# Diffraction Features from (101¯4) Calcite Twins Mimicking Crystallographic Ordering

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## Abstract

**:**

_{3}) pseudomorph after ikaite (CaCO

_{3}·6H

_{2}O), from Victoria Cave (Russia) were studied using transmission electron microscopy (TEM). This paper demonstrates the occurrence of extra reflections at positions halfway between the Bragg reflections of calcite in 0kl electron diffraction patterns and the doubling of d

_{104}spacings (corresponding to 2∙3.03 Å) in high-resolution TEM images. Interestingly, these diffraction features match with the so-called carbonate c-type reflections, which are associated with Mg and Ca ordering, a phenomenon that cannot occur in pure calcite. TEM and crystallographic analysis suggests that, in fact, (10$\overline{1}$4) calcite twins and the orientation change of CO

_{3}groups across the twin interface are responsible for the extra reflections.

## 1. Introduction

_{3}·6H

_{2}O), as a result of transformation. Glendonite is commonly associated with cold paleotemperature [8,9,10]. However, issues have been raised with regard to using it as an indicator for cold temperature [11] because, in a laboratory setting, ikaite formation was reported even above 20 °C [11,12]. Ikaite rapidly disintegrates into a mush of water and recrystallizes to calcite during slight warming or pressure release, resulting in a highly porous crystal mesh [13,14,15,16]. Aragonite (unit cell parameters a = 4.9611 Å, b = 7.9672 Å, c = 5.7404 Å; space group: Pmcn) has also been observed from ikaite transformation in marine and alkaline lake environments [17,18]. Studies on the transformation of synthetic ikaite suggest that it can also transform to amorphous calcium carbonate [19] and vaterite (unit cell parameters a = 4.13 Å, b = 7.15 Å, c = 8.48 Å; space group: Pbnm) (e.g., [20]). Macroscopic calcite pseudomorphs after ikaite are traditionally called glendonite, although other names also are used [8]. According to [11], the pseudomorph replacement of ikaite by calcite occurs through a coupled dissolution–reprecipitation mechanism at the ikaite–calcite interface. Since glendonites preserved the parent phase morphology, structural relicts indicating phase transition can be expected [21]. In fact, the TEM data here reported indicated an interesting lamellar structure with the occurrence of diffraction features that are inconsistent with ordinary calcite and that could mistakenly be associated with crystallographic ordering and superstructures.

_{3}triangular groups along the [0001] (Figure 1a). The orientation change of the carbonate groups implies a c glide that is revealed by systematic absences (l = 2n + 1 for 0kl reflections) in the corresponding reciprocal lattice (Figure 1b). In dolomite, (10$\overline{1}$4) Mg and Ca cation layers alternate along [0001]; as a result, the R$\overline{3}$c symmetry is reduced to R$\overline{3}$ and b-type reflections (l = 2n + 1 for 0kl reflections) occur (e.g., [22]). Although such b-type reflections do not occur in pure conventional calcite, they are present in a disordered phase of calcite (space group: R$\overline{3}$m) as a consequence of the rotational disorder of the CO

_{3}groups. This polymorph was reported at high temperature (>1260 K) and at high pCO

_{2}[23]. The reflections halfway between those of the a-type (l = 2n for the 0kl reflections) and b-type are the so-called c-type reflections (Figure 1c), which have been associated with ordering and attributed to various superstructures in Mg-bearing calcite and dolomite [22,24,25]. In contrast to these explanations, Larsson and Christy [5] showed that the c-type reflections can arise from submicron-sized calcite twins. Shen et al. [26] followed this explanation and demonstrated that multiple diffraction between the host dolomite and twinned Mg-calcite nano-lamellae could give rise to the c-type reflections in Ca-rich dolomite.

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. c-Type Reflections and the Twin Lattice

_{3}(Figure 2a,b). Its water content is negligible [21] and its X-ray diffraction pattern is consistent with ordinary calcite, having the unit cell parameters a = 4.989 (2) and c = 17.08 (1) (Figure 2c). However, TEM reveals that the sample has a complex nanostructure. In particular, BFTEM images taken along [01$\overline{1}$0] show linear features parallel to (10$\overline{1}$4) and indicate the occurrence of 10–15 nm size nano-domains in the calcite matrix (Figure 3a). SAED patterns of the nano-domains reveal weak c-type reflections that are incompatible with the R$\overline{3}$c space group of calcite (Figure 3b).

