A classical view on nonclassical nucleationPaul J. M. Smeetsa,b,c,1,2, Aaron R. Finneyd,e,f,1,3, Wouter J. E. M. Habrakena,b,g, Fabio Nudelmana,b,h, Heiner Friedricha,b,c,Jozua Lavena,b, James J. De Yoreoi,j, P. Mark Rodgerd,e,4, and Nico A. J. M. Sommerdijka,b,c,3

aLaboratory of Materials and Interface Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MBEindhoven, The Netherlands; bCenter for Multiscale Electron Microscopy, Department of Chemical Engineering and Chemistry, Eindhoven University ofTechnology, 5600 MB Eindhoven, The Netherlands; cInstitute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven,The Netherlands; dCentre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom; eDepartment of Chemistry, University ofWarwick, Coventry CV4 7AL, United Kingdom; fDepartment of Materials Science and Engineering, University of Sheffield, Sheffield S1 3JD, UnitedKingdom; gDepartment of Biomaterials, Max Planck Institute of Colloids and Interfaces, Research Campus Golm, D-14424 Potsdam, Germany; hEaStCHEM,School of Chemistry, University of Edinburgh, Edinburgh EH9 3FJ, United Kingdom; iPhysical Sciences Division, Pacific Northwest National Laboratory,Richland, WA 99352; and jDepartment of Materials Science and Engineering, University of Washington, Seattle, WA 98195

Edited by Patricia M. Dove, Virginia Polytechnic Institute and State University, Blacksburg, VA, and approved July 28, 2017 (received for reviewJanuary 6, 2017)

Understanding and controlling nucleation is important for manycrystallization applications. Calcium carbonate (CaCO3) is oftenused as a model system to investigate nucleation mechanisms.Despite its great importance in geology, biology, and many indus-trial applications, CaCO3 nucleation is still a topic of intense dis-cussion, with new pathways for its growth from ions in solutionproposed in recent years. These new pathways include the so-called nonclassical nucleation mechanism via the assembly of ther-modynamically stable prenucleation clusters, as well as the formationof a dense liquid precursor phase via liquid–liquid phase separation.Here, we present results from a combined experimental and com-putational investigation on the precipitation of CaCO3 in diluteaqueous solutions. We propose that a dense liquid phase (contain-ing 4–7 H2O per CaCO3 unit) forms in supersaturated solutionsthrough the association of ions and ion pairs without significantparticipation of larger ion clusters. This liquid acts as the precursorfor the formation of solid CaCO3 in the form of vaterite, whichgrows via a net transfer of ions from solution according to z Ca2+ +z CO3

2− → z CaCO3. The results show that all steps in this process canbe explained according to classical concepts of crystal nucleation andgrowth, and that long-standing physical concepts of nucleation candescribe multistep, multiphase growth mechanisms.

calcium carbonate | nucleation | crystal growth | cryo-electronmicroscopy | molecular simulation

In the process of forming a solid phase from a supersaturatedsolution, nucleation is the key step governing the timescale of

the transition. Controlling nucleation is an essential aspect inmany crystallization processes, where distinct crystal polymorphism,size, morphology, and other characteristics are required. It is,therefore, important to obtain a fundamental understanding ofnucleation mechanisms.More than 150 years ago, a basic theoretical framework,

classical nucleation theory (CNT) (1, 2), was developed to describesuch nucleation events. CNT describes the formation of nucleifrom the dynamic and stochastic association of monomeric units(e.g., ions, atoms, or molecules) that overcome a free-energy bar-rier at a critical nucleus size and grow out to a mature bulk phase.Calcium carbonate (CaCO3) is a frequently used model system tostudy nucleation (3–5); however, despite the many years of effort,there are still phenomena associated with CaCO3 crystal formationwhere the applicability of classical nucleation concepts have beenquestioned (6). These include certain microstructures and habits ofbiominerals formed by organisms (7), or geological mineral depositswith unusual mineralogical and textural patterns (8).Three anhydrous crystalline polymorphs of CaCO3 are observed

in nature: vaterite, aragonite, and calcite in order of increasingthermodynamic stability. In many cases, the precipitation of CaCO3from solution is described as a multistep process, with amorphousphases first precipitated before transformation to more stablecrystalline forms according to Ostwald’s rule of stages (9). Moreover,

in biological systems, time-dependent spectroscopy measurementsindicated that a hydrated amorphous calcium carbonate (ACC) isfirst deposited and then undergoes dehydration before crystalli-zation (10). Liquid–liquid phase separation has been proposed tooccur in CaCO3 solutions. Faatz et al. (11) presented the basis fora phase stability diagram including liquid–liquid phase separation.Wolf et al. (12) performed experiments in acoustically levitateddroplets and observed the formation of emulsion-like structures intransmission electron microscopy (TEM), which were proposed tobe a dense liquid phase (DLP). Bewernitz et al. (13) performedtitration experiments at moderate pH levels, in which they sup-ported the proposed emergence of a DLP by 13C nuclear magneticresonance (NMR) T2 relaxation and 13C pulsed field gradientstimulated-echo self-diffusion NMR measurements. Later, Wallaceet al. (14) developed the phase stability diagram to include regionsfor direct nucleation of solid CaCO3. They also performed latticegas simulations, which showed that upon classical nucleation of adense liquid close to the critical temperature, a wide distribution ofcluster sizes could be found in dilute solution. Recently, Zou et al.(15) proposed a stability diagram for calcium carbonate with ametastable solution region—where mineral phases or dense liquids

Significance

Nucleation is the process by which constituent building blocksfirst assemble to form a new substance. In the case of mineralformation from initially free ions in solution, the emergence ofintermediary phases often determines the thermodynamicsand kinetics of formation for the most stable phase. Our workon CaCO3 mineralization reevaluates a topic of intense discus-sion: Can nucleation be explained by theories established overa century ago, or should new physical concepts, as recentlyproposed, be adopted? Our data show that classical theoriescan indeed be used to describe complex mechanisms of crys-tallization. In addition, we provide information about theproperties of intermediate phases, which will aid in the designof additives to control mineralization.

Author contributions: P.J.M.S., A.R.F., P.M.R., and N.A.J.M.S. designed research; P.J.M.S.and A.R.F. performed research; P.J.M.S. and A.R.F. analyzed data; and P.J.M.S., A.R.F.,W.J.E.M.H., F.N., H.F., J.L., J.J.D.Y., P.M.R., and N.A.J.M.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1P.J.M.S. and A.R.F. contributed equally to this work.2Present address: Department of Materials Science and Engineering, Northwestern Uni-versity, Evanston, IL 60208.

3To whom correspondence may be addressed. Email: a.finney@sheffield.ac.uk orn.sommerdijk@tue.nl.

4Deceased March 23, 2017.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1700342114/-/DCSupplemental.

