# The Effect of Stoichiometry, Mg-Ca Distribution, and Iron, Manganese, and Zinc Impurities on the Dolomite Order Degree: A Theoretical Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{01.5}/I

_{11.0}intensity ratios in the X-ray powder diffractograms are frequently measured to quantify dolomite cation order in dolomites. However, the intensity of diffraction peaks can be affected by factors other than the Mg-Ca distribution in the dolomite structure. The most relevant among these factors are (i) deviations from the ideal dolomite stoichiometry, and (ii) the partial substitution of Mg and Ca atoms by Fe, Mn, and Zn impurities. Using the VESTA software, we have constructed crystal structures and calculated I

_{01.5}/I

_{11.0}ratios for dolomites with Mg:Ca ratios ranging from 0.5 to 1.5, and with Fe, Mn, and Zn contents up to 30%. Our results show that both deviations from dolomite ideal stoichiometry and the presence of impurities in its structure lead to a significant decrease in I

_{01.5}/I

_{11.0}intensity ratios, an effect which must be considered when cation orders of natural dolomites from different origins are compared.

## 1. Introduction

_{3})

_{2}, is an abundant carbonate mineral with a structure characterized by a highly ordered alternation of magnesium and calcium layers along the c axis. However, at temperatures below ~100 °C, the formation of dolomites with such a high cation order cannot occur by direct precipitation from aqueous solutions, but it requires a Mg-Ca ordering process or processes after first crystallisation [1,2,3]. The investigation of both the mechanisms and kinetics of dolomite ordering process in nature first requires to accurately quantify the degree of Mg-Ca order within the dolomite structure. Since the dolomite structural order depends on the distribution of Mg and Ca cations in their corresponding crystallographic positions, the following order parameter can be defined:

_{Mg}is the occupancy factor of Mg atoms in the magnesium sublattice in the dolomite structure [4,5,6,7].

_{Mg}in the dolomite structure have a clear effect on diffraction patterns [8], the degree of the cationic order of dolomites can be conveniently evaluated from X-ray powder diffractograms. One method to proceed is to calculate the ratio of the intensities of a selected ordering peak (i.e., a Bragg reflection which only appears in the dolomite diffractograms when Mg-rich and Ca-rich alternate along the dolomite c-axis) and the nearest non-ordering peak to the selected ordering peak (i.e., a dolomite Bragg reflection not related to the Mg-Ca order) [8,9,10,11]. Ordering peaks, also known as superstructure peaks or superstructure reflections, must fulfill the following condition: h0.l and 0k.l with l odd (e.g., 00.3, 10.1, and 01.5 peaks) [12].

_{01.5}/I

_{11.0}ratio is the most frequently intensity ratio used to quantify dolomite cation order (e.g., [9,10,13,14] and references therein). Using the I

_{01.5}/I

_{11.0}ratio, researchers have not only characterized some natural dolomites, but also monitored crystallisation processes of dolomites under controlled experimental conditions [1,2,15]. Nevertheless, it is important to take into account that two main factors can affect I

_{01.5}/I

_{11.0}ratios other than Ca-Mg distribution in dolomite structure: (i) the dolomite stoichiometry, i.e., deviations from Mg:Ca = 1 ratio, and (ii) the presence of impurities, which can partially substitute Mg atoms. Therefore, an adequate use of the I

_{01.5}/I

_{11.0}ratio as dolomite order index requires to precisely quantity the effects of these factors on the intensities of dolomite diffraction peaks. Otherwise, the degree of cation order in the dolomite structure might be underestimated.

## 2. Calculation Procedure

_{01.5}/I

_{11.0}ratios were measured in the calculated diffractograms using a standard protocol that can be found elsewhere (e.g., [9,10,13,14,20,21]). This method consists in calculating the intensity I

_{01.5}/I

_{11.0}ratios by measuring peak intensities in counts, and without conducting any previous treatment of the diffractograms (e.g., Rietveld method).