_{110}(5.849 Å) and d

_{2-1-1}(3.882 Å) of ikaite. In addition, the calculated angle between (110) and (2$\overline{1}\overline{1}$) is 75.7°, which is close to the measured value of 73°. However, ikaite loses its water content in vacuum within seconds; thus, it cannot be studied with TEM. Furthermore, Fourier transform infrared spectroscopy does not indicate a detectable amount (<1 wt%) of crystalline water inside the sample [21]. Similarly, the interpretation of c-type reflections with cation ordering is not viable, because both EDX and ICP-OES analysis (Figure 2) suggest that the sample does not contain a detectable amount (<1 wt%) of foreign cations.

#### 3.2. HRTEM Images of the (10$\overline{1}$4) Calcite Twins and Doubled d_{104} Spacings

_{012}spacings (3.85 Å) and they can be localized from their corresponding FFTs (Figure 4a–c). The HRTEM image (Figure 4a) obtained from the thin part also shows fringes with 3.03 Å corresponding to d

_{104}spacing. However, 6.05 Å spacing can be measured from the thicker areas (>10 nm) of the image (white lines in Figure 4a) and its corresponding FFT (Figure 4d), as well as the FFT calculated from the entire HRTEM image (Figure 4e). This d-spacing, which is also evident in Figure 5a, erroneously indicates cell doubling.

_{104}spacings (2∙3.03 Å) of the HRTEM image and the c-type reflections occurring along [104]* of the FFTs (Figure 4d,e and Figure 5b). In fact, Christy and Larson [5] have demonstrated that, by considering twins in an underlying calcite matrix, even the doubled d

_{012}corresponding to a 2∙3.85 Å spacing can be generated. Thus, the doubled d

_{104}and the d

_{012}spacings measured on the thick part (>10 nm) of the HRTEM images can be used as evidence for nanosized calcite twins.

#### 3.3. Crystal Structure of the (10$\overline{1}$4) Calcite Twins

_{3}groups and the (10$\overline{1}2)$ calcite planes across the twin interface, which agrees well with the observed features (Figure 4a and Figure 5a). Based on geometry optimizations of 2D twinned slabs, Bruno et al. [35,36] demonstrated that the twinned individuals are translated and, at the twin interface, tilting and rotation of the CO

_{3}groups occur, which gives rise to variations of the Ca−O distances. Following the construction of the twin model, the crystal structure of a (10$\overline{1}$4) stacking fault can also be generated (Figure 6b).

#### 3.4. Possible Origin of the (10$\overline{1}$4) Calcite Twins

## 4. Conclusions

_{3}(Figure 2), it turned out that the c-type reflections cannot mimic the diffraction features associated with crystallographic ordering. TEM and crystallographic analysis suggested that, in fact, twinning by reticular pseudomerohedry (twin plane: (10$\overline{1}$4); twin index: 4; obliquity: 0.74°) successfully explains these reflections (Figure 3). The twin individuals could be recognized from thin areas (~10 nm) of the HRTEM images through the direction change of the fringes corresponding to d

_{10-2}spacings (3.85Å). From the thicker part of the sample (>10 nm), the small-sized twin individual (5–10 nm) hosted in the calcite matrix and dynamically scattered electrons gave rise to double d

_{104}spacings corresponding to 2∙3.03 Å measured on HRTEM images (Figure 4 and Figure 5). Streaked c-type reflections were also observed, and they were explained by (10$\overline{1}$4) stacking faults occurring inside the small (5–15 nm wide) twin domains. It was shown that the orientation change of carbonate groups across the (10$\overline{1}$4) calcite planes (Figure 6) gave rise to the (10$\overline{1}$4) twins and stacking faults. Although in the glendonite sample Mg and Ca ordering could not occur, this phenomenon may be present in Mg-containing calcite, from which c-type reflections have been reported. This paper strongly supports (1) the interpretation of Larsson and Christy [5] associating c-type reflections with (10$\overline{1}$4) twins and with the orientation change of carbonate groups across the twin interface and (2) the final conclusion of considering the occurrence of (10$\overline{1}$4) twins before attributing c-type reflections to Mg and Ca ordering.

