Thermodynamic and Kinetic Studies of Dolomite Formation: A Review

Abstract

The “dolomite problem”, which has confused scientists for nearly two centuries, is an important fundamental geological problem. The mineralogical characteristics of carbonate minerals show that the dolomite structure consists of an ordered arrangement of alternating layers of Ca²⁺ and Mg²⁺ cations interspersed with ${\mathrm{C}\mathrm{O}}_3^{2-}$ anion layers normal to the c-axis. The dolomite structure violates the c glide plane in the calcite structure, which means that dolomite has R$\overline{3}$ space group symmetry. The ordered dolomite has superlattice XRD reflections [e.g., (101), (015) and (021)], which distinguish it from calcite and high-Mg calcite. The calculation of thermodynamic parameters shows that modern seawater has a thermodynamic tendency of dolomite precipitation and the dolomitization reaction can be carried out in standard state. However, the latest thermodynamic study shows that modern seawater is not conducive to dolomitization, and that seawater is favorable for dolomitization in only a few regions, such as Abu Dhabi, the Mediterranean and the hypersaline lagoons in Brazil. The kinetic factors of dolomite formation mainly consist of the hydration of Mg²⁺, the presence of sulfate and the activity of carbonate. Current studies have shown that the presence of microorganisms, exopolymeric substances (EPS), organic molecules, carboxyl and hydroxyl functional groups associated with microorganisms and organic molecules, clay minerals with negative charges and dissolved silica facilitate magnesium ions to overcome hydration and thus promote Mg²⁺ incorporation into growing Ca-Mg carbonates. Similarly, the metabolic activity of microorganisms is conducive to the increase in alkalinity. However, the inhibitory effect of sulfate on dolomite formation seems to be overestimated, and sulfate may even be a catalyst for dolomite formation. Combining the carbonate crystallization mechanism with thermodynamic and kinetic factors suggests that the early stage of dolomite precipitation or the dolomitization reaction may be controlled by kinetics and dominated by unstable intermediate phases, while metastable intermediate phases later transform to ordered dolomite via an Ostwald’s step rule.

1. Introduction

Dolomite [CaMg(CO₃)₂] is a common carbonate mineral and is the main component of dolostone. Dolomite was first discovered in 1791 by French naturalist Deodal de Dolomieu [1]. Dolostone, an important type of sedimentary rock, can form important oil and gas reservoirs [2], and most Mississippi Valley-type (MVT) Pb-Zn deposits are hosted in dolostone [3], which indicates that dolostone has important economic value.

Dolomite is widely developed in deep-time marine carbonate rocks [4,5]. Although modern seawater is supersaturated with respect to dolomite [6], dolomite is a rare precipitate in Holocene sediments [4,7,8]. Additionally, dolomite is notoriously difficult to precipitate experimentally at ambient temperature and pressure [9]. This is known as the “dolomite problem” [10,11]. Carbonate precipitation is controlled by both kinetic and thermodynamic considerations [12]. Therefore, many scholars have conducted a great deal of research in thermodynamics and kinetics to solve the dolomite problem.

In terms of thermodynamics, the solubility product of dolomite was experimentally determined by scholars as early as the 1950s [13,14,15,16,17,18,19,20], but due to the difficulty in determining equilibrium in laboratory experiments, the values of the dolomite solubility product determined experimentally at ambient temperature have wide discrepancies. Therefore, it is difficult to accurately determine the solubility product of dolomite in standard state. Additionally, many scholars have proposed stoichiometric reactions to form dolomites [21,22,23,24], and some have been used for thermodynamic considerations. At the same time, thermodynamic parameters of related minerals and ions that can be used to determine the direction of the dolomitization reaction have been also published [19,25,26,27,28,29,30,31]. Although these reactions are all in the direction of dolomite precipitation, these reactions have not been demonstrated in the laboratory at low temperatures, and the scarcity of dolomites in modern environments may indicate that reaction kinetics may be a major control in the formation of dolomite [7,9]. In terms of kinetics, it is believed that the main kinetic factors of dolomite precipitation are the hydration of Mg²⁺ [22], the presence of sulfate [32] and the activity of carbonate [22]. The hydration of Mg²⁺ is an important factor in inhibiting dolomite precipitation because magnesium ions are tightly bound to water at low temperatures, which makes it difficult for Mg²⁺ to enter the carbonate lattice. Accordingly, working out how to make magnesium ion dehydrate is the key to solving the dolomite problem. In addition, the presence of sulfate will cause ${\mathrm{S}\mathrm{O}}_4^{2-}$ and Mg²⁺ in water to form tight ion pairs, thus inhibiting the incorporation of Mg²⁺ into the dolomite lattice [32]. However, recent studies indicate that the inhibitory effect of sulfate is not strong at low temperatures [33]. Lippmann [22] pointed out that the activity of carbonate in seawater is also a kinetic factor affecting dolomite precipitation. Garrels and Thompson [34] calculated a chemical model for seawater at 25 °C and found that the activity of carbonate (4.7 × 10⁻⁶) is much lower than the molality (2.69 × 10⁻⁴). Thus, working out how to weaken the kinetic barriers to dolomite formation has become a focus of research in recent years.

Accordingly, in order to better understand the dolomite problem, this paper reviews the research progress in kinetic and thermodynamic studies of dolomite genesis in recent decades. Firstly, this paper reviews the literature on the mineralogy of dolomite in order to distinguish other Ca-Mg carbonate minerals. Secondly, thermodynamic and kinetic studies related to dolomite origin in recent decades are reviewed. Finally, based on the thermodynamic and kinetic considerations of dolomite formation, we discuss the possible formation process of dolomite and propose directions for the study of the genesis of dolomite.

