isotope ratios are widely used in geo-and cosmochemical provenance analysis, paleoenvironmental studies, and forensics (Hoefs, 2009).For elements with more than two stable isotopes, traditionally, a single isotope ratio of the second most abundant isotope to the most abundant isotope is reported (e.g., 18 O/ 16 O, 30 Si/ 28 Si, 34 S/ 32 S).However, measurements of all stable isotopes are useful, for example, for the identification of mass-independent effects (e.g., Clayton et al., 1973, for O;Lee et al., 1977, for Mg;Armytage et al., 2011, for Si;Farquhar et al., 2000, for S).But high-precision measurements of multiple stable isotope ratios also bear information about specific, purely mass-dependent processes (see Young et al., 2002).Examples are mass-dependent multiple isotope variations of O in water (Barkan & Luz, 2007) or rocks (Pack & Herwartz, 2014), variations of S in sedimentary rocks (Ono et al., 2006), variations of Mg in chondrules (Galy et al., 2000) and carbonates (Tatzel et al., 2019), or combined triple O and Fe isotope variations in cosmic spherules (Pack et al., 2016).
For mass-dependent processes, the fractionation in δ 29 Si is about half of that in δ 30 Si.For a particular fractionation process (equilibrium or kinetic) between two phases or two reservoirs A and B, δ 29 Si and δ 30 Si are coupled through the exponent θ with  29 Si  10 3 + 1 30 Si  10 3 + 1 Graphically, the θ value (here referred to as the "triple isotope fractionation exponent") is the slope of the line that connects the data point of A with that of B in a δ' 29 Si versus δ' 30 Si diagram with δ' 29 Si and δ' 29 Si standing for the linearized form of the δ-notation (Hulston & Thode, 1965;Miller, 2002): and  ′30 Si = 10 3 In ( In the framework of this study, the θ value is related to mass-dependent fractionation in a particular physical process.It is distinct from the slope λ of a regression line in a δ' 29 Si versus δ' 30 Si diagram that is defined by a set of samples that are, in general, not genetically related.Such a line would be defined, for example, by analyses of a set of different terrestrial samples (rocks, water, and biominerals).Because such an array is the result of various equilibrium and kinetic processes, all having different θ values, λ has no particular physical meaning.
Now, what is the meaning of θ?For simple kinetically controlled transport processes (e.g., effusion, Graham, 1863), θ can be approximated with The masses   Si− denote the total masses of the moving species to which the silicon isotopes with masses i are bound.The lower limit for such kinetic θ is 0.5 (silicon bond to a moving molecule of infinite mass) and the upper limit is 0.5086 (diffusion of atomic silicon).The relation shown in Equation 5, however, only applies if the free path length is larger than the diffusion width considered.We want to note here that this situation was practically never realized in nature.
For the diffusion of Si(OH) 4 in water, one may use the reduced masses μ i of i Si(OH) 4 and water (  H 2 O = 18.0153 g mol −1 ) instead of the molecular mass m i in Equation 5with In ( and 10.1029/2023GC011243 3 of 15 Combining Equations 6 and 7 gives a θ = 0.5053 associated with the diffusion of Si(OH) 4 in water, which differs considerably from the number obtained by applying Graham's law (Equation 5; Figure 1).
The reduced masses μ in Equation 6, however, could also refer to a diatomic harmonic oscillator (as approximation), which bond is broken during the rate controlling reaction step.In this case, Si isotopes shall be bonded to a partner with the atomic mass m R with The accurate mass numbers should be taken instead of the numbers with two decimals given in Equation 8.The θ value for such kinetic processes would fall in a range between 0.509 and 0.5175 (Figure 1).Typically, kinetic fractionation is associated with a θ lower than the high-T equilibrium value, but can approach such a high value if Si is bond to a low-mass molecule.
Kinetically-controlled isotope fractionation can also occur when another bond (i.e., without breaking a bond to the Si atom) is broken within a molecule that Si is bound (e.g., within a protein; Hennig et al., 2005).Such an effect is termed secondary kinetic isotope effect.The secondary effect is based on the fact that the vibrational structure and thus bond strengths of an entire molecule are modified by the substitution of an isotope at any position within the molecule.This effect, however, is likely small and will not be discussed in more detail here.
Secondly, we discuss variations of θ associated with mass-dependent equilibrium processes.It has been pointed out by Matsuhisa et al. (1978) that equilibrium θ is a function of T and the phases participating.The value for high-T equilibrium silicon isotope fractionation can be estimated from quantum mechanical calculations (Young et al., 2002) and is approximated by As for Equation 8, the accurate isotope masses should be used in Equation 9. A priori, however, it is unknown what "high temperatures" are.Also, the T dependence can be variable.For the O isotope fractionation between water and vapor, little T dependence of θ has been observed (Barkan & Luz, 2005;Meijer & Li, 1998); whereas a strong T dependence has been suggested for the silica-water equilibrium (Pack & Herwartz, 2014;Sharp et al., 2016).Also, the calcite-water equilibrium θ exhibits a considerable T-dependence (Wostbrock et al., 2020).The few data for O demonstrate that there is no single equilibrium θ value and that the equilibrium θ is a function T and of the studied system.Sun et al. (2023) assumed that low-T equilibrium fractionation is associated with a θ that is not different from the high-T approximation of 0.5178 (Equation 9).Currently, no empiric data are available on equilibrium θ for any Si isotope fractionation process.

