Effect of temperature on the transformation of amorphous calcium magnesium carbonate with near-dolomite stoichiometry into high Mg-calcite†

High Mg-calcite (HMC) is thermodynamically unstable under ambient conditions, yet it has been found in many biogenic and abiotic depositional settings with Mg contents up to 50 mol%. The elevated Mg content of HMC was frequently attributed to an amorphous calcium magnesium carbonate (ACMC) precursor, but the effects of transformation conditions on the Mg content of HMC are still debated and far from being quantified. Therefore, the transformation of ACMC with near-dolomite stoichiometry (∼48 mol% Mg) into HMC has been studied in a MgCl2–NaHCO3 buffered solution at moderate pH (7.6) and temperatures from 10 to 80 °C. The obtained chemical data show that the apparent solubility of ACMC (KACMC) is lower at higher temperature and the relative increase of KACMC as a function of the Mg content is similar between 10 and 80 °C which can be assessed by the equation: log(KACMC) = 0.01629 * [Mg]ACMC − 0.0001096 T + 0.0545 T −12.919, where T is reported in Kelvin and [Mg]ACMC refers to the amount of Mg in ACMC in mol%. The Mg content of the final HMC increases from 5 to 40 mol% with increasing temperature, thus is significantly lower compared to the Mg content of the ACMC precursor. Our findings argue for a dissolution and re-precipitation process during ACMC transformation, where at higher temperatures the Mg incorporation into HMC is enhanced due to (i) the reduced solvation energy barrier of aqueous Mg and (ii) the high prevailing molar Mg/Ca ratio of the solution after its reaction with the ACMC. Notably, the Mg/Ca ratio of the latter solution is controlled by the temperature-dependent solubility of ACMC. Finally, the findings indicate that the nanocrystalline HMCs formed via transformation of ACMC are physically defective from rapid crystal growth and have higher solubilities compared to well-crystallized Mg-bearing calcites.


Introduction
Calcite is the most abundant calcium carbonate (CaCO 3 ) mineral in marine and terrestrial environments. 1,2 In the crystal structure of calcite, Ca 2+ can be substituted by other divalent cations present in natural waters. Predominant in these replacement reactions is the substitution of Ca 2+ by Mg 2+ . [3][4][5] In the literature, calcite containing >4 mol% Mg is usually referred to as high Mg-calcite (HMC; Ca 1−x Mg x CO 3 , x > 0.04), whereas calcite with lower Mg content is referred to as low Mg-calcite (LMC; Ca 1−x Mg x CO 3 , x < 0.04). 5,6 Abiogenic HMCs with <20 mol% Mg form marine cements consolidating sedimentary materials, e.g. in shallow tropical carbonate factories, 3 in zones affected by anaerobic oxidation of methane 7 and in coastal sabkha settings. 8 Biogenic HMCs with up to 25 mol% Mg are a common building material of e.g. skeletons of coralline algae, foraminifers and echinoderms. 3,[9][10][11][12] The Mg content can be even higher (40-45 mol%) in structural elements of sea urchin teeth. 13,14 A few examples of HMC with up to nearly 50 mol% Mg have been reported in natural depositional settings which are usually rich in microbial activity such as in algal sediments from a hypersaline lake (salt pond) of San Salvador Island, Bahamas, 15 in microbial mats of the Lagoa Vermelha, Brazil, 16 in microbial films of the Seroe Domi Formation of Curacao, The Netherlands 17 and in sediments of the shallow, alkaline Lake Neusiedl, Austria. 18 Note here that HMC phases with near-dolomite stoichiometry, but lacking cation ordering, are also referred to as very high Mg-calcite (VHMC) or protodolomite. 5 Despite several decades of research, the formation of HMC and VHMC in natural systems is a poorly understood process because (i) the (V)HMC structure is destabilized by the uptake of Mg 2+ (ref. 19) and (ii) the inorganic precipitation of HMC with >20 mol% Mg in the laboratory under ambient conditions remains an enigma as high aqueous Mg 2+ /Ca 2+ ratios inhibit the nucleation and growth of HMC from solution and favour the precipitation of aragonite (CaCO 3 ). [20][21][22][23] The inhibiting effect of aqueous Mg 2+ on the formation of calcite originates from the strong affinity of the Mg 2+ ion for the aqueous solution which is reflected by its high hydration Gibbs free energy 24 and low rate of exchange of water molecules in its hydration sphere. 25,26 The dehydration of the hydrophilic Mg 2+ ion at the lattice growth site is therefore one of the most rate-limiting steps during the formation of (V)HMC.
