Slide 1Slide 2Earth = anion balls with cations in the spaces…Closest PackingPauling’s Rules for ionic structuresC.N. calculationsSlide 7Slide 8Bond strength – Pauling’s 2nd RuleMesodesmic subunit – SiO44-Slide 11Slide 12Slide 13•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 oxidesClosest 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…Pauling’s Rules for ionic structures1. 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 possibleC.N. calculations•Application of pythagorean theorem: c2=a2+b2•End up with ranges of Rc/Ra values corresponding to different C.N.Rc/RaExpected coordination C.N.<0.15 2-fold coordination 20.15 Ideal triangular 30.15-0.22 Triangular 30.22 Ideal tetrahedral 40.22-0.41 Tetrahedral 40.41 Ideal octahedral 60.41-0.73 Octahedral 60.73 Ideal cubic 80.73-1.0 Cubic 81.0 Ideal dodecahedral 12>1.0 dodecahedral 12Pauling’s Rules for ionic structures2. 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 anionBond strength – Pauling’s 2nd RuleSi4+Bond Strength = 4 (charge)/4(C.N.) = 1Bond Strength of Si = ½ the charge of O2-O2- has strength (charge) to attract either anotherSi or a different cation – if it attaches to another Si, the bonds between either Si will be identicalO2-Si4+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)Nesosilicates – SiO44-Sorosilicates– Si2O76-Cyclosilicates – Si6O1812-Inosilicates (single) – Si2O64-Inosilicates (double) – Si4O116-Phyllosilicates – Si2O52-Tectosilicates – SiO20Pauling’s Rules for ionic structures3. Sharing of edges or faces by coordinating polyhedra is inherently unstable–This puts cations closer together and they will repel each otherPauling’s Rules for ionic structures4. Cations of high charge do not share anions easily with other cations due to high degree of repulsion5. 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
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