2. Dolomite Mineralogy

2.1. Calcite and Dolomite

When we study the crystal structure of rhombohedral carbonates, the crystal structure of calcite should be considered first. Because some important carbonate mineral constituents of sedimentary rocks, e.g., magnesium- and iron-bearing carbonates, have structures that are identical to or closely related to the crystal structure of calcite [22]. Accordingly, the structure of calcite can be used as a basis for describing the structure of such minerals. Calcite, a rhombohedral carbonate mineral, is a typical trigonal system. The vast majority of diagenetic calcite in the rock record formed from shallow burial in marine-derived fluids [35]. The calcite crystal structure consists of alternating layers of calcium cations (Ca²⁺) and carbonate anions (${\mathrm{C}\mathrm{O}}_3^{2-}$) oriented normal to the c-axis (Figure 1a). The calcite crystal structure is of space group R$\overline{3}$c [22], and the unit cell of calcite is hexagonal [dimension: a = 4.9896 (Å), c = 17.0610 (Å)] [36,37,38]. The (104) reflection peak is the most intense reflection in calcite and dolomite, which corresponds to the cleavage rhombohedron planes [38], but there are no ‘ordering’ reflections of dolomite in the XRD pattern of calcite.

Dolomite (CaMg(CO₃)₂) is a special rhombohedral carbonate mineral containing Ca and Mg. Very few sedimentary dolomites are truly stoichiometric and are more suitable to be represented by Ca_xMg_1−x(CO₃)₂. The stoichiometric compositions of natural dolomite vary from Ca_1.16Mg_0.84(CO₃)₂~Ca_0.96Mg_1.04(CO₃)₂ [7]. Dolomite is a trigonal system mineral whose crystal structure is a derivative of the calcite crystal structure. Dolomite is distinguished from calcite and other rhombohedral carbonates by its stoichiometry [39], and the ideal dolomite crystal structure consists of alternating layers of Mg²⁺ and Ca²⁺ interspersed with ${\mathrm{C}\mathrm{O}}_3^{2-}$ groups oriented normal to the c-axis (Figure 1b) [38]. In addition, the dolomite structure violates the c glide plane in the calcite structure, which means that dolomite has R$\overline{3}$ symmetry [22]. The hexagonal unit cell dimensions of dolomite are a = 4.8069 (Å), c = 16.0034 (Å) [40,41]. Additionally, single-crystal dolomite is often rhombohedral {10$\overline{1}$1} and sometimes columnar {11$\overline{2}$0} [40]. Analysis of the XRD pattern shows that the crystal structure of dolomite is different from that of calcite. The ordered dolomite has superlattice XRD reflections [e.g., (101), (015) and (021)] (Figure 2a) [5,42,43]. The ratio of the diffraction intensity of the (015) crystal plane to that of the (110) crystal plane is used to calculate the degree of cation ordering in dolomite [δ = r (015)/r (110)] [44]. Ancient sedimentary dolomite tends to have a much more regular lamellar structure than Holocene dolomite. In addition, ancient sedimentary dolomite typically possesses a pervasive modulated microstructure (wavelengths ≈ 200 Å) that is generally parallel to {1014} [7].

2.2. High-Mg Calcite

Calcites containing > 4 mol% MgCO₃ are considered to be high-Mg calcite [38]. Liu et al. [45] pointed out that the MgCO₃ content of high-Mg calcite ranges from 4 mol% to 36 mol%, while calcite with a MgCO₃ content ranging from 36 mol% to 55 mol% is called disordered dolomite. High-Mg calcite is characterized by a large number of Mg²⁺ cations randomly substituting for Ca²⁺ cations in a single cation position in the calcite lattice, and the disordered distribution of Ca²⁺ and Mg²⁺ in high-Mg calcite is in contrast to the ordered distribution of cations in dolomite. High-Mg calcite usually does not reproduce the ‘ordering’ reflections seen in the XRD pattern of dolomite (Figure 2b), and the (104) diffraction peak position (2θ) of high-Mg calcite is between that of dolomite and calcite [38]. So high-Mg calcite is often rhombohedral [46,47]. At present, it is believed that the genesis of high-Mg calcite is mainly through biological origin [48,49,50,51] and inorganic precipitation in seawater [52]. Biogenic species include red corals [49], red coralline algae [53,54], calcareous sponges [50], sea urchin [55] and so on, and the magnesium contents of these biogenic high-Mg calcites range from 4 mol% to 45 mol% [50]. Moreover, high-Mg calcite is unstable with respect to dolomite and calcite under ambient conditions [56].

2.3. Protodolomite, Very High-Mg Calcite and Disordered Dolomite

Protodolomite, very high-Mg calcite and disordered dolomite are terms used to describe products that have near-dolomite stoichiometry (ca 40 to 50 mol% MgCO₃) in experiments. The discussion of these terms has been documented in detail in the review of Gregg et al. [38]. We endorse their view that a rhombohedral Ca-Mg carbonate mineral is dolomite if its XRD pattern does display evidence of ordering reflections. If the mineral does not show evidence of cation ordering, then it is not dolomite and is very high-Mg calcite. This view is also supported by other authors [57,58]. They think the absence of two out of the three principal ordering reflections (the XRD pattern of ideal dolomite has (101), (015) and (021) ‘ordering’ reflections) indicates the arrangement of Ca²⁺ and Mg²⁺ in the mineral crystal is not ordered, and it should belong to the calcite space group (R$\overline{3}$c) rather than the dolomite space group (R$\overline{3}$).

