Ionic Coordination andIonic Coordination andSilicate StructuresSilicate Structures

Lecture 4Lecture 4

Elemental Abundance in CrustElemental Abundance in Crust

ElementElement % by wt% by wt mol wtmol wt % by mol% by mol

OO 46.646.6 16.016.0 62.662.6

SiSi 27.727.7 28.128.1 21.221.2

AlAl 8.18.1 27.027.0 6.46.4

FeFe 5.05.0 55.855.8 1.91.9

CaCa 3.63.6 40.140.1 1.91.9

NaNa 2.82.8 23.023.0 2.62.6

KK 2.62.6 39.139.1 1.41.4

MgMg 2.12.1 24.324.3 1.91.9

Elemental Abundance in CrustElemental Abundance in CrustElementElement Ionic Radius (R)Ionic Radius (R) R/RR/ROxygenOxygen

O O 2-2- 1.321.32 1.001.00

Si Si 4+4+ 0.300.30 0.230.23

Al Al 3+3+ 0.39/0.540.39/0.54 0.30/0.420.30/0.42

Mg Mg 2+2+ 0.720.72 0.550.55

Fe Fe 2+2+ 0.780.78 0.590.59

Fe Fe 3+3+ 0.650.65 0.490.49

Ca Ca 2+2+ 1.00/1.121.00/1.12 0.76/0.860.76/0.86

Na Na ++ 1.02/1.181.02/1.18 0.78/0.890.78/0.89

K K ++ 1.51/1.641.51/1.64 1.14/1.241.14/1.24

C C 4+4+ 0.080.08 0.060.06

Atoms and Ions Have Different RadiiAtoms and Ions Have Different Radii

Pauling’s RulesPauling’s RulesRULE 1:RULE 1:

Around every cation, a coordination Around every cation, a coordination polyhedron of anions forms, in which polyhedron of anions forms, in which the cation-anion distance is determined the cation-anion distance is determined by the radius sums and the by the radius sums and the coordination number is determined by coordination number is determined by the radius ratio.the radius ratio.

Cation-Anion Distance (Ionic)Cation-Anion Distance (Ionic)

Covalent Radius IS Smaller than Covalent Radius IS Smaller than Ionic RadiusIonic Radius

Coordination NumberCoordination Number

Coordination numberCoordination number (c.n.) is the sum of (c.n.) is the sum of the total number of neighbors of a central the total number of neighbors of a central atom in a compound atom in a compound

Controlled by the ratio of radii of the ionsControlled by the ratio of radii of the ionsWhat arrangement of ions of a given size will What arrangement of ions of a given size will

allow them to be the most closely packed?allow them to be the most closely packed?Coordination number affects ionic radiiCoordination number affects ionic radii

Larger CN results in larger ionic radiusLarger CN results in larger ionic radius

CN=2: LinearCN=2: Linear

Not important in mineralsNot important in minerals

Carbon Dioxide

CN=3: TriangularCN=3: Triangular

CN=4: TetrahedralCN=4: Tetrahedral

CN=6: OctahedralCN=6: Octahedral

CN=8: CubicCN=8: Cubic

CN=12: Hexagonal orCN=12: Hexagonal orCubic Close PackedCubic Close Packed

Coordination of Common Crustal IonsCoordination of Common Crustal Ions

ElementElement R/RR/ROxygenOxygen CNCN Coordination with OCoordination with O

Si Si 4+4+ 0.230.23 44 TetrahedralTetrahedral

Al Al 3+3+ 0.30/0.420.30/0.42 4/64/6 Tetrahedral/OctahedralTetrahedral/Octahedral

