40.1 1.9 23.0 2.6 39.1 1.4 24.3 1.9 Elemental Abundance in Crust Element Ionic Radius (R) R/ROxygen O 2Si 4+
1.32 0.30 1.00 0.23 Al 3+ 0.39/0.54 0.30/0.42 Mg 2+ Fe 2+ 0.72
0.78 0.55 0.59 Fe 3+ 0.65 0.49 Ca 2+ Na + 1.00/1.12 1.02/1.18
0.76/0.86 0.78/0.89 K+ C 4+ 1.51/1.64 0.08 1.14/1.24 0.06 Atoms and Ions Have Different Radii Paulings Rules RULE
1: Around every cation, a coordination polyhedron of anions forms, in which the cation-anion distance is determined by the radius sums and the coordination number is determined by the radius ratio. Cation-Anion Distance (Ionic) Covalent Radius IS Smaller than Ionic Radius Coordination Number Coordination number (c.n.) is the sum of
the total number of neighbors of a central atom in a compound Controlled by the ratio of radii of the ions What arrangement of ions of a given size will allow them to be the most closely packed? Coordination Larger number affects ionic radii CN results in larger ionic radius CN=2: Linear Carbon Dioxide
Not important in minerals CN=3: Triangular CN=4: Tetrahedral CN=6: Octahedral CN=8: Cubic CN=12: Hexagonal or Cubic Close Packed Coordination of Common Crustal Ions
Element R/ROxygen CN Coordination with O Si 4+ 0.23 4 Tetrahedral Al 3+
0.30/0.42 4/6 Tetrahedral/Octahedral Mg 2+ 0.55 6 Octahedral Fe 2+
0.59 6 Octahedral Fe 3+ 0.49 6 Octahedral Ca 2+ 0.76/0.86
6/8 Octahedral/Cubic Na + 0.78/0.89 6/8 Octahedral/Cubic K+ 1.14/1.24
8/12 Cubic/Closest General Formula for Silicates Ions in silicates will be in tetrahedral, octahedral, or cubic/closest packed coordination General Formula: Xm Yn (Zp Oq) Wr
X = 8-12 CN Y = 6 CN Z = 4 CN O = Oxygen W = OH, F, Cl Site CN Ions Z
4 Si4+, Al3+ Y 6 Al3+, Fe3+, Fe2+, Mg2+, Mn2+, Ti2+ X 8
Na+, Ca2+ 8-12 K+, Ba2+, Rb+ Mineral Formula Examples General Formula Xm Yn (Zp Oq) Wr Augite (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)2O6 Muscovite
KAl2(Si3Al)O10(OH,F)2 Plagioclase (Na,Ca)(Si,Al)4O8 Paulings Rules RULE 2: Ionic Bond Strength An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an ion equal the charge on that ion. Electrostatic Valency = Cation Charge/CN Measure of bond strength
Requirements of Rules 1 and 2 Stable coordination numbers for Si and Al result in complex ions Si tetrahedra and Al octahedra must bond with other ions to balance negative charge Insufficient cations to balance negative charge Tetrahedra and octahedra must commonly share oxygens with other complex ions Paulings Rules RULE 3:
Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability. Maximizes distance between cations, and therefore minimizes repulsion Requirements of Rule 3 In silicates the tetrahedra will share oxygens with neighboring tetrahedra, as well as with neighboring octahedra Paulings Rules RULE 4:
In a crystal structure containing several cations, those of high valency and small coordination number tend not to share polyhedral elements. A follow-up to Rule 3 Requirements of Rules 3 and 4 Si4+ has a high valency and low coordination number (4 with oxygen), so silica tetrahedra will not share sides or faces Arrangements of silica tetrahedra must be based on the sharing of apices
Isolated Tetraheda Silicates (Nesosilicates) Tetrahedra do not share any oxygens with neighboring silicon ions Charge balance achieved by bonding with cations e.g., Olivine, Garnet, Kyanite Paired Silicates (Sorosilicates) Pairs
of tetrahedra share one oxygen Remaining charge balance achieved by bonding with cations e.g., Epidote Ring Silicates (Cyclosilicates) Sets of tetrahedra share two oxygens to form a ring Remaining charge balance achieved by bonding with cations
e.g., tourmaline, beryl Single-Chain Silicates (Inosilicates) Sets of tetrahedra share two oxygens to form a chain Remaining charge balance achieved by bonding with cations e.g., pyroxenes Double-Chain Silicates (Inosilicates) Sets
of tetrahedra share oxygens (2 and 3 alternation) to form a chain Remaining charge balance achieved by bonding with cations e.g., amphiboles Sheet Silicates (Phyllosilicates) Sets of tetrahedra share three oxygens to form a sheet Remaining charge
balance achieved by bonding with cations e.g., micas Framework Silicates (Tectosilicates) Sets of tetrahedra share all 4 oxygens in 3 dimensions to form a 3-D network If all tetrahedra are cored by silicon then there is no charge imbalance
e.g., quartz If some tetrahedra are cored by Al, then the remaining charge balance achieved by bonding with cations e.g., feldspars Silicon Content of Silicates STRUCTURE
EXAMPLE FORMULA Si:O Ratio Nesosilicates Mg2SiO4 1:4 Sorosilicates Zn4(OH)2Si2O7.H2O 1:3.5 Cyclosilicates Al2Be3Si6O18
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