Experimental studies on mineral formation, however, have shown that besides direct precipitation from solution (classical formation pathway), carbonate minerals can be formed via the transformation of amorphous precursor phases. 27,28 Evidence for this alternative formation pathway also comes from calcifying organisms, where calcite formation often proceeds through an amorphous calcium carbonate (ACC) precursor phase. 29,30 In this context, it has been suggested that Mg-containing ACC is a necessary prerequisite for the formation of HMC 10 and VHMC. 31 In most studies, the formation of amorphous calcium magnesium carbonate (ACMC) was induced by mixing a Na 2 -CO 3 solution (pH > 11) with (Ca, Mg)Cl 2 solutions (pH = 6-7) at room temperature. 10,[31][32][33][34][35] The chemical composition of the initial solution for ACMC synthesis (e.g. Mg/Ca ratio, pH) has been suggested to control the amount of Mg incorporated into the ACMC and the final HMC. [36][37][38] Specifically, the formation of VHMC via ACMC has been achieved from synthesis in aqueous solutions with high Mg/Ca ratios at high pH (∼ 10), high carbonate-to-calcium ratios (>2 : 1) or by thermal treatment (>40°C). 31,36,[38][39][40] However, in most studies, the chemical compositions of the reactive solutions and solids during the formation of ACMC and its transformation into Mg-calcite were not concerned or even not documented. In particular, the effect of temperature on the Mg content of HMC formed via the amorphous pathway in aqueous solution has not been investigated in earlier studies. In order to better understand the fate of Mg during the transformation of ACMC into HMC, we investigated the transformation behaviour of synthetic ACMC with neardolomite stoichiometry (48 mol% Mg) in solution at moderate pH (7.6) and reaction temperatures ranging from 10 to 80 ± 1°C. The aim of the present study is to provide a more detailed understanding of the interplay between the chemical composition of (i) ACMC, (ii) the corresponding reactive solution and (iii) (V)HMC formed via ACMC in the apparent aqueous environment. Moreover, the obtained chemical data were used to assess the solubility of ACMC and HMC.

Synthesis of amorphous calcium magnesium carbonate
The synthesis of ACMC material with 47.9 ± 1.5 mol% Mg was carried out by a previously developed protocol. 33,41 Briefly, a 0.25 M (Ca, Mg)Cl 2 solution (Mg/Ca ratio = 2.1) and a 0.25 M Na 2 CO 3 solution were prepared using CaCl 2 ·2H 2 O, MgCl 2 ·6H 2 O, and Na 2 CO 3 chemicals (p.a. Roth) and ultrapure water (Millipore Integral 3; 18.2 MΩ cm −1 ). The two stock solutions were cooled in a fridge for 4 hours (T = 10 ± 2°C). The precipitation of ACMC was induced by pouring 100 mL of the (Ca, Mg)Cl 2 solution into a beaker containing 100 mL of the Na 2 CO 3 solution. The ACMC was separated from solution by a 0.2 μm cellulose filter using a suction filtration unit and was subsequently freeze-dried for 12 hours (Virtis Benchtop 3 L). The synthesis protocol was repeated several times until about 20 g of ACMC were produced. The obtained ACMC material was analysed by X-ray diffraction (Fig. S1A †) and was stored in a desiccator with silica gel.

