Nuclear reactions determine element abundance Is the earth homogeneous though? Is the solar system?? Is the universe???
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 R c /R a 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: c 2 =a 2 +b 2 End up with ranges of R c /R a values corresponding to different C.N.
R c /R a Expected coordination C.N. <0.15 2-fold coordination 2 0.15 Ideal triangular 3 0.15-0.22 Triangular 3 0.22 Ideal tetrahedral 4 0.22-0.41 Tetrahedral 4 0.41 Ideal octahedral 6 0.41-0.73 Octahedral 6 0.73 Ideal cubic 8 0.73-1.0 Cubic 8 1.0 Ideal dodecahedral 12 >1.0 dodecahedral 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 (SO 4 2-, NO 3-, CO 3 2- ) Mesodesmic cation-anion bond strength = ½ charge, meaning identical bond strength available for further bonding to cation or other anion
Bond strength Pauling s 2 nd Rule Bond Strength of Si = ½ the charge of O 2- Si 4+ O 2- 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 O 2- Si 4+ O 2- Si 4+
Mesodesmic subunit SiO 4 4- Each Si-O bond has strength of 1 This is ½ the charge of O 2- O 2- then can make an equivalent bond to cations or to another Si 4+ (two Si 4+ then share an O) Reason silicate can easily polymerize to form a number of different structural configurations (and why silicates are hard)
Nesosilicates SiO 4 4- Sorosilicates Si 2 O 7 6- Inosilicates (double) Si 4 O 11 6- Cyclosilicates Si 6 O 18 12- Phyllosilicates Si 2 O 5 2- Inosilicates (single) Si 2 O 6 4- Tectosilicates SiO 2 0
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.