The Δ' 29 Si Notation
The Δ' 29 Si value is introduced in order to better display small variations in the δ' 29 Si versus δ' 30 Si space (see also Sun et al., 2023;Pack & Herwartz, 2014, 2015, for detailed discussion on Δ-notation in isotope systems with more than two isotopes).The absolute magnitude of Δ' 29 Si depends on the choice of an arbitrary reference line (RL) in the δ' 29 Si versus δ' 30 Si space.The RL can have any slope and may have an intercept different from zero (see Pack & Herwartz, 2014, 2015, for discussion on the RL for the case of O).Here, we adopt the definition of Δ' 29 Si as the deviation in δ' 29 Si from a RL by Sun et al. (2023) with Figure 1.Plot of θ for kinetic silicon isotope fractionation for ideal effusion (Graham's law, blue, Equation 5) and for reaction rate-controlled processes (red, for diatomic harmonic oscillator, Equations 6 and 8) versus mass m R of the partner that Si atoms are bond to.The high-T approximation for equilibrium fractionation (black, Equation 9) is shown for comparison.
Although being an arbitrary choice, 0.5178 has some physical meaning as it is identical to the high-T equilibrium approximation of θ for mass-dependent processes.The high-T approximation for equilibrium fractionation is also used as λ RL for the definition of Δ' 33 S, Δ' 36 S, Δ' 25 Mg, and Δ' 17 O (Galy et al., 2002; Hulston & Thode, 1965;  Pack & Herwartz, 2014).For the sake of inter-community (rock vs. water communities) consistency, for oxygen, a slope of the reference line of 0.528 is now used by many laboratories.A zero intercept is chosen so that the NBS-28 quartz standard has a Δ' 29 Si = 0 ‰; similar to the cases for S (Δ'

