Nuclear reactions determine element abundance… Is the earth homogeneous though? Is the solar...
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Transcript of Nuclear reactions determine element abundance… Is the earth homogeneous though? Is the solar...
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• Nuclear reactions determine element abundance…
• Is the earth homogeneous though?
• Is the solar system??
• Is the universe???
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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
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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…
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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
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C.N. calculations
• Application of pythagorean theorem: c2=a2+b2
• End up with ranges of Rc/Ra values corresponding to different C.N.
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Rc/Ra 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
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Pauling’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 (SO4
2-, NO3-, CO3
2-)• Mesodesmic – cation-anion bond strength =
½ charge, meaning identical bond strength available for further bonding to cation or other anion
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Bond strength – Pauling’s 2nd Rule
Si4+
Bond Strength = 4 (charge)/4(C.N.) = 1
Bond 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 identical
O2-Si4+ Si4+O2-
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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)
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Nesosilicates – SiO4
4-
Sorosilicates– Si2O7
6-
Cyclosilicates – Si6O18
12-
Inosilicates (single) – Si2O6
4-
Inosilicates (double) – Si4O11
6-
Phyllosilicates – Si2O5
2-
Tectosilicates – SiO2
0
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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
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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.