Earth anion balls with cations in the spaces View of the earth as a system of anions packed together By size and abundance Si and O are the most important If we consider anions as balls then their arrangement is one of efficient packing with smaller cations in the interstices Closest packed structures are ones in which this idea describes atomic arrangement OK for metals sulfides halides some oxides Packing Spheres and how they are put together HCP and CCP models are geometrical constructs of how tightly we can assemble spheres in a space Insertion of smaller cations into closest packed arrays yield different C N s based on how big a void is created depending on arrangement Closest Packing Coordination number C N of anions bonded to a cation larger cation higher C N Anions are much larger than most cations anion arrangements in 3 dimensions packing Hexagonal Closest Packed HCP spheres lie atop each other vertical sequence ABABAB Cubic closest packed CCP spheres fill in gaps of layer below vertical sequence ABCABC Exceptions to closest packing Body centered cubic BCC polyhedra and others Packing Coordination and C N Principle difference between hexagonal and cubic closest packing is repeat sequence ABABAB for hexagonal ABCABCABC for cubic To classify there are different types of hexagonal and cubic packed possibilities A close packed plane can yield either 3D structure depending on how it is layered and a single type of structure does not yield a single type of site more than one site with different C N is possible Which is this Pauling s Rules for ionic structures 1 Radius Ratio Principle cation anion distance can be calculated from their effective ionic radii cation coordination depends on relative radii between cations and surrounding anions Geometrical calculations reveal ideal Rc Ra ratios for selected coordination numbers Larger cation anion ratio yields higher C N as C N increases space between anions increases and larger cations can fit Stretching a polyhedra to fit a larger cation is possible C N calculations Application of pythagorean theorem c2 a2 b2 End up with ranges of Rc Ra values corresponding to different C N Rc Ra Expected coordination C N 0 15 0 15 0 15 0 22 0 22 0 22 0 41 0 41 0 41 0 73 0 73 0 73 1 0 1 0 1 0 2 fold coordination Ideal triangular Triangular Ideal tetrahedral Tetrahedral Ideal octahedral Octahedral Ideal cubic Cubic Ideal dodecahedral dodecahedral 2 3 3 4 4 6 6 8 8 12 12 Pauling s Rules for ionic structures 2 Electrostatic Valency Principle Bond strength cation valence C N Sum of bonds to a ion charge on that ion Relative bond strengths in a mineral containing 2 different ions Isodesmic all bonds have same relative strength Anisodesmic strength of one bond much stronger than others simplify much stronger part to be an anionic entity SO42 NO3 CO32 Mesodesmic cation anion bond strength charge meaning identical bond strength available for further bonding to cation or other anion Bond strength Pauling s 2nd Rule Bond Strength of Si the charge of O2 Si 4 O2 has strength charge to attract either another Si or a different cation if it attaches to another Si the bonds between either Si will be identical Bond Strength 4 charge 4 C N 1 O2 Si4 O2 Si4 Mesodesmic subunit SiO Each Si O bond has strength of 1 This is the charge of O2 O2 then can make an equivalent bond to cations or to another Si4 two Si4 then share an O Reason silicate can easily polymerize to form a number of different structural configurations and why silicates are hard 44 Nesosilicates SiO44Sorosilicates Si2O76 Cyclosilicates Si6O1812 Inosilicates single Si2O64 Inosilicates double Si4O116 Phyllosilicates Si2O52 Tectosilicates SiO20 Pauling s Rules for ionic structures 3 Sharing of edges or faces by coordinating polyhedra is inherently unstable This puts cations closer together and they will repel each other Pauling s Rules for ionic structures 4 Cations of high charge do not share anions easily with other cations due to high degree of repulsion 5 Principle of Parsimony Atomic structures tend to be composed of only a few distinct components they are simple with only a few types of ions and bonds
View Full Document
Unlocking...