Over the two decades, the microbial model of dolomite formation has attracted much attention from geologists. Many scholars have carried out simulation experiments in the laboratory on the dolomite precipitation induced by microorganisms at ambient temperature and pressure [59,60,61,62,63,64,65,66]. However, Gregg et al. [38] and Kaczmarek et al. [57] reevaluated the XRD data of the experimental products of microbial-induced experiments and found that the products precipitated by microbial mediation actually lack cation ordering. Therefore, these minerals are not strictly dolomite, but calcite group minerals. They suggested that these products may be very high-Mg calcite that is close to the ideal stoichiometric composition of dolomite (Figure 3). Qiu et al. [66] also found in their experiment using halophilic archaea to mediate dolomite precipitation that XRD and SAED patterns of the products did not have the ordering characteristics of dolomite (Figure 3), and it was likely that disordered dolomite (very high-Mg calcite) formed. The experimental results of Zhang et al. [67] showed that in the presence of ~113 mg L⁻¹ of non-living biomass, disordered dolomite with ~41 and 45 mol% of MgCO₃ was precipitated in solutions with initial Mg:Ca ratios of 5:1 and 8:1, respectively. They believed that non-living biomass of the methanogen Methanosarcina barkeri can enhance the incorporation of Mg into the calcitic structure and induce the crystallization of disordered dolomite. Additionally, microbially mediated very high-Mg calcite was observed in coralline algae from Australia [53,68]. These scholars regarded the observed Ca-Mg carbonate minerals (ranging from 38 to 62 mol% MgCO₃) as ‘dolomite’ only based on the magnesium content, without considering the cation ordering. Accordingly, the Ca-Mg carbonate minerals these authors observed are probably very high-Mg calcite, not dolomite. Based on the above facts, the products of most microbially induced experiments are still strictly disordered and are more likely to be very high-Mg calcite in nature.

3. Advances in Thermodynamic Studies of Dolomite Origin

Dolomite dissolution can be expressed by the reaction:

$$\mathrm{CaMg}({\mathrm{CO}}_3{)}_2={\mathrm{Ca}}^{2+}+{\mathrm{Mg}}^{2+}+2{\mathrm{C}\mathrm{O}}_3^{2-},$$

(1)

This gives an equilibrium constant K_sp-dol defined by:

$${\mathrm{K}}_{\text{sp-dol}}={\mathrm{a}}_{{\mathrm{M}\mathrm{g}}^{2+}}{\left({\mathrm{a}}_{{\mathrm{C}\mathrm{O}}_3^{2-}}\right)}^2,$$

(2)

where K_sp-dol represents the solubility product of dolomite and ai refers to the activity of the subscripted aqueous species at equilibrium [19]. Ideally, the solubility product should be determined using a saturated solution at the desired temperature/pressure conditions [69]. However, even under highly supersaturated conditions, it is difficult to precipitate ordered, stoichiometric dolomite under standard state conditions (25 °C, 1 atm) [7,9]. Therefore, it is difficult to determine the equilibrium in solubility experiments, which makes the values of dolomite solubility products reported in the literature vary widely from 10^−16.5 to 10^−19.33 at low temperatures. For instance, Yanat’eva [13] reported a K_sp-dol value of 10^−18.37 at 25 °C, measured from dolomite dissolution experiments performed in pure water over 100 days. Garrels et al. [14] obtained a K_sp-dol value of 10^−19.33 through dolomite dissolution experiments at 25 °C and 1atm pCO₂. Hsü [15] assumed that water from the Florida Aquifer was in equilibrium with dolomite and obtained a mean K_sp-dol value of 10⁻¹⁷. Hsü [16] estimated that the stoichiometric dolomite solubility product constant under standard state was ≈10⁻¹⁷, based on modern metastable dolomites. Hardie [17] estimated that the solubility product constant of metastable Ca-rich dolomite was ≈10^−16.5. Sherman and Barak [18] performed dissolution experiments with dolomite in Ca-Mg-HCO₃/CO₃ solutions at 25 °C for 672 days and calculated a K_sp-dol value of 10^−17.2±0.2. The solubility product of dolomite was experimentally determined to be 10^−17.56~10^−26.44 at 50~253 °C using dolomite of hydrothermal origin by Bénézeth et al. [19]. They then fitted a K_sp-dol value at 25 °C of 10^{−17.19±0.3} from these experimental data. Robertson et al. [20] used groundwater methods instead of experimental methods to determine K_sp-dol. They assumed that calcite-dolomite has reached equilibrium with a large residence time in the subsurface fluid. A K_sp-dol value of 10^{−17.27±0.35} at 25 °C was then evaluated by a mixed-effects model.

Generally speaking, the direction of the reversible reaction can be determined by comparing the ion product (Q) with the solubility product constant (K_sp) [30]. The ion product is the ion concentration product under any state studied, and the expression is:

$${\mathrm{Q}}_{\mathrm{dol}}=\left[{\mathrm{Ca}}^{2+}\right] \left[{\mathrm{M}\mathrm{g}}^{2+}\right] {\left[{\mathrm{C}\mathrm{O}}_3^{2-}\right]}^2,$$

(3)

where the parentheses [x] indicate ionic concentration. The solubility product constant is the ion product in the reaction equilibrium state. When K_sp-dol = Q_dol, it is at equilibrium, and K_sp-dol is a constant under the condition of constant temperature. When Q_dol > K_sp-dol, the mineral precipitates. While Q_dol < K_sp-dol, the mineral dissolves. The ion activity product of modern seawater is 10^−15.01 [7], so modern seawater has a thermodynamic tendency to precipitate dolomite. Unfortunately, dolomite is scarce in modern environments. Accordingly, we have to consider the dolomitization of calcite and/or aragonite.

According to the second law of thermodynamics, the direction and degree of a phase transition between minerals can be described by the total entropy (the sum of the entropy of the system and the entropy of the environment) or the Gibbs free energy. Changes in natural minerals always tend to increase in total entropy or decrease in Gibbs free energy. Gibbs free energy is defined by a change in enthalpy substituted with a change in entropy multiplied by some reference temperature, as shown in the following equation:

∆G = ∆H − T∆S,

(4)

where ∆G represents Gibbs free energy change (kJ·mol⁻¹), ∆H is the enthalpy change (kJ·mol⁻¹), ∆S is the entropy change (J·mol⁻¹·K⁻¹) and T (K) is the temperature of each reaction. The change in entropy and change in enthalpy are found to determine the Gibbs free energy of a reaction because Gibbs free energy is a combination of enthalpy change and entropy change.