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Structure of calcite seen along [01$\overline{1}$0]. In order, the large blue circles and red and black dots represent Ca, O and C atoms. The (10$\overline{1}$4) plane is marked with a blue line. (

**b**) 0kl diffraction plane of R$\overline{3}$c calcite with a-type reflections (empty circles). (

**c**) 0kl diffraction plane with c-type reflections (blue dots) occurring halfway between a-type reflections.

**Figure 2.**(

**a**) BSE image and EDX data of the studied glendonite. (

**b**) Elements present in glendonite. (

**c**) X-ray powder diffraction pattern of glendonite calcite. Si standard was added for measuring the cell parameters.

**Figure 3.**(

**a**) BFTEM image of a ~10 nm size (10$\overline{1}$4) twinned domain within the calcite matrix. The areas 1 and 2, marked by white circles, are magnified in Figure 4 and Figure 5, respectively. (

**b**) The SAED pattern along [01$\overline{1}$0] obtained from a ~200 nm size region shown in (

**a**) reveals weak c-type reflections (white arrows). (

**c**) The interpretation of the SAED pattern (

**b**) via (10$\overline{1}$4) twinning. The splitting of the overlapping reflections (white squares) increases with increasing diffraction angle (white arrows). Black arrows mark reflections arising from dynamically scattered electrons of the (10$\overline{1}$4) twin hosted within a calcite matrix. (

**d**) The interpretation of the SAED pattern (

**b**) with the pseudo-orthorhombic twin cell (hk0 diffraction plane). Large-size black dots denote the reflections marked by black arrows in (

**c**).

**Figure 4.**(

**a**) HRTEM image of a ~10 nm size (10$\overline{1}$4) twinned domain within calcite along [01$\overline{1}$0] (area shown in Figure 3a with white circle 1). Blue and red lines show d

_{10-2}spacings of three polysynthetic twinned individuals. Black and white lines show single and doubled d

_{104}spacings, respectively. FFTs calculated from regions 1 (

**b**) and 2 (

**c**) correspond to twin individuals 1 and 2. (

**d**) FFT calculated from region 3 corresponds to an area where individual 2 is hosted in the calcite matrix. (

**e**) FFT calculated from the entire HRTEM image (

**a**) shows a diffraction pattern similar to inset (

**d**). Dynamically scattered electrons arising from the thick part of the sample result in reflections marked by black arrows in (

**d**) and (

**e**). The FFTs of (

**d**) and (

**e**) are interpreted with the pseudo-orthorhombic twin cell. White arrows mark the streaked reflections for (

**d**) and (

**e**), which are indicative for (10$\overline{1}$4) stacking faults.

**Figure 5.**(

**a**) HRTEM image of a ~15 nm size (10$\overline{1}$4) twin domain within calcite along [01$\overline{1}$0] (area shown in Figure 3a with white circle 2). Blue and red lines mark d

_{10-2}spacings of the twin individuals. White lines mark doubled d

_{104}spacings. (

**b**) FFT calculated from the HRTEM image (

**a**) showing c-type reflections (black arrow). The FFT is indexed according to rhombohedral calcite. The white arrow shows streaked reflections, which can indicate (10$\overline{1}$4) stacking faults.

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**MDPI and ACS Style**

Németh, P.
Diffraction Features from (101¯4) Calcite Twins Mimicking Crystallographic Ordering. *Minerals* **2021**, *11*, 720.
https://doi.org/10.3390/min11070720

**AMA Style**

Németh P.
Diffraction Features from (101¯4) Calcite Twins Mimicking Crystallographic Ordering. *Minerals*. 2021; 11(7):720.
https://doi.org/10.3390/min11070720

**Chicago/Turabian Style**

Németh, Péter.
2021. "Diffraction Features from (101¯4) Calcite Twins Mimicking Crystallographic Ordering" *Minerals* 11, no. 7: 720.
https://doi.org/10.3390/min11070720