## 3. Results and Discussion

#### 3.1. Stoichiometric Dolomites

_{Mg}= 1. In turn, the order degree reaches a minimum when both sites are occupied by 50% of magnesium cations and 50% of calcium cations, i.e., X

_{Mg}= 0.5. Other occupancy factors of the Mg- and Ca-sites result in intermediate order degrees.

_{Mg}= 0.5). In a different way, when the calcite R$\overline{3}$c structure is used for the calculations [18], both crystallographic sites are identical, and superstructure peaks vanish for X

_{Mg}= 0.5 (see Figure S1 in the Supporting Information).

_{01.5}/I

_{11.0}ratios, indicating a very low cation order [14,20]. However, the minimum order to distinguish between a dolomite and a VHMC, i.e., when its structure changes from an R$\overline{3}$ to an R$\overline{3}$c, has not yet been clearly defined. Taking this into account, we consider that a significant overestimation of the order indexes observed for a completely disordered dolomite will only occur for dolomites with an Mg mole fraction close to 0.5. Above that value, all dolomites will present a structure with R$\overline{3}$ space group and, therefore, superstructure peaks will be present in the diffractograms.

_{Mg}ranging from 0.5 to 1.0, I

_{01.5}/I

_{11.0}, ratios were systematically measured. These intensity ratios were found to increase nonlinearly from 0.13 to 0.53 as the X

_{Mg}increases (Figure 3a). Since intensity ratios were measured from diffractograms simulated using a dolomite structure [17], an I

_{01.5}/I

_{11.0}value of 0.13 was obtained for a completely disordered dolomite (i.e., for x

_{Mg}= 0.5). As explained above, this “residual order” for a fully disordered dolomite structure results from the symmetry constraints of the R$\overline{3}$ space group.

_{01.5}/I

_{11.0}ratios can be also related to the order parameter, s, using Equation (1). Figure 3b shows the non-linear increase of I

_{01.5}/I

_{11.0}ratio as the s parameter increases from s = 0 to s = 1. Noticeably, for the maximum value of the order parameter (s = 1), a superstructure/non-superstructure intensity ratio is not equal to one, as previously assumed in the analysis by Luth [5] of the Schultz-Güttler [11] method for quantifying the cation degree of order in dolomites. From this assumption, Luth [5] concluded that measurements of dolomite superstructure/non-superstructure intensity ratios might lead to a systematic underestimation of the s parameter. Our calculations do not support this conclusion, but they instead indicate that a precise correlation between intensity ratios and s requires a previous calibration with the experimental dolomite diffractograms.

#### 3.2. Non-Stoichiometric Dolomites

_{0.5}Mg

_{1.5}(CO

_{3})

_{2}to Ca

_{1.5}Mg

_{0.5}(CO

_{3})

_{2}. Structurally, the cation in excess can fill its corresponding sites and a fraction of the sites of the minority cation (see Figure 4a), or alternatively, Mg:Ca ratios can vary in both cation sites, while keeping the same Mg:Ca ratio of the given stoichiometry (see Figure 4b). Dolomites of both types have been found in nature, i.e., dolomites with excess of Ca atoms which fill completely its own site and a fraction of the magnesium sites [22], and dolomites with an excess of Ca atoms which occupy both magnesium and calcium sites [23].

_{01.5}/I

_{11.0}ratios in the diffractograms calculated for non-stoichiometric dolomites with x ranging from 0.5 to 1.5 in the Ca

_{2−x}Mg

_{x}(CO

_{3})

_{2}formula, and for which one of both cation sites is always fully occupied by the corresponding cation. As can be seen in this figure, deviations from the dolomite stoichiometry towards an excess of calcium have a more pronounced effect on the I

_{01.5}/I

_{11.0}ratios than in the case of an excess of magnesium in the dolomite structure. The reason for this asymmetry lies in the larger atomic scattering factor of calcium compared to that of magnesium. Thus, the intensity of the I

_{01.5}peak is more effectively reduced when calcium atoms increasingly occupy Mg-sites than in the case of magnesium atoms occupying Ca-sites. In other words, dolomite order quantified by I

_{01.5}/I

_{11.0}ratios will be more underestimated for Ca-rich dolomites than for Mg-rich dolomites.