The change in enthalpy of the reaction in each process is defined by a change in the enthalpy of the product substituted with a change in the enthalpy of reactants as shown in the following equation:

∆H = H_products − H_reactants,

(5)

The change in the entropy of the reaction is defined by a change in the entropy of the product substituted with a change in the entropy of the reactants as shown in the following equation:

∆S = S_products − S_reactants,

(6)

Dolomitization of limestone can be expressed by the reaction:

2CaCO₃ + Mg²⁺ = CaMg(CO₃)₂ + Ca²⁺,

(7)

The reaction is reversible and the direction of the reaction is determined by the Gibbs free energy change (∆_rG°). The reaction proceeds positively when ∆_rG° < 0. The reaction proceeds in the reverse direction when ∆_rG° > 0. The thermodynamic parameters of reactants and products in dolomitization are shown in

Table 1. Thermodynamic parameters of dolomitization reactants and products in standard state (25 °C, 1 bar) as reported in the literature.

Solid Phase	∆fG° (kJ·mol−1)	∆fH° (kJ·mol−1)	S° (J·mol−1·K−1)	Reference
Dolomite	−2162.354	−2325.248	154.890	Berman [25]
	−2161.7 ± 1.1	−2324.5 ± 1.1		Hemingway and Robie [26]
	−2161.51	−2324.56	156.0	Holland and Powell [28]
	−2147.82 ± 2.2			Rock et al. [29]
	−2163.576	−2329.86	115.2	Values given in Chen et al. [30]
	−2160.9 ± 2	−2323.1 ± 2	156.9 ± 2	Bénézeth et al. [19]
Calcite	−1128.295	−1206.819	91.725	Berman [25]
	−1128.81	−1207.54	92.50	Holland and Powell [28]
	−1128.76	−1206.87	92.9	Values given in Chen et al. [30]
Aragonite	−1128.03	−1207.65	89.5	Holland and Powell [28]
Gypsum	−1797.2	−2022.2	193.8	Nordstrom [31]
ions	∆fG° (kJ·mol−1)	∆fH° (kJ·mol−1)	S° (J·mol−1·K−1)	Reference
Ca2+	−553.16	−543.45	−56.52	Shock et al. [27]
	−553.04	−542.96	−56.43	Values given in Chen et al. [30]
Mg2+	−454.29	−466.27	−138.16	Shock et al. [27]
${\mathrm{C}\mathrm{O}}_3^{2-}$	−528.34	−675.69	−50.03	Shock et al. [27]
${\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$	−587.33	−690.39	98.49	Shock et al. [27]
${\mathrm{S}\mathrm{O}}_4^{2-}$	−742.628			Nordstrom [31]
	−744.96	−910.21	18.84	Shock et al. [27]
H+	0	0	0	Shock et al. [27]
H2O(l)	−237.141	−285.83	69.95	Nordstrom [31]

Note: The ion data are the standard thermodynamic data in aqueous solution at 298.15 K; ∆_fG°, standard Gibbs free energy of formation; ∆_fH°, standard enthalpy of formation; S°, standard entropy

. Thermodynamic calculations indicate that calcite can be replaced by dolomite at ordinary temperatures because ∆_rG° < 0 (

Table 2. The change in entropy, change in enthalpy and Gibbs free energy change for the dolomitization reactions.

Reactions	∆rG1° = ∆fG°products − ∆fG°reactants (kJ·mol−1)	∆H (kJ·mol−1)	∆S (J·mol−1·K−1)	References to the Original Data
2CaCO3 + Mg2+ = CaMg(CO3)2 + Ca2+	−2.15	14.8	53.54	Bénézeth et al. [19]; Shock et al. [27]; Holland and Powell [28]; Nordstrom [31]
CaCO3 + Mg2+ = CaMg(CO3)2	−49.46	26.4	252.59
1.89CaCO3 + Mg2+ = CaMg(CO3)2 + 0.89Ca2+	−66.94	−58.04	75.6
1.75CaCO3 + Mg2+ = CaMg(CO3)2 + 0.75Ca2+	−146.06	−151.22	90.8
$3{\mathrm{CaCO}}_3\left(\mathrm{s}\right)+\mathrm{M}{\mathrm{g}}^{2+}+{\mathrm{S}\mathrm{O}}_4^{2-}$ + H+ + 2H2O = CaSO4·$2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)+\mathrm{CaMg}\left({\mathrm{CO}}_3{)}_2\right(\mathrm{s})+{\mathrm{Ca}}^{2+}+{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$	−13.808	−140.62	101.08

) for dolomitization in standard state. However, carbonate ions must present in various aquifers and Mg-rich fluids, and not just from the dissolution of calcite or aragonite, as neither calcite nor dolomite can be stable in aqueous solution if there is no dissolved carbonate in the system [70]. Obviously, it is indispensable to consider the effect of ${\mathrm{C}\mathrm{O}}_3^{2-}$or ${\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$ on the thermodynamic equilibrium. Therefore, reaction (7) may not be suitable for the real dolomitization reaction and thermodynamic equilibrium in the natural environment. Some scholars have proposed other reaction equations for dolomitization. For example, Lippmann [21] proposed a chemical formula for the formation of dolomite based on the synthesis of norsethite (BaMg(CO₃)₂) at 20 °C:

$${\mathrm{CaCO}}_3 +{\mathrm{Mg}}^{2+}+{\mathrm{C}\mathrm{O}}_3^{2-}=\mathrm{CaMg}{\left({\mathrm{CO}}_3\right)}_2,$$

(8)

The conclusion obtained by the calculation of thermodynamic parameters of reactants and products is consistent with reaction (7), however, reaction (8) requires not only the supply of magnesium but also the supply of carbonate ions. Lippmann [21] explained that the alkalinity required for this process of dolomitization may be derived from the hydrolysis connected with silicate weathering, or it may be produced from magnesium sulfate and organic matter by sulfate-reducing bacteria in buried carbonate sediments. In reaction (7), the dolomitizing fluid supplies the Mg²⁺ required and removes the Ca²⁺ released into the fluid; while in reaction (8), the dolomitizing fluid needs to supply Mg²⁺ and Ca²⁺ without removing any reaction products. In addition, the enthalpy changes in reactions (7) and (8) are 14.8 kJ·mol⁻¹ and 26.4 kJ·mol⁻¹, respectively, indicating that these two reactions are heat-absorbing and require higher temperatures to proceed spontaneously.

