Lifting Symmetries

[UncleAl]

Chemists play with symmetries.

 

Identical-radius spheres densely pack. An octahedrally coordinated metal ion is mostly spherical. Symmetric bidentate chelate ligands give chiral point group C3 three-bladed propeller molecules, with a /_-(delta) right hand screw or a /-(lambda) left hand screw. Do identical radius homochiral cations and anions give a chiral cubic lattice with only rotational symmetries?

 

Inorg. Syn. 6 186 (1960)

{Co(en)3}(3+)

en = 1,2-diaminoethane

 

Inorg. Syn. 8 204 (1966)

{Co(ox)3}(3-)

ox = oxalate dianion

 

Both complex ions occur as fully resolved optical isomers. Will the homochiral 1:1 salt be FCC/CCP close packed? Will the unit cell have its axes tilted out of cubic? Will the macroscopic crystal have interesting optical properties?

 

http://www.mazepath.com/uncleal/trisco.png

 

Trivalent ions of identical size build a strongly bonded lattice. It's a nice science project.

[Turtle]

___I'm no chemist, but I have an intimate knowledge of aspects of symmetry. Offhand, I recall 2 different arrangements for close packing identical spheres; one has the spheres in a "box" arrangement with alligned columns & rows & the other the spheres are nested. I don't have my references at hand as I'm in the middle of a move, but I seem to recall in the symmetrey of nested spheres the ratio of sphere volume to interspaces volume is 6 to 1.

___Neither do I have at hand the mathematical expression for counting the succesive layers of close packed spheres, but somewhere I have subjected the elements generated by that expression to my Katabatak analysis (reference thread "Katabatak Math..." for more on Katabataks).

___I hope I have contributed something here, or at least not detracted. :naughty: :hihi: