Relative Contributions of Mg Hydration and Molecular Structural Restraints to the Barrier of Dolomite Crystallization: A Comparison of Aqueous and Non-Aqueous Crystallization in (BaMg)CO 3 and (CaMg)CO 3 Systems

: Carbonate mineralization is reasonably well-understood in the Ca–CO 2 –H 2 O system but continuously poses difﬁculties to grasp when Mg is present. One of the outstanding questions is the lack of success in dolomite MgCa(CO 3 ) 2 crystallization at atmospheric conditions. The conventional view holds that hydration retards the reactivity of Mg 2+ and is supported by solvation shell chemistry. This theory however is at odds with the easy formation of norsethite MgBa(CO 3 ) 2 , a structural analogue of dolomite, leading to the premise that crystal or molecular structural constrains may also be at play. The present study represents our attempts to evaluate the separate contributions of the two barriers. Crystallization in the Mg–Ba–CO 2 system was examined in a non-aqueous environment and in H 2 O to isolate the effect of hydration by determining the minimal relative abundance of Mg required for norsethite formation. The results, showing an increase from 1:5 to 6:4 in the solution Mg/Ba ratio, represented a ~88% reduction in Mg 2+ reactivity, presumably due to the hydration effect. Further analyses in the context of transition state theory indicated that the decreased Mg 2+ reactivity in aqueous solutions was equivalent to an approximately 5 kJ/mol energy penalty for the formation of the activated complex. Assuming the inability of dolomite to crystallizes in aqueous solutions originates from the ~40 kJ/mol higher (relative to norsethite) Gibbs energy of formation for the activated complex, a hydration effect was estimated to account for ~12% of the energy barrier. The analyses present here may be simplistic but nevertheless consistent with the available thermodynamic data that show the activated complex of dolomite crystallization reaction is entropically favored in comparison with that of norsethite formation but is signiﬁcantly less stable due to the weak chemical bonding state.


Introduction
Interests in carbonates trace back to 1870s, with the first recognition that CaCO 3 may form different polymorphs [1]. Since then, our knowledge base in this field has expanded immensely in virtually all fronts of related areas, first in crystallography [2,3] and mineralogy [4,5], followed by crystallization/dissolution as well as mineral-water interfacial reactions [6][7][8][9][10][11]. Modern-time motivation to study carbonates lies chiefly in the need to understand biomineralization [12] and the unique chemistry of mineral crystallization and dissolution where the thermodynamic equilibria between CO 2 (g), HCO 3 − and CO 3 = (aq), and alkali earth metals control long-term climate [13,14]. To date, significance advances have revealed various physiochemical aspects of carbonate behavior and reactivity, both in geological and biological settings.
Looking at carbonate minerals in the Earth's crust as a whole, however, one cannot help but notice the puzzling question of dolomite mineralization [15]. Despite belonging far, norsethite can precipitate readily in a room temperature aqueous environment [34][35][36]. Although the results from a number of recent studies [37][38][39][40][41][42] indicated that the reaction pathway may involve dissolution-recrystallization of certain precursors, the routineness of norsethite formation clearly demonstrates that Mg 2+ can dehydrate efficiently to enter the lattice of anhydrous carbonate crystals at ambient conditions. More importantly, the relative cation size (Mg to Ba vs. Mg to Ca) and the anion orientation are all structural factors, and the mere fact that a change in such parameters can result in the crystallization of ordered binary magnesium carbonate MgBa(CO 3 ) 2 argue strongly for a more important role of atomic arrangement along the reaction coordinate of dolomite formation, aside from Mg hydration. We suspect the aspect of structural restraints may lie chiefly in the transition state of the crystallization reactions because the Gibbs energy of formation for dolomite (−2148.90 kJ/mol) [43] and norsethite (−2167 ± 2 kJ/mol) [40] is not significantly different. The goal of this study is to test this hypothesis and to assess the relative weight of Mg hydration and the structural limitation. We carry out crystallization experiments in H 2 O solutions and a non-aqueous solvent to determine the minimal relative abundance of Mg needed to form norsethite and use the difference in the determined minima to estimate the magnitude of the hydration effect. We then apply the transition state theory (TST) to further evaluate the contribution of Mg hydration to the reduction in the activated complex. Finally, we compare the Mg hydration effect and the activation free energy of dolomite crystallization to gauge the approximate scale of the structural restraints in the overall reaction process.

Crystallization Experiments
Aqueous stock solutions were prepared from BaCl 2 , MgCl 2 , and NaHCO 3 using distilled deionized water. Chloride solutions containing 1, 10, 40, and 50 mM/L of metal ions were prepared first for Mg and Ba separately, followed by mixing varied proportions of the MgCl 2 and BaCl 2 solutions to achieve the desired levels of the Mg-to-Ba ratio (Mg/Ba, from 4:6 to 9:1). The concentration of sodium bicarbonate solution varied from 5 to 250 mM. In a typical synthesis experiment, 20 mL of NaHCO 3 solution were slowly titrated into 20 mL of a mixed cation chloride solution, sealed, and left still for ten days. Speciation, ionic activities, and supersaturation states of each experimental solution were calculated via the computer code PHREEQC. The solubility product for witherite and norsethite were assumed to be K sp,wt = 10 −8.56 (PHREEQC database) and K sp,nr = 10 −17.73 [40].
Non-aqueous experiments were carried out in formamide (O=CH-NH 2 , FMD) that has a weaker (relative to H 2 O) autoionization (autoprotolysis constant 10 −16 vs. 10 −14 ) but a stronger polarity (dielectric constant 109 vs. 78) [44] and can dissolve inorganic salt easily to make experimental solutions. Stock solutions of 0.2M MgCl 2 , 0.2M BaCl 2 , and 0.2 Cs 2 CO 3 were prepared by dissolving the corresponding salt compounds that were pre-dried in an oven at 60 • C. The experimental solutions with varied Mg/Ba content (5:1, 2:1, 1:1, 1:2, and 1:5) were then made by mixing that of MgCl 2 and BaCl 2 in desired proportion, followed by slow titration into the Cs 2 CO 3 stock. The final solution was kept closed and still for 24 h.
All experiments were conducted at room temperature (25 ± 1 • C). At the end of crystallization experiments, individual solutions were centrifuged (10,000 rpm, 10 min) and the solid was collected; washed extensively in ethanol to remove the residual Na + , Cs + , and Cl − ; and oven-dried at below 30 • C. Chemicals and solvent used in the synthesis experiments were of analytical grade and purchased from Shanghai Aladdin Bio-Chem Technology Co.

Precipitate Identification
The crystallinity and mineral composition of the precipitates were characterized by powder X-ray diffraction (XRD) using a Riguka MiniFlex 600 instrument (Cu K α1 radiation). The diffractograms were collected from 3−70 • with a scanning rate of 2 • /min. Prior to instrumental analysis, the precipitates were dispersed in alcohol and pipetted on a zerobackground monocrystalline silicon sample holder and placed into the diffractometer once dried. The diffractograms were analyzed using the package of MDI Jade 6. Other than XRD characterization, the precipitates were not checked for impurity contents of Na, Cs, and Cl through chemical analyses.

Results
A total of 82 synthesis experiments (Table 1) were carried out in aqueous solutions with various combinations of supersaturation, cation-to-anion ratio ([Mg + Ba]/CO 3 ), and relative concentrations of Mg to Ba (Mg/Ba). All experiments were performed in supersaturated solutions with reference to norsethite (0.3 < logΩ N < 5.46, where Ω N is the ratio of ionic activity product to the solubility product of norsethite), with all but six of them undersaturated with respect to witherite (−0.63 < logΩ W < 2.33). Altogether, crystal formation was observed in 74 of the experimental runs (Table 1), of which 26 exhibited XRD signals of norsethite crystallization. The experiments that did not show crystallization either had low supersaturation with respect to norsethite (logΩ N < 1) and undersaturation to witherite or had a high level of Mg presence (Mg:Ba > 7:3) but low supersaturation relative to witherite (logΩ W < 0.4).
Exclusive formation of norsethite required a strong presence of Mg (Mg/Ba > 7/3); decreasing Mg usually led to co-precipitation of norsethite and witherite first, followed by sole occurrence of witherite ( Figure 1). The minimal requirement of Mg/Ba for norsethite to be a component of the crystallization product was 6/4, and this value appeared to be positively correlated with Ω N and the cation-to-anion ratio in the experimental solutions. For example, at logΩ N ≈ 2 to 2.5 and cation/anion ≈ 0.28, norsethite crystallized along with witherite in solutions with Mg:Ba = 6:4; when logΩ N increased to approximately 5-5.5 and cation/anion ≈ 21-22, norsethite was only detected at the conditions of Mg:Ba = 8:2. On the other hand, the exclusion of norsethite from crystallization (i.e., witherite was the sole product) could occur at any level of Mg/Ba and any supersaturation (with respect to both norsethite and witherite) as long as the cation-to-anion ratio was sufficiently large (usually > 80~100). For example, at logΩ N ≈ 2.2 to 2.7 and cation/anion ≈ 130−140, witherite was the only phase found in solution at logΩ W ≈ 0.3-1.0, same as the experiments where logΩ N ≈ 4.0-4.5, cation/anion ≈ 161-177, and logΩ W ≈ 1.2-1.8.
A much simpler outcome was observed in formamide containing varied amounts of Mg 2+ and Ba 2+ at a fixed concentration of ([Mg] + [Ba]). Unlike the results in aqueous environment where norsethite formation required Mg dominated solution chemistry and in fact was never observed once Mg/Ba < 6/4, norsthite was shown to be a major component of the precipitate at Mg:Ba = 1:2 along with witherirte and the single solid phase at Mg/Ba = 1 ( Figure 2). Similar to the observations in H 2 O, a reduction in the relative abundance of Mg suppressed norsethite crystallization and ultimately led to a dominant occurrence of witherite at Mg/Ba = 1/5 ( Figure 2, traces of norsethite still visible). Different from aqueous experiments, however, a strong Mg presence with Mg/Ba = 2 and 5 in FMD did not promote norsethite crystallization but instead led to the formation of an amorphous phase in both cases (Figures 2 and 3). The amorphous precipitate appeared as nano-aggregate (  Exclusive formation of norsethite required a strong presence of Mg (Mg/Ba > 7/3); decreasing Mg usually led to co-precipitation of norsethite and witherite first, followed by sole occurrence of witherite ( Figure 1). The minimal requirement of Mg/Ba for norsethite to be a component of the crystallization product was 6/4, and this value appeared to be positively correlated with ΩN and the cation-to-anion ratio in the experimental solutions. For example, at logΩN ≈ 2 to 2.5 and cation/anion ≈ 0.28, norsethite crystallized along with witherite in solutions with Mg:Ba = 6:4; when logΩN increased to approximately 5-5.5 and cation/anion ≈ 21-22, norsethite was only detected at the conditions of Mg:Ba = 8:2. On the other hand, the exclusion of norsethite from crystallization (i.e., witherite was the sole product) could occur at any level of Mg/Ba and any supersaturation (with respect to both norsethite and witherite) as long as the cation-to-anion ratio was sufficiently large (usually > 80 ~ 100). For example, at logΩN ≈ 2.  A much simpler outcome was observed in formamide containing varied amounts of Mg 2+ and Ba 2+ at a fixed concentration of ([Mg] + [Ba]). Unlike the results in aqueous environment where norsethite formation required Mg dominated solution chemistry and in fact was never observed once Mg/Ba < 6/4, norsthite was shown to be a major component of the precipitate at Mg:Ba = 1:2 along with witherirte and the single solid phase at Mg/Ba = 1 (Figure 2). Similar to the observations in H2O, a reduction in the relative abundance of   All visible peaks below 2θ of 55 • were able to be assigned to norsethite and witherite, suggesting that those two minerals may be the only phases that occurred in the experiments. Notice the lack of crystallinity at conditions of 2Mg:1Ba and 5Mg:1Ba as well as the presence of norsethite (10.1) and (00.3) peaks at 1Mg:5Ba.

Hydration Hindrance
Two observations stand out distinctively from the aqueous experiments. (1) Incongruent crystallization ([Mg/Ca]s olid /[Mg/Ca] solution = 1) occurred for exclusive norsethite formation as the solutions were required to have more Mg than Ba with an observed minimal value of Mg/Ba ≈ 7/3, and (2) norsethite was never detected in solutions with Mg/Ba < 6/4, whereas witherite could crystallize in Mg 2+ dominated (as strong as Mg:Ba = 9:1) conditions (provided that the cation-to-anion ratio is high). The requirement of Mg-enriched solution to precipitate norsethite was observed previously by Lippmann [4] and Hood et al. [36] with a relative abundance of Mg/Ba ≈1.6 while maintaining CO 3 2− at a fixed concentration (0.5 M). A plausible conclusion we can draw from these findings is that the stronger hydration of magnesium (than of Ba 2+ ) may have limited Mg 2+ from being in the free (dehydrated) state, so much so that 50% more Mg 2+ was needed to match the quantity of free Ba 2+ ions in the solutions. At the opposite end, although witherite appeared to form more easily in the Mg-Ba-CO 2 -H 2 O system given that the logΩ W is smaller throughout the experiments by a factor of 2-10 in comparison with logΩ N , norsethite nevertheless crystallizes readily and can often be the exclusive precipitate at specific conditions (Mg/Ba >~7/3, cation/anion <~60). Aqueous crystallization of norsethite at ambient conditions is known all along [4,35,38,45,46] but is not known to require additional energy input other than supersaturation, and thus, it is inconsistent with the view that Mg 2+ -H 2 O interactions act as a barrier to preventing magnesium ions from entering the rhombohedral carbonate lattice.
Contrasting with the Mg-rich requirement for norsethite precipitation in aqueous environment, norsethite can crystallization in Mg-depleted FMD solutions with Mg/Ba = 1/2-1/5. These observations on the one hand appear to be largely in line with the expectations of the Mg hydration theory, considering that the binding energy of Mg 2+ with FMD (~125 kcal/mol [47]) is significantly smaller than with H 2 O (~260 kcal/mol [22,48]), and the hydrogen bonds between formamide molecules (8-13 kJ/mol for NH···O and NH···N) are meaningfully weaker than that between water molecules (21 kJ/mol for OH···O) [49]. Simply put, it is reasonable to assume that, while the stronger (relative to Ba 2+ ) hydration of Mg 2+ dictates that magnesium ions stay largely in a hydrated form in aqueous solutions, the FMD solvation shell around Mg 2+ is not as rigid and tight as the hydration shell, allowing for the presence of sufficient amount of free magnesium ion to participate in the crystallization reactions. On the other hand, the same rationale would lead one to expect the crystallization of anhydrous magnesium carbonate in FMD when this assumption is extended to Mg dominated conditions. However, experimental results, showing the lack of crystallinity in precipitates formed at conditions of Mg/Ba > 1 (Figure 2), defied this logic reasoning. Furthermore, in comparison with the amorphous calcium carbonate (ACC) formed in the presence of Mg ions, the Mg-Ba-CO 3 amorphous precipitate (Figure 3 upper) had a rather evenly distributed particle size instead of a mixture of distinctly sized populations [50], suggesting the occurrence of a monotonous short range order (the recurrence of Ba-O and Mg-O coordination) rather than the commonly observed Ca-ACC (mainly Ca-O order) and Mg-ACC (both Ca-O and Mg-O order) in the Mg-Ca-CO 3 system.

Structural Restraints
The lack of long-range orders in carbonate precipitates formed in Mg-rich FMD solutions was first observed in the Ca-Mg-CO 2 system [51], where different from the Ba-Mg-CO 2 system of concern in this study, congruent crystallization of MgCa(CO 3 ) 2 (dolomite) did not occur; high Mg (37% mole ratio) calcite instead formed at Mg/Ca = 1. Given the absence of H 2 O in the experiments, the authors deduced that hydration may be an external force that is partially responsible for hindering dolomite and magnesite formation at ambient conditions, and crystal structural restraints, particularly reduced freedom of the CO 3 groups and the increased lattice strains resulting from the size difference between Mg 2+ and Ca 2+ ions, may be the inherent factor preventing magnesium from entering the trigonal carbonate structure at ambient conditions. A later study [52] presented additional evidence embracing the premise that Mg for Ca substitution in calcite is limited to < 40%. In the context of lacking dolomite formation in the Ca-Mg-CO 2 -FMD system, the unhindered crystallization of norsethite at Mg/Ba = 1 observed in the present study appears to be consistent with the view of structural restraints. This is because, unlike dolomite (R3), the CO 3 groups in the norsethite (low temperature polymorph, R3c) are not as rigidly constrained. The refined norsethite structure by Effenberger et al. [33] indicates that the carbonate groups stacked along the c direction do not strictly alternate their orientations in adjacent layers but instead rotate clockwise and anti-clockwise successively within a plane and in the c-axix (compare Figure 9a,c in Effenberger et al., 2014 [33]). In doing so, the unit cell doubles its size in the c-direction and the resultant structure allows for the large cation Ba 2+ to increase its coordination number while maintaining the octahedral coordination of the smaller ion Mg 2+ without creating much stress. In contrast, the dolomite structure does not have the luxury to relax because the R3 symmetry dictates that the planar CO 3 rotates 60 • in alternate layers. Thus, it appears that the lack of flexibility in the a-b plane is a key parameter limiting dolomite crystallization at ambient conditions. In their study of PbMg(CO 3 ) 2 and norsethite crystallization, Pimentel and Pina [39] observed a reduction in the formation rate associated with the cation size decrease from Ba to Pb and proposed that the shape and relative size of the constituent coordination polyhedra may play a fundamental role (may be more relevant than magnesium hydration) in controlling the stability of dolomite-like structures such as those involving Mg 2+ , Ca 2+ , Ba 2+ , Pb 2+ , and Sr 2+ . Together, the findings to date suggest that structural flexibility in terms of adapting to the variable coordination of the non-Mg cations is critical for long range order development in all rhombohedral binary carbonate systems.
Considerations in structural restraints also lead us to speculate that magnesium carbonate formation may be an initial step in the reaction pathways of dolomite and norsethite crystallization. Two lines of thought are factored in this proposition. First, anhydrous carbonate can crystallize into two crystal systems: trigonal or orthorhombic. A general understanding [53][54][55] is that minerals with cations smaller than Ca 2+ (ionic radius r = 100 pm) adopt the trigonal structure (metal ions coordinated by six oxygens), whereas those larger than Ca 2+ usually take on the orthorhombic form (metal ions coordinated by nine oxygens). Calcium, being the pivot, can be either trigonal (calcite) or orthorhombic (aragonite). As such, it is expected that magnesite MgCO 3 and witherite Ba(CO 3 ) 2 are exclusively trigonal and orthorhombic, respectively, given the cation size of Mg 2+ (r = 72 pm) and Ba 2+ (r = 152 pm). When binary systems are concerned, while it is conceivable that dolomite and proto-dolomite adopt a trigonal structure (because of the structural flexibility of calcium carbonate), the rationale for norsethite's structural preference is not so distinctly discernable due to the trigonal and orthorhombic combination of the end members. The fact that norsethite ends up in the trigonal system indicates that the rhombohedral structure in principle is the thermodynamically more stable one for a Mg-Ba binary carbonate crystal. Moreover, the occurrence of norsethite and witherite co-precipitation signals that, while Ba can be incorporated in both trigonal and orthorhombic structures, magnesium on the other hand can only enter crystals with trigonal symmetry. Thus, on the basis that magnesium and barium do not form solid solution (Ba,Mg)CO 3 , we deduce that the initial step of norsethite crystallization is more likely the formation of magnesite units, which allow for a later or subsequent incorporation of Ba for the nucleation to continue. Conversely, if witherite is the first unit to form, the inability of Mg to enter the orthorhombic structure leads to a discontinuation of the crystallization process without the formation of norsethite in the end. Second, a common behavior of the Ca-Mg-CO 2 and Ba-Mg-CO 2 system in non-aqueous environment is the lack of crystalline precipitates in Mg-dominated solutions. This is surprising because~33% to~17% of solvated cations in those scenarios (Mg/Ba and Mg/Ca = 2 and 5, this study and Xu et al., 2013 [51]) are barium and calcium and should result in witherite and calcite crystallization, as they did in aqueous environments. A plausible interpretation is that Mg 2+ , which may be less stable in an un-hydrated form due to the high charge density relative to Ba and Ca ions, has the advantage to bind with CO 3 2− first. When Mg is the minority ion in the solution and binds preferentially with carbonate ions, Ba 2+ and Ca 2+ can interact with the remaining CO 3 2− to form witherite and calcite or can be incorporated in the prior-formed Mg-CO 3 unit to crystallize in norsethite and high-Mg calcite. In Mg-dominating solutions, however, rapid interactions of Mg with CO 3 ions lead to amorphous magnesium carbonate precipitation (on the assumption that the Mg-CO 3 units cannot stack to form 3D crystalline structures due to the entropy penalty in the CO 3 groups) [51] and a quick consumption of CO 3 2+ , leaving Ba 2+ and Ca 2+ behind to stay in the solution without their host minerals witherite and calcite or to occur as minor components in the amorphous phases.