_{01.5}/I

_{11.0}ratios can be further reduced by allowing Mg and Ca atoms to occupy both sites in different ratios, i.e., by removing the previous constraint of filling first the layer corresponding to the atom in excess. Figure 5b illustrates the effect on the I

_{01.5}/I

_{11.0}ratios when both the molar ratio of Mg atoms in Ca-sites (Mg excess region in the plot) and the molar ratio of Ca atoms in Mg-sites (Ca excess region in the plot) increase. As in the case shown in Figure 5a, the decrease in I

_{01.5}/I

_{11.0}ratios is more pronounced in the Ca-excess region of the plot.

_{01.5}/I

_{11.0}ratios will be always underestimated, i.e., the experimental value of I

_{01.5}/I

_{11.0}of a non-stoichiometric dolomite is always lower than that of a stoichiometric dolomite. Therefore, in order to precisely quantify the order of a dolomite crystal it is necessary to know first the maximum theoretical I

_{01.5}/I

_{11.0}ratio for its particular stoichiometry and Ca-Mg distribution in the two cation sites.

#### 3.3. Dolomites with Iron, Manganese, and Zinc Impurities

_{01.5}/I

_{11.0}ratios. Although cation impurities can be accommodated in both Ca- and Mg-sites, in this work, we will only analyse this effect in the case of the partial substitution of Mg

^{2+}by Fe

^{2+}, Mn

^{2+}, or Zn

^{2+}cations in the Mg-site of dolomites. Moreover, we have assumed that these dolomites fulfill the condition: (Mg+M):Ca = 1 (where M = Fe, Mn, or Zn atoms). Therefore, the general formula of the dolomites considered is Ca(Mg

_{1−x}M

_{x})(CO

_{3})

_{2}. As an example, Figure 6 shows a dolomite structure in which a 20% of the Mg-sites are occupied by Fe

^{2+}.

_{01.5}/I

_{11.0}when Fe was progressively substituted in the Mg-site up to 30%. In this compositional range, I

_{01.5}/I

_{11.0}ratios decrease from 0.53 (dolomite without iron impurities) to 0.21 (dolomite with X

_{Fe}= 0.3 in the Mg-site). A similar decrease in the dolomite cation order also occurs when Mg atoms are partially substituted by Mn and Zn impurities in the Mg-site (see Figure S2 in the Supporting Information). However, the significantly larger atomic scattering factor of the Zn atoms compare to those of Fe and Mn atoms results in a more pronounced decrease of I

_{01.5}/I

_{11.0}ratios when magnesium is gradually substituted by Zn. Thus, for X

_{Zn}= 0.3 in the Mg-site, I

_{01.5}/I

_{11.0}is only 0.14.

## 4. Conclusions

_{01.5}/I

_{11.0}intensity ratios when the amount of calcium and magnesium was varied in the Mg- and Ca-sites of a dolomite structure with Mg:Ca = 1 (i.e., an ideally stoichiometric dolomite). Similarly, when non-stoichiometric dolomites were considered (i.e., dolomites with Mg:Ca ≠1), I

_{01.5}/I

_{11.0}values decreased significantly when x was varied in the Ca

_{2−x}Mg

_{x}(CO

_{3})

_{2}dolomite formula. We found that such a decrease is more pronounced for dolomites with an excess of calcium than for dolomites with and excess of magnesium. Finally, we calculate the decrease in I

_{01.5}/I

_{11.0}intensity ratios as the Mg-site was progressively occupied by Fe, Mn, or Zn impurities up to 30%. Since both the deviations from stoichiometry and the presence of impurities result in a significant decrease in the I

_{01.5}/I

_{11.0}intensity ratios, these factors should be considered to quantify the degree of cation order of natural and experimentally produced dolomites.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Structures of stoichiometric dolomite: (

**a**) completely ordered: X

_{Mg}= 1; (

**b**) completely disordered: X

_{Mg}= 0.5. The Ca

^{2+}cations are depicted in blue, the Mg

^{2+}in orange, and the CO

_{3}

^{2−}anionic groups in black (carbon atoms) and red (oxygen atoms). The Mg:Ca ratio in each site is represented by spherical sectors with radii proportional to occupancy factors.