Mg Mg 2+2+ 0.550.55 66 OctahedralOctahedral

Fe Fe 2+2+ 0.590.59 66 OctahedralOctahedral

Fe Fe 3+3+ 0.490.49 66 OctahedralOctahedral

Ca Ca 2+2+ 0.76/0.860.76/0.86 6/86/8 Octahedral/CubicOctahedral/Cubic

Na Na ++ 0.78/0.890.78/0.89 6/86/8 Octahedral/CubicOctahedral/Cubic

K K ++ 1.14/1.241.14/1.24 8/128/12 Cubic/ClosestCubic/Closest

General Formula for SilicatesGeneral Formula for Silicates

Ions in silicates will be in Ions in silicates will be in tetrahedral, octahedral, or tetrahedral, octahedral, or cubic/closest packed cubic/closest packed coordinationcoordination

General Formula:General Formula:

XXm m YYn n (Z(Zp p OOqq) W) Wrr

X = 8-12 CNX = 8-12 CN Y = 6 CNY = 6 CN Z = 4 CNZ = 4 CN O = OxygenO = Oxygen W = OH, F, ClW = OH, F, Cl

SiteSite CNCN IonsIons

ZZ 44 SiSi4+4+, Al, Al3+3+

YY 66 AlAl3+3+, Fe, Fe3+3+, , FeFe2+2+, Mg, Mg2+2+, , MnMn2+2+, Ti, Ti2+2+

XX 88 NaNa++, Ca, Ca2+2+

8-128-12 KK++, Ba, Ba2+2+, Rb, Rb++

Mineral Formula ExamplesMineral Formula Examples

General FormulaGeneral Formula

XXm m YYn n (Z(Zp p OOqq) W) Wrr

AugiteAugite(Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)(Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)22OO66

MuscoviteMuscoviteKAlKAl22(Si(Si33Al)OAl)O1010(OH,F)(OH,F)22

PlagioclasePlagioclase(Na,Ca)(Si,Al)(Na,Ca)(Si,Al)44OO88

Pauling’s RulesPauling’s Rules RULE 2: Ionic Bond StrengthRULE 2: Ionic Bond Strength

An ionic structure will be stable to the extent that An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds the sum of the strengths of the electrostatic bonds that reach an ion equal the charge on that ion. that reach an ion equal the charge on that ion. Electrostatic Valency = Cation Charge/CNElectrostatic Valency = Cation Charge/CNMeasure of bond strengthMeasure of bond strength

Requirements of Rules 1 and 2 Requirements of Rules 1 and 2

Stable coordination numbers for Si and Al Stable coordination numbers for Si and Al result in complex ionsresult in complex ions

Si tetrahedra and Al octahedra must bond Si tetrahedra and Al octahedra must bond with other ions to balance negative chargewith other ions to balance negative charge

Insufficient cations to balance negative Insufficient cations to balance negative chargecharge

Tetrahedra and octahedra must commonly Tetrahedra and octahedra must commonly share oxygens with other complex ions share oxygens with other complex ions

Pauling’s RulesPauling’s RulesRULE 3:RULE 3:

Shared edges, and particularly faces of two Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases anion polyhedra in a crystal structure decreases its stability.its stability.Maximizes distance between cations, and Maximizes distance between cations, and

therefore minimizes repulsiontherefore minimizes repulsion

Requirements of Rule 3 Requirements of Rule 3

In silicates the tetrahedra will share In silicates the tetrahedra will share oxygens with neighboring tetrahedra, as oxygens with neighboring tetrahedra, as well as with neighboring octahedrawell as with neighboring octahedra

Pauling’s RulesPauling’s RulesRULE 4:RULE 4:

In a crystal structure containing several In a crystal structure containing several cations, those of high valency and small cations, those of high valency and small coordination number tend coordination number tend notnot  to share   to share polyhedral elements.polyhedral elements.A follow-up to Rule 3A follow-up to Rule 3

Requirements of Rules 3 and 4 Requirements of Rules 3 and 4

SiSi4+4+ has a high valency and low has a high valency and low coordination number (4 with oxygen), coordination number (4 with oxygen), so silica tetrahedra will not share sides so silica tetrahedra will not share sides or facesor faces

