Silicate Minerals: Pauling s s Rules and Silicate Structures February 6, 2007 Elemental Abundance in Crust Fe Ion O 2- Si 4+ Al 3+, 3+ Ca Na + K + Mg mol % 2.6 1.4 mol% x charge 4.8 3.8 2.6 1.4 3.8 Sum of Charges 62.6-125.2-125.2 4+ 21.2 84.8-40.4 3+ 6.4 19.2 21.2 16.4, 3+ -21.2-12.6-16.4-10.0 8.6-4.8-8.6 Elemental Abundance in Crust: 8 Elements Constitute 99.9% of Atoms in the Crust Fe Ion O 2-46.6 16.0 62.6 Si 27.7 28.1 21.2 Al 8.1 27.0 6.4 Al 3+, 3+ Ca Na + K + Mg % by wt 5.0 3.6 2.8 2.6 39.1 1.4 2.1 mol wt 55.8 40.1 23.0 24.3 % by mol, 3+ 6.4 2.6 Pauling s s Rules RULE 1: Every cation is surrounded by anions. The number of anions (coordination ( number) ) is determined by the ratio of ionic radii. 1
Atoms and Ions Have Different Radii Ionic Radii Relative to O 2- Element O 2- Si 4+ Al 3+ Ionic Radius (R) 1.32 0.30 0.39/0.54 R/R Oxygen 1.00 0.23 0.30/0.42 Mg Fe Fe 3+ Ca Na + K + C 4+ 0.72 0.78 0.65 1.00/1.12 1.02/1.18 1.51/1.64 0.08 0.55 0.59 0.49 3+ 0.59 0.76/0.86 0.49 0.78/0.89 1.14/1.24 0.06 Coordination Number Coordination number (CN) is the sum of the total number of anion neighbors around a central cation in a compound CN=3: Triangular CN is controlled by the ratio of radii of the ions What arrangement of ions of a given size will allow What arrangement of ions of a given size will allow them to be the most closely packed? Note that the control on the arrangement of ions (crystal structure) is controlled by size, not charge) CN can also be described by the 3D shape made by the coordinating anions 2
CN=4: Tetrahedral CN=6: Octahedral CN=8: Cubic CN=12: Hexagonal or Cubic Close Packed 3
Styrofoam Ball Investigation of Coordination Number Three sizes of styrofoam balls Exercise 1: CN of Si and O Large balls = Oxygen, Small Balls = Silicon Exercise 2: CN of Al and O Large balls = Oxygen, Medium Balls = Aluminum Exercise 3: CN of C Large balls = Carbon General Formula for Silicates Ions in silicates will be in tetrahedral, octahedral, or cubic/closest packed coordination General Formula: X m Y n (Z p O q ) W r X = 8-12 8 CN Y = 6 CN Z = 4 CN O = Oxygen W = OH, F, Cl Site Z Y X CN 4 6 8 8-12 Al 3+, Fe 3+ Fe, Mg Mn, Ti Fe Ions Si 4+, Al 3+ 3+,, Na +, Ca K +, Ba, Rb + Coordination of Common Crustal Ions Element Si 4+ Al 3+ R/R Oxygen 0.23 0.30/0.42 CN 4 4/6 Coordination with O Tetrahedral Tetrahedral/Octahedral Mg Fe Fe 3+ Ca Na + K + 0.55 0.76/0.86 0.78/0.89 1.14/1.24 6 6/8 6/8 8/12 Octahedral 0.59 6 Octahedral 3+ 0.49 6 Octahedral Octahedral/Cubic Octahedral/Cubic Cubic/Closest Mineral Formula Examples General Formula X m Y n (Z p O q ) W r Augite (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al) 2 O 6 Muscovite KAl 2 (Si 3 Al)O 10 (OH,F) 2 Plagioclase (Na,Ca)(Si,Al) 4 O 8 4
Requirements of Rule 1 Stable coordination numbers for Si and Al result in complex ions (SiO 4-4, AlO 5-4, AlO 9-6 ) 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 RULE 3: Pauling s s Rules If neighboring coordinated polyhedra (e.g., tetrahedra, octahedra) ) share edges or faces the stability of the crystal structure will decrease. Decreased distance between cations results in increased repulsion between the cations Pauling s s Rules RULE 2: Ionic Bond Strength A measure of bond strength can be calculated based on cation charge and coordination number Electrostatic Valency = Cation Charge/CN Pauling s s Rules RULE 4: Cations with high charge and small coordination number tend not to share polyhedral elements (sides and faces). A follow-up to Rule 3 5