Morrow [23] proposed a dolomitization reaction (reaction (9)) based on the conservation of volume. This reaction is intermediate between reactions (7) and (8).

$$(2-\mathrm{x}){\mathrm{CaCO}}_3+{\mathrm{Mg}}^{2+} +\mathrm{x}{\mathrm{C}\mathrm{O}}_3^{2-}={\mathrm{CaMg}({\mathrm{CO}}_3)}_2+(1-\mathrm{x}){\mathrm{Ca}}^{2+}$$

(9)

where x = 0.11 and 0.25 for the dolomitization of aragonite and calcite, respectively. For x = 0.11 and 0.25, reaction (9) is characterized by a free energy change at equilibrium of ∆_rG° < 0 (Table 2) for dolomitization of aragonite and calcite. In addition, this reaction can reflect the degree of gain or loss of rock volume during dolomitization [23].

Recently, Wang [24] found that in pure carbonate solution, the saturation exponential model of dolomite cannot fully reflect its precipitation trend due to the inherent relationship between dolomite and calcite and their stoichiometry competition for ions Ca²⁺ and ${\mathrm{C}\mathrm{O}}_3^{2-}$. Thereby, he developed a new CDGPE (Calcite-Dolomite-Gypsum Phase Equilibrium) phase equilibrium model as shown in the following formula:

$$3{\mathrm{CaCO}}_3\left(\mathrm{s}\right)+{\mathrm{Mg}}^{2+}+{\mathrm{S}\mathrm{O}}_4^{2-}+{\mathrm{H}}^{+}+2{\mathrm{H}}_2\mathrm{O}={\mathrm{CaSO}}_4·2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)+\mathrm{CaMg}\left({\mathrm{CO}}_3{)}_2\right(\mathrm{s})+{\mathrm{Ca}}^{2+}+{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-},$$

(10)

The new model uses the phase equilibrium among calcite, dolomite and gypsum to describe the precipitation/dissolution trend of dolomite, and the Gibbs free energy change in reaction (10) is still less than zero. Reaction (10) takes the other ions in solution into account in the thermodynamic equilibrium, which is clearly closer to the natural environment than reactions (7) and (8). This model indicates that the increase in activity ratios of Mg²⁺ to Ca²⁺ and ${\mathrm{S}\mathrm{O}}_4^{2-}$ to ${\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$, as well as the more acidic condition, will promote dolomite precipitate [24]. In addition, this model has proved reliable and useful in predicting the surface water reported in dolomitization and dedolomitization (including in modern seawater) (Figure 4); Modern seawater is located in the dedolomitization zone, and the seawater of Abu Dhabi, the Mediterranean, and the Persian Gulf is located in the dolomitization zone. However, the author did not elaborate on why sulfates or gypsum are so important for dolomite precipitation. Therefore, it is necessary to further clarify the relationship between dolomite and gypsum in future studies because dolomite is often associated with gypsum in ancient strata. Undeniably, this model theoretically provides us with a new perspective on dolomite origin, but it needs to be verified by simulation experiments or natural examples in the future.

Additionally, there is a difference in the Gibbs free energy between ordered and disordered dolomite. The free energy differences due to order–disorder is sizeable, and there may be a more than 1.3 kcal/mol difference in ∆_fG° (25 °C, 1 atm) between ordered dolomite and disordered dolomite [7,17,71], which indicates a significant difference of 1.5 orders of magnitude in the solubility constant of dolomite in standard state only due to the degree of cation ordering. Accordingly, completely disordered dolomites (very high-Mg calcite) are the most soluble and least stable, but also the easiest to precipitate at ambient temperatures [7,17].

In summary, from the analysis of thermodynamic data, it can be concluded that: (1) normal seawater has a thermodynamic tendency to precipitate dolomite; (2) calcite and aragonite can be replaced by dolomite at ambient conditions; and (3) the new phase equilibrium model needs to be verified by simulation experiments or natural examples. Nevertheless, the scarcity of modern dolomite leads us to believe that dolomite precipitation may be more controlled by kinetic factors.

4. Advances in Kinetic Studies of Dolomite Origin

Based on the theory of chemical dynamics, in any reaction, not all molecules can take part in the reaction, but molecules (ions) with a certain level of energy can. These molecules are called activated molecules, and the difference between the average energy of activated molecules and the average energy of all molecules is called the activation energy. The reaction first needs to overcome the activation energy to occur. Therefore, even reactions that can proceed spontaneously according to thermodynamic principles may not occur, depending on the energy level of the reacting molecules and the magnitude of the activation energy.

Thermodynamic studies indicate that modern seawater has a thermodynamic tendency to precipitate dolomite. The widespread distribution of dolomite in ancient sedimentary strata also strongly suggests that dolomite is a stable phase in carbonate diagenesis at low temperatures and pressure [16]. However, carbonate rocks precipitated in modern normal marine environments contain little or no dolomite, even if the seawater is supersaturated with dolomite. Similarly, it has so far been difficult to precipitate/synthesize ordered stoichiometric dolomite in the laboratory at low temperatures [9,72]. Many geologists attribute this to kinetic inhibition [7,9,16,73]. To date, the main kinetic factors that inhibit the nucleation or precipitation of dolomite at low temperatures are thought to include: (1) the high hydration energy of the magnesium ion [22,45,51,66,74,75,76,77,78,79,80]; (2) the presence of sulfate (even in very low concentrations), related to the formation of complex MgSO₄⁰ [32,74,81,82]; and (3) the low activity of ${\mathrm{C}\mathrm{O}}_3^{2-}$ in most natural solutions [22,70].