It is worth noting that a number of previous studies actually found [4,38,40,45,56] BaCO 3 , instead of MgCO 3 being a precursor of norsethite at atmospheric conditions. Considering the recent finding that norsethite formation proceeds through a crystallization (chiefly of Na 3 Mg(CO 3 ) 2 Cl, with minor witherite and norsethite)-dissolution-recrystallization (of norethite) pathway [38], we suspect the incorporation of Ba into the trigonal carbonate structure (or the transformation of BaCO 3 from orthorhombic to rhombohedral class) is a kinetically unfavored process. This may be especially true at low T, where the formation of ordered MgCO 3 is challenging and the orthorhombic template for BaCO 3 to epitaxially grow on is lacking. As such, witherite is expected to form first but dissolves subsequently to release Ba 2+ once MgCO 3 units are in place to crystallize MgBa(CO 3 ) 2 . At higher T when magnesite can readily form and the orthorhombic to rhombohedral transformation for BaCO 3 is less hindered, one should expect MgCO 3 to be a precursor of norsethite. This view is in fact consistent with the experimental observation that magnesite is the only precursor during norsethite crystallization at temperatures above 100 • C [57].

Relative Effect of Mg Hydration and Structural Restraints
The above discussion seems to converge on a conclusion that both Mg hydration and lattice structure are in play in limiting dolomite formation at ambient conditions. We now try to evaluate the relative importance of the two barriers. At a microscopic level, crystallization is characterized by the process of particle attachment and detachment. One effective approach to quantify this process is through the application of the transition state theory. Since dolomite (and magnesite in the same sense) is the thermodynamically stable phase at ambient conditions [18,[58][59][60][61], the difficulty to crystallize such minerals is safely ascribed to the reaction kinetics. In the TST approach, the kinetic limitations can be assessed specifically by examining the concentration of the activated complex at constant temperature. To a first-degree approximation, we assume the nucleation of norsethite proceeds through the following reaction (Equation (1)): where (BaCO 3 ·MgCO 3 ) ‡ refers to the activated complex and Mg 2+ , Ba 2+ , and CO 3 2− are the effective concentrations of the reactant ions. As the TST model is thermodynamics based, the following relations exist in the Ba-Mg-CO 2 system (Equation (2)): where K ‡ N and ∆G ‡ N are the equilibrium formation constants and the activation free energy (Gibbs energy of formation of the activated complex) for norsethite crystallization. It then follows that the concentration of the activated complex satisfies the following expression (Equation (3) Note that the maximal concentration for the activated complex implicated by Equation (3) can only be achieved at the conditions of [Mg 2+ ]/[Ba 2+ ] = 1. This is because the charge neutrality requirement for chemical reactions stipulates the total cation concentration ([Mg 2+ ] + [Ba 2+ ]) in the system to be a fixed value, and consequently, the ionic activity product of the cations reaches the maximum at equal relative abundance for each individual cations. As the minimal relative abundance of Mg for norsethite to form in FMD is Mg/Ba = 1/5, the increased value of Mg/Ba = 6/4 in water suggests that hydration may have reduced the availability of free Mg ions (or the reactivity of Mg 2+ ) by~88%. Applying the TST theory to the Ca-Mg-CO 2 system, we may have the following relations (Equations (4)-(6)): The similarity of these equations to Equations (1) (Table 2) [40,[62][63][64][65][66] reveal that (MgCO 3 ·CaCO 3 ) ‡ is in fact an entropically more favored species than (MgCO 3 ·BaCO 3 ) ‡ is, stating that the high ∆G ‡ D is derived primarily from the enthalpic contribution, i.e., weaker bonding in the activated complex. The Ca-O bond is only~17% weaker than the Ba-O bond (dissociation energy 464 kJ/mol and 563 kJ/mol, respectively), indicating the ∆H ‡ for (MgCO 3 ·CaCO 3 ) ‡ and (MgCO 3 ·BaCO 3 ) ‡ should only differ slightly as long as the spatial arrangement of atoms (i.e., bond angle and distance) in the two species are similar. The fact that ∆H ‡ D (132 kJ/mol) is more than~80% higher than ∆H ‡ N (77.52 kJ/mol) suggests the existence of a significant structural difference between the two activation states, consistent with the entropic factor of the two species (∆S ‡ N = −18.1 J/K/mol and ∆S ‡ D = 29.7 J/K/mol). A potential explanation is that (MgCO 3 ·BaCO 3 ) ‡ may have a more ordered structure due to the inability of Mg 2+ and Ba 2+ to form a single mixed layer, so that the oxygens in the CO 3 groups can bind to Mg in the +c direction and Ba in the −c direction without distorting the bond lengths on either side. On the contrary, (CaCO 3 ·MgCO 3 ) ‡ may be