Experimental setup for ACMC transformation into HMC
Transformation of ACMC in solution was performed at 10, 20, 40, 60 and 80°C (see Table 1). Initially, 50 mM NaHCO 3 solutions were prepared in 150 mL gas-tight glass bottles which were placed either in a cooling chamber (10 ± 2°C), a temperature-controlled room (20 ± 2°C) or in ovens (40 ± 2°C , 60 ± 2°C and 80 ± 2°C) over a period of 24 to 60 h. 52 mL of the pre-cooled/heated NaHCO 3 solution was added into a 150 mL borosilicate glass reactor containing 6.099 g MgCl 2 ·6H 2 O to obtain a Mg concentration of 30 mM. 2 mL of the NaHCO 3 -MgCl 2 solution was collected with a pipette to measure its initial Mg and alkalinity concentration ( Table 2). The MgCl 2 -NaHCO 3 solutions exhibit an initial pH value of 8.02 ± 0.15 ( Table 2). The reactor was placed in an Easy Max System (Max™ 102; Mettler Toledo) in order to control the stirring of the solution at 200 rpm and its temperature at 10.0, 20.0, 40.0, 60.0 or 80.0 ± 0.1°C (Fig. 1). Subsequently, 1.5 g of the synthesized ACMC was introduced into the buffered NaHCO 3 -MgCl 2 solution (Fig. 1). After a short homogenization period between the ACMC material and the solution, a homogeneous sub-sample of the suspension (2 mL) was collected with a pipette (t = 0.3 min). Subsequently, the pH of the experimental solution was adjusted to 7.58 ± 0.04 (within ≤ 3 min) by computer-controlled titration of a 2 M HCl solution (Schott; TitroLine alpha plus) (Fig. S2 †). Note here that the pH of the solution was adjusted to 7.6 to prevent the precipitation of hydrous Ca-or Mg-carbonate phases, such as monohydrocalcite and nesquehonite. 36,42,43 Further homogeneous sub-samples of the experimental suspension (2 mL) were collected with a pipette at 5 min, 11 min, 21 min, 32 min and 61 min. After 61 min of reaction time, the experimental solutions were transferred into 100 mL gastight bottles which were again placed in the fridge (10 ± 2°C), temperature-controlled room (20 ± 2°C) and ovens (40 ± 2°C, 60 ± 2°C and 80 ± 2°C) over a period of 2 months. Additional homogeneous sub-samples were collected after 1 day, 1 week and 2 months of reaction time. The solids were separated from the solutions by a 0.2 μm cellulose acetate filter using a suction filtration unit and washed with ethanol. Subsequently, the solids were dried overnight in an oven at 40°C and stored in a desiccator with silica gel.

Analytical procedures
Thermogravimetric analyses (TGA) of the freeze-dried ACMC was realized using a PerkinElmer STA8000. The ACMC was heated from 25°C to 800°C at 10°C min −1 in the presence of 99.999% N 2 atmosphere. The mineralogy of the precipitates collected during the ACMC transformation experiments was determined by a PANalytical X'Pert PRO diffractometer using Co-Kα radiation (40 mA, 40 kV) at a 2θ range from 4 to 85°with a step size of 0.008°2θ and 40 s count time per step. The mineral phases of the reaction products were quantified using Rietveld refinement (software HighScore Plus, PANalytical) using the crystal structure data given in Table S1. † The estimated analytical uncertainty of the quantification lies within 1 wt%. The refinement values consisted of the specimen displacement, a 7-term polynomial background function and scale factors and lattice parameters for all phases. For major phases, the peak shape was refined using a pseudo-Voigt profile function and peak asymmetry. The preferred orientation of calcite was refined for the (104) plane with the March-Dollase function. If two separate calcite phases were present, all their refined values, except of the scale factor and lattice parameters, were constrained with each other to ensure a stable refinement. The d-value and the left full-width at half-maximum (left FWHM, for asymmetric peaks) of the (104) reflection (hereafter referred to as d 104 and FWHM d104 , respectively) was obtained from the refinement results. The d 104 value of the calcite phases was used to calculate their Mg content ([Mg] XRD ) according to Goldsmith et al. 44 and this content was then used to adapt the occupancy of Ca and Mg in the structure data used for the refinement. Note that the accuracy of the determination of the d 104 value and the FWHM d104 is limited by the step size of the XRD measurement (0.008°2θ). Selected precipitates were gold-coated and imaged using a scanning electron microscope (SEM, ZEISS DSM 982 Gemini). The total alkalinity of the experimental solutions was measured by a Schott TitroLine alpha plus titrator using a 10 mM HCl solution with a precision of ±2%. The aqueous Ca and Mg concentrations of experimental solutions and solids (digested in 6% HNO 3 ) were determined using inductively coupled plasma optical emission spectrometry (ICP-OES, Perkin Elmer Optima 8300 DV) with an analytical precision of ±3% for Ca and Mg analyses. The Mg content of the bulk solid ([Mg] solid in mol%, Table 2) was calculated according to the equation: where [Mg] s and [Ca] s are the measured concentrations of Ca and Mg of the solid (mol kg −1 ) determined by chemical digestion and ICP-OES analysis.

Geochemical modeling
The aqueous speciation and ion activities of the reactive solutions were calculated using the PHREEQC computer code with the minteq.v4 database. The apparent solubility product (K) for amorphous calcium magnesium carbonate (ACMC, Ca 1−x Mg x CO 3 ·nH 2 O) and high Mg-calcite (HMC, Ca 1−x Mg x -CO 3 ) was calculated using the equation where aCa 2+ , aMg 2+ and aCO 3 Table 2). In the latter case the Mg and Ca content of the solid was measured by acid digestion and subsequent ICP-OES analysis, thus representing bulk composition ion-balanced by cation ions. Although water molecules are present in ACMC, the activity  Subsequently, XRD peaks appear due to the transformation of ACMC into high Mg-calcite (HMC) and partly into aragonite (ARG) and hydromagnesite (HMG). XRD analyses reveal that for all experiments at ≤60°C, the reaction products consist mainly of HMC (≥98 wt%) and traces of ARG (<2 wt%) ( Table 1). In experiment T_10°C two peaks were detected in the XRD pattern corresponding to high Mg-calcites with distinct Mg contents, hereafter mentioned as HMC_I and HMC_II (Table 1 and Fig. 2A). The reflection peaks of HMC_I appear in the XRD pattern at ≥21 min (during ACMC transformation), while those of HMC_II can be detected at ≥61 min of reaction time ( Fig. 2A and S3A †). Note that in experiment T_40°C, minor amounts of HMG (9 wt%) were detected beside HMC and ARG after 2 weeks of reaction time (Table 1, Fig. S3C †). At 80°C, XRD patterns show the transformation of ACMC into HMC, HMG and ARG which account for 78, 15 and 7 wt%, respectively, after 1 day of reaction time ( Fig. S3E; † Table 1). After 2 months of reaction time, the presence of HMG was no longer detected (Fig. S3E †). Instead, a reflection peak at 2.77 Å indicates the presence of new phase (labeled as * in Fig. S3E †), which could correspond to magnesite (MgCO 3 ). 2 Indeed, earlier studies reported the formation of magnesite by the transformation of pre-existing hydrated Mg-carbonate phases such as hydrogmagnesite and dypingite at elevated temperatures (e.g. Montes-Hernandez et al. 46 ). Fig. 2F shows that the XRD reflection peaks of the final HMCs are broader in comparison to the reference calcite (Merck). This observation is confirmed by comparing the FWHM d104 values, which shows that the FWHM d104 is higher for the HMCs (0.351-0.644; Table 1) than for the reference calcite (0.094). The obtained FWHM d104 values of the HMCs however are similar to that determined for the reference Coorong dolomite (FWHM d104 = 0.649; Fig. S4A †). Broad XRD reflection peaks are referred to non-ideal crystal structure phenomena which can be caused by small (nanocrystalline) particle sizes 39,40,47 and inhomogeneities in the Ca and Mg composition 48 of the crystalline solid. Indeed, the broad XRD peaks obtained for the HMCs and the reference Coorong dolomite (Fig. 2F) can result from their small crystal sizes: SEM images reveal aggregates composed of nanocrystals with <100 and <300 nm in size for the HMCs (Fig. 3D) and the Coorong dolomite (Fig. S4B †), respectively.
To get insights into the evolution of the Mg content of the forming HMC via ACMC, the characteristic d 104 -peak value of HMC was used to calculate its Mg content ([Mg] XRD ) according to Goldsmith et al. 44 (Table 1). The Mg content of the HMCs obtained after 1 day of reaction time is higher at elevated temperature as indicated by lower d 104 -values (corresponds to higher 2θ values in Fig. 2F). Note that a maximum concentration of 40 ± 1 mol% Mg in HMC was obtained in experiments T_60°C and T_80°C (Table 1). In experiment T_10°C, the HMC_I that was detected in the samples collected at ≥21 min exhibits 6 ± 1 mol% Mg, which is ∼9 mol% lower than the Mg content of HMC_II (15 ± 1 mol%) that was detected in the samples obtained at ≥61 min of reaction time ( Fig. 2A, Table 1). Rietveld refinement of the reaction products after 1 day shows that the amount of HMC_I (7 mol% Mg) and HMC_II (15 mol% Mg) is 56 and 42 wt%, respectively (Table 1). In experiments performed between 20°C and 60°C, the initial HMC phase that was detected beside ACMC (at 11 min in Fig. 2B-E; Table 1) shows a significant lower Mg content than the HMC that was obtained during ACMC transformation (Table 1). This indicates that the Mg uptake in HMC is not uniform  (Table 1).