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are able to nucleate from solution—bounded by a limit of solutionstability at 3–4 mM calcium and carbonate concentrations (understandard conditions). At a limit of solution stability, dense liquidsor solids and dilute ionic (“lean”) solution phases spontaneouslyphase separate (i.e., they undergo spinodal decomposition).Transformations from free ions in solution to dense liquid or

solid phases may occur according to classical concepts. However,recent studies have described so-called nonclassical nucleationpathways (16) involving thermodynamically stable, nanometer-sized prenucleation clusters (PNCs) (17, 18) that are already pre-sent in undersaturated solutions. In fact, ∼75% of bound calciumin solution was proposed to be present in PNCs in typical titrationexperiments (17). In this scenario, the first solid mineral phase isproduced upon aggregation of PNCs, as indicated by an increase inthe sedimentation coefficients for solution species in analyticalultracentrifugation (AUC) measurements (17).Computer simulations indicate that PNCs are dynamically

ordered liquid-like oxyanion polymers (DOLLOPs) with an av-erage twofold cation–anion coordination (18). The loose bindingof ions allows for a wide range of cluster configurations, and alimiting size to clusters was attributed to the pH dependence ofbicarbonate incorporation. While the structural and dynamicalproperties of DOLLOPs may appear similar to nanodroplets ofdense liquids, PNCs are defined as stable solutes, that is, they donot have a phase boundary with the surrounding solution (19).Recently, evidence from AUC (17) and cryogenic TEM (cryo-TEM) (20) reporting PNCs with well-defined (sub)nanometersizes has been disputed (21). The role of PNCs in the nucleationprocess has also been questioned, considering that their pro-posed thermodynamic stability should increase the barrier tonucleation, relative to the one from ions in solution (22).Attempts have been made to incorporate PNCs into pathways

for liquid–liquid separation (13, 19); nevertheless, no direct evi-dence for these mechanisms have been provided. Computer sim-ulations have shown that liquid–liquid separation provides thepossibility for a wide distribution of cluster sizes in solution, but nospecial thermodynamic status for clusters of a well-defined sizewas demonstrated (14). Thus, an open debate remains about theinvolvement of stable PNCs in the nucleation of CaCO3.In this work, a combined experimental and computational in-

vestigation of CaCO3 precipitation is reported using a titration setupwith ion-selective electrodes (ISEs) as described by Gebauer et al.(17), and molecular-dynamics (MD) simulations of clusters and freeions in water with the force field reported by Demichelis et al. (18).This system is additionally studied using cryo-TEM with imageanalysis, TEM simulations, and dynamic light scattering (DLS). Ourstudies confirm that a significant fraction (>60%) of Ca2+ in so-lution is bound before nucleation, in agreement with earlierstudies (17, 18). However, we find no evidence for the formationof PNCs. Before nucleation of solid CaCO3 in the form of vaterite,we find the emergence of a dense liquid calcium carbonate phasein both experiments and simulations. In titration experiments, thevaterite grows following nucleation via a net transfer of stoichio-metric calcium and carbonate ions from solution, which eventuallyexhibits Ostwald ripening as determined from DLS measurements.All of the observed results can be completely explained within theconcepts of classical nucleation in a multiple-step, multiple-phasereaction from predominantly free ions and ion pairs in solution.

ResultsPrenucleation Species. As in the report of Gebauer et al. (17), atypical LaMer curve (23) was obtained (Fig. 1A) with high re-producibility, which showed a steady increase in the concentrationof free Ca2+, c(Ca2+free), followed by a sudden drop indicating thenucleation of a new phase. Following nucleation, c(Ca2+free) con-verged toward the equilibrium solution concentration of the newlyformed solid phase. In the following, we used a dimensionless time,tσ max, normalized by the time of maximum c(Ca2+free) to account

for the stochastic nature of nucleation. The high reproducibility ofthe experiments is then evident in Fig. 1.The difference between the total concentration of titrated

Ca2+, c(Ca2+tot), and c(Ca2+free), defines the concentration ofbound Ca2+ in solution: c(Ca2+bound). Fig. 1B shows that, in ac-cordance with previous data (17), on average 65–75 ± 1.0%(mean ± SE) of the Ca2+ was bound in solution before nucleation.During the prenucleation stage (K0.90 tσ max), the activity ratio ofbound to free calcium ions in solution (SI Appendix, Fig. S3), andconcentration ratio of bound to total calcium ions in solution (Fig.1B) was nearly constant until the nucleation point (the deviation att K 0.1 tσ max is attributed to electrode signal instability during thecalibration at very low ionic strength, see SI Appendix, section 2.3).At the same time, during linear Ca2+ addition, the linear additionrate of NaOH to maintain the pH indicated a constant chemicalcomposition of the reaction mixture in the prenucleation stage (SIAppendix, Fig. S4). It can be concluded from these considerationsthat the carbonate activity is virtually constant.From the definition of the equilibrium for any prenucleation

species of the type Cax(CO3)y, it follows that

a�CaxðCO3Þ2ðx–yÞy

�

a�Ca2+free

�x = constant · a�Ca2+free

�x−1.

This is true if over a large range of Ca2+ concentrations x = 1 (seeSI Appendix, section 2.3.4, for more details), and suggests that

A

C D

B

Fig. 1. (A) Titration curve for n = 10 experiments showing the averagedevelopment of concentration of free Ca2+ ions as measured by the Ca2+-ISE[c(Ca2+free); red line] compared with the total average concentration of Ca2+

dosed [c(Ca2+tot); black line] as a function of time normalized with respect tothe time of maximum c(Ca2+free): tσ max. The average concentration of boundCa2+ [c(Ca2+bound) = c(Ca2+total) − c(Ca2+free)] is given by the blue curve. Errorbars show SDs of the distribution. (B) Ratio of bound and total Ca2+ ionconcentrations up until tσ max (intervals are 100 s). The arrow indicates nu-cleation at ∼0.90 tσ max, as the fraction of bound Ca2+ starts to increasecompared with the constant ratio of c(Ca2+bound)/c(Ca

2+tot) determined in

the prenucleation stage (K0.90 tσ max). The deviation of c(Ca2+bound)/c(Ca2+

tot)at K0.1 tσ max is attributed to electrode signal instability during the cali-bration at very low ionic strength. Error bars are standard errors of mea-surement (SEMs). (C) MINTEQ model data for c(Ca2+free), c(Ca

2+bound), and

c(Ca2+total), shown as red, blue, and black squares, respectively, overlaid onthe experimentally measured time-dependent concentration curves with thesame color. (D) The concentration of free Na+ in solution c(Na+free) as de-termined by the MINTEQ speciation program (magenta squares) and theaverage c(Na+free) determined from n = 3 Na+-ISE measurements (magentaline), with corresponding SDs of the distribution.