Silicon Isotope Ratios in Diatom Frustules and Sponge Spicules
Isotope ratios of biominerals are used as proxy for a wide range of paleo-environmental properties (e.g., seawater T, CO 2 partial pressure, weathering rates, etc.; Hoefs, 1996;Sharp, 2005).The correct interpretation of the observed isotope ratios requires that the biomineralization process itself fractionates isotope ratios at known magnitude (e.g., T dependent equilibrium fractionation).However, as this is not always the case, the use of isotope ratios of biominerals for paleo-environmental studies is limited.
Non-equilibrium effects associated with biomineralization are summarized as "vital effects" (see Weiner & Dove, 2003 for more details); a term that was introduced by Urey et al. (1951).An example is echinoderms, which precipitate carbonate in oxygen isotope disequilibrium with ambient water and are thus not well suited for oxygen isotope palaeo-thermometry.The presence of vital effects has been demonstrated for a variety of species and chemical and isotope systems (Weiner & Dove, 2003, and references therein).Wostbrock et al. (2020) demonstrated that triple O isotopes of calcite can be used to obtain precipitation temperatures even if the equilibrium composition is not preserved.
Marine sponges show a large and variable vital effect with respect to Si isotopes (De La Rocha, 2003;Douthitt, 1982;Hendry et al., 2010;Hendry & Robinson, 2012).The source of Si in marine organisms is dissolved silicic acid that is mainly brought into the oceans through rivers.Silicon is an important nutrient for marine phytoplankton.
It occurs in the ocean as dissolved silicic acid (Si[OH] 4 ) with variable concentrations up to 150 μM (De La Rocha et al., 2000;Hendry et al., 2010;Hendry & Robinson, 2012).The Si concentration generally decreases with a decrease in water depth due to the uptake of Si by phytoplankton in the surface layers (e.g., de Souza, 2011;Tréguer et al., 2021).The bulk Si budget of modern ocean water is controlled by opal-precipitating diatoms and sponges.The δ 30 Si of modern seawater ranges between 0.5 and 3.5‰ with deep ocean water (>1000 m) being more homogenous with 0.5 ≤ δ 30 Si ≤ 1.7‰ (De La Rocha et al., 2000;de Souza, 2011;de Souza et al., 2014).
In the modern oceans, phytoplankton largely controls the concentration and isotope composition of Si in shallow water.Diatoms are an extremely abundant group of eukaryotic algae (class Bacillariophyceae) that live in seaand freshwater environments and contribute up to 40% of the modern total oceanic primary production (Sumper & Brunner, 2008).
Diatoms fractionate silicon by −2.1 to −0.5‰ in δ 30 Si relative to available Si(OH) 4 with no strong dependence of the fractionation on the Si(OH) 4 concentration or temperature (De La Rocha et al., 1997;Hendry & Robinson, 2012;Sun et al., 2014;Sutton et al., 2013).The absence of any effect of the Si concentration on the Si isotope fractionation may suggest that this is an equilibrium effect.The absence of a measurable T effect, however, may be taken as an indication of a kinetic effect.
However, because of the negligible variations in Si isotope fractionation between diatoms and dissolved Si(OH) 4 , they can be used as a proxy for the δ 30 Si of seawater that provides information about the abiotic (weathering) and biotic (opal formation) Si cycle (De La Rocha et al., 1997, 1998).The δ 30 Si value of diatoms, however, gives limited information about the isotope composition of the bulk oceans (i.e., Si-rich abyssal water masses) because of their restriction to the isotopically variable surface layer.
The largest Si isotope fractionation is observed in siliceous sponges and triple Si isotope data may help to shed light on the underlying fractionation process.Sponges are basic metazoans and traditionally divided into siliceous sponges (Silicispongia sensu, Schmidt, 1862) and calcareous sponges (Calcarea).Sponges of both groups form spicules either in form of opaline silica or in form of high-Mg calcite.Modern phylogenetic analyses have shown that sponges are a monophyletic group with the two main clades Silicea (including Hexactinellida, Demospongiae, and Homoscleromorpha) and Calcarea (Philippe et al., 2009;Reitner & Mehl, 1996;Wörheide et al., 2012).Some taxa of the Homoscleromorpha produce siliceous spicules.Demosponges that do not form spicules are classified into Myxospongiae and Keratosa (Erpenbeck et al., 2012).
Three groups of siliceous sponges are distinguished: • Demospongiae: the most abundant and diverse sponges • Hexactinellida: less common and representative of deep-water environments • Homoscleromorpha: small group, probably related to the Calcarea, live in the same environments as the Demospongiae Demospongiae and Hexactinellida exhibit spicules, which are intracellularly secrete around a protein backbone structure (axial filament).In contrast, silica spicules of the Homoscleromorpha do not contain an axial filament and the formation mechanism is not yet fully understood.The proteinous axial filament of demospongid spicules is silicatein, a modified proteolytic capthepsin L enzyme (Shimizu et al., 1998).Intriguingly, long chained polyamines as observed in diatoms are also found in some demosponges such as Axynissa.The proteinous axial filament of hexactinellid spicules mostly shows coincidences with cathepsin.In very few hexactinellid taxa (e.g., Aulosaccus schulzei) transcripts with silicatein affinities were found which are identical to the demosponge silicateins (Veremeichik et al., 2011).This observation strongly supports the phylogenetic close relationship between Demospongiae and Hexactinellida (Silicispongia).Within the Homoscleromorpha no silicatein was observed.This observation shows that within the siliceous spicules-forming sponges three different modes were developed.
Deep-sea siliceous sponges live on the ocean floor, where the concentration and isotope composition (0.9 ‰ ≤ δ 30 Si ≤ 1.8 ‰; average 1.1 ‰) of silicic acid are less variable than in surface water (De La Rocha et al., 2000;Hendry et al., 2010) and more representative for the bulk oceans.Therefore, sponges should be more suitable as tracers for bulk ocean silicon isotope composition than diatoms.Douthitt (1982), De La Rocha (2003), Hendry et al. (2010), and Hendry and Robinson (2012), however, reported highly variable δ 30 Si values in marine sponges between −5.7 and −0.7 ‰, which limits the usability of sponge spicules as a proxy for the Si isotope composition of seawater.The fractionation between spicules and seawater was attributed to kinetic fractionation (i.e., a vital effect).Hendry et al. (2010), Wille et al. (2010), and Hendry and Robinson (2012) showed that the fractionation in δ 30 Si between sponge spicules is paradoxically inversely correlated with the Si(OH) 4 concentration.Paradoxically, because kinetic fractionation (e.g., diffusion toward the site of biomineralization) is typically larger at low concentrations.They suggest a growth-rate effect, that is, low Si(OH) 4 concentrations result in slow growth and hence a small kinetic isotope effect (i.e., small vial effect) during growth.High Si(OH) 4 concentration results in fast growth with a more pronounced kinetic control on the δ 30 Si value of the spicules.In this study, we first present a new technique for the measurement of triple silicon isotope ratios.We then report data on standards and present data on sponge silica spicules.We discuss data with respect to information on the Si isotope fractionation process during spicule formation.