Scanning electron microscope images show that in experiments performed at ≤20°C, the precipitates obtained at 5 min of reaction time consist of amorphous spherical particles (Fig. 3A), similar to the synthesized ACMC standard material (Fig. S1B †). In experiments performed ≥40°C, traces of HMC or HMG nanocrystals were observed beside the ACMC particles at 5 min of reaction time (Fig. 3A), although XRD results show that the solids obtained at 5 min are solely amorphous (Fig. 2C-E). The HMC (T_40°C and T_60°C) consists of spindle-shaped aggregates composed of nanocrystals, whereas the HMG crystals (T_80°C) show a plate-like morphology. These morphologies are similar to those observed for HMC and HMG obtained at a later stage in the experimental runs ( Fig. 3B-D). At a reaction time of 21 min (Fig. 3B), large amounts of spherical ACMC particles were observed in the precipitates obtained in experiments performed at ≤20°C, whereas at ≥40°C ACMC was rarely observed in the collected solids. Note here that no ACMC particles were observed in the collected solids at ≥21 min in experiment T_80°C (Fig. 3B), at ≥32 min in experiments T_40°C and T_60°C (not shown) and at ≥61 min in experiments T_10°C and T_20°C (Fig. 3C).
SEM images of the final HMC show aggregates composed of spindle-shaped assemblages of nanocrystals at lower temperatures (≤20°C), whereas at higher temperatures (≥40°C) the HMC-nanocrystals coalesced into spheroidal aggregates ( Fig. 3C and D). These spindle-shaped and spherical morphologies are consistent with those of high Mgcalcites formed via amorphous precursors from previous studies. 39,[48][49][50][51] In experiment T_10°C, large amounts of star-shaped aggregates composed of linearly arranged nanoparticles were detected beside the spindle-shaped HMC aggregates (Fig. 3D). These star-shaped aggregates most likely correspond to HMC_II that was detected beside HMC_I in the XRD-pattern at ≥61 min in experiment T_10°C ( Fig. 2A). Trace amounts of those aggregates could also be observed in the final solids of experiments T_20°C and T_40°C (Fig. 3D). Note here that the aragonite detected in experiments T_10°C, T_20°C and T_40°C (2-7 wt%, Table 1) could not be found in SEM images.

Chemical evolution of the reactive solutions and solids
The addition of ACMC into the MgCl 2 -NaHCO 3 solutions induced an increase of pH as well as of Ca, Mg and alkalinity concentrations (at 0.3 min in Fig. 4A-C, Table 2) which is attributed to the dissolution of ACMC. At lower temperatures, higher amounts of ACMC likely dissolved as it is indicated by higher Ca, Mg and alkalinity concentrations at 0.3 min of  Table 2). Moreover, the obtained data from experiments performed at lower temperatures show a preferential release of Mg ions into the solution, resulting in ACMCs with slightly lower Mg contents (e.g. 46 mol% Mg in T_10°C) compared to original composition of the synthetic ACMC material introduced in the reactors (48 mol% Mg) (Fig. 4D).
After a short initial homogenization period between the ACMC material and the solution, the pH of the experimental solutions was adjusted to 7.58 ± 0.04 by automatic titration of HCl solution (Fig. S2 †). The adjustment of the pH resulted in the further dissolution of ACMC, which causes an increase in alkalinity, Ca and Mg concentrations of the experimental solutions between 0.3 and 5 min (Fig. 4A-C). After about 5 min, the Ca and alkalinity concentrations of the experimental solutions decrease (Fig. 4A and C) due to the transformation of ACMC into crystalline Ca-Mg carbonate phases (Fig. 2). With the exception of experiment T_80°C, the aqueous Mg concentrations of the solutions increase in the same time frame (Fig. 4B). The net release of Mg into the solution with an uptake of Ca into the solid during the ACMC transformation step results in HMCs with lower Mg contents compared to that of the initial ACMC precursor in experiments performed at ≤60°C (Fig. 4D). In contrast, in experiment T_80°C, the Mg content of the bulk solid increases slightly during the ACMC transformation step (Fig. 4D) Fig. S3 †). Note that in experiment T_40°C, the Mg content of the bulk solid increased between 1 week and 2 months of reaction time, owing to the additional formation of HMG at this stage of the experiment (Fig. 4D).