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bound calcium in solution is therefore present in single Ca2+-basedion association complexes, such as the classical ion pair CaCO3

0,similar to what was previously demonstrated for the case of calciumphosphate (24). Complexes with y = 2, 3. . . and containing bicar-bonate would also agree with these data. An alternative that hasbeen proposed could be the formation of polymeric assemblies ofthe type [ion association complex]n, where, using a multiple bindingapproach, the free energy of binding would be equal for all sub-sequent additions of monomeric units to n = 2, 3, 4. . . assemblies.Such polymeric assemblies were indeed proposed for [CaCO3

0]n onthe basis of AUC (17) and molecular simulations (18), and for [Ca(HPO4

2−)3]n on the basis of titration experiments and cryo-TEMobservations (24).To verify whether the titration data could indeed be fully

explained by the formation of classical species, the activities of allrelevant ions (Ca2+, CO3

2−, HCO3–, Na+, Cl–, OH–) were calculated,

taking into account the ionic strength at different time points, andentered into an equilibrium speciation model (Visual MINTEQ; SIAppendix, section 2.4). The model not only correctly described theexperimentally determined concentrations of calcium (Fig. 1C) andsodium (Fig. 1D), but also requires that the only relevant speciesbefore nucleation are dissolved ions and the classical ion pairsCaCO3

0 and CaHCO3+ in a 96/4 ratio (SI Appendix, Table S4). This

contrasts the suggestion that relatively large ionic assemblies areaccessible to the system. Indeed, DLS did not indicate any signifi-cant population of nanoparticles in the prenucleation stage com-pared with the buffer background (SI Appendix, Fig. S5).Cryo-TEM was used to investigate the presence of ionic as-

semblies of the type [CaCO30]n in the prenucleation stage. An

example TEM image is shown in SI Appendix, Fig. S5, demon-strating that no such objects were found in any of the acquiredimages. At the applied imaging conditions, objects ≥0.9 nm (25)can be detected, which would permit the observation of polymericprenucleation clusters for which average diameters of 2–3 nm havebeen proposed (19). The obtained images were also systematicallyanalyzed using an in-house computational process (SI Appendix,section 1.9), but no prenucleation clusters were found to be presentin solution. Specifically, at K0.90 tσ max, a significant population ofclusters with sizes ≥0.9 nm, as proposed for PNCs (17, 26), was notobserved in cryo-TEM, in good agreement with titration analysisand DLS measurements.The lack of polynuclear assemblies contrasts with the proposed

stability of DOLLOPs, which were shown to emerge spontaneouslyin computer simulations and proposed as the structural form forPNCs (18). For high Ca2+ concentrations (500 mM), 50- to 70-nssimulations identified DOLLOPs containing up to ∼60 ions atpH = 10. Using a speciation model incorporating the multiplebinding assumption, Demichelis et al. (18) predicted that, at thesepH levels and c(Ca2+) = 0.4 mM, around 25% and 75% of boundcalcium would be present in ion pairs and DOLLOPs, respectively.To investigate cluster sizes at close-to-experimental concentrations,we performed similar simulations, generating trajectories of at least20 ns and using total Ca2+ concentrations (20–30 mM) and pHvalues as close as computationally feasible to those used in theexperiments (SI Appendix, Table S1).At equilibrium, the concentrations of free calcium and (bi)car-

bonate were measured as 3–5 and 16–26 mM, respectively (SIAppendix, Table S1). In agreement with previous simulations (18),from an initial single cluster in water, polymeric chains with char-acteristics of DOLLOP were observed during the first few nano-seconds of simulation. However, upon continuing the simulationup to 10 ns, these polymers dissociated into free ions, ion pairs,and, occasionally, clusters of at most four ions in size with anyreasonable probability (Fig. 2). A second series of simulations wasinitiated from random distributions of free ions (Materials andMethods). These equilibrated to the same cluster size distributionfound with the first series (Fig. 2 and SI Appendix, section 3.1) andthe frequencies for both ion attachment and detachment to/from

clusters were equivalent. Furthermore, while density fluctuations inall simulations produced—albeit rarely—larger clusters, thesequickly dissociated. While the system size may limit the size towhich clusters can grow in solution, multiple simulations withvarying total numbers of ions produced, qualitatively, the sameexponential decay in cluster size distribution that is predicted byclassical theories (SI Appendix, Fig. S12).In the present work, 60–65% of the bound calcium was found

in ion pairs in the system where the pH at equilibrium was 8.3 ± 0.8,and we would expect this to be higher still for lower Ca2+ con-centrations, in line with the speciation model data above. Theaffinities for calcium binding to carbonate or bicarbonate showeda preference for CaCO3

0 ion pairs in all simulations (Fig. 2D,Inset, and SI Appendix, section 3.1). In the random system atequilibrium, the same ionic species were also found, with 66% ofthe ion pairs being of the type CaCO3

0 (SI Appendix, Fig. S13).During the simulation, the pH decreased due to the preferredbinding of Ca2+ to CO3

2−, which enriches the solution in HCO3−.

Another simulation performed at higher initial pH (pH = 10.3)showed an increased preference for the formation of CaCO3

0 ionpairs (87%) and a further reduction of the larger clusters, withonly 3% of the Ca2+ bound to two carbons (Fig. 2D, Inset).Values closer to the predicted 96/4 ratio for CaCO3

0/CaHCO3+

(SI Appendix, Table S4) are expected at higher equilibrium pH,but simulations very much larger in system size would be re-quired to obtain statistically meaningful values.The size of clusters was determined according to radius of gy-

ration, Rg. Fig. 2E shows Rg probability densities for a simulationwhich started from a random distribution of ions. The distributionindicates a high probability to find clusters with Rg = 0.2 nm (ion

Nions

P(N

ions

)

NCa-C

P(N

Ca-

C)

P

t (ns)

A B

C

D

Rg (nm)

f( Rg)

0 0.1 0.2 0.3 0.40

5

10

15

20

25

30E

00.20.40.60.8

1

0 5 10 15

Ca-CCa-2CCa-3C

1 2 3 4 5 6 7 8 9 1000

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 400.20.40.60.8

1

Fig. 2. Simulations at low CaCO3 concentrations starting from (A–C) apreformed cluster and (D–E) a random distribution of ions in solution.Snapshots of (A) a cluster present at the beginning of a simulation (wherethe initial Ca2+ concentration was 32 mM), and (B) ionic species found atequilibrium in a 20-ns MD simulation. Calcium, carbon of carbonate, andcarbon of bicarbonate are shown in yellow, purple, and blue, respectively.Green lines show carbon and calcium within 4.2 Å. (C) Time dependence ofthe relative probability for calcium to bind to one (black), two (blue), orthree (red) (bi)carbonates. (D) Size probability distribution at equilibrium (innumber of ions, Nions; Nions = 1 indicates free ions) for ionic species in waterfor a system with an initial Ca2+ concentration of 26 mM; averages wereobtained from the final 2 ns of simulation. Inset is the probability of a Ca2+

ion coordinating to NCa-C carbon atoms (black) in associated species recordedover the same time window. Red and blue data are for binding to CO3

2− andHCO3

−, respectively. Error bars represent 1 SD in the distribution. (E) Radiusof gyration (Rg, in nanometers) probability densities for ionic species in so-lution at equilibrium for the simulation described in D. The peak at Rg = 0 isdue to free calcium, which is modeled as a charged point mass.

