Mineralogists, I always thought that it was impossible to fill all the tetrahedral sites in a close-packed array since this violates one of Pauling's rules about sharing of polyhedral elements. However, the fluorite structure is described in precisely this manner: "The fluorite structure can be generated by starting with a FCC lattice of cations (A) and filling all of the tetrahedral holes with anions (X)" (https://chemistry.osu.edu/~woodward/ch754/struct/CaF2.htm). Does this rule only apply when CATIONS are placed in tetrahedral sites? Does the charge of the tetrahedral anion matter here...i.e., F- has a small charge so its OK to fill all the tet sites, but this wouldn't happen if the anions had a larger negative charge. ?? Thanks for your help. - Kent Ratajeski ------------ Kent Ratajeski, Ph.D. 301 Slone Research Building Department of Earth and Environmental Sciences University of Kentucky Lexington, KY 40506-0053 Phone: 859-257-4444 Fax: 859-323-1938 http://www.as.uky.edu/users/krata2

Kent, if a student would come up with this question I would argue that the cations form a CCP sub-lattice, but they are not close-packed, because they are separated from each other by the larger anions. I do not know any Pauling Rule that opposes the presence of the anions (or cations, respectively) in all tetrahedral sites if there is enough space. The fluorite structure works with oxygen as well, Uraninite is a prominent example. Ralf > > Mineralogists, > > I always thought that it was impossible to fill all the tetrahedral sites > in a close-packed array since this violates one of Pauling's rules about > sharing of polyhedral elements. However, the fluorite structure is > described in precisely this manner: "The fluorite structure can be > generated by starting with a FCC lattice of cations (A) and filling all of > the tetrahedral holes with anions (X)" > (https://chemistry.osu.edu/~woodward/ch754/struct/CaF2.htm). > > Does this rule only apply when CATIONS are placed in tetrahedral sites? > Does the charge of the tetrahedral anion matter here...i.e., F- has a > small charge so its OK to fill all the tet sites, but this wouldn't happen > if the anions had a larger negative charge. ?? > > Thanks for your help. > > - Kent Ratajeski > > ------------ > Kent Ratajeski, Ph.D. > 301 Slone Research Building > Department of Earth and Environmental Sciences > University of Kentucky > Lexington, KY 40506-0053 > > Phone: 859-257-4444 > Fax: 859-323-1938 > http://www.as.uky.edu/users/krata2 > _______________________________________________ > MSA-talk mailing list > MSA-talk@minlists.org > http://lists.minlists.org/mailman/listinfo/msa-talk >

Kent, The ccp-hcp-mixed cp paradigm works well for alloys, etc., where electrostatic repulsion is not an issue and, on the contrary, where atoms are sharing electrons. When applied to structures with significant ionic bonding, you obviously need to take repulsion into account because you cannot have two chlorine atoms in halite, for example, sitting snugly next to each other as they would be in a truly close-packed arrangement (i.e., in the halite "ccp" they are about 4 A away vs. 2 x IR = 3.6 A). In native copper, this distance is 2.56 A, i.e. slightly less than twice the covalent radius of Cu (1.35 A). Incidentally, there are many ionic hcp structures where anions are where they are supposed to be and cations occupy ALL tetrahedral interstices - for example, alkali oxides and chalcogenides (Li2O, Na2S, etc.) - they are often referred to as "antifluorites". Anton R. Chakhmouradian University of Manitoba -----Original Message----- From: msa-talk-bounces@minlists.org [mailto:msa-talk-bounces@minlists.org] On Behalf Of Ratajeski, Kent Sent: Friday, February 05, 2016 9:57 AM To: msa-talk@minlists.org Subject: [MSA-talk] fluorite structure and Pauling's Rules Mineralogists, I always thought that it was impossible to fill all the tetrahedral sites in a close-packed array since this violates one of Pauling's rules about sharing of polyhedral elements. However, the fluorite structure is described in precisely this manner: "The fluorite structure can be generated by starting with a FCC lattice of cations (A) and filling all of the tetrahedral holes with anions (X)" (https://chemistry.osu.edu/~woodward/ch754/struct/CaF2.htm). Does this rule only apply when CATIONS are placed in tetrahedral sites? Does the charge of the tetrahedral anion matter here...i.e., F- has a small charge so its OK to fill all the tet sites, but this wouldn't happen if the anions had a larger negative charge. ?? Thanks for your help. - Kent Ratajeski ------------ Kent Ratajeski, Ph.D. 301 Slone Research Building Department of Earth and Environmental Sciences University of Kentucky Lexington, KY 40506-0053 Phone: 859-257-4444 Fax: 859-323-1938 http://www.as.uky.edu/users/krata2 _______________________________________________ MSA-talk mailing list MSA-talk@minlists.org http://lists.minlists.org/mailman/listinfo/msa-talk