At higher temperatures, the transformation of ACMC into HMC occurs faster as revealed by XRD and SEM observations ( Fig. 2 and 3). This is further supported by the temporal evolution of pH and HCl solution addition derived from titration data (Fig. S2 †). In experiments performed at ≤60°C, , showing the transformation of amorphous calcium magnesium carbonate (ACMC) into high Mg-calcite (HMC) at ≤60°C and into HMC and hydromagnesite (HMG) at 80°C (see Table 1).
our data reveal that additional amounts of HCl solution were automatically added into the experimental solution to keep the pH constant at 7.58 ± 0.04 during the transformation of ACMC into HMC (Fig. S2A-D †). The rise in pH and consequent titration of HCl may be explained by a fast dissolution of ACMC and slow precipitation of HMC during the ACMC transformation step. At higher temperatures, the HCl solution was added into the experimental solution in shorter periods of time (e.g. 17 min in T_60°C) than at lower temperatures (e.g. 34 min in T_20°C), indicating that the transformation of ACMC into HMC occurs faster at elevated temperatures. Note that in experiment T_80°C, where ACMC transformed into HMC, HMG and ARG (Fig. 2E, Table 1), no additional HCl was added into the solution (Fig. S2E †). In the latter case, the pH decreased slightly from 7.59 to 7.41 during the ACMC transformation step.

Effect of temperature on the Mg content of HMC formed via ACMC with near-dolomite stoichiometry
Earlier studies showed a strong correlation between the physicochemical parameters of the initial solution used for ACMC synthesis and the amount of Mg incorporated into ACMC and the final HMC. 31,37,49,51 In this context, it has been suggested that tuning the amount of Mg in ACMC controls the amount of Mg incorporated into HMC. In contrast, the results of this study show that the Mg content of the HMC is by far not pre-determined by the Mg content of the initial ACMC (48 mol% Mg) that was introduced into the solution (Fig. 5A). In experiments performed at temperatures ≤40°C, the Mg content of the final HMC is significantly lower (e.g. 18 mol% Mg in experiment T_20°C) than of the initial ACMC, whereas at higher temperatures (≥60°C), the final HMCs reach Mg contents comparable to those of VHMC (40 mol% ; Fig. 5A). These findings clearly document that the Mg content of the forming calcite is strongly regulated by the reaction temperature prevailing during ACMC transformation. It is generally acknowledged that the transformation mechanism of ACMC into (V)HMC involves (i) dissolution of ACMC and (ii) nucleation and crystal growth of (V)HMC. 31,36,40,51 The relationship in Fig. 5A suggests that the Mg content of calcite forming at the ACMCsolution interface is significantly controlled by the temperature-dependent dehydration kinetic of aqueous Mg 2+ . The incorporation of Mg into anhydrous carbonates is generally postulated to be kinetically limited under low-  Table 1) at 10, 20, 40, 60 and 80°C. Stage I: ACMC is the sole solid phase (open diamonds); stage II: ACMC transforms to the crystalline phases (shaded diamonds); stage III: solid phase is crystalline (solid diamonds). Note that the pH of the solution was adjusted to 7.58 ± 0.04 within ≤3 min by computer-controlled titration of a 2 M HCl solution (Fig. S2 †). temperature conditions, due to the strong hydration of Mg 2+ compared to Ca 2+ . 20,52 In contrast, higher temperatures reduce the Mg-solvation energy barrier and favour anhydrous Ca-Mg-carbonate formation. 53 Thus, the amount of Mg incorporated into calcite formed via ACMC is enhanced at higher reaction temperatures (Fig. 5A).
The obtained results further support previous observations 51 that the incorporation of Mg into calcite formed via ACMC is controlled by the Mg 2+ /Ca 2+ ratio of the reactive solution at the time of transformation. Blue et al. 51 synthesized ACMCs with different Mg contents under constant pH conditions (pH 8.3-9.1) using a mixed flow reactor and investigated their crystallization pathway in aqueous solution under stirred and unstirred conditions. Their results document a positive correlation between the Mg content of calcite and the Mg 2+ /Ca 2+ ratio of the solution from which the mineral formed. In the experimental setup used in the present study, Mg 2+ and CO 3 2− ions were present in the initial solution, whereas Ca 2+ ions exclusively originated from the dissolution of the ACMC. At higher temperatures, lower amounts of ACMC dissolved in the NaHCO 3 -MgCl 2 solution as indicated by less Ca 2+ ions released into the reactive solution (Fig. 4A). This can be explained by the anticorrelation between amorphous carbonate mineral solubility and temperature (for ACC: Brečević & Nielsen 28 ). Thus, at 5 min of reaction time, the reactive solutions exhibit higher aqueous Mg 2+ /Ca 2+ ratios as a function of increasing temperature ( Fig. 5B; Table S2 †). Indeed, by comparing the Mg content of the initial HMC with the Mg 2+ /Ca 2+ ratio of the solution after its reaction with the ACMC, we find a good agreement of the results obtained at 25°C and those reported by Blue et al. 51 (Fig. 5C).
