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… They are going to do a lab on this Need picture of hexagonal and cubic close packing (Box 13.1) – or better yet a physical model to have in class Discuss exceptions – try to get discussion going of what causes problems – refer to figure 13.2 (get in here somewhere) to guide it towards sizes and then recognize that CCP and HCP structures have only tetragonal and octahedral sites. Many silicates have polyhedral sequences are more complicated stacked structures which we will discuss in more detail later.

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 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 Discuss who Linus Pauling was… First to integrate quantum mechanics (wait to now to tell them the orbitals discussed earlier was quantum mechanics) and x-ray diffraction (study of how X-rays interact with repeating structures of minerals). Won 2 nobels – chemistry and peace! For Radius ratio principle – just discussed ionic radii Bigger cations – more room to put ions around it… Thought exercise – stretching a polyhedra – space between cations and anions increases  larger cations will fit and C.N. would increase. Oppose this to the other direction – can you compress the polyhedra? High P – would you expect the anions to get smaller and lower the Rc/Ra?  would metamorphic minerals then exhibit lower c.n.? This would require that the anions themselves compress  difference between distorting the structure (easy with higher P) and making the ions themselves smaller (very difficult) and additionally making them change size at different rates relative to one another. Therefore, metamorphic minerals exhibit more distortion, which raises the C.N.!! Garnet a common example – dodecahedral mineral - bring one in for discussion!

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 2-fold coordination 2 0.15 Ideal triangular 3 0.15-0.22 Triangular 0.22 Ideal tetrahedral 4 0.22-0.41 Tetrahedral 0.41 Ideal octahedral 6 0.41-0.73 Octahedral 0.73 Ideal cubic 8 0.73-1.0 Cubic 1.0 Ideal dodecahedral 12 >1.0 dodecahedral

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 = ½ charge, meaning identical bond strength available for further bonding to cation or other anion

Bond strength – Pauling’s 2nd Rule Si4+ Bond Strength of Si = ½ the charge of O2- 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-

Mesodesmic subunit – SiO44- Each Si-O bond has strength of 1 This is ½ 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) SiO44- -piz orbitals – add picture of tetrahedra filled in (mesh?) Discuss why they are hard – strong and equivalent bonds, no zone of weakness Compare to a mineral like muscovite, which has very weak bonds

Nesosilicates – SiO44- Inosilicates (double) – Si4O116- Sorosilicates Phyllosilicates – Si2O52- Cyclosilicates – Si6O1812- Picture of structure of 6 major types of silicates- Klein has one I think – not for painful detail at this point – in later section on silicate minerals we will get into this Inosilicates (single) – Si2O64- 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 Need picture of a tetraheda to illustrate this sharing princliple – after figure 13.13

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.