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pairs), while larger clusters (up to a maximum of Rg = 0.4–0.5 nm)were found with only very low probability. Thus, no larger clusters≥0.9 nm could be found, entirely consistent with our cryo-TEM data.As HCO3

− limits DOLLOP growth, simulations at moderatelybasic pH could lead to an underestimation of equilibrium clustersizes. Therefore, we investigated a series of cluster simulationsfrom an initial (CaCO3)20 structure, where ionic coordinationand ionic density were consistent with the structure of liquid-likeclusters, at the limit of high pH and at 20–50 mM. These clustersdissociated at all concentrations, with the dissolution rate beinghighest at the lowest concentration. Here, ion pairs (70%) and alow probability of clusters containing four ions were found after45 ns of simulation (SI Appendix, section 3.2 and Table S7).While some dissolution of clusters in water might be expected,the continued, gradual dissociation of smaller polymeric speciesover tens of nanoseconds is further suggestive of the instability ofliquid-like clusters in homogeneous, low-salinity solutions.Wallace et al. (14) showed the free energy of liquid-like clusters

from a low-density calcium carbonate solution to consistently de-crease with cluster size in replica exchange simulations sampling300–400 K at 15 mM. While their all-atom approach is adequate tounderstand the energetics of cluster growth, it does not provide theequilibrium cluster size distribution at low concentrations.To summarize, we do not observe larger nanometer-sized

polymeric species at our experimental conditions in cryo-TEM,nor detect them by DLS, and additionally demonstrate that PNCsdissipate in solution via our simulations. Instead, MINTEQ cal-culations, titration data, and our simulations demonstrate that ionpair formation of the form of CaCO3

0 dominates calcium-bound

species in solution. Therefore, we are confident that we can ex-clude the formation of PNCs to describe our data.

Nucleation of a DLP. Before 0.96 tσ max, DLS showed an initialincrease in the count rate starting from ≥0.90 tσ max, indicatingthe nucleation of a new phase (Fig. 3A). The associated corre-lation diagrams (Fig. 3B) indicated that around these time points(∼0.88–0.96 tσ max) objects with a size of ∼200–400 nm werepresent (Fig. 3C). DLS demonstrated that after 0.96 tσ max afurther increase in count rate and particle size occurred (Fig. 3 Aand B, and SI Appendix, Fig. S9) where the average particle ra-dius, r, at time, t, scales approximately as r(t) ∼ t1/3 (Fig. 3D),which fits particle growth through coalescence by Browniancollisions (27) and through coarsening by Ostwald ripening (28,29) (SI Appendix, section 2.7.2).To investigate the evolution of morphology and structure of

the formed CaCO3 in more detail, samples for cryo-TEM weretaken from the titration experiment at time points close beforetσ max and vitrified by plunge freezing (Materials and Methods).At >0.90 tσ max, cryo-TEM images showed the presence of roundamorphous objects of ∼200–400 nm (Fig. 4 A, B, and D), with

BA

C D

Fig. 3. DLS results showing (A) evolution of the derived count rate (blackdashed line) during 0.8–1.2 tσ max around the nucleation point at ∼0.90 tσ max

(red arrow). The dotted red line indicates the average count rate in theprenucleation stage, while the blue curve represents the amount of freeCa2+ (right axis). (B) The correlation coefficient (G′) given for the time points1–4 in A, showing a significant increase between measurement 2 and 3. Thepurple arrow indicates the single descent in curves 1 and 2, as also found forthe carbonate buffer solution. Pink arrows point at two distinct descents incurves 3 and 4 indicating the presence of a populations of micrometer-sizedparticles (around 105 μs) alongside a population of smaller particles (at 102–103 μs)after 0.96 tσ max. The intercept G′ > 1 at 1.01 tσ max at 100 μs is indicative ofsedimentation. (C) Volume size distribution of a typical DLS measurementbetween 0.88 and 0.96 tσ max (at 0.92 tσ max; bin size, 33 nm) demonstratingthe presence of ∼200–400 nm particles in solution. (D) Rate of particleOstwald ripening/coalescence as determined by DLS. The average radiusr at time t scales with r(t) ∼ t1/3 from approximately ∼0.90–0.96 tσ max

onward, as indicated by the linear fits with corresponding R2 for n = 3measurements in red, blue, and black.

C

050

100150200250300350400450

Ave

rage

siz

e (n

m) cryoTEM

DLS

C

B

FE

D

backgroundDLP

DLP

T = 5.6688P-value = 0.0051

0.36 0.37 0.38 0.39

A

0 200 400 600120

130

140

150

160

Inte

nsit

y (a

.u.)

Distance (nm)

d-spacing (nm)

0.2 0.3 0.4 0.5

Inte

nsity

(a.u

.)

d-spacing (nm)

Fig. 4. (A and B) Cryo-TEM image of the DLP in titration experiments insupersaturated solution conditions at (A) 0.92 tσ max and (B) 0.96 tσ max

showing objects with diameters of ∼320 and ∼420 nm, respectively (whitearrows). (Scale bars: A and B, 500 nm.) C shows a line scan through the upperobject in B (indicated in B by the black dashed line). The black dashed lines inC indicate the object boundaries, while the blue line indicates the meanintensity value of the dilute background solution. The low contrast relatedto the maximum intensity in the line scan indicates a high degree of hy-dration. (D) Low-dose selected area electron diffraction (LDSAED) shows theamorphous nature of the objects in B. (Scale bar: 2 nm−1.) The Inset showsthe integrated radial average profile over the diffraction pattern in D, withthe large peak reflecting the ring closest to the center. (E) Bar plots in-dicating the d-spacing of the background solution of the DLP at 0.96 tσ max

(red), and of the submicrometer-sized DLP at 0.96 tσ max (blue) of n = 5 sampleswith corresponding error bars (SD of the distribution). Statistical analysis (via aWelch–Aspin generalized T test; SI Appendix, section 2.7) shows a significantdifference between the DLP and its background solution by the indicatedP value. (F) Mean size ± SD for the DLP particles in cryo-TEM (blue) and the DLSsize distribution at 0.96 tσ max (green). DLS distributions correspond to the firstdecay in the correlation function recorded at 0.96 tσ max (Fig. 3B).