During the ongoing transformation of ACMC into HMC, the Mg 2+ /Ca 2+ ratio of the solution increases (Table S2 †) due to stronger uptake of Ca 2+ compared to Mg 2+ from the solution into the solid. This increasing Mg 2+ /Ca 2+ ratio likely results in the formation of HMC with higher Mg contents as a function of reaction time ([Mg] XRD values in Table 1). Hence, the final HMCs exhibit higher Mg contents compared to the initial HMCs (Fig. 5A). This effect is temporally better resolved at low temperatures, due to slower transformation kinetics of ACMC into HMC (Table 1). For example, at 20°C the Mg content of HMC increases slowly from 12 to 17 mol% between 11 and 61 min of reaction time (Table 1). In contrast, at higher temperatures, the transformation of ACMC into HMC occurs faster and the transition from lower to higher Mg contents for HMCs occurs in shorter time intervals (Table 1).
The positive relationship between aqueous Mg 2+ /Ca 2+ ratios and Mg content of the forming HMC from ACMC transformation (Fig. 5C) 51,54 However the process by which physical mixing influences the formation of distinct crystalline Ca-Mg-carbonates and the Mg content of calcite is still poorly understood and needs further investigations.   Table 2). (B) Temperature of the solution versus the Mg 2+ /Ca 2+ ratio of the solution at 5 min of reaction time (Table S2 †). (C) Mg 2+ /Ca 2+ ratio of the solution at 5 min versus the Mg content of (i) initial HMC from this study, of initial HMC from experiments conducted at stirred conditions reported by Blue et al. 51

Solubility considerations of ACMC and HMC
At higher reaction temperatures, less ACMC dissolved in the NaHCO 3 -MgCl 2 solutions as it is indicated by the lower concentrations of Ca, Mg and CO 3 ions in the reactive solutions at 0.3 min of reaction time (Fig. 4A). In order to assess the effect of temperature on the solubility (K) of ACMC, the activities of Ca 2+ , Mg 2+ and CO 3 2− ions in the reactive solution (Table S3 †) and the ACMC stoichiometry (at 0.3 min) were used to calculate K ACMC values according to eqn 2 (see also Purgstaller et al. 33 ). The obtained K ACMC values for ACMC with 47.0 ± 1.5 mol% Mg (t = 0.3 min) indicate that the solubility of ACMC is lower at higher temperature (Fig. 6A), analogous to the temperaturedependent solubility of ACC determined by Brečević and Nielsen. 28 A similar behaviour is also well known for anhydrous carbonate minerals such as calcite 55 and magnesite 56 which exhibit lower K values at higher temperatures (Fig. 6A). The relationship between the solubility of ACMC (with 47.0 ± 1.5 mol% Mg) and temperature (T in Kelvin) can be described by the polynomial function: log(K ACMC ) = −0.0001434 ± 0.0000137 T 2 + 0.0760 ± 0.0087 T − 15.537 ± 1.375 (R 2 = 0.99) It is strongly emphasized that in the present study the experimental data for calculating K ACMC values are limited (Table S3 †) and further experimental work is needed to verify the obtained relationship between K ACMC and temperature (Fig. 6A).