**Figure 3.**(

**a**) I

_{01.5}/I

_{11.0}ratio versus the molar fraction of Mg in the Mg-site, X

_{Mg}, for a stoichiometric dolomite. (

**b**) I

_{01.5}/I

_{11.0}ratio versus order parameter, s.

**Figure 4.**Non-stoichiometric dolomite structures: (

**a**) a dolomite structure in which 100% of Mg-sites and 30% of Ca-sites are occupied by magnesium atoms, while only 70% of Ca-sites are occupied by calcium atoms; (

**b**) a dolomite structure in which 90% of magnesium sites and 40% of calcium sites are occupied by magnesium atoms, while 60% of calcium sites and 10% of magnesium sites are occupied by calcium atoms. The Mg:Ca ratio in each site is represented by spherical sectors with radii proportional to occupancy factors. In both structures, the total Mg:Ca ratio is 1.3:0.7.

**Figure 5.**I

_{01.5}/I

_{11.0}versus x in the range from x = 0.5 to x = 1.5 for non-stoichiometric dolomites with formula Ca

_{2−x}Mg

_{x}(CO

_{3})

_{2}: (

**a**) variation of I

_{01.5}/I

_{11.0}by changing x in the dolomite formula while always maintaining Mg- or Ca-sites filled with the corresponding cation, as shown in Figure 5a; (

**b**) variation of I

_{01.5}/I

_{11.0}by changing Mg:Ca ratios in both Ca- and Mg-sites for a given x, as shown in Figure 5b. Numbers along the dashed vertical red lines indicate the molar fraction of the cation in excess in the site of the other cation.

**Figure 6.**Dolomite structure with 20% of iron impurities in the magnesium sites. Ca

^{2+}cations are shown in blue, Mg

^{2+}in orange, Fe

^{2+}in green, and the CO

_{3}

^{2−}anionic groups in black (carbon atoms) and red (oxygen atoms). The Fe:Mg ratio of 0.2 in the Mg-sites is represented by spherical sectors with radii proportional to the occupancy factors.

Dolomite | Calcite | |
---|---|---|

a = b (NM) | 0.4811 | 0.4988 |

c (NM) | 1.6047 | 1.7068 |

α = β (º) | 90 | 90 |

γ (º) | 120 | 120 |

S.G. | R$\overline{3}$ | R$\overline{3}$c |

Ca (X, Y, Z) | 0, 0, 0 | 0, 0, 0 |

Mg (X, Y, Z) | 0, 0, 0.5 | - |

C (X, Y, Z) | 0, 0, 0.2430 | 0, 0, 0.25 |

O (X, Y, Z) | 0.2476, 0.9650, 0.2441 | 0.257, 0, 0.25 |

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**MDPI and ACS Style**

Zvir, Y.; Pimentel, C.; Pina, C.M.
The Effect of Stoichiometry, Mg-Ca Distribution, and Iron, Manganese, and Zinc Impurities on the Dolomite Order Degree: A Theoretical Study. *Minerals* **2021**, *11*, 702.
https://doi.org/10.3390/min11070702

**AMA Style**

Zvir Y, Pimentel C, Pina CM.
The Effect of Stoichiometry, Mg-Ca Distribution, and Iron, Manganese, and Zinc Impurities on the Dolomite Order Degree: A Theoretical Study. *Minerals*. 2021; 11(7):702.
https://doi.org/10.3390/min11070702

**Chicago/Turabian Style**

Zvir, Yuliya, Carlos Pimentel, and Carlos M. Pina.
2021. "The Effect of Stoichiometry, Mg-Ca Distribution, and Iron, Manganese, and Zinc Impurities on the Dolomite Order Degree: A Theoretical Study" *Minerals* 11, no. 7: 702.
https://doi.org/10.3390/min11070702