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image contrast that was very low compared with what would beexpected for solid CaCO3 particles of the same size (30). For thissystem, the observed low contrast implies a phase of low density,and therefore it is sensible to assume that the objects contain ahigh degree of hydration. Amorphous calcium carbonate withhigh levels of hydration behaved as a liquid in computer models(14). Furthermore, low image contrast in TEM was observed fora polymer-induced liquid precursor phase (31), as well as intetrahydrofuran–water mixtures which underwent liquid–liquidphase separation (32). Importantly, the ion activity product de-rived from the titration curve at all times remained significantlybelow the solubility of ACC as reported by Brecevi�c and Nielsen(33) (see Fig. 8A). This also contrasts with the earlier assignmentof the solubility to different forms of ACC, which—althoughhaving similar ion activity products—were not corrected for theinfluence of ionic strength (17, 34). The fact that we still observean amorphous phase, and considering the above discussion, wepropose that the observed objects are vitrified droplets of a DLP,rich in calcium carbonate that forms from the solution through aliquid–liquid phase separation process. We note, however, thatour TEM data cannot provide information surrounding the dy-namical behavior of ions in the observed objects. Low-dose se-lected area electron diffraction (LDSAED) was used to assessthe differences in short range order between the backgroundsolution after nucleation and the DLP (at 0.96 tσ max). Thisanalysis revealed broad rings indicating the absence of any long-range order in the DLP (Fig. 4D) and representing a d-spacinglarger than that of the background solution (Fig. 4E), in line withan increased ion density within the droplets (20).Simulations at high calcium and carbonate concentrations sup-

port the experimental observations. From initially free ions inwater at 0.57 M, a Ca2+ and CO3

2− ion-rich liquid domain formedover 40 ns of MD simulation. The spherical-like nanoparticle (withdiameter ∼3.0 nm; Fig. 5A) which emerged was in equilibrium witha lean aqueous solution containing free ions, ion pairs, and occa-sional larger associates (SI Appendix, Figs. S18 and S19). This is in

line with predictions from lattice-gas simulations of liquid–liquidphase separation (14). While the initial ion concentrations herewere much higher than in experiments, this was chosen to reduceany barrier to nucleation. At still higher concentrations (1.1 and 1.7M), cylindrical ionic networks spanned the periodic simulation cells(Fig. 5B and SI Appendix, section 3.3.1). This transition is explainedby a crossover in the minimum surface energy between a sphereand percolating cylinder at limited system sizes, as would beexpected for a liquid phase. The concentrations of free ions in leansolution at equilibrium (SI Appendix, Table S2) were comparable tothose found from solutions at relatively low concentrations, andcalcium concentrations [c(Ca2+) = 1–2 mM] were less than thatproposed for the limit of solution stability at 300 K (15), furthersupporting the proposed phase separation mechanism.From our analyses, the structure and dynamic properties of

dense liquid CaCO3 at all concentrations were consistent andcomparable to a viscous fluid (SI Appendix, section 3.4). Ca2+ inthe DLP was found to bind preferentially to two carbonates(∼45%, Fig. 5C; see SI Appendix, section 3.3.2, for details); anincrease in three-coordinate Ca2+ was observed compared withionic associates in lean solution, but not enough (35%) to con-dense and rigidify the dense liquid. Our coordination levels werein reasonable agreement with those found in the high pH sim-ulations of Demichelis et al. (18) and for dense liquid nano-particles simulated by Wallace et al. (14), where the averagecoordination in the largest clusters was around 2.8. Furtheranalysis showed that ion coordination was relatively high in thecore of the DLP, while a gradual decrease was observed awayfrom the core in a wide and diffuse interfacial region (Fig. 5 Eand F, and SI Appendix, section 3.3.2). Ion diffusion coefficients,Dion, varied as a function of distance from the center of the denseliquid toward the interfacial region and were 10−8 to 10−6 cm2/s(SI Appendix, section 3.4): at least two orders of magnitudehigher than Dion in ACC with a 1:1 CaCO3:H2O stoichiometry(35). The dynamic nature of ion coordination was confirmed byshort Ca–C coordination lifetimes (Fig. 5D and SI Appendix,

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Fig. 5. (A and B) Snapshots taken from simulationsdemonstrating the existence of a DLP in CaCO3 so-lutions at initial concentrations of (A) 0.57 M and (B)1.1 M. Averages were measured from the final 5 nsof simulation. Calcium and carbonate are shown aspurple and yellow, respectively, and a van der Waalssurface (from ion atom centers) is highlighted. In B, a16-Å slice through a large cylindrical cluster is taken,which intersected the simulation cell boundaries. Watermolecules are represented by the blue circles. (C) Clustercoordination probabilities for Ca2+ to bind to NCa–C car-bons with corresponding SD at 1.1 M. (D) Probabilitydensity for Ca–C bond lifetimes (distance cutoff: 4.2 Å) at1.1 M, with data smoothed using a running average. (E)Mass density, ρ, of ions (red) and water (blue) in the DLPas a function of distance from the center of mass at1.1 M with regression curves fitted (bandwidth: 0.6 nm).(F) Coordination probability map generated from in-terpolated data. Ca2+ coordination numbers in the firstcoordination shell to carbonate oxygen atoms, Ca2+ co-ordination, and water, Ca2+ solvation, are plotted withthe distance of calcium from the center of mass high-lighted by the map color on the right (scale in nano-meters). (G) Calculated TEM image at 1.7 M. Bottom toTop: a schematic of the supercell used in the calculation,showing orientation of the DLP with respect to the in-cident electrons; a selected region of the calculated TEMimage; smoothed line scans taken from the image asshown by the blue and black curves.

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section 3.3.2). In the core of the dense phase, the water wasrelatively tightly bound and on average a high level of hydrationwas found (4–7 H2O/CaCO3; SI Appendix, section 3.3.3).TEM images for these dense phases (Fig. 5G) were calculated

using a multislice algorithm (SI Appendix, section 1.12) and basedon the method by Rullgård et al. (36). These were in goodagreement with the experimental cryo-TEM data showing 85 ±5% vs. ∼93% transmission compared with the low-density back-ground solution, respectively (see Figs. 4C and 5G, noting that thesize of the simulated system limits the defocus values that can beused; SI Appendix, section 3.5.1). This agrees with our cryo-TEMobservations which gave no evidence for clusters >1.1 nm withinand surrounding the DLP phase (SI Appendix, Fig. S10).To substantiate the estimated levels of hydration in the DLP in

our simulations, experimental cryo-electron micrographs of theDLP droplets were compared with those of solid ACC. Since ourvitreous ice layers have a thickness of ∼130 nm (37), which issmaller than the measured lateral diameter of a DLP droplet(Fig. 4 A and B), we propose that the observed DLP droplets areoblate structures that fit the thickness of the ice layer. Wetherefore compared these with spherical ACC particles (miner-alized and analyzed in situ according to ref. 38), having a di-ameter approximately equal to the ice layer thickness. Analysisof such images showed that the contrast of an ACC particlerelative to the background solution and the carbon support film(i.e., independent of imaging conditions) was significantly higherthan that of the DLP (≈3.5 times, as demonstrated in Fig. 6).To obtain quantitative information on differences in hydration

level between the DLP and ACC from the cryo-TEM experiments,we compared electron transmission properties of ACC with varyinghydration in TEM simulations. As a primary step, ACC was pro-duced in MD simulations by relaxing random distributions of ions