As it can be seen in Fig. 6A the solubility products of ACMC are higher compared to Mg-free ACC at any temperature suggesting that ACMC is more soluble than ACC. This feature can be attributed to the increasing water content and changes in short-range order, as Ca is substituted by Mg in the amorphous structure. 33 The relationship between the solubility of ACMC and its Mg content is displayed in Fig. 6B. Note that the slopes of the regression lines between the K ACC value of Brečević and Nielsen 28 and the K ACMC value of this study are similar at 10, 20, 40, 60 and 80°C (slope = 0.01634 ± 0.00066; Fig. 6B and Table S4 †) and are in good agreement with the slope value of the linear relationship between K ACMC and the Mg content of ACMC at 25°C (slope = 0.01602; Mg content of ACMC = 2 to 51 mol%, Table S4 †) presented by Purgstaller et al. 33 Considering the close agreement between K values obtained in this study and those of Brečević and Nielsen 28 and Purgstaller et al. 33 a quantitative description of the variations of K ACMC with temperature and Mg content of ACMC can be obtained starting from the relationship between ACC solubility (K ACC ) and temperature (T in Kelvin) determined by Brečević and Nielsen: 28 Based on the assumption that the relative increase of K ACMC values as a function of the Mg content is independent of temperature and can be described by the same linear function with an average slope of 0.01629 ± 0.00060 (see Table S4 Fig. 6B). However, the impact of temperature on the solubility of HMC is not fully elucidated and to our knowledge only Bertram et al. (1991) 57 studied the solubility of synthetic Mg-calcites with 1.9 to 15 mol% Mg between 25 to 64°C and showed that the decrease in solubility of Mg-calcite with increasing temperature parallels that of calcite (see K data of Mg-calcite with 15 mol% Mg in Fig. 6A). No experimental data, however, exist for the solubility dependence of HMC with >15 mol% Mg at elevated temperatures. Fig. 6A Fig. 2A) and those of T_40°C and T_80°C include HMG (6-15 wt%, Table 1). As it can be seen in Fig. 6B, the HMC formed via ACMC at 20°C (with 18 mol% Mg) is significantly more soluble (log(K HMC ) = −7.83) than the biogenic and synthetic Mg-calcites of group II reported by Busenberg and Plummer,19 which exhibit similar Mg contents (e.g. log(K HMC ) = −8.16 for biogenic Mg-calcite with 19 mol% Mg at 25°C). Note that Busenberg and Plummer 19 distinguished two groups of Mg-calcites with distinct solubilities, reflecting crystal structure defects (Fig. 6B). Group I consists of metamorphic and hydrothermal Mg-calcites and synthetic Mg-calcites prepared at high temperatures and pressures or low temperatures and low supersaturations (saturation index ≤0.2). Group II Mg-calcites are of either biogenic origin or synthetic Mg-calcites prepared at high supersaturations (saturation index ≥0.5). The Mg-calcites of group I are thought to be relatively free of structural defects, whereas group II Mg-calcites were described as more defective Mgcalcites which exhibit higher solubilities. The discrepancy between the reported solubility value of Busenberg and Plummer 19 and of the present study might be explained by different physical defects originating from rapid crystal growth during HMC formation. Considering an ACMC transformation step, the solution in equilibrium with ACMC is highly supersaturated with respect to calcite (saturation index >2 (ref. 31) and 49)). Such high calcite supersaturation degrees probably promote rapid precipitation of HMC at the ACMC-solution interface. Indeed, in the present study, ACMC transformed into nanocrystalline HMC at relatively short time intervals (<60 min, Fig. 2 and 3). These solids are likely more defective and thus exhibit higher solubilities compared to well-crystallized HMC (Fig. 6B). The elevated solubilities of nanocrystalline HMC appears to be consist with recent results of Davis et al. 58 who demonstrated, based on microscopic observations, enhanced solubilities of Mgcalcites at the nanometric scale.

Conclusions
In the present study, the transformation of ACMC with neardolomite stoichiometry (47.9 ± 1.5 mol% Mg) into HMC was investigated in a MgCl 2 -NaHCO 3 buffered solution at pH 7.6 and in the temperature range from 10 to 80 ± 1°C. The results provide an advanced understanding of the complex interplay between the chemical composition of ACMC, the corresponding solution and the finally formed Mg-calcite. At first, the experimental data indicate that the apparent solubility of ACMC is lower at higher temperature and the relative increase of solubility as a function of the Mg content of ACMC is similar from 10 to 80°C which can be assessed by eqn 5. At ambient temperatures, the Mg content of HMC formed via the transformation of ACMC is as low as 18 mol%, whereas at 60 and 80°C, the final HMCs reach Mg levels comparable with those of VHMC (40 mol%). Hence, the Mg content of the HMC is not pre-determined by the Mg content of the amorphous precursor, but strongly influenced by the reaction temperature during ACMC transformation. The transformation of ACMC to HMC proceeds via a dissolution and re-precipitation mechanism where at higher temperatures the amount of Mg incorporated into calcite is enhanced due to (i) the reduced solvation energy barrier of aqueous Mg 2+ and (ii) the high Mg 2+ /Ca 2+ ratio of the reactive solution after its reaction with the ACMC. The high Mg 2+ / Ca 2+ ratio of the latter solution can be explained by low solubility of ACMC at elevated temperatures. The obtained solubilities of the final HMC are higher compared to those of well-crystalline Mg-bearing calcites, which is most likely caused by nanometric-sized HMC crystals with structural defects originated from fast crystal growth.

Conflicts of interest
There are no conflicts to declare.