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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 (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  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… 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)

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

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 with neighboring ions  Charge balance achieved by bonding with cations  e.g., , 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., bonding with cations  e.g., tourmaline,

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.,

Tourmaline Beryl

Double-Chain Silicates 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.,

Amphibole Cleavage (120 / 60) 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.,

Pyroxene

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., (SiO2)  If some tetrahedra cored by Al, remaining charge balance achieved by bonding with cations Biotite () Biotite (Broken)  e.g., (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 () 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

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