(300 CaCO3 units) and a varying number of water molecules(CaCO3·n H2O, where n = 0 7; SI Appendix, section 1.12.4).Radial distribution functions confirmed an amorphous arrange-ment of ions and the final configuration was then used in TEMimage simulations. Supercells were created to ensure the sampledepth was set approximately equal to that of the experimentalTEM analysis (i.e., 130 nm).Fig. 7A shows the simulated electron intensities measured at the

detector for ACC, as informed by calculating mean intensities of anumber of line scans from simulated TEM images in the region ofthe bulk phases. The mean intensities show that the contrast isgreatest for ACC with low water content. Experimentally obtainedrelative mean values for ACC intensities were close to those forsimulated CaCO3·1H2O (67% vs. 76 ± 4%). As both the samples insimulation and experiment are approximately equal in depth, thedifference in relative intensities is most likely due to the differencein the defocus parameters adopted (the chosen defocus did notaffect the assignment of DLP vs. ACC in the experiments; SI Ap-pendix, section 3.5.1).Within uncertainties, the electron intensity measured for the

DLP in simulations is in good agreement with ACC containing5–7 H2O/CaCO3 (Fig. 7A), that is, distinctly different from ACCwith CaCO3:1H2O. The experimentally determined TEM elec-tron intensity for the DLP also falls within this range; hence,these data show that it is possible to quantitatively differentiatebetween low hydration amorphous solids and dense liquids usingTEM. We can compare the mass density of the DLP from sim-ulations (ρ = 970–1,500 kg·m–3; Figs. 5E and 7B) to the massdensities of bulk ACC with varying levels of hydration (Fig. 7B).Both the total mass and ionic mass densities of the DLP areconsistent with ACC containing 4–6 H2O/CaCO3. Combined,these results allow us to place bounds on the hydration level inthe DLP as 4–7 H2O/CaCO3, which is consistent with the resultsfrom structural analyses in SI Appendix, section 3.3.3.

Formation of Vaterite. Following the prenucleation stage and for-mation of the DLP, at ∼0.96 tσ max an increase in the amount of

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Fig. 6. (A) Cryo-TEM image showing a line scan (red box) through one of thetwo ACC particles in the direction of the red arrow. The width of the line scan istaken as ∼0.5 times the observed particle diameter. (B) Intensity vs. distance ofthe line scan in A, where the boundaries of the ACC particle are indicated bythe two black dashed lines. The intensity difference with the mean intensity ofthe background solution (dark blue line) is given by the indicated black arrowand value. (C) Cryo-TEM image of Fig. 4B with indicated line scan (light bluebox) through a DLP particle in the direction of the blue arrow. The width of theline scan is taken as ∼0.5 times the observed DLP diameter. (D) Intensity vs.distance of the line scan in C, where the DLP droplet boundaries are indicatedby the two black dashed lines. The intensity difference with the mean intensityof the background solution (dark blue line) is given by the indicated arrow andvalue. (Scale bars: A, 100 nm; B, 500 nm.)

A B

Fig. 7. (A) Electron transmission intensities measured for bulk ACC withvarying levels of hydration; and (B) comparison of mass densities of ACC andDLP in simulations. (A) Mean electron intensities measured at the detector inTEM simulations for bulk ACC with a range of hydration levels, n (i.e.,CaCO3·nH2O) are given by black data points. The data were averaged using anumber of line scans, and errors shown in black are 1 SD of the sampleddistribution. The blue and red lines are the mean intensities measured forbulk water and DLP (with SD in the blue shaded area) using the same inputparameters. The mean intensity of low concentration CaCO3 solution wasthe same as that for pure water within statistical uncertainties. The experi-mental mean intensity for the DLP was ∼135 (i.e., ∼93% of the backgroundsolution; Fig. 4C) and for ACC ∼100 (i.e., 67% relative to the backgroundsolution; Fig. 6B), and we note the difference in the microscope parametersin experiments compared with TEM simulations. (B) Calculated mass densi-ties from simulations of bulk ACC with n water molecules per calcium car-bonate (i.e., CaCO3·nH2O), where the blue data show the ionic mass densityin ACC and the red data provide the total mass density (i.e., ions and water).The shaded blue and red areas provide the ionic and total mass densities inthe core region of the DLP observed in high concentration simulations (Fig.5E and SI Appendix, Fig. S21).

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NaOH required to maintain a constant pH of 9.75 (due to releaseof H+ in solution) marked the nucleation and growth of the firstsolid CaCO3. This increase reflects the withdrawal of carbonate ionsfrom the buffer equilibrium while its binding behavior implies thatgrowth of CaCO3 occurs via a net transfer of ions from solutiononto the growing CaCO3 according to the below (SI Appendix,section 2.5):

z Ca2+free + z  CO2-3 → z  CaCO3.

Simultaneously, at 0.96 tσ max, polarized optical microscopy(POM) showed objects with diameters of 1–3 μm that did notshow birefringence when viewed through crossed polarizers (i.e.,the material showed optically isotropic behavior; SI Appendix,Fig. S7), but these observations did not give any indication aboutthe liquid or solid nature of the objects.From 1.03 tσ max onward, the particles displayed birefringence

during or after drying of the surrounding solution, implying arapid transformation of the disordered precursor to one of thecrystalline forms of CaCO3 (Fig. 8B). SEM demonstrated that thesebirefringent particles had a corrugated spherical morphology char-acteristic of vaterite (39) (Fig. 8C and SI Appendix, Fig. S8). Thisidentification was confirmed by in situ attenuated total reflection–Fourier transform infrared spectroscopy (ATR-FTIR) (Fig. 8D),which showed the growth over time of vibrational peaks charac-teristic of vaterite at 875 cm−1, 1,072 cm−1, and 1,087 cm−1 (SIAppendix, Fig. S8). In contrast to the report of Gebauer et al. (17),no experimental evidence was obtained that indicated the formationof solid ACC. ATR-FTIR did not show characteristic peaks asso-ciated with ACC, nor did the SEM results demonstrate a typicalsolid, spherical morphology. Indeed, the ion activity product derived

from the titration curve exhibited a good resemblance to the solu-bility product of vaterite (Fig. 7A, dotted line). We note that we donot observe a shift in the carbonate ν2 band from 863 cm−1 (ACC)toward 873 cm−1 (vaterite), which would indicate that vaterite growsat the expense of ACC (40). This agrees with our data in Fig. 8A thatwe never surpass the solubility of ACC in our titration experiments.

