Introduction to MineralogyDr. Tark Hamilton

Chapter 4: Lecture 12The Chemical Basis of Minerals

(Pauling’s Rules)

Camosun College GEOS 250

Lectures: 9:30-10:20 M T Th F300

Lab: 9:30-12:20 W F300

Pauling’s Rules

• 1: Coordination Principle: all ions in polyhedra• 2: Electrostatic Valency Principle: Σ bonds = charge• 3: Sharing of Polyhedral Elements decreases

stability (e.g. corners OK, edges rare or faces empty)

• 4: Hi valence & Low C.N. Cations don’t share• 5: Principle of Parsimony (few geometries, common

environments, high symmetry)

Pauling Rule 2: Electrostatic Valency Principle ("Bond Strength")

• "In a stable ionic structure the charge on an ion is balanced by the sum of electrostatic bond strengths to the ions in its coordination polyhedron"

• i.e. A stable ionic structure must be arranged to preserve Local Electroneutrality

• (Ions in a crystal are surrounded by ions of opposite charge so as not to produce large volumes of similar charge in the crystal - this maximizes Madelung potential!)

• Ion-ion or ion-radical all the same or unstable

2: Bond Strength (e.v.) = Z+ / C.N.

Na+ or F- in NaClC.N. = 6, e.v. = 1

Ca+2 in CaF2

C.N. = 8, e.v. = 2

F- in CaF2

C.N. = 4, e.v. = 1

Octahedrale.b.s. = 1/6

Cubice.b.s. = 2/8 = ¼

Tetrahedrale.b.s. = ¼

Only 1 Bond Strength

• Uniform Bond Strength – Isodesmic crystals• NaCl Chloride all bonds = 1 (ordinary ionic crystal implied,

but preference for C.N.=6 due to Cl- ‘s 3 normal p-orbitals.)

• MgAl2O4 Aluminate, FeCr2O4 Chromrate (mol. radicals?)

• Spinels: AB2O4 Radicals or Isodesmic?

• Mg+2 or Fe2+ , tetrahedral, 2/4 = ½• Al+3 or Cr+3 , octahedral, 3/6 = ½• So isodesmic and no radicals!• Different I.R. & valence made up for by varying C.N.• 1 bond strength = 1 uniform energy level throughout

Unequal Bond Strengths• Small highly charged cations form radicals with

larger low valence anions, Anisodesmic• (CO3)-2 , (NO3)- , (PO4)-3 , (SO4)-2 , (WO4)-2

• C+4 in Carbonate is 3 C.N. so bond is 4/3 = 1.33• N+5 in Nitrate is 3 C.N. so bond is 5/3 = 1.67• S+6 in Sulphate is 4 C.N. so bond is 6/4 = 1.5• These are more than half of O-2 valence, so O in

these groups is more tightly bonded than to Cations• Oxygens much more tightly bonded to core atom

(C,N,S,P, W, V, Cr…) than to surrounding cations• These molecular radicals usually persist through

melting, decrepitation or mineral-chemical reactions• Carbonatite melts, Apatite-Magnetite melts

Tightly Bonded Radicals (Viva Che!)

3 Isomers in solutions1 radical in solid minerals

4 isomers in solutions1 radical in solid minerals

3 Lone Pairs

2 Lone Pairs

(-2)

Pauling Rule 3: Polyhedral Linking

• "The stability of structures with different types of polyhedral linking is vertex-sharing > edge-sharing > face-sharing"

• effect is largest for cations with high charge and low coordination number

• especially large when r+/r- approaches the lower limit of the polyhedral stability

• Why? Sharing edges/faces brings ions at the centre of each polyhedron closer together, hence increasing electrostatic repulsions

• i.e. disposition of ions of similar charge will be such as to minimize the Electrostatic Energy between them

• Linked polyhedra act as a single ionic structural unit

2+- 4+: Sharing Polyhedral Elements

OK

Empty+sites,

too muchcation

repulsion

RareTetrahedra+4 cations

not +3, 1.5 e.v.

+2 cations

Edge contracts

Octahedra

Pauling’s Rules 1-4 all:

• Tend to maximize cation-anion interactions due to attraction

• Tend to minimize cation-cation or anion-anion interactions due to repulsion

#5 - Principle of Parsimony

• # of contrasting elements are small because there are few anion or cation sites

• Complex compositions tend toward several constituents (cations) in the same kind of site

• This is termed solid solution: Fe for Mg, Si for Al, Ca for Na (definite not exact compositions)

• Goldschmidt’s rules say ions have to be similar size +/-15% and +/- 1 charge unit

Limited Types of Coordination

Octahedral – Na & Cl

Cubic – CaTetrahedral – F

Octahedral – emptyTetrahedral - S

Halite

Fluorite

Sphalerite