Sponge Samples
We have obtained samples of 11 individual sponges collected at different locations worldwide (for details, see Table 2; see also Heinrich et al., 1992, for information of samples from RV Polarstern cruise VII/1).The sponge materials include Demospongiae, Hexactinellida and Homoscleromorpha.The spicules were removed from the sponge soft tissue using concentrated sodium hypochloride solution.

Analytical Protocol
We extracted SiF 4 by infrared laser-assisted fluorination of ∼3 mg silica samples.Samples are loaded into an evacuated sample chamber and fluorinated following a protocol first described by Sharp (1990).Instead of O 2 , we use the SiF 4 that is produced in the fluorination reaction.Purified F 2 (∼20 mbar, corresponding to a ∼2-fold excess in F 2 ) gas was used as a reaction agent.SiF 4 was separated from excess F 2 and O 2 in a cold trap (−196°C).
After the removal of O 2 and F 2 , SiF 4 was released by heating the cold trap to room temperature and re-trapping in a ¼"-stainless steel cold finger in front of the inlet to the sample bellow of a ThermoElectron MAT253 multicollector gas mass spectrometer.The spectrometer was equipped with collectors for masses 85, 86 and 87.SiF 4 was analyzed as SiF 3 + because of the higher intensity of the isotopologues of this radical (Figure 2).Bottled SiF 4 (Linde) was used as reference gas.Data are reported relative to the isotope ratios measured on NBS-28 quartz (δ 2 9 Si = δ 30 Si = Δ' 29 Si = 0).Sulfur-and carbon compounds lead to isobaric interferences in the mass range of SiF 3+ (see Molini-Velsko et al., 1986).We removed all S and C from our samples by heating samples in air at 900°C for 30 min.We have not applied gas chromatographic separation of interfering species (see Molini-Velsko et al., 1986) as this procedure has been shown to introduce a shift in δ 30 Si.Because the associated θ value is not known, we preferred to remove any contaminant before fluorination to obtain pure SiF 4 .A mass scan is shown in Figure 2.
We report the 2σ uncertainties (standard deviation, SD; standard error, SE) throughout the manuscript.

Reference SiF 4 (Zero Test)
The external reproducibility of a single dual inlet analysis of reference gas versus reference gas ("zero enrichment test") was ±0.008 ‰ for δ 29 Si and ±0.009 ‰ for δ 30 Si (single analysis, 2σ SD).The standard deviation of Δ' 29 Si of a single analysis was ±0.01 ‰.The averages of δ 29 Si, δ 30 Si and Δ' 29 Si were zero within analytical uncertainty.Refilling of the sample bellows with SiF 4 did not cause any resolvable fractionation (Figure 3a).

NBS-28 Quartz
The analytical uncertainties in δ 29 Si and δ 30 Si are considerably higher for analyses of silicates in comparison with reference SiF 4 gas (Figure 3b).For NBS-28, the standard deviation (2σ) is 0.06 ‰ for δ 29 Si and 0.1 ‰ for δ 30 Si.As analytical uncertainties in δ 29 Si and δ 30 Si show a high degree of correlation (Figure 3c), the uncertainty in Δ' 29 Si is only 0.01 ‰ (2σ SD).

