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   Carbon dioxide crystals 

Cubic symmetry crystals. Left to right, cubic, cuboctahedral, octahedral and rhombic dodecahedral forms. The crystals need not be regular provided the interfacial angles are preserved, as in the cuboctahedral platelet habit.
  
















































 
We do not yet know what shapes CO2 crystals actually have in Martian clouds - but we can make reasonable predictions.

All crystals belong to one of only six symmetry systems. Water-ice in Earth's cirrus clouds, Ice Ih, has hexagonal symmetry and forms hexagonal prisms and pyramids. In contrast, solid carbon dioxide has cubic symmetry.

This does not mean that CO2 crystallizes only into microscopic cubes. Imagine walking around an enormously magnified crystal where the individual atoms are visible. They lie in very orderly rows and planes - in several particular directions there are clear avenues and pathways through the lattice. These are the directions taken up by the crystal faces. Facets running in other directions would entail an overall increased energy and disorder and would be less stable. Thus each of the six crystallogrphic symmetry systems in turn produces a limited number of precise crystal forms. A cubic symmetry lattice could give cubic, octahedral, twelve sided rhobic-dodecahedral and other more complicated crystals. Combinations of these forms can occur and so cuboctahedra, solids with six faces having the same direction as a cube and eight more that of an octahedron, might also occur. As with hexagonal water-ice, the crystals need not be regular - provided the interfacial angles stay constant. The relative sizes of the faces can change to produce a variety of habits of each form.

Microscopic CO2-ice was found as long ago as 1912 (ref 1) to have cubic, octahedral and cuboctahedral crystals and recently (ref 2) they have been rephotographed with modern techniques. All these could exist in clouds and rhombic dodecahedral crystals might also exist. Each of these crystal forms might also have flat platelet type habits - imagine the shape being made by machining down the opposite faces of a regular crystal. As with Earth's crystals, the plate habits allow even more fascinating halo possibilities!

Finally, CO2 is transparent at visible wavelengths and is much more strongly refractive than water-ice. Armed with these predictions and data it is quite possible to make accurate predictions of possible halo in Martian skies.
 
Recent electron micrographs of laboratory CO2 crystals. At top is a cuboctahedron, the lower frame shows several octahedra.  These particular crystals are less than a micron across and would not form halos and,of course, existence in the laboratory is no proof that these forms occur in clouds!
 
Ref. 1   (a) H.E. Behnken, Phys. Rev. 35, 66-73 (1912)
(b) W. Wahl, Z. Physik. Chem. 88, 129-171 (1914)
Ref. 2   (a) Wergin, W. P., J. L. Foster, A. T. C. Chang, D. K. Hall, A. Rango and E. F.Erbe. 1997. Structure of carbon dioxide crystals (Martian snow) as observed in TEM replicas and low temperature SEM images. Microsc. and Microanalysis. (suppl 2): 1235-36.     
 (b) Foster, J. L., W. P. Wergin, E. Erbe, A. T. C. Chang, and D. K. Hall. 1997.Observations and comparisons of H2O (snow) and CO2 crystals using low-temperature scanning electron microscopy. Workshop on remote sensing of planetary ices: Earth and other solid bodies. Flagstaff, AZ June.