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Coordination Number Determined by Radius Ratio

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Coordination Number Determined by Radius Ratio Coordination and Silicate Structures Pauling’s Rules A coordination polyhedron of anions forms around a cation Ionic Coordination and Ionic distance determined by radii Silicate Structures Coordination number determined by radius ratio. May result in a complex ion Atoms and Ions Have Different Radii Elemental Abundance in Crust Element Ionic Radius (R) R/ROxygen O 2- 1.32 1.00 Si 4+ 0.30 0.23 Al 3+ 0.39/0.54 0.30/0.42 Mg 2+ 0.72 0.55 Fe 2+ 0.78 0.59 Fe 3+ 0.65 0.49 Ca 2+ 1.00/1.12 0.76/0.86 Na + 1.02/1.18 0.78/0.89 K + 1.51/1.64 1.14/1.24 C 4+ 0.08 0.06 1 Coordination and Silicate Structures Styrofoam Ball Investigation of Coordination Number Coordination Number Coordination number: total number of neighbors around a central atom Four sizes of styrofoam balls Exercise 1: CN of Si and O Element Ionic R/ROxygen Largest = O, Smallest = Si Radius Controlled by (R) ratio of ionic radii Exercise 2: CN of Fe and O O 2- 1.32 1.00 Largest = O, Medium = Al Si 4+ 0.30 0.23 Arranged for Fe 2+ 0.78 0.59 closest packing Exercise 3: CN of Ca and O Largest balls = O, Large = Ca Ca 2+ 1.12 0.85 CN=4: Tetrahedral CN=6: Octahedral 2 Coordination and Silicate Structures CN=12: Hexagonal or CN=8: Cubic Cubic Close Packed Coordination of Common Crustal Ions General Formula for Silicates Element R/R CN Coordination with O Ions in silicates… Oxygen tetrahedral, octahedral, Si 4+ 0.23 4 Tetrahedral or cubic/closest packed Site CN Ions 3+ Al 0.30/0.42 4/6 Tetrahedral/Octahedral coordination Z 4 Si4+, Al3+ Mg 2+ 0.55 6 Octahedral Y 6 Al3+, Fe3+, General Formula: Fe 2+ 0.59 6 Octahedral Fe2+, Mg2+, Xm Yn (Zp Oq) Wr 2+ 2+ 3+ Mn , Ti Fe 0.49 6 Octahedral X = Cubic/Closest X 8 Na+, Ca2+ Ca 2+ 0.76/0.86 6/8 Octahedral/Cubic Y = Octahedral + 2+ + Na + 0.78/0.89 6/8 Octahedral/Cubic Z = Tetrahedral 8-12 K , Ba , Rb O = Oxygen + K 1.14/1.24 8/12 Cubic/Closest W = OH, F, Cl 3 Coordination and Silicate Structures Mineral Formula Examples Requirements of Pauling’s Rules General Formula Stable coordination numbers for Si 4- Xm Yn (Zp Oq) Wr produces complex anion (SiO4) Augite 4- (SiO4) must bond to balance charge (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)2O6 Insufficient cations Muscovite KAl2(Si3Al)O10(OH,F)2 Tetrahedra commonly bond with other Plagioclase complex anions (Na,Ca)(Si,Al)4O8 Pauling’s Rules Requirements of Pauling’s Rules Shared edges or faces of polyhedra decrease stability. Si4+ has high charge and low coordination The closer the cations… the greater the number repulsion Silica tetrahedra will not share sides or faces The higher the cation charge… the greater the repulsion Arrangements of silica tetrahedra based on sharing of apices 4 Coordination and Silicate Structures Isolated Tetraheda Silicates Isolated Tetrahedra Silicates (Nesosilicates) Tetrahedra do not share any oxygens with neighboring silicon ions Charge balance achieved by bonding with cations e.g., Olivine, Garnet, Kyanite Olivine Garnet Paired Silicates (Sorosilicates) Ring Silicates (Cyclosilicates) Pairs of tetrahedra Sets of tetrahedra share one oxygen share two oxygens to Remaining charge form a ring balance achieved by Remaining charge bonding with cations balance achieved by e.g., Epidote bonding with cations e.g., tourmaline, beryl 5 Coordination and Silicate Structures Ring Silicates 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 Tourmaline Beryl Double-Chain Silicates Chain Silicates: Cleavage (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 Amphibole Cleavage (120 / 60) Pyroxene Cleavage (90) 6 Coordination and Silicate Structures Sheet Silicates Chain Silicates: Habit (Phyllosilicates) Sets of tetrahedra share three oxygens to form a sheet Remaining charge balance achieved by bonding with cations e.g., micas Pyroxene Amphibole Sheet Silicates Framework Silicates (Tectosilicates) Tetrahedra share all 4 oxygens to form a 3-D network If all tetrahedra cored by silicon then no charge imbalance e.g., quartz (SiO2) If some tetrahedra cored by Al, remaining charge balance achieved by bonding with cations Biotite (Crystal) Biotite (Broken) e.g., feldspar (NaAlSi3O8 ) 7 Coordination and Silicate Structures Silicon Content of Silicates Framework Silicates STRUCTURE EXAMPLE FORMULA Si:O Ratio Nesosilicates Mg2SiO4 1:4 Sorosilicates Zn4(OH)2Si2O7.H2O 1:3.5 Cyclosilicates Al2Be3Si6O18 1:3 Inosilicates CaMgSi2O6 1:3 (Single Chain) Inosilicates Ca2Mg2(Si4O11)OH2 1:2.75 (Double Chain) Phyllosilicates Al Si O (OH) 1:2.5 Feldspar (Orthoclase) Nepheline 2 4 10 2 Tectosilicates SiO2 1:2 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 8 .
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