Requirements of Rules 3 and 4 Si 4+ has a high charge 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 only Isolated Tetraheda Silicates Is there a distinct shape to the crystal lattice? take when they grow? Is there a difference in the bonds in different directions? take when they break? (Nesosilicates Nesosilicates) Isolated Tetraheda Silicates Tetrahedra do not share any oxygens with neighboring silicon ions (Nesosilicates Nesosilicates) Charge balance achieved by bonding with cations e.g., Olivine, Garnet Isolated Tetrahedra Silicates Olivine Garnet 6
Paired Silicates (Sorosilicates ( Sorosilicates) Pairs of tetrahedra share one oxygen Remaining charge e.g., Epidote Uncommon structure Ring Silicates (Cyclosilicates ( Cyclosilicates) Is there a distinct shape to the crystal lattice? take when they grow? Is there a difference in the bonds in different directions? take when they break? Ring Silicates (Cyclosilicates ( Cyclosilicates) Sets of tetrahedra share two oxygens to form a ring Remaining charge e.g., tourmaline, beryl Ring Silicates Tourmaline Beryl 7
Single-Chain Silicates (Inosilicates ( Inosilicates) Sets of tetrahedra share two oxygens to form a chain Remaining charge e.g., pyroxenes Chain Silicates: Habit Pyroxene Amphibole Double-Chain Silicates (Inosilicates Inosilicates) Sets of tetrahedra share oxygens (2 and 3 alternation) to form a chain Remaining charge e.g., amphiboles Chain Silicates: Cleavage Amphibole Cleavage (120 / 60) Pyroxene Cleavage (90) 8
Sheet Silicates (Phyllosilicates Phyllosilicates) Sets of tetrahedra share three oxygens to form a sheet Remaining charge e.g., micas, clays Sheet Silicates Biotite (Crystal) Biotite (Broken) Sheet Silicates (Phyllosilicates Phyllosilicates) Is there a distinct shape to the crystal lattice? What shape will they take when they grow? Is there a difference in the bonds in different directions? What shape will they take when they break? Framework Silicates (Tectosilicates ( Tectosilicates) Sets of tetrahedra share all 4 oxygens in 3 dimensions to form a 3-D 3 network network If all If all tetrahedra are cored by silicon then there is no charge imbalance charge imbalance e.g., quartz If some tetrahedra are cored by Al, then the remaining charge cations e.g., feldspars 9
Framework Silicates (Tectosilicates ( Tectosilicates) Is there a distinct shape to the crystal lattice? take when they grow? Is there a difference in the bonds in different directions? take when they break? Silicon Content of Silicates STRUCTURE EXAMPLE FORMULA Si:O Ratio Nesosilicates Mg 2 SiO 4 1:4 Sorosilicates Zn 4 (OH) 2 Si 2 O 7.H 2 O 1:3.5 Cyclosilicates Al 2 Be 3 Si 6 O 18 1:3 Inosilicates (Single Chain) Inosilicates (Double Chain) Phyllosilicates CaMgSi 2 O 6 Ca 2 Mg 2 (Si 4 O 11 )OH 2 Al 2 Si 4 O 10 (OH) 2 1:3 1:2.75 1:2.5 Tectosilicates SiO2 1:2 Framework Silicates Feldspar (Orthoclase) Nepheline 10