more disordered because Ca and Mg can replace each other in any binding geometry, resulting in oxygen-metal bonds in any orientation of the CO 3 groups having both Ca and Mg attached. Consequently, the bonds cannot adopt the optimal length and angle due to the size difference of Ca and Mg ions (bond length Mg-O 2.082 Å, Ca-O 2.382 Å in dolomite). After all, activated complexes differ from but resemble the products one way or the other. It is therefore reasonable to speculate that the ordered structure of norsethite and the common occurrence of disordered (Ca,Mg)CO 3 phases may be a reflection of the corresponding activated complex one way or the other. Finally, the estimated~88% reduction in [Mg 2+ ] due to hydration leads to a reaction quotient~eight times smaller than the equilibrium formation constant (K ‡ N ) for the activated complex (Equation (2)), equivalent to a~5 kJ/mol energy deficiency to reach the required ∆G ‡ N . The magnitude of fluctuation in the reported ∆G ‡ N (~79-84 kJ/mol, Table 3) in solutions with various levels of the Mg:Ba ratio seems to agree with such a small effect of Mg hydration. While this energy penalty can be compensated by raising the relative abundance of Mg in solutions for norsethite formation, the same cannot be said for dolomite. Assuming that dolomite crystallizes in aqueous solutions if the ∆G ‡ of the reaction (~125 kJ/mol) is lowered to a value close to that for norsethite (~80 kJ/mol, which incidentally is nearly identically to that for calcite, Table 2), on the basis that thẽ 45 kJ/mol difference between ∆G ‡ D and ∆G ‡ N ( Table 2) results from a combination of Mg hydration and structural constraints, our data suggest that the former accounts for~12% while the latter accounts for~88% of the dolomite mineralization barrier. Table 3. Thermodynamic properties of the activated complexes for norsethite formation in solutions with different values of the Mg-to-Ba ratio [40].

Summary
The Mg-Ba-CO 2 system was investigated through crystallization experiments at various conditions in water and a non-aqueous environment to determine the minimal Mg/Ba values at which norsethite can crystallize, and the measured difference was used to estimate the hydration effect on Mg 2+ reactivity in the crystallization reactions. The experimental data suggest that hydration may have suppressed the reactivity of Mg 2+ by close to 88% relative to that in FMD. Application of the TST model to the norsethite system revealed that the hydration effect on Mg has resulted in a reaction quotient that is approximately eight-fold smaller than the equilibrium formation constant for the activated complex, equivalent to~5 kJ/mol energy penalty. In comparison to dolomite, the TST parameters indicate that the activated complex for norsethite crystallization appears to be entropically unfavored but has a significantly stronger bonding strength, leading to the activation free energy~50% lower than for dolomite crystallization. The~5 kJ/mol energy penalty originating from Mg 2+ hydration is approximately equivalent to~12% of the difference between ∆G ‡ D and ∆G ‡ N , suggesting the hindrance for ambient condition dolomite mineralization may be derived primarily from the weaker bonding state in the transition state.
It is important to note that the simple approach adopted in this study may not be completely appropriate and can lead to erroneous conclusions. An important assumption made here is that the reaction pathway, the activated complex in specific, is similar for dolomite and norsethite crystallization reactions. Although less likely, it is still possible that the transition states of the reactions in Equations (1) and (4) differ to a certain degree. In addition, the assumption that ∆G ‡ D needs to be lowered to a level close to ∆G ‡ N in order for dolomite to crystallize may also be overly simplistic. For example, laboratory synthesis of dolomite is often possible at conditions near or above 100 • C [67]. At this temperature, ∆G ‡ D is in fact approximately 5 kJ/mol lower than that at 298 K (Table 2) and can be fully accounted for by the Mg hydration effect. Despite the uncertainties, the results from the approach appear to be able to rationalize the fact that crystallization of the ordered binary carbonate MgBa(CO 3 ) 2 can proceed at the relative Mg abundance of Mg:Ba = 6:4 in ambient aqueous solutions, while at the similar conditions, not even disordered (MgBa)CO 3 with Mg content greater than 10% [68][69][70][71][72][73][74] can readily form.
Author Contributions: H.T. conceptualized this study and drafted the manuscript. S.Z. and Y.W. carried out the crystallization experiments and material characterization and helped to finalize the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China, grand No. NNSFC-41972041.

Data Availability Statement:
The data presented in this study are available in the article.