Kent and Ralf: Its a snowy day in southern New England, everything is shut down, and Kent's observations and questions make for some interesting fireside discussion. Probably best to begin with description of the fluorite structure in terms of its space group (F 4/m -3 2/m) - or simply fcc lattice, and a unit cell consisting of Ca4F8, with Ca (2+) on site 4a @ (0, 0, 0) + F-centering and 2F(1-) site 8a @ +/-( ¼, ¼, ¼). So, Ca is on the lattice points at the corners of the cell and centers of faces (4 per cell) , and F occupies all 8 of the tetrahedral sites. This is the fundamental description, although it can be a little abstract. Here's is where I pitch using CrystalMaker for visualization. Students can look at whole structure, but is can be useful to look at pattern of cations alone - its fcc, or look at anions alone - it simple cubic. An alternate description of the fluorite structure is an 8-cell simple cubic superlattice (we often do this to better visualize spinel structure) with F(1-) on on the supercell lattice points (there are 8 of them) and with ½ of the 8 body-center sites occupied by Ca(2+) - Ca4F8. Now it is obvious that Ca(2+) is VIII-coordinated with F(1-). (I have intentionally avoided using the terms "cation sub lattice" and "anion sublattice"! They might be called "cation- or anion-substructures" or better, fcc cation array and simple cubic anion array, but I rant). Pauling focused on cation-anion polyhedra, consisting of a cation at the center, surrounded by anions at the corners. Cations and anions "touch" - that is the "bond length" we can measure in a structure (Paulings 1st rule), whereas electrostatic repulsion separates adjacent anions . Polyhedral frame structures are built by linking polydedra through their anions at the corners. Note that while each F(1-) is bonded to 4 Ca(2+), each Ca(2+) is bonded to 8 F(1-). The resulting CaF8(4-) cubes are Pauling's polyhedra and linking through adjacent corners, they share 8 of 12 edges. This arrangement balances the charge of the anion by those of first neighbor cations - Pauling's 2nd rule. It is unfortunate that Pauling's "Rules" are called "rules, as they were originally devised as a set of generalizations that Pauling applied successively to "guess" the most likely starting structure for refinement. In an era when a Reitveld refined structure is obtained from a powder XRD scan with the click of a mouse, it's hard to imagine the tedious effort involved in refining a structure from intensities estimated from photographs and tables of transcendental functions, calculating structure factors etc with an adding machine. Time to put another log in the fire. Ray On 2/5/2016 11:35 AM, Ralf Milke wrote: > Kent, > > if a student would come up with this question I would argue that the > cations form a CCP sub-lattice, but they are not close-packed, because > they are separated from each other by the larger anions. I do not know any > Pauling Rule that opposes the presence of the anions (or cations, > respectively) in all tetrahedral sites if there is enough space. > > The fluorite structure works with oxygen as well, Uraninite is a prominent > example. > > Ralf > > >> Mineralogists, >> >> I always thought that it was impossible to fill all the tetrahedral sites >> in a close-packed array since this violates one of Pauling's rules about >> sharing of polyhedral elements. However, the fluorite structure is >> described in precisely this manner: "The fluorite structure can be >> generated by starting with a FCC lattice of cations (A) and filling all of >> the tetrahedral holes with anions (X)" >> (https://chemistry.osu.edu/~woodward/ch754/struct/CaF2.htm). >> >> Does this rule only apply when CATIONS are placed in tetrahedral sites? >> Does the charge of the tetrahedral anion matter here...i.e., F- has a >> small charge so its OK to fill all the tet sites, but this wouldn't happen >> if the anions had a larger negative charge. ?? >> >> Thanks for your help. >> >> - Kent Ratajeski >> >> ------------ >> Kent Ratajeski, Ph.D. >> 301 Slone Research Building >> Department of Earth and Environmental Sciences >> University of Kentucky >> Lexington, KY 40506-0053 >> >> Phone: 859-257-4444 >> Fax: 859-323-1938 >> http://www.as.uky.edu/users/krata2 >> _______________________________________________ >> MSA-talk mailing list >> MSA-talk@minlists.org >> http://lists.minlists.org/mailman/listinfo/msa-talk >> > > _______________________________________________ > MSA-talk mailing list > MSA-talk@minlists.org > http://lists.minlists.org/mailman/listinfo/msa-talk -- Ray Joesten Professor Emeritus Chemistry and Geoscience Email: joesten@uconn.edu Department of Chemistry Center for Integrative Geosciences 55 North Eagleville Rd U-3060 354 Mansfield Road U-2045 University of Connecticut University of Connecticut Storrs, CT 06269-3060 Storrs, CT 06269-2045