DiscussionWe present an extensive study of the nucleation of CaCO3 from asupersaturated solution that forms via liquid–liquid phase separa-tion. Experiments and simulations agree that no clusters, or poly-meric assemblies thereof, larger than 0.9 nm in size are stablebefore nucleation. Furthermore, they demonstrate that the boundcalcium in solution is predominantly present in the form of ionpairs alongside a population of clusters stochastically formed fromthe association of ions/ion pairs, of which the abundance decaysrapidly with increasing cluster size in accordance with CNT.Our results are incongruent with the findings of Gebauer et al.

(17). However, it is important to note that, after initially pro-posing a narrow size distribution for PNCs based on AUC ex-periments, it was later realized that the sharp peaks in the AUCtraces reflected the average value for all species in equilibriumon the timescale of the experiment (>8 h), rather than a distri-bution of cluster sizes (21). Particle sizes were determinedaccording to the Stokes–Einstein equation or by using the sedi-mentation coefficients and the densities of ACC and ikaite, afterfitting with a discrete species model. However, considering thatStokes–Einstein breaks down for systems where the solute sizeapproaches that of the solvent (41), and that DOLLOPs arelikely to have a much lower density than any phase of reference,we remain skeptical about the inference of particle size from theAUC data. Moreover, to date, analysis of AUC data has notaccounted for the impact on cluster size distribution that mustarise in the concentration gradient caused by the centrifugationprocess. Hence, the interpretation of the small associates foundhere as thermodynamically stable prenucleation clusters hinges onthe proposed binding model for cluster formation in which theequilibrium binding energy for every ion pair is equal (17) andnegative by about 20 kJ/mol (18). Based on ratios of species con-centrations in our simulations, we find that the binding constant, β,for ion pairing is entirely consistent with earlier measurements (i.e.,

A

B D

C

Fig. 8. (A) Free ion product development vs. normalized time (black solid line)during a typical titration experiment. The black dashed line indicates the solu-bility product Ksp, compared with the reported solubility product of ACC (Ksp ACC)(33) and vaterite (Ksp vat) (56). (B) POM indicating micrometer-sized entities at1.03 tσ max (yellow arrows), which show birefringence when the surroundingsolution (dark gray) retracts (Inset). (C) SEM at 1.03 tσ max showing a typicalspherical–framboidal vaterite morphology. (D) In situ ATR-FTIR spectra fromtσ max to 1.40 tσ max showing typical vibrations of vaterite at 875 cm−1 (CO3

2− ν2out of plane bend), 1,087/1,072 cm−1 (CO3

2− ν1 symmetric stretch), and1,467 cm−1 (CO3

2−, ν3 asymmetric bond stretch) (57) gradually increasing in time.The Top Inset shows an enlargement of the ν1 peak at 1.40 tσ max, while thespectrum on the far Right displays the magnified ν2 spectral region.

Fig. 9. Schematic demonstrating the development of CaCO3 structureduring the titration experiment in dilute calcium carbonate solutions. In theprenucleation stage, predominantly CaCO3

0 and CaHCO3+ ion pairs exist

alongside free ions in solution. After a critical concentration at ∼0.90 tσ max, aliquid–liquid phase separation leads to the formation of a dense liquid phase(DLP) and a lean ionic solution of free ions and ion pairs. At the nucleationpoint (∼0.96 tσ max), the DLP reacts with free Ca2+ and free CO3

2− undermacroscopic release of H+ and after ∼tσ max converts to vaterite, until after∼1.30 tσ max equilibrium has been reached.

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∼104) (18, 42). The formation of (CaCO3)2 in a single step fromtwo ion pairs, on the other hand, suggests that β is reduced byorders of magnitude. While small system sizes limit statistical ac-curacy and activities are not included, the large difference in β valuesraises doubts about the assumptions which underlie the model.Wolf et al. (43) and Pouget et al. (20) both suggested the

presence of PNCs in an outgassing supersaturated Ca(HCO3)2solution—the “Kitano method” (44)—using mass spectrometryand cryo-TEM in combination with AUC, respectively. However,the injection in the vacuum system of a mass spectrometer willdrive the outgassing of the solution and the resulting increase insupersaturation will promote the formation of clusters with largerdiameters, similar to what has been observed in simulations at highconcentration (18, 45, 46). Moreover, the defocus conditions thatPouget et al. applied for HRTEM imaging on the same electronmicroscope, are of the order of microns. The corresponding con-trast transfer function (CTF) in this case (Materials and Methodsand SI Appendix, section 1.9) indicates a direct interpretable res-olution substantially larger than 1 nm, and we thus conclude thatthese data cannot prove the existence of 0.6-nm clusters, as wasindicated in the original publication. Since, as indicated previously,it is now realized that also the AUC data do not unambiguouslyprove the presence of clusters with a defined particle size, wetherefore conclude that neither of these reports provide solid evi-dence supporting the formation of prenucleation clusters.Our results also run counter to the conclusions from a study

where CaCO3 was nucleated in the presence of a silica precursor,in which nanometer-sized objects observed by cryo-TEM andDLS in solution were attributed to PNCs (26). These results canbe explained by the presence of silica primary particles, asdemonstrated recently (47). In fact, it is not possible to dis-criminate between primary particles of silica and the proposedPNCs based on the data presented in that study (26).At higher supersaturation, we provide evidence for the formation

of objects consistent with a dense liquid before the growth of solidmineral phases, which has recently been proposed to feature ina multistep CaCO3 mineralization pathway (6, 14). AmorphousCaCO3 is commonly considered to have the formula CaCO3·1 H2O,and to our knowledge the highest water content reported for ACC is∼1.4 H2O/CaCO3 (48), which is still clearly distinct from the 4–7H2O/CaCO3 we suggest for the DLP. Recently, Nielsen et al. (49)investigated CaCO3 nucleation with the use of in situ liquid phaseTEM and observed that the dissolution behavior of amorphousparticles under the electron beam showed extreme qualitative dif-ferences and that dissolution rates differed by more than an order ofmagnitude. They tentatively related these differences to either solidor liquid-like behavior of the particles (where liquid-like particlesdissolve faster). It is important to note, however, that these observeddifferences in dissolution rate will also depend on other factors suchas the difference in particle size, thickness of the imaged liquid layer,and applied electron dose rate. In any case, the apparent differencein electron-scattering intensities between these particles showingdifferent dissolution rates is significantly lower compared with thedifference we observe between the ACC and the DLP, and suggestsa significantly lower degree of hydration for any of the amorphousphases reported by Nielsen compared with the DLP observed here.In contrast to the scenarios proposed previously for other sys-

tems (11, 14), we conclude that liquid–liquid separation in thestudied system happens via an activated process. Our total calciumand carbonate concentrations of ∼1 mM at tσ max are well belowthe spinodal limit reported by Zou et al. (15), although we notethat their solutions were not prepared identically. Moreover, it isunlikely that the slow addition of Ca2+ ions allows the system tocross the spinodal line before the appearance of the DLP. Thus,liquid–liquid separation in our experiment is more likely to involvenucleation and growth of the DLP within the binodal regime. OurDLS data in Fig. 2D fits the growth of phase-separated domainsboth through coalescence by Brownian collisions and through

Ostwald ripening (50). The light-scattering data do not allow us todistinguish between either of the two mechanisms for liquid–liquidphase separation; however, we note that we do not observecoarsening behavior displaying power-law regimes of the form tα

with α ≠ 1/3 as is often associated with late postseparation pro-cesses in spinodal decomposition in light-scattering data (51–53)(for details, see SI Appendix, section 2.7.2). Moreover, our simu-lations predict a noticeable free-energy barrier to the nucleation ofdense liquid clusters at relatively low supersaturation (SI Appendix,section 3.3.1). We therefore propose that the formation of the∼200-nm liquid droplets occurs through density fluctuations thatsubsequently ripen/coalesce to form larger (sub)micrometer-sizedobjects, from which eventually vaterite nucleates.In summary, our work provides a comprehensive reevaluation

of the nucleation mechanism for CaCO3 in controlled dilutesolutions (as presented in Fig. 9). Although the nucleation pro-cess depends critically on many parameters, such as temperature,pH, and composition, we conclude that nucleation can be de-scribed by the concepts of CNT. While the mechanism of growthinvolves intermediate phases, the fundamental concepts ofclassical nucleation still hold, as for the recently reported casesof calcium phosphate (24) and iron oxide (54) nucleation.

Materials and MethodsTitration Experiments. In the titration experiment, a 10mMCaCl2 solution wasslowly added into a 10 mM carbonate buffer at 20 ± 1 °C and pH 9.75 (SIAppendix, section 1.1–1.4). This pH was selected since it reflects a highbinding tendency of calcium with carbonate species due to the high fractionof carbonate ions in the carbonate buffer (17). The free Ca2+ concentration[c(Ca2+free)] was monitored using a Ca2+-ISE, and the amount of NaOH addedto maintain a constant pH was registered. In addition, we measured the freeNa+ concentration [c(Na+free)] using a Na+-ISE (SI Appendix, section 1.3).

To analyze solution species, samples were extracted from the titrationexperiment at regular time intervals. In the prenucleation stage, DLSwas usedto detect nanometer-sized objects in solution (SI Appendix, section 1.5). Inaddition, cryo-TEM was used to investigate the presence of clusters, as wasdone in calcium phosphate experiments (24). To this end, the samples werevitrified by plunge freezing (SI Appendix, section 1.9). For imaging, we used aTitan Krios microscope, which offers high resolution, detector sensitivity, anddetector size (4,000 × 4,000 pixels CCD). Imaging contrast was optimized byapplying a nominal defocus of −0.5 μm. This defocus value resulted in a CTFthat allowed the direct interpretation of dark contrast objects ≥0.9 nm (25).

Formed CaCO3 after the prenucleation stage was observed in (polarized)light microscopy, SEM, and cryo-TEM (FEI Tecnai G2 operated at 200 kV andequipped with a LaB6 filament). Analysis was performed using in situ ATR-FTIR, DLS, and electron diffraction.

Simulations.MD at 298 K and 1 atm was used to investigate the speciation ofcalcium (bi)carbonate in solution (see SI Appendix, section 1.10, for full de-tails). Configurations were prepared to achieve an initial pH of 9.9 by settingthe CO3

2−/HCO3− ratio determined by the Henderson–Hasselbalch equation

and using a pKa of 10.328 for HCO3− ⇄ CO3

2− + H+. Subsequently, Ca2+ wasadded to neutralize the total charge in the system, generating total Ca2+

concentrations of 20–30 mM (SI Appendix, Table S1, provides the initialsystem compositions). Two different initial arrangements of the ions wereused: in the first type of simulation (cluster system), ions were inserted into abox of water as a single, low-energy cluster with an average ionic co-ordination consistent with DOLLOP, as taken from extensive random struc-ture searches (45), and allowed to relax. In the second type (random system),ions were randomly introduced into a volume of water and equilibrated.The 20-ns trajectories were generated with averages calculated in 2-nswindows at equilibrium. The total number of ions and water molecules wasthe same in both the cluster and random systems.

Random systems were also prepared for simulations at high initial free Ca2+

concentrations [c(Ca2+free)] of 0.57, 1.1, and 1.7 M (SI Appendix, Table S2). Thesesimulations contained only carbonate anions; otherwise, they were preparedfollowing the methods used for lower concentration simulations. Simulationswere performed at 298 K and 1 atm for 60 ns, with the final 5-ns window usedto analyze equilibrium states. TEM simulations were performed using a multi-slice algorithm for the system at 1.7 M initially and bulk amorphous phases withvarying degrees of hydration. For full details, see SI Appendix, section 1.12.

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The force field of Demichelis et al. (18) was used to model the interactionsbetween atoms. This is an adaptation of earlier force fields and has been shownto accurately reproduce the properties of bulk phases and, crucially, the freeenergies of solvation for ions in water (18, 42, 55). Clusters were definedaccording to a geometric criterion where the distance between Ca and C (ofcarbonate and bicarbonate) was within 4.2 Å: slightly larger than the minimumin Ca–C radial distribution functions for low-density amorphous CaCO3 clusters.

ACKNOWLEDGMENTS. Experimental work was performed at the EindhovenUniversity of Technology. The computational part of this study was performed atthe Centre for Scientific Computing and Department of Chemistry (University ofWarwick). Computational resources were provided by the Scientific Computing

Research Technology Platform (Warwick University), the MidPlus Regionale-Infrastructure Centre (Grant EP/K000128/1), and ARCHER, the UK nationalsupercomputing service. The work of P.J.M.S. and N.A.J.M.S. is supported by aVICI grant of the Netherlands Organization for Scientific Research. The work ofA.R.F. and P.M.R. was supported under Engineering and Physical SciencesResearch Council Grant EP/I001514/1, and A.R.F. acknowledges support fromthe University of Sheffield under a Doctoral Prize Fellowship. The work of J.J.D.Y.was supported by the US Department of Energy, Office of Basic Energy Sciences,Division of Materials Science and Engineering at the Pacific Northwest NationalLaboratory (PNNL). PNNL is operated by Battelle for the US Department ofEnergy under Contract DE-AC05-76RL01830. This work is dedicated to thememory of P.M.R., who sadly passed away on March 23, 2017.

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