4.1. Hydration of the Magnesium Ion

Lippmann [22,83] showed that the supersaturation of dolomite in seawater can last for a long time without precipitating dolomite. He suggested that this reflects the relative strength of the electrostatic bonding of Mg²⁺ to H₂O (greater than that for Ca²⁺ and ${\mathrm{C}\mathrm{O}}_3^{2-}$), i.e., the enthalpy of hydration of Mg²⁺ is greater than that of Ca²⁺ (1926 kJ/mole vs. 1579 kJ/mole). Although seawater is supersaturated with dolomite, ${\mathrm{C}\mathrm{O}}_3^{2-}$ cannot overcome the hydrated shell to bond with Mg²⁺, and Mg²⁺ is difficult to incorporate into the carbonate mineral lattice. Accordingly, sedimentologists have determined that the hydration of Mg²⁺ in seawater is an important factor in preventing dolomite precipitation [4,7,22,45,51,64,66,74,75,76,77,78,79,80,84].

In recent years, many researchers have found through experiments factors that can weaken Mg²⁺ hydration. Very high-Mg calcite with 43 mol% MgCO₃ was precipitated by Oomori and Kitano [84] at 40 °C from seawater containing dioxane and Na₂CO₃. They speculated that the presence of an organic compound reduces the dielectric constant of the solution, thus reducing the hydration of Mg²⁺ and making it easier to incorporate into the carbonate phase. Zhang et al. [75] showed that the addition of polysaccharides to a solution may help to weaken the chemical bonding between Mg²⁺ and water molecules, thereby reducing the energy barrier of desolvation of the Mg²⁺-H₂O complex and promoting the bonding of Mg²⁺ with precipitating carbonate to form very high-Mg calcite. Zhang et al. [76] determined that the addition of a small amount of dissolved sulfide also enhances the bonding of Mg²⁺ onto the growing carbonate surfaces and reduces the dehydrating energy barrier of the Mg²⁺-H₂O complex, which facilitates the precipitation of very high-Mg calcite. Liu et al. [79] demonstrated through laboratory carbonation experiments that highly negatively charged clay minerals such as illite and montmorillonite can aid the precipitation of abiotic protodolomite under ambient conditions. They speculated that Mg and Ca ions are favorably adsorbed by electrostatic force onto clay surfaces, forming metal–hydroxyl complexes and facilitating the dehydration of Mg²⁺ and Ca²⁺ (Figure 5). In addition, Fang and Xu [85] demonstrated experimentally that dissolved silica (Si(OH)₄), which has a low dipole moment and dielectric constant, can reduce the dehydration energy barrier of the Mg²⁺-H₂O complex and promote Mg²⁺ incorporation into the Ca-Mg carbonates.

In the last two decades, some microorganisms, e.g., sulfate-reducing bacteria (SRB) [86,87,88], methanogenic archaea [89,90], aerobic halophilic bacteria [78,91] and anaerobic fermentation bacteria [92], have successfully been used to synthesize Ca-Mg carbonate minerals in the laboratory, which shows that microbial activity can indeed precipitate Ca-Mg carbonate minerals (e.g., disordered dolomite or high magnesium calcite). Some scholars have proposed that the nucleation and growth of Ca-Mg carbonate minerals usually occur on cell walls and/or extracellular polymers (EPS), which not only act as nucleation sites but also facilitate the dehydration of Mg²⁺ and increase the concentration of available Mg²⁺, thereby facilitating the formation of high-Mg calcite or disordered dolomite [45,51,65,78,86,88,90,91,92,93,94]. Kenward et al. [64] and Roberts et al. [77] suggested that Mg²⁺ is complexed and dehydrated by surface-bound carboxyl groups, thereby reducing the energy required for carbonization (i.e., [Mg(H₂O)₆]²⁺ + R-COO⁻ → [Mg(H₂O)₅(R-COO)]⁺ + H₂O). Accordingly, natural surfaces with high carboxyl groups (including organic matter and microbial matter) may be a mechanism for the formation of ordered dolomite. Additionally, high-Mg calcite and very high-Mg calcite were precipitated by Liu et al. [45] from a solution containing microbially derived carboxylic acids at 25 °C. They argued that microbially derived carboxylic acids (i.e., citric acid, succinic acid) are effective in diminishing the hydration effect of Mg²⁺, thereby facilitating the incorporation of Mg²⁺ into Ca-Mg carbonate minerals.

To summarize, although Mg²⁺ hydration is an important factor hindering dolomite precipitation, it has been proved in the laboratory that there are many ways to overcome Mg²⁺ hydration and make Mg²⁺ incorporate into carbonate minerals to form high-Mg calcite or very high-Mg calcite; and very high-Mg calcite is considered to be a precursor or intermediate product in the dolomite formation [38,57], which shortens the intermediate process of dolomite formation to some extent.

