GAMGI Tutorials: Calcite crystalline structure

# Calcite crystalline structure

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Calcite (CaCO3) is the stable form of calcium carbonate and is one of the most widely available minerals, present in sedimentary (limestone) and metamorphic (marble) rocks. Stalactites and stalagmites in caves are usually formed by calcite.

First we create a cell with the calcite lattice parameters and space group, then one atom of Ca, C and O, to model the atoms of the structure, and finally link the cell with the atoms to build the crystal, using the Wyckoff positions reported in the literature for calcite.

A lateral view of the calcite structure, for a single conventional cell, can be seen in the figure at http://www.gamgi.org/images/screenshot10_4b.png.

### Calcite

1. Press Cell->Create and set Group to 167, the R-3c space group for calcite. As the lattice is rombohedral, System and Lattice are automatically set to h and R, respectively.
2. Set lattice parameters a and c to 4.9896 and 17.0610, respectively, the reported values for calcite. Entries b, ab, ac and bc are automatically disabled, as these parameters are known for the hexagonal system.
3. Press Atom->Create and set Style to Solid. Write Ca in the Element entry and press the mouse over the screen (outside the cell), to create a Ca atom. Repeat the task to create C and O atoms. These three atoms will act as models to create the structure.
4. Press Cell->Link and select the Crystal link method. Initially, the Wyckoff menu (in Position page) only has the option, 1 Basis 1, which is the usual crystallographic base or motif. The first "1" indicates the number of objects that will be linked to each crystallographic node, and the last "1" the point symmetry.
5. Press the mouse over the cell to identify it. The cell belongs to space group 167, so the Wyckoff menu is automatically updated to include options for all the Wyckoff positions available for this space group: 12 f 1, 6 e .2, 6 d -1, 4 c 3., 2 b -3. and 2 a 32.
6. Press the mouse over the Ca atom, to identify the atom used as a model to create the Ca atoms of the crystal.
7. According to literature, Ca atoms occupy Wyckoff positions b, so select these positions in the Wyckoff menu: 2 b -3.. For these positions, all coordinates are known in advance, so x, y and z entries are all automatically disabled.
8. Press Ok. 2 atoms of Ca are added to each node of the cell (and removed if they fall outside the cell volume).
9. Repeat the link procedure, to add the C atoms. Press the mouse first over the cell, and then over the C atom. Carbon atoms occupy positions a, so select these positions in the Wyckoff menu: 2 a 32. For these positions, all coordinates are known in advance, so x, y and z entries are all automatically disabled.
10. Press Ok. 2 atoms of C are added to each node of the cell (and removed if they fall outside the cell volume).
11. Repeat the link procedure, to add the O atoms. Press the mouse first over the cell, and then over the O atom. Select positions e, in the Wyckoff menu: 6 e .2. For these positions, only the y,z coordinates are fixed by symmetry. Enter 0.257 for x and press Ok. 6 atoms of O are added to each node of the cell (and removed if they fall outside the cell volume).
12. Select Light->Create and press Ok, to add a light and give atoms a three dimensional look.
13. The atomic structure is now created. To remove the Ca,C,O atoms used as models during the building process, press Atom->Remove and click the mouse over them.
14. The conventional rombohedral cell thus created has 30 atoms inside. For Ca: 4 x 1/6 + 4 x 1/12 (corners) + 2 x 1/3 + 2 x 1/6 (edges) + 4 (inside) = 6 atoms. For C: 4 x 1/3 + 4 x 1/6 (edges) + 4 (inside) = 6 atoms. For O: 8 x 1/2 (faces) + 14 (inside) = 18. As expected, the CaCO3 stoichiometry is obeyed.
15. Rotate,move,scale the calcite cell with the mouse. Press Atom->Measure to determine lengths and angles between atoms.

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