Crystal Structure of 3MgO·2CO2 Solved by Monte Carlo Simulation
Kohei WATABE, Yusuke SETO and Hiroyuki MIURA
In the thermal decomposition process of basic magnesium carbonates, hydromagnesite, 4MgCO3·Mg(OH)2·4H2O, and nesquehonite, MgCO3·3H2O, show an endothermic reaction around 500°C and an intermediate crystal phase together with an amorphous phase were obtained [1 - 7]. The chemical formula of the intermediate phase was determined to be 3MgO·2CO2 by thermogravimetry . However, the crystal structure of this intermediate phase has not been determined due to the lack of availability of single-crystal specimens suitable for structural analysis. In the present study, a Monte-Carlo-based simulation developed by Miura and Kikuchi  was employed to solve for the initial model of the crystal structure using the observed d values and the intensity data. The crystal structure was then refined by the Rietveld method.
2 Sample preparation
The intermediate phase was synthesized in two steps. In the first step, nesquehonite was synthesized using the process described by Iwai et al. . In the second step, the nesquehonite was heated from room temperature to 500°C in air with a heating rate of 30 °C/min; the sample was then removed from the electric furnace and quenched to room temperature . The powder XRD pattern of the intermediate phase was collected using a Mac Science MX-Labo diffractometer with Cu-Ka radiation (40 kV, 30 mA, 0.5° - 0.5° - 0.15 mm slit) in a step scanning mode over a 2q range of 10° - 100° in increments of 0.02° (20 seconds/step). The intensities of the XRD peaks were measured after monochromatization using pyrolytic graphite. The background due to the amorphous portion was removed in the data processing process of the diffractometer. The observed X-ray powder diffraction data were indexed by a cubic cell based on the procedure described by Sawada et al.  and a cell constant a = 8.516(13) A was obtained. The X-ray powder diffraction data of the obtained material is listed in Table 1 together with data for the intermediate phase reported by Hladky  and Sawada et al. . The observed data, which agree with the previous data, indicate that we were successful in obtaining the intermediate phase.
Table 1. X-ray diffraction data for 3MgO·2CO2
|This study||Sawada ||Hladky |
3 Structural analysis
The systematic absence, h + k + l = 2n, which was observed in the XRD data, limits the possible space groups to I23, I213, Im3, I43m, I432 and Im3m. As reported by other authors [1, 2], the recovered intermediate phase consisted of a crystalline part and an amorphous part, as shown in the SEM image (Figure 1). Both the crystalline and amorphous components were measured by energy dispersive EPMA (JEOL JSM-5310 + OXFORD -7068). Since the polished specimens were coated with carbon, the observed carbon content was not accurate. However, nearly constant O/Mg ratios were obtained indicating that the compositions of the crystalline and amorphous components are the same, 3MgO·2CO2, as determined by thermogravimetry ()Table 2. The Z-number was calculated to be 4 from the assumed specific gravity. The x, y and z coordinates of magnesium, carbon and oxygen atoms were determined using the Structure Model-Assembly Program (SMAP) developed by Miura and Kikuchi . Since it was not possible to determine the space group of the intermediate phase by systematic absence, all of these six possible space groups were examined by Monte Carlo simulation. Here, we describe the case of I43m, which yielded the best R-factor (R = |Iobs - Icalc| / Iobs). There are 12 magnesium, 8 carbon and 28 oxygen atoms in a unit cell. These atoms are assumed to occupy the following Wyckoff positions; Mg: 12d or 12e; C: 8c; O1: 24f or 24g; O2: 6b. The total number of oxygen atoms in a unit cell is 28 and the average site occupancy of oxygen was fixed at 0.933(= 28/30). The SMAP search program selects the Wyckoff positions of Mg and O1 at random, then sets the x, y, and z coordinates using a random number. The obtained structure model was then evaluated using the R-factor. The program repeats this process and the best structure model was found in which Mg and O1 atoms are located at the 12d and 24g positions respectively with R = 0.077, in 20 minutes. This structure model was used as the initial model for the Rietveld simulation.
Figure 1. Back-scattered electron image of 3MgO·2CO2 White circles show the analysis points.
Table 2. Chemical compositions of products (mol%)
Numbers indicate the analysis points shown in Figure 1.
Figure 2. Rietveld Refinement of 3MgO·2CO2
4 Structure refinement
The RIETAN-2000 program developed by Izumi and Ikeda  was used for the Rietveld refinement. The structure model obtained by employing the above-mentioned Monte Carlo search was used as the initial intermediate phase structure. The background parameters, peak shift parameters, profile parameters, cell constants, atomic coordinates, and isotropic temperature factors were optimized in the calculation. The site occupancies of O1 and O2 were fixed at 1.00 and 0.667 respectively to satisfy the bond-valence calculation described below. The final R-values for pattern fitting are Rwp = 8.89 and Rp = 6.32%. The R-values based on the intensity and structure factors are RI = 8.90% and RF = 12.23%, S = 2.28. The results of the Rietveld refinement are shown in Figure 2, and the clinographic view of the crystal structure is shown in Figure 3. The atomic coordinates and the selected bond distances are listed in Table 3 and Table 4, respectively.
Figure 3. Crystal structure of 3MgO·2CO2 drawn by VICS-II , (A)clinographic view, (B)Mg4O17block on (001) plane.
Table 3. Atomic coordinates of 3MgO·2CO2
aWyckoff positionbSite occupancy
Table 4. Selected interatomic distances(A)
|Mg Octahedra||CO3 Triangle|
|Mg-O1||2.068(3) × 4||C-O1||1.273(6) × 3|
|Mg-O2||2.129(3) × 2||Average||<1.273>|
Table 5. Bond-valence sum of 3MgO·2CO2
|O1||0.363 × 4||1.372 × 3||2.098|
|O2||0.308 × 2||1.232|
The Rietveld refinement of 3MgO·2CO2 confirmed the crystal structure obtained by the Monte Carlo simulation based on the set of d values and the intensity data. The unit cell thus determined consists of independent magnesium and carbon atoms and two independent oxygen atoms. The magnesium atom is surrounded by six oxygen atoms in an octahedral coordination. Four symmetrically identical MgO6 octahedra in an edge-sharing arrangement form an Mg4O17 block in the (100) planes of a unit cell. The Mg4O17 blocks share edges to form a framework structure. A CO3 triangle in the  direction connects three Mg4O17 blocks. Bond valence calculations, as described by Brese and O'Keeffe  and Brown  were carried out to determine the site occupancy of the oxygen atoms. The bond valence sums of the O1 and O2 atoms in the intermediate phase are 2.098 and 1.232 respectively (Table 5). These data coincide with the assumption that the site occupancies of O1 and O2 are 1.00 and 0.667 respectively. The bond-valence calculation indicates that the 3MgO·2CO2 structure model is electrochemically reasonable.
This work was financially supported by Grant-in-Aid for Scientific Research No. 17540449.
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