4.2. Sulfate Inhibitor

It is generally believed that ${\mathrm{S}\mathrm{O}}_4^{2-}$ and Mg²⁺ in water form tight ion pairs, thus inhibiting the incorporation of Mg²⁺ into the dolomite lattice. This observation originated from Baker and Kastner’s high-temperature (200 °C) synthesis experiment [32]. Later, some scholars also agreed that the presence of sulfate can preclude the formation of dolomite because Mg²⁺ and ${\mathrm{S}\mathrm{O}}_4^{2-}$ form strong ion pairs [7,61,86,87,95,96,97,98,99,100]. To address this issue, many researchers have suggested that microbial sulfate reduction can mediate/promote dolomite formation by removing sulfate from solution and releasing magnesium ions from strong ion pairs [61,86,87,95,96,97,98,99]. The resolution of the inhibitory effect of dissolved sulfate also facilitated the proposal of the microbial model. However, Sánchez-Román et al. [101] through their culture experiments proved that it is possible to form dolomite when the sulfate concentration was as high as 56 mM. Similarly, the experimental results of Wang et al. [33] demonstrate that at high temperatures, ${\mathrm{S}\mathrm{O}}_4^{2-}$ combines with Mg²⁺ to form a tight contact ion pair (CIP). Thermochemical sulfate reduction (TSR) can remove sulfate to release Mg²⁺ and generate CO₂ (${\mathrm{C}\mathrm{O}}_3^{2-}$/${\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$), which facilitates the formation of hydrothermal dolomite; whereas at low temperatures, sulfate primarily exists as unassociated ${\mathrm{S}\mathrm{O}}_4^{2-}$, solvent-separated ion pairs and solvent-shared ion pairs, particularly in very dilute sulfate-bearing solutions (Figure 6). Therefore, they concluded that dissolved sulfate does inhibit the formation of dolomite at high temperatures due to the strong ion pairing between Mg²⁺ and ${\mathrm{S}\mathrm{O}}_4^{2-}$ but is indeed overestimated at low temperatures. It has also been noted that ${\mathrm{S}\mathrm{O}}_4^{2-}$ may even be a catalyst for dolomite precipitation [102,103], as there are numerous sulphate-rich natural environments and culture experiments that do form very high-Mg calcite and dolomite [8,61,80,86,97,104,105]. The concentration of dissolved sulfate in solution or pore water in areas where dolomite is still precipitating today is still greater than that in seawater (

Table 3. Sulfate concentration where dolomite is still precipitated today vs. seawater sulfate concentration.

Field Sites	${\mathbf{SO}}_4^{2-}$ (mM)	Reference
Early Holocene dolomite in Lake Sayram, Central Asia	16.88	Cheng et al. [8]
Hypersaline dolomitic lakes in the Coorong Region, S. Australia	100.7–589.5	Wright and Wacey [61]
Lake Jibuhulangtu Nuur, Inner Mongolia, China	117.5	Liu et al. [80]
Hypersaline coastal lagoon, Lagoa Vermelha, Brazil	41–60	Warthmann et al. [86]
Hypersaline coastal lagoon, Lagoa Vermelha, Brazil	50	Van Lith et al. [87]
Hypersaline coastal lagoon, Brejo do Espinho, Brazil	69	Van Lith et al. [87]
Pore water of slightly saline Qinghai Lake, NW China	17.9	Deng et al. [105]
Seawater	~28.125	Corzo et al. [111]
	29	Brennan et al. [112]

). Additionally, the symbiosis of dolomite and evaporite in ancient strata is common at different periods of geological history around the world [106,107,108,109,110]. This shows a close correlation between dolomite and gypsum/anhydrite. Thus, dolomitized fluids may be enriched in sulfate. In addition, the thermodynamic phase equilibrium model proposed by Wang [24] suggests that the presence of sulfate is particularly important for dolomite formation; however, this requires further study in simulation experiments and in nature.

In summary, from these current studies, it can be concluded that the removal of sulfate by microbial sulfate reduction at surface temperatures is not the key factor in inhibiting the formation of low-temperature dolomite; rather, sulfate may promote the formation of dolomite [24,102,103].

4.3. The Activity of ${CO}_3^{2-}$

Another factor inhibiting dolomite formation is the disproportionate concentrations in seawater of the component ions of dolomite. In particular, ${\mathrm{C}\mathrm{O}}_3^{2-}$ content is extremely low in comparison to the cations [22]. Lippmann [22] argued that only very few carbonate ions have enough kinetic energy to penetrate the hydration barrier due to hydrated Mg²⁺ on crystal surfaces. The microbial model suggests that the metabolic activity of microorganisms can form ${\mathrm{C}\mathrm{O}}_3^{2-}$and ${\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$ [e.g., sulfate reduction process Equation (11)], which increases the carbonate alkalinity of the surrounding environment and facilitates the formation of dolomite.

$$2{\mathrm{CH}}_2\mathrm{O}+{\mathrm{S}\mathrm{O}}_4^{2-} \to 2{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}+{\mathrm{H}}_2\mathrm{S},$$

(11)

5. Thermodynamic and Kinetic Considerations of Dolomite Nucleation and Growth

For a typical chemical reaction, it is often necessary to distinguish whether it is thermodynamically or kinetically controlled. When the reaction is controlled by kinetics, the reaction system is far from the equilibrium state, and the products are mainly in the transition state or intermediate phase, which can form easily. When the reaction is thermodynamically controlled, the reaction system has reached equilibrium and the products are mainly thermodynamically stable minerals. Thermodynamics deals with the driving force of a system moving from the initial state to the product state, whereas kinetics is concerned with the energy barriers of the specific pathways in this process [113].

Classical nucleation theory suggests that a solid phase forms within a supersaturated solution by adding an atom or a molecule to a growing cluster, whereas the non-classical nucleation theory involves the aggregation of pre-nucleation clusters of ions or primary particles before crystal formation (Figure 7) [114]. Recent studies have shown that a variety of precursor phases exist in the early stages of carbonate crystallization, including pre-nucleation clusters, metastable liquid-like precursors, mesocrystals and amorphous and nanophase precursors [114,115,116,117,118,119,120,121,122,123].

Crystal nucleation and growth are free-energy-driven phenomena and reflect solution supersaturation [121]. The interfacial free energy of the mineral with respect to its solution is a key parameter that determines its nucleation rate. Metastable phases (e.g., (very) high Mg-calcite) with relatively low interfacial free energy and activation energy form at a higher rate than the most stable phases (e.g., ideal dolomite or calcite) [124,125,126].