Sponges
The isotopic compositions of the analyzed sponge spicules are listed in Table 2.The δ 30 Si of sponge spicules vary between −3 and 0 ‰.Demospongiae and Homoscleromorpha vary in a range of −2 < δ 30 Si < 0 ‰ and Hexactinellida show δ 30 Si down to −3 ‰.The Δ' 29 Si values of sponges are exclusively >0 ‰ and vary between 0.008 and 0.023 ‰.

Laser Fluorination for Si Isotope Analyses and Results for Standards
The uncertainty of our laser fluorination method (0.01‰ for Δ '29 Si, 1σ SD) is comparable to ICP-MS analyses (Sun et al., 2023) and thus is an alternative for high-precision triple Si isotope studies.
Diatoms fractionate the 30 Si/ 28 Si ratio by −1.1 ‰ relative to dissolved silica (De La Rocha et al., 1997), that is, they should closely mirror the Δ' 29 Si of dissolved silica; except that we assume an unrealistic low Graham's law θ value.The Diatomite standard, indeed, has Δ' 29 Si = 0.000 ± 0.005‰, which is in agreement with the reported Δ' 29 Si of seawater and confirms that this −1.1‰fractionation (even if it's kinetic) is associated with a negligible shift in Δ' 29 Si.
The data from this study and from the literature suggest that Hexactinellida fractionate the 30 Si/ 28 Si ratio by ∼−4.5 ‰, whereas the Demospongiae typically have 30 Si/ 28 Si ratios that are ∼2 ‰ lower than seawater (Figure 6).The Homoscleromorpha that have been analyzed in this study fall into the field of the Demospongiae (Figure 6).
It has been demonstrated that, irrespective of the class, sponges fractionate Si isotopes as a function of Si concentration (Hendry & Robinson, 2012;Wille et al., 2010).The lower δ 30 Si suggests that hexactinellid sponges prefer ecosystems with high concentrations of Si (∼>40 μM Si[OH] 4 ), whereas the higher δ 30 Si of Demospongiae and Homoscleromorpha reflect their habitats with lower concentrations of dissolved Si (∼<40 μM Si[OH] 4 ).This is in agreement with the deep-water habitats of Hexactinellida.
All sponge data fall on a distinct trend in the Δ' 29 Si versus 1000 ln 30/28 α sponge-seawater space and, along with seawater, define a line with slope λ = 0.512 ± 0.04 (2σ SD; Figure 6).This suggests that the cause of the fractionation is the same for all studied species, a conclusion that was based on the observation of universal concentration-dependence of fractionation in 30 Si/ 29 Si (Cassarino et al., 2018;Hendry et al., 2019;Hendry & Robinson, 2012;Wille et al., 2010).The source of Si in sponges is dissolved seawater Si in the form of silicic acid.Polymeric silicic acid may fractionate 30 Si/ 28 Si relative to the monomeric form (Oelze et al., 2015, and references therein).Hence, increasing affinity of heavy Si isotopes in polymerized, dissolved silicic acid may be discussed as a cause for decreasing δ 30 Si spicule -δ 30 Si seawater with increasing Si concentrations.This is because,   in general, concentrations of polymers increase with increasing concentrations of Si (Gerya et al., 2005).In such a scenario, equilibrium Si isotope fractionation would change with Si concentration, a relation observed for sponges (Hendry et al., 2010;Hendry & Robinson, 2012;Wille et al., 2010).Concentrations of Si in the oceans, however, are generally low, with Si occurring almost exclusively as monomer (Tréguer et al., 2021); therefore, we do not favor this model as an explanation for the observed relation between Si isotope fractionation and seawater Si concentration.Also, the observed θ for the fractionation between dissolved Si and spicules is much lower than that predicted for high-T equilibrium fractionation (Equation 9).We therefore suggest that one or multiple equilibrium fractionation steps are unlikely to be the cause for the low δ 30 Si of sponge spicules.
Kinetic fractionation that follows Graham's law (Equation 5), such as that considered by Sun et al. (2023) for cherts, is expected to give 0.5 ≤ θ ≤ 0.509 (Figure 1) and is significantly lower than the observed value of 0.512 as observed for sponges and seawater (Figure 4).As the free path length is small Note.The isotope compositions (δ 29 Si, δ 30 Si, Δ' 29 Si) are given relative to NBS-28.The average values (with 2σ SE) are also given (italic).