Arrangements of silica tetrahedra must Arrangements of silica tetrahedra must be based on the sharing of apices be based on the sharing of apices

Isolated Tetraheda Silicates Isolated Tetraheda Silicates (Nesosilicates)(Nesosilicates)

Tetrahedra do not Tetrahedra do not share any oxygens share any oxygens with neighboring with neighboring silicon ionssilicon ions

Charge balance Charge balance achieved by bonding achieved by bonding with cationswith cations

e.g., Olivine, Garnet, e.g., Olivine, Garnet, KyaniteKyanite

Paired Silicates (Sorosilicates)Paired Silicates (Sorosilicates)

Pairs of tetrahedra Pairs of tetrahedra share one oxygenshare one oxygen

Remaining charge Remaining charge balance achieved by balance achieved by bonding with cationsbonding with cations

e.g., Epidotee.g., Epidote

Ring Silicates (Cyclosilicates)Ring Silicates (Cyclosilicates)

Sets of tetrahedra Sets of tetrahedra share two oxygens to share two oxygens to form a ringform a ring

Remaining charge Remaining charge balance achieved by balance achieved by bonding with cationsbonding with cations

e.g., tourmaline, beryle.g., tourmaline, beryl

Single-Chain Silicates (Inosilicates)Single-Chain Silicates (Inosilicates)

Sets of tetrahedra Sets of tetrahedra share two oxygens to share two oxygens to form a chainform a chain

Remaining charge Remaining charge balance achieved by balance achieved by bonding with cationsbonding with cations

e.g., pyroxenese.g., pyroxenes

Double-Chain Silicates Double-Chain Silicates (Inosilicates)(Inosilicates)

Sets of tetrahedra share Sets of tetrahedra share oxygens (2 and 3 oxygens (2 and 3 alternation) to form a alternation) to form a chainchain

Remaining charge Remaining charge balance achieved by balance achieved by bonding with cationsbonding with cations

e.g., amphibolese.g., amphiboles

Sheet SilicatesSheet Silicates(Phyllosilicates)(Phyllosilicates)

Sets of tetrahedra Sets of tetrahedra share three oxygens share three oxygens to form a sheetto form a sheet

Remaining charge Remaining charge balance achieved by balance achieved by bonding with cationsbonding with cations

e.g., micase.g., micas

Framework Silicates (Tectosilicates)Framework Silicates (Tectosilicates) Sets of tetrahedra share Sets of tetrahedra share

all 4 oxygens in 3 all 4 oxygens in 3 dimensions to form a 3-D dimensions to form a 3-D networknetwork

If all tetrahedra are cored If all tetrahedra are cored by silicon then there is no by silicon then there is no charge imbalancecharge imbalance e.g., quartze.g., quartz

If some tetrahedra are If some tetrahedra are cored by Al, then the cored by Al, then the remaining charge balance remaining charge balance achieved by bonding with achieved by bonding with cationscations e.g., feldsparse.g., feldspars

Silicon Content of SilicatesSilicon Content of Silicates

STRUCTURESTRUCTURE EXAMPLE FORMULAEXAMPLE FORMULA Si:O RatioSi:O Ratio

NesosilicatesNesosilicates MgMg22SiOSiO44 1:41:4

SorosilicatesSorosilicates ZnZn44(OH)(OH)22SiSi22OO77.H.H22OO 1:3.51:3.5

CyclosilicatesCyclosilicates AlAl22BeBe33SiSi66OO1818 1:31:3

Inosilicates Inosilicates (Single Chain)(Single Chain)

CaMgSiCaMgSi22OO66 1:31:3

Inosilicates Inosilicates (Double Chain)(Double Chain)

CaCa22MgMg22(Si(Si44OO1111)OH)OH22 1:2.751:2.75

PhyllosilicatesPhyllosilicates AlAl22SiSi44OO1010(OH)(OH)22 1:2.51:2.5

TectosilicatesTectosilicates SiO2SiO2 1:21:2