Previous studies have shown that dolomite precipitation or dolomitization is more likely to be controlled by kinetics. Current studies on the formation of dolomite are also gradually showing the existence of intermediate phases in the formation process [38,72,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143]. For instance, Montes-Hernandez et al. [139] proved that ordered dolomite can precipitate via simultaneous dissolution of calcite and magnesite under hydrothermal conditions (from 100 to 200 °C) (CaCO₃ + MgCO₃) → CaMg(CO₃)₂. Two kinetic steps are clearly identified: first, protodolomite formation after about 5 days of reaction; and second, protodolomite to dolomite transformation, probably produced by a coupled dissolution–recrystallization process. Montes-Hernandez et al. [140] showed that Mg-calcite precipitating at ambient temperature (Figure 8a) is quickly dissolved at higher temperatures (200~300 °C) to form dolomite and other Mg-Ca anhydrous carbonates (including protodolomite) (Figure 8b). These metastable mineral phases dissolve in turn to form new dolomite particles or nourish the existing dolomite particles by a crystal growth process. Finally, micron-sized rhombohedrally ordered dolomite particles precipitate (Figure 8c). Rodriguez-Blanco et al. [141] experimentally concluded that the crystallization of dolomite from an aqueous solution at temperatures between 60~220 °C requires three stages. In the first stage, a nanoparticulate magnesium-deficient, amorphous calcium carbonate (Mg-ACC) forms. During the second stage, the Mg-ACC partially dehydrates and orders prior to its rapid (<5 min) crystallization to non-stoichiometric protodolomite (Figure 8d,e). In stage three of the reaction, the protodolomite transforms to highly crystalline and stoichiometric dolomite spheroids on a much longer timescale (hours to days), via an Ostwald-ripening mechanism (~5–50 μm, Figure 8f), but these are made up of larger (>50 and <600 nm) and highly crystalline rhombohedral crystals (Figure 8g). Moreover, metastable very high-Mg calcite (protodolomite) can also transform into dolomite under experimental conditions. For instance, Zheng et al. [5] demonstrated that low-temperature protodolomite (very high-Mg calcite) transforms into dolomite in the absence of external fluid by dry-heating experiments (protodolomites were added into clean quartz tubes filled with ultra-pure nitrogen gas and then sealed under vacuum and heated for two months in the temperature range of 100 °C–300 °C). The superlattice reflections emerge, and the XRD reflections of protodolomite become sharper after protodolomite transforms into dolomite under dry-heating conditions. Furthermore, the products have a more stoichiometric composition (close to 50 mol% MgCO₃). The newly formed dolomite retains the spheroidal morphology but exhibits a coarser texture with larger, euhedral nanoscopic grains.

Furthermore, as mentioned in Section 4, the presence of microorganisms, exopolymeric substances (EPS), organic molecules, carboxyl and hydroxyl functional groups associated with microorganisms and organic molecules, clay minerals with negative charges and dissolved silica facilitate the formation of very high-Mg calcite, which is analogous to the reaction paths observed in high-temperature laboratory experiments. Therefore, many scholars believe that very high-Mg calcite is a key precursor mineral during dolomite formation [57,67,79,93,141]. However, this does not indicate that the subsequent conversion of very high-Mg calcite to dolomite must be under high-temperature conditions. It is possible that the process takes a long time under ambient conditions [72,132,144], but this may not be long on a geologic timescale.

The above facts indicate that metastable intermediate phases are easier to generate than thermodynamically stable dolomite during dolomite formation. In the subsequent phase transition stage, it has been suggested that the transformation of high-Mg calcite or very high-Mg calcite to dolomite can be qualitatively described by Ostwald’s step rule [126,138,141,142,143,145,146]. Ostwald’s step rule states that in the course of the transformation of an unstable or metastable system into a stable one (under earth-surface conditions), the system does not go directly to the most stable conformation, but prefers to reach intermediate stages having the closest free energy to the initial state [122], and the process is driven by the surface energy of various crystals [147]. These early-formed, very high-Mg calcites can act as the nuclei for dolomite crystallization during the later dolomitization stage [148]. Metastable intermediate phases recrystallize to ideal dolomite under certain temporal and changing environmental conditions [39]. However, the ordering process of these metastable transition phases has not been studied in detail.

In summary, dolomite nucleation and growth may be consistent with a non-classical crystallization mechanism. Dolomitization proceeds through various disordered phases. The early stage of dolomite precipitation or the dolomitization reaction may be controlled by kinetics and dominated by unstable intermediate phases. These early-formed, very high-Mg calcites transform to dolomite via an Ostwald’s step rule under certain temporal and changing environmental conditions.

6. Conclusions and Prospect

Dolomite [CaMg(CO₃)₂] is a rhombohedral carbonate mineral. The dolomite structure consists of an ordered arrangement of alternating layers of Ca²⁺ and Mg²⁺ cations interspersed with ${\mathrm{C}\mathrm{O}}_3^{2-}$ anion layers normal to the c-axis, which is in contrast to the disordered distribution of Ca²⁺ and Mg²⁺ in the (high-Mg) calcite structure.

The thermodynamic characteristics of dolomite formation indicate that modern seawater has a thermodynamic tendency to precipitate dolomite and a thermodynamic drive exists for the conversion of calcite and aragonite to dolomite. However, the latest thermodynamic models predict that modern seawater is not conducive to dolomitization, and that seawater is favorable for dolomitization in only a few regions, such as Abu Dhabi, the Mediterranean and the hypersaline lagoons in Brazil. In terms of kinetics, the presence of microorganisms, exopolymeric substances (EPS), organic molecules, carboxyl and hydroxyl functional groups associated with microorganisms and organic molecules, clay minerals with negative charges and dissolved silica facilitate the incorporation of Mg²⁺ into growing Ca-Mg carbonates. Microbial metabolic activity also favors an increase in alkalinity and, therefore, dolomite formation. We speculate that the early stage of dolomite precipitation or the dolomitization reaction may be controlled by kinetics and dominated by metastable intermediate phases, while metastable intermediate phases later transform to ordered dolomite via an Ostwald’s step rule.

Finally, since dolomite precipitation or dolomitization reactions are controlled more by kinetics, it is necessary to understand the transition states in simulation experiments and natural environments. The formation process and mechanism of the transformation from metastable high-Mg calcite to dolomite (i.e., ordering process) in low temperatures need to be further explored in the future in the existing small natural salt lakes and evaporative sea areas such as the Lagoa Vermelha lagoon in the east coast of Brazil, Abu Dhabi and in simulation experiments.