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Crystal Structure of Fluorite

Calcium fluoride occurs naturally as the mineral fluorite.

The ionic radius of the calcium ion is 1.26 Å and that of the fluoride ion is 1.17 Å. In this case the cation is the larger ion, and the ratio of radii for the anion and cation is r-/r+ = 1.17/1.26 = 0.929. The two ions are essentially the same size; thus it makes little difference whether one talks about inserting fluoride ions into holes in a calcium ion lattice or vice versa.

With a radius ratio of 0.929 (essentially unity), the smaller ion is expected to prefer a cubic hole.

The images below depict the structure of fluorite. The light blue spheres represent the fluoride ions and the red spheres represent the calcium ions. The top two images illustrate the cubic holes occupied by calcium ions; however, these two images do not show the unit cell. The bottom two images show the fluorite unit cell.

Examine the images and note how the fluoride ions lie in a cubic arrangement. The calcium ions, which are nearly the same size as the fluoride ion, are inserted into the cubic holes in the fluoride ion array, which expands the array so that no two fluoride ions are in contact with each other. This structure is illustrated in the top two figures, which show only a portion of the fluorite unit cell.

There is a 1:1 ratio of atoms and holes in a simple cubic structure. The Ca2+ ion, however, has twice the charge of a F- ion, and thus every hole cannot be filled with a Ca2+ without violating electroneutrality. Consequently, only half of the cubic holes in fluorite are occupied by a Ca2+ ion, which results in a 2:1 ratio of F- to Ca2+ ions.

The bottom two virtual reality displays depict the actual unit cell for fluorite. Observe how the cubic hole in the exact center of the unit cell is vacant. The cubic holes situated in the center of each face, however, are occupied by a calcium ion.

Rotate the display of the unit cell and observe that the calcium ions form an expanded cubic closest-packed structure with fluoride ions occupying the tetrahedral sites. This packing is backwards from what one normally expects, which is that the larger ion would adopt the closest-packed structure and a relatively small counter-ion would locate in tetrahedral sites. In this case it is the smaller ion that forms the ccp structure so that it may existing in cubic holes formed by the larger ion. (Recall that closest-packed structures do not inherently contain cubic holes.) Thus fluorite has (8,4)-coordination.

The dimensions of the fluorite unit cell are a = b = c = 5.4626 Å.

  1. How many fluoride ions lie inside the unit cell?
  2. How many calcium ions like inside the unit cell? The structure as a whole is electrically neutral and thus the unit cell must be electrically neutral. Therefore Ca2+ and F- ions must be present in a 1:2 ratio.
  3. What is the volume of the fluorite unit cell (in cm3)?
  4. What is the density of fluorite (in g cm-3)?
  5. The measured density of naturally occuring fluorite lies in the range 3.175 to 3.184 g cm-3. How does your calculated density compare with the experimental values?
Cubic Arrangement of Fluoride Ions Portions of Atoms lying inside the Cube of Fluoride Ions

Unit Cell Portions of Atoms lying inside the Unit Cell

This virtual reality display requires Java3D. If the display is not visible, consult the Java3D FAQ. Dragging with the left mouse button rotates the display. Dragging with the center mouse buttons expands the display, and dragging with the right mouse button moves the display.

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