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 ^[1][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 ^[2][35]. The calcite crystal structure consists of alternating layers of calcium cations (Ca²⁺) and carbonate anions (CO2−3CO32−) oriented normal to the c-axis. The calcite crystal structure is of space group R3̲3¯c ^[1][22], and the unit cell of calcite is hexagonal [dimension: a = 4.9896 (Å), c = 17.0610 (Å)] ^[3][4][5][36,37,38]. The (104) reflection peak is the most intense reflection in calcite and dolomite, which corresponds to the cleavage rhombohedron planes ^[5][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 ^[6][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 ^[7][39], and the ideal dolomite crystal structure consists of alternating layers of Mg²⁺ and Ca²⁺ interspersed with CO2−3CO32− groups oriented normal to the c-axis ^[5][38]. In addition, the dolomite structure violates the c glide plane in the calcite structure, which means that dolomite has R3̲3¯ symmetry ^[1][22]. The hexagonal unit cell dimensions of dolomite are a = 4.8069 (Å), c = 16.0034 (Å) ^[8][9][40,41]. Additionally, single-crystal dolomite is often rhombohedral {101̲1¯1} and sometimes columnar {112̲2¯0} ^[8][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)] ^[10][11][12][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)] ^[13][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} ^[6][7].

Calcites containing > 4 mol% MgCO₃ are considered to be high-Mg calcite ^[5][38]. Liu et al. ^[14][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, and the (104) diffraction peak position (2θ) of high-Mg calcite is between that of dolomite and calcite ^[5][38]. So high-Mg calcite is often rhombohedral ^[15][16][46,47]. At present, it is believed that the genesis of high-Mg calcite is mainly through biological origin ^{[17][18][19][20]}[48,49,50,51] and inorganic precipitation in seawater ^[21][52]. Biogenic species include red corals ^[18][49], red coralline algae ^[22][23][53,54], calcareous sponges ^[19][50], sea urchin ^[24][55] and so on, and the magnesium contents of these biogenic high-Mg calcites range from 4 mol% to 45 mol% ^[19][50]. Moreover, high-Mg calcite is unstable with respect to dolomite and calcite under ambient conditions ^[25][56].

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. ^[5][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 ^[26][27][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 (R3¯c) rather than the dolomite space group (R3¯).

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 ^{[28][29][30][31][32][33][34][35]}[59,60,61,62,63,64,65,66]. However, Gregg et al. ^[5][38] and Kaczmarek et al. ^[26][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. Qiu et al. ^[35][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, and it was likely that disordered dolomite (very high-Mg calcite) formed. The experimental results of Zhang et al. ^[36][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. 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.