Table 2 Continued
Figure 5. Plot of Δ' 29 Si versus δ' 30 Si of river (blue) and seawater (orange) (Georg et al., 2006;Grasse et al., 2017).Note that the slope for the underlying low-T fractionation is identical to the high-T approximation of θ for Si.
for the diffusion of Si(OH) 4 in water, Equation 6 instead of Equation 5 is a better approximation to describe diffusion of silicic acid.The observed value of 0.512 (regression through all sponge data and seawater), however, is also significantly higher than the θ value associated with collision-dominated diffusion of Si(OH) 4 in water (θ = 0.505, Equation 6).If Si isotope fractionation during sponge spicule formation is related to bond-breaking as the rate-limiting step (red curves in Figure 1), θ is described by Equation 8 and we would expect θ between 0.509 and 0.5175 depending on the mass of the isotopologues, with the observed value of 0.512 being well within that range.
The triple Si isotope data on sponge spicules confirm the observation by Sun et al. (2023) that distinct fractionation processes leave a signature in Δ '29 Si, which allows us to obtain information about geo-and biogeochemical pathways.Furthermore, knowledge of the θ for the fractionation between sponge spicule silica and seawater (Figure 4) and assuming a Δ '29 Si of seawater of zero (Figure 5; buffered by the composition of the continental crust) allows the reconstruction of seawater δ 30 Si from measured sponge Δ' 29 Si data (Equation 10).
′30 Siseawater = Δ ′29 Sisponge (0.5178 − 0.512) +  ′30 Sisponge (11) The current analytical precision for the kinetic slope of 0.512 ± 0.004 (Figure 4), however, would allow reconstruction of δ 30 Si seawater not better than a few permil, which is large compared to the expected variations.In order to better use this proxy, more data with higher precision in Δ' 29 Si than presented here are required.Infrared absorption spectroscopic determination of Si isotopes on laser fluorination liberated SiF 4 may be an alternative to mass spectrometry and may provide data with improved precision (e.g., see Hare et al., 2022or Perdue et al., 2022, for the case of triple O isotopes of CO 2 ).2) with Δ '29 Si taken from Grasse et al. (2017).The uncertainty in δ 30 Si was assumed as 0.3‰.Karen Ziegler (University of New Mexico) generously provided the material of BigBatch and Diatomite.Reinhold Przybilla (Göttingen) supported this work through his invaluable service in keeping the stable isotope laboratory running.Zach Sharp (University of New Mexico) and Daniel Herwartz (University of Cologne) are thanked for discussions and helpful comments on the manuscript.The ThermoElectron MAT 253 was purchased from Grant INST 186/744-1 FUGG (AP, German Science Foundation and State of Lower Saxony).We thank Justin Hayles and Katharine Hendry for their thorough and most helpful reviews.Branwen Williams is thanked for the editorial handling.Open Access funding enabled and organized by Projekt DEAL.
Wille et al. (2010) suggested that the fractionation between seawater and sponge spicules comprises two parts: (a) a variable kinetic effect (vital effect) during the spicule formation, which is related to the ambient silicon concentration and (b) a constant Δ 30 Si spicule-water = −1.34‰ fractionation during silicon uptake.Hendry and Robinson (2012) developed a kinetic fractionation model on the basis of three fractionation steps: (a) Si uptake by the cell, (b) polymerization and (c) outflux of Si out of the cell.

Figure 2 .
Figure2.Magnetic mass scan of SiF 4 liberated from NBS-28 quartz (Thermo MAT253 mass spectrometer).The highest intensity is observed for the SiF 3 fragment on masses 85 (off scale), 86, and 87, which was therefore used for the isotope analysis.

Figure 3 .
Figure 3. Plot of (a) δ 29 Si versus δ 30 Si in reference gas versus reference gas (with and without He in the source) and (b) laser fluorination δ 29 Si versus δ 30 Si data of NBS-28 quartz (normalized to NBS-28).Note the high degree of correlation between δ 29 Si and δ 30 Si (b), which is a result of mass-dependent fractionation during gas extraction.The 2σ error ellipse (SD, single analysis) is shown.(c) Plot of Δ '29 Si versus δ 30 Si of NBS-28 quartz with 2σ error bars.The errors in δ 30 Si and Δ '29 Si are independent.
Data are reported relative to NBS-28.For each number, a new aliquot was extracted.Also given are averages with 2σ SE (italic).List of Isotope Ratios